Question

Select one of the factors of 5x^2 + 7x + 2.

A) (5x − 2)
B) (x + 2)
C) (5x + 1)
D) None of the above

Answer 1

Answer:

Correct choice is D

Step-by-step explanation:

Consider the quadratic expression $5x^2 + 7x + 2.$

First, find the discriminant:

$D=7^2-4\cdot 5\cdot 2=49-40=9.$

Now find the roots of the quadratic expression $5x^2 + 7x + 2:$

$x_{1,2}=\dfrac{-7\pm \sqrt{9}}{2\cdot 5}=\dfrac{-7\pm 3}{10}=-1,\ -0.4.$

Then

$5x^2 + 7x + 2=5(x-(-1))(x-(-0.4))=5(x+1)(x+0.4)=(x+1)(5x+2).$