Factorising Quadratics SACHS
Which factors can work [ sum = + 8, product = + 12 ] ?
sum of 'end terms'
1, 12
2, 6
3, 4
x2 + 8x + 12
product of 'end terms'
sum of 'end terms'
x2 + 8x + 12 = (x + 2)(x +       )
Factors: +2 & +6
x2 + 8x + 12
product of 'end terms'
Which factors can work [ sum = + 5, product = – 24 ] ?
sum of 'end terms'
1, 24
2, 12
3, 8
4, 6
x2 + 5x – 24
product of 'end terms'
sum of 'end terms'
x2 + 5x – 24 = (x +      )(x –      )
Factors: 3 & 8
x2 + 5x – 24
product of 'end terms'
Which factors can work [ sum = – 10, product = + 16 ] ?
sum of 'end terms'
1, 16
2, 8
4, 4
x2 – 10x + 16
product of 'end terms'
sum of 'end terms'
x2 – 10x + 16 = (x – 2)(x –      )
x2 – 10x + 16
Factors: 2 & 8
product of 'end terms'
x2 – 2x – 15 =
(x + 5)(x + 3)
(x – 5)(x + 3)
(x – 5)(x – 3)
(x + 5)(x – 3)
x2 + 13x + 30 =
(x + 3)(x + 10)
(x – 3)(x + 10)
(x – 3)(x – 10)
(x + 3)(x – 10)
x2 – 7x + 12 =
(x + 4)(x + 3)
(x – 4)(x + 3)
(x – 4)(x – 3)
(x + 4)(x – 3)
x2 + x – 20 =
(x + 5)(x + 4)
(x – 5)(x + 4)
(x – 5)(x – 4)
(x + 5)(x – 4)
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