Question

+5x+3.

What are the factors of the polynomial?
(2x+3)(x+1)
(2x-3)(x-1)
(3x+2)(x+1)
(3x-2)(x-1)

Answer 1

Question:

2x^2 + 5x + 3

What are the factors of the polynomial?

(2x+3)(x+1)

(2x-3)(x-1)

(3x+2)(x+1)

(3x-2)(x-1)

Answer:

Option A

The factors are:

`2x^2+5x+3 = (2x+3)(x+1)`

Solution:

Given that, the quadratic equation is:

`2x^2 + 5x + 3`

We have to find the factors of polynomial

Find the factors:

`2x^2+5x+3`

Split 5x as 2x and 3x

`2x^2+5x+3 = 2x^2 +2x + 3x + 3`

`\mathrm{Break\:the\:expression\:into\:groups}`

`2x^2+5x+3=\left(2x^2+2x\right)+\left(3x+3\right)`

`\mathrm{Factor\:out\:}2x\mathrm{\:from\:}2x^2+2x\mathrm{:\quad }2x\left(x+1\right)`

Thus we get,

`2x^2+5x+3 = 2x(x+1) + (3x+3)`

`\mathrm{Factor\:out\:}3\mathrm{\:from\:}3x+3\mathrm{:\quad }3\left(x+1\right)`

Thus we get,

`2x^2+5x+3 = 2x(x+1) + 3(x+1)`

`\mathrm{Factor\:out\:common\:term\:}x+1`

Thus we get,

`2x^2+5x+3 = (2x+3)(x+1)`

Thus the factors are found for given polynomial