Factorising Quadratics SACHS

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

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