factorise the following polynomials: x3+13x2+31x-45,given that (x+9) is a factor
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Answered by
60
x^3 +13x^2 + 31x - 45
= x^3 - x^2 + 14x^2 - 14x + 45x - 45
= x^2 ( x - 1) + 14x (x - 1) + 45 (x - 1)
= (x - 1)(x^2 + 14x + 45)
= (x-1) [x^2 + 5x + 9x + 45]
= (x-1)[ x(x +5) + 9 (x +5)]
= (x-1)(x+5)(x+9)
= x^3 - x^2 + 14x^2 - 14x + 45x - 45
= x^2 ( x - 1) + 14x (x - 1) + 45 (x - 1)
= (x - 1)(x^2 + 14x + 45)
= (x-1) [x^2 + 5x + 9x + 45]
= (x-1)[ x(x +5) + 9 (x +5)]
= (x-1)(x+5)(x+9)
Answered by
11
Answer:
x^3 +13x^2 + 31x - 45
= x^3 - x^2 + 14x^2 - 14x + 45x - 45
= x^2 ( x - 1) + 14x (x - 1) + 45 (x - 1)
= (x - 1)(x^2 + 14x + 45)
= (x-1) [x^2 + 5x + 9x + 45]
= (x-1)[ x(x +5) + 9 (x +5)]
= (x-1)(x+5)(x+9)
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