Question

factorize x3+13x2+31x-45
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Answer 1

Step-by-step explanation:

x³ + 13x² +31x - 45

if x = 1 then

1³ + 13(1)² +31(1) – 45

1+13+31 - 45

0

thefore x - 1 is a root of this polynomial

now ,

x³ + 13x² +31x − 45

x³ - x² +14x² - 14x + 45x - 45

x²(x − 1) + 14x(x − 1) + 45(x − 1)

(x − 1)(x² + 5x + 9x +45)

(x − 1)(x² + 14x +45)

(x − 1)(x + 5) (x +9)

Hope it helps you...

Answer 2

Answer:

(x - 1)(x + 5)(x + 9)

Step-by-step explanation:

$x^{3} + 13x^{2} + 31x - 45\\= x^{3} + 14xx^{2} + 45x - 1x^{2} - 14x - 45\\= x(x^{2} + 14x + 45) - 1(x^{2} + 14x + 45)\\= (x - 1)(x^{2} + 14x + 45)\\= (x - 1)(x^{2} + 5x + 9x + 45\\= (x - 1)(x(x + 5) + 9(x + 5)) \\= (x - 1)(x + 5)(x + 9)$