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:
[tex]2x^2+5x+3 = (2x+3)(x+1)[/tex]
Solution:
Given that, the quadratic equation is:
[tex]2x^2 + 5x + 3[/tex]
We have to find the factors of polynomial
Find the factors:
[tex]2x^2+5x+3[/tex]
Split 5x as 2x and 3x
[tex]2x^2+5x+3 = 2x^2 +2x + 3x + 3[/tex]
[tex]\mathrm{Break\:the\:expression\:into\:groups}[/tex]
[tex]2x^2+5x+3=\left(2x^2+2x\right)+\left(3x+3\right)[/tex]
[tex]\mathrm{Factor\:out\:}2x\mathrm{\:from\:}2x^2+2x\mathrm{:\quad }2x\left(x+1\right)[/tex]
Thus we get,
[tex]2x^2+5x+3 = 2x(x+1) + (3x+3)[/tex]
[tex]\mathrm{Factor\:out\:}3\mathrm{\:from\:}3x+3\mathrm{:\quad }3\left(x+1\right)[/tex]
Thus we get,
[tex]2x^2+5x+3 = 2x(x+1) + 3(x+1)[/tex]
[tex]\mathrm{Factor\:out\:common\:term\:}x+1[/tex]
Thus we get,
[tex]2x^2+5x+3 = (2x+3)(x+1)[/tex]
Thus the factors are found for given polynomial
