Question

Factorise

4x^2+8x+3

Answer 1

For a polynomial of the form ax2+bx+c, rewrite the middle termas a sum of two terms whose product is a⋅c=4⋅3=12 and whose sum is b=8



Factor 8 out of 8x
4x2+8(x)+3
Rewrite 8
as 2 plus 6
4x2+(2+6)x+34
Apply the distributive property.
4x2+(2x+6x)+3
=4x2+2x+6x+3
Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.
(4x2+2x)+(6x+3)
Factor out the greatest common factor (GCF) from each group.
2x(2x+1)+3(2x+1)
Factor the polynomial by factoring out the greatest common factor, 2x+1
(2x+1)(2x+3)