Alg. II Polynomial Problems
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a2+4a-3 7a2+8a+3 (4a2+2a+14) - (3a2+6a+11) Simplify 7a2+8a+25 a2-4a+3 Simplify -4y2+y-4 10y2-y-4 (3y2+5y-8) - (7y2+4y-4) 10y2+y+12 10y2+y-4 Simplify 1/2m2-3/2m+1 1/2m2+3/2m-1 (m2-m+1) - (1/2m2+ 1/2m) 1.5m2+1.5m+1.5 m2-m+1  How many real solutionsdoes the function have? Decide whether f(x) is a polynomial function. yes, it's a polynomial no, it's not a polynomial f(x) = 9x4 + 8x3 - √x Given g(x), determine the following.... How many possible curves can its graph have? Degree g(x) = 9x3+8x2-6x+10 What type of polynomial is f(x)? f(x) = 7x2 - 10x4 + 2x -1 linear quartic cubic quadratic Evaluate the function for the given value of x. g(x) = -3x4 + 2x3 -12x - 6; x = -2 g(-2) = x↦+∞ f(x) ↦ -∞ & x↦-∞, f(x) ↦ -∞ x↦+∞ f(x) ↦ -∞ & x↦-∞, f(x) ↦ +∞ x↦+∞ f(x) ↦ +∞ & x↦-∞, f(x) ↦ -∞ What is the end behavior of the polynomial? Find the solutions (x-intercepts) of the function. List answers in order from smallest to biggest. Round to tenths place where necessary. x= Using a graphing calculator, f(x) = 4x3 - 2x2 - 24x -18 When typing in your answer... 3. If you have a 1x, do not type the 1. Just type x. 2. For exponents, use ^ (above the #6 on keyboard) Ex. 2x³ .... 2x^ 3 1. Do NOT type in spaces between terms. Find the sum. (-5x2 + 4x - 2) + (-8x2 + 2x +1) = Find the sum. When typing in your answer... 3. If you have a 1x, do not type the 1. Just type x. 2. For exponents, use ^ (above the #6 on the keyboard) Ex. 2x³ .... 2x^ 3 1. Do NOT type in spaces between terms. (8x4 + 2x2 - 1) + (-5x2 + 7x + 1) = When typing in your answer... 2. For exponents, use ^ (above the #6 on the keyboard) Ex. 2x³ .... 2x^ 3 3. If you have a 1x, do not type the 1. Just type x. 1. Do NOT type in spaces between terms. Find the difference (4x5 -7x3 +18) - (14x5 + 4x3 -2) = When typing in your answer... 3. If you have a 1x, do not type the 1. Just type x 1. Do NOT type in spaces between terms. 2. For exponents, use ^ (above the #6 on the keyboard) Ex. 2x³ .... 2x^ 3 Find the product (3x-4)(3x+4) = When typing in your answer... 3. If you have a 1x, do not type the 1. Just type x 1. Do NOT type in spaces between terms. 2. For exponents, use ^ (above the #6 on the key board) Ex. 2x³ .... 2x^ 3 Find the product (x-3)2= When typing in your answer... 3. If you have a 1x, do not type the 1. Just type x 1. Do NOT type in spaces between terms. 2. For exponents, use ^ (above the #6 on the keyboard) Ex. 2x³ .... 2x^ 3 Divide the following (3x2 - 14x -5)÷(x-5) Using long division, divide the following and find the When typing in your answer... 3. If you have a 1x, do not type the 1. Just type x 1. Do NOT type in spaces between terms. 2. For exponents, use ^ (above the #6 on the keyboard) Ex. 2x³ .... 2x^ 3 (7x3 + x2 + x)÷(x2 +1) = REMAINDER x2+1 Divide using synthetic division to find the REMAINDER When typing in your answer... 3. If you have a 1x, do not type the 1. Just type x 1. Do NOT type in spaces between terms. 2. For exponents, use ^ (above the #6 on the keyboard) Ex. 2x³ .... 2x^ 3 The remainder is (4x2 - 13x -5)÷(x-2) = x-2 f(2) = f(x) = 5x3- x2 + 30x -1 for x = 2 Use synthetic division to evaluate. Input solutions smallest to largest. Factor and solve the equation. a= a= a3 - 4a2 + 4a = 0 Input solutions smallest to largest. Using Factor by Grouping v= v= v= Solve the following v3 - 2v2 -16v + 32=0 If not whole number answers, round to the tenths. Input solutions smallest to largest. Factor and Solve the equation. m= m= m= 9m5 - 27m3 = 0 When typing in your answer... 3. If you have a 1x, do not type the 1. Just type x 1. Do NOT type in spaces between terms. 2. For exponents, use ^ (above the #6 on the keyboard) Ex. 2x³ .... 2x^ 3 Factor x3 - 8 When f(x)→∞, then When f(x)→∞, then When f(x)→-∞, then ? f(x)=3x3-6x2+x-5 Find the end behavior of f(x) x→∞ ? x→ -∞ x→-∞ Degree: x= What are the x-intercepts for g(x)? g(x) = (x+1)4(x-4)(x+5) List answers from lowest to highest i7 = Simplify i136 = Simplify Do not put any spaces in your answer. (4+5i)+(-6+10i) Simplify How many real solutionsdoes the function have? Decide whether f(x) is a polynomial function. yes, it's a polynomial no, it's not a polynomial f(x) = x6 + 8x3 - 6 How many possible curves can its graph have? Degree g(x) = 9x5+8x2-6x+10 What type of polynomial is f(x)? f(x) = 7x3 - 8x2 + 2x -1 quartic linear cubic quadratic x↦+∞ f(x) ↦ -∞ & x↦-∞, f(x) ↦ -∞ x↦+∞ f(x) ↦ +∞ & x↦-∞, f(x) ↦ -∞ x↦+∞ f(x) ↦ -∞ & x↦-∞, f(x) ↦ +∞ What is the end behavior of the polynomial? Degree 4 3 2 1 0 quadratic ? quartic ? cubic ? linear ? constant ? Match the following. Octic doubled When f(x)→∞, then When f(x)→∞, then When f(x)→-∞, then ? f(x)=3x3-6x2+x-5 Find the end behavior of f(x) x→∞ ? x→ -∞ x→-∞ Degree: x= What are the x-intercepts for g(x)? g(x) = (x+1)6(x-4)3(x+5) List answers from lowest to highest i7 = Simplify i136 = Simplify (3+5i)+(-5+8i) Do not put any spaces in your answer. Simplify What is the leading coefficient? What is the linear term? g(x) = 9x5+8x2-6x+10 degree: How many possible curves? x-intercepts: f(x) = ⅛(x+3)(x-2)2 , 2 -2 4 -4 6 -6 2 -2 4 -4 6 -6 8 -8 10 -10 Increase: On how many intervals does the polynomial.... decrease: x-intercepts: degree: f(x) = -5(x+1)3(x+2)(x-1) How many possible curves? , , √-25 - √-9 + √-81= Do not put any spaces in your answer. Simplify How many are there.... local maximums: local minimums: 2 -2 4 -4 2 -2 4 -4 6 -6 If the answer is all real numbers, then type R. What is the domain of the function? 2 -2 4 -4 2 -2 4 -4 6 -6 If the answer is all real numbers, then type R. What is the range of the function? 2 -2 4 -4 2 -2 4 -4 6 -6 If the answer is all real numbers, then type R. What is the domain of the function? between the terms and signs. When typing in your answer, do NOT put spaces Multiply and write the answer in standard form. 5i(-4 + 2i) = 2x2-8x-4 10x2+2x-4 (6x2-5x) - (4x2-3x-4) Simplify 2x2+8x+4 2x2-2x+4 For example: 3x4 would be typed as When typing in your answer, do NOT put spaces between the terms. If you need an exponent, use ^ 5x2(3x2 + 7x + 6) Simplify 3x^ 4 10y2+y+12 -4y2+y-4 (3y2+5y-8) - (7y2+4y-4) Simplify 10y2-y-4 10y2+y-4 4x+4 5x2-9x+8 (5x2-4x+6) - (5x-2) Simplify 5x2+9x-8 5x2+9x+8 For example: 3x4 would be typed as When typing in your answer, do NOT put spaces between the terms. If you need an exponent, use ^ (2x2-11x+7) - (2x2+11x-7) Simplify 3x^ 4 For example: 3x4 would be typed as When typing in your answer, do NOT put spaces between the terms. If you need an exponent, use ^ (6m2+3) - (m-5) Simplify 3x^ 4 2y2-15y-16 2y2+18y-16 (5y2+15y) - (3y2-16) Simplify 2y2+15y+16 2y2-15y+16 1/2m2+3/2m-1 1.5m2+1.5m+1.5 (m2-m+1) - (1/2m2+ 1/2m) Simplify 1/2m2-3/2m+1 m2-m+1 For example: 3x4 would be typed as When typing in your answer, do NOT put spaces between the terms. If you need an exponent, use ^ (a2+1/2a+1) - (a2-a/2-1) Simplify 3x^ 4 For example: 3x4 would be typed as When typing in your answer, do NOT put spaces between the terms. If you need an exponent, use ^ (8x2 -3x +1)(-3x +2) Find the product 3x^ 4 11b2+8b+9 11b2+3b-1 (5b2+3b+4) + (6b2-5) Simplify 5b2-2b+9 5b2+9b-1 For example: 3x4 would be typed as When typing in your answer, do NOT put spaces between the terms. If you need an exponent, use ^ (2y2-3y+7) + (6y2-8y-9) Simplify 3x^ 4 For example: 3x4 would be typed as When typing in your answer, do NOT put spaces between the terms. If you need an exponent, use ^ (-x2-6x-1) + (4x2+12x+10) Simplify 3x^ 4
1. Polynomial 3. Possible number of curves 4. Possible number of solutions 5. Even Function 6. Odd Function 2. Degree of polynomial the lowest exponent Polynomials with the correct definition/example. Match the following vocabulary/concepts about all exponents of x are whole numbers > 1and positive ? symmetrical about the origin ? symmetrical about a vertical line ? symmetrical about a horizontal line the highest exponent ? degree - 1 ? degree of the polynomial ? -7x5 - 6x4 + 3x2 + x7 -12 -7x5 - 6x4 + 3x2 + x7 -12 -7x5 - 6x4 + 3x2 + x7 -12 -7x5 - 6x4 + 3x2 + x7 -12 linear term Match the highlighted term/number with it's label leading coefficient constant term ? degree of polynomial ? quartic term ? quadratic term ? -9 - 8i 4 + 5i i2 -1 ? Match the highlighted term/number with it's label imaginery term ? real number ? i12 i7 i9 -i ? i ? 1 ? Fill in the blanks... -7 ? Given: (9x4 + 3x2 - 5x -10)÷(x+7) + 9 ? 9 -63 ? 0 ? 3 ? -3 -5 ? 7 -10 ? between the terms and signs. When typing in your answer, do NOT put spaces Multiply and write the answer in standard form. 3i(8 - 3i)= between the terms and signs. When typing in your answer, do NOT put spaces Multiply and write the answer in standard form. (4 + 6i)(9 -2i) = √-16 = √-64 = Simplify 3√-4 = √-100 = Simplify √-16 - √-36 + √-25= Do not put any spaces in your answer. Simplify -7x5 - 6x4 + 3x2 + x7 -12 -7x5 - 6x8 + 3x2 + x>7 -12 -7x5 - 6x4 + 3x2 + x7 -12 -7x7 - 6x4 + 3x2 + x -12 linear term Match the highlighted term/number with it's label quartic term quadratic term ? degree of polynomial ? constant term ? leading coefficient ? -9 + 4i 3+ 5i i2 -1 ? Match the highlighted term/number with it's label imaginery term ? real number ? i16 i7 i9 -i ? i ? 1 ? 2 -2 4 -4 6 -6 2 -2 4 -4 6 -6 8 -8 10 -10 If need symbols, copy/paste Domain: Find the Domain & Range Range: ≤ ≥ > < If answer is "All Real Numbers", type R When typing in your answer... 3. If you have a 1x, do not type the 1. Just type x 1. Do NOT type in spaces between terms. 2. For exponents, use ^ (above the #6 on the keyboard) Ex. 2x³ .... 2x^ 3 ( 3x3 + 6x2 - 4x -8 using Factor by grouping Factor the given Polynomial ) ( ) |
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