Question

Which expression is equal to the polynomial below?

2x4 5x3 – 8x – 20



x3(2x 5) 4(2x – 5)


x3(2x 5) – 4(2x 5)


x3(2x – 5) – 4(2x – 5)


x3(2x 5) 4(2x 5)

Answer 1

Option (b) is correct.

`\Rightarrow x^3(2x+5)-4(2x+5)` is equal to the given polynomial
`2x^4+5x^3-8x-20`

Explanation:

Given polynomial
`2x^4+5x^3-8x-20`

We have to choose form the given option that is equal to the given polynomial
`2x^4+5x^3-8x-20`

Consider the given polynomial
`2x^4+5x^3-8x-20`

We will factorize the given polynomial by grouping like terms.

Taking
`x^3` common from first two term and -4 common from last two term , we have,

`2x^4+5x^3-8x-20`

`\Rightarrow x^3(2x+5)-4(2x+5)`

Again taking (2x +5) common from both terms, we get

`\Rightarrow (x^3-4)(2x+5)`

Thus, Option (b) is correct.

Answer 2

If you would like to find the equal expression to the polynomial 2x^4 + 5x^3 - 8x - 20, you can do this using the following steps:

2x^4 + 5x^3 - 8x - 20 = x^3 * (2x + 5) - 4 * (2x + 5)

The correct result would be x^3 * (2x + 5) - 4 * (2x + 5).