Factor each polynomial?

2x^2 + 5x + 2

I missed a week of school and my teacher will not re-teach so please help.

2 Answers
May 26, 2018

rarr2x^2+5x+2=(x+2)(2x+1)

Explanation:

rarr2x^2+5x+2

=2x^2+4x+x+2

=2x(x+2)+1(x+2)

=(x+2)(2x+1)

May 26, 2018

(x+2)(2x+1)

Explanation:

"given a quadratic in "color(blue)"standard form"

•color(white)(x)ax^2+bx+c color(white)(x);a!=0

"to factor consider the factors of the product ac which"
"sum to b"

2x^2+5x+2" is in standard form"

"with "a=2,b=5" and "c=2

"consider the factors of the product "2xx2=4
"which sum to + 5"

"the factors required are + 4 and + 1"

"split the middle term using these factors"

2x^2+4x+x+2larrcolor(blue)"factor by grouping"

=color(red)(2x)(x+2)color(red)(+1)(x+2)

"take out the "color(blue)"common factor "(x+2)

=(x+2)(color(red)(2x+1))

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