Question

Use the grouping method to factor the polynomial below completely. X^3+2x^2+5x+10

Answer 1

(X^3+2x^2) +(5x+10)

X^2(x+2) +5(x+2)

(X^2+5)(x+2)

Answer 2

`(x+2)\text{ and }(x^2+5)` are the factors of given polynomial,

Explanation:

We are given the following information in the question:

We are given a polynomial:

`x^3 + 2x^2 + 5x + 10`

We have to factor this polynomial with the help of grouping method.

Grouping can be dine with the help of taking the common factors.

Working:

`\text{Taking } x^2 \text{ common from the first two terms and 5 from the other two terms, we have}\\\Rightarrow x^2(x + 2) +5(x + 2)\\\text{Aain taking the common term}\\\Rightarrow (x+2)(x^2+5)`

Hence, the two factors of the given polynomial are:

`(x+2)\text{ and }(x^2+5)`