Question

factorise x^3 + 13x^2 + 31x - 45 if it given that x + 9 is it factor

Answer 1

hope this answer will help you!!

Answer 2

Answer:

$(x-1),(x+5)$ and $(x+9)$ are the factors of polynomial $f(x)$.

Step-by-step explanation:

Let $f(x)=x^{3}+13 x^{2}+31 x-45$ be the given polynomial.

Therefore $(x+9)$ is a factor of the polynomial  $f(x)$.

Now,

$\begin{aligned}&f(x)=x^{2}(x+9)+4 x(4 x(x+9)-5)(x+9) \\&=(x+9)\left\{x^{2}+4 x-5\right\} \\&=(x+9)\left\{x^{2}+5 x-x-5\right\} \\&=(x+9)(x-1)(x+5)\end{aligned}$

Hence $(x-1),(x+5)$ and $(x+9)$ are the factors of polynomial $f(x)$.