can someone completly factor these two equations and tell me how its done step by step for each? 2x^2 + 13x + 15
2x^2 + 27x + 13

Question

can someone completly factor these two equations and tell me how its done step by step for each?  2x^2 + 13x + 15
2x^2 + 27x + 13

saifoo.khan · Answer

http://www.youtube.com/watch?v=X7B_tH4O-_s

directrix · Answer

What follows is a step-by-step procedure for factoring a trinomial using the "bust the 'b' technique. The expression 4 x²  -1x + 18 was factored. If you want to read this and after doing so, would like to see how it works to factor the expression 2x^2 + 13x + 15, then I will help you with it.

"Bust the b" Technique

4 x²  -1x + 18

a = 4 and c = 18 and b = -1.

The task on "bust the b" is to find numbers that mutiply to a*c AND add to b.

In this case, numbers that multiply to 4*18 and add to -1.

14 * 18 breaks aparts into the product of prime factors : 2*2*2*3*3 

Look at those five factor of 14 * 18 and try to put them in the form of 2 numbers that differ by -1. 

2*2*2 and 3*3 appear to differ by 1. That would be 8 and 9.

"b" has been "busted into 8 and - 9 whose sum is -1 which equals "b" in this problem.

4x - x+ 18 = 4 x² + 8 x - 9 x - 1.

The "b" has been busted.

Factoring by grouping comes next.

4 x² + 8 x - 9 x - 18 =

4x ( x + 2) - 9  ( x + 2 ) = --> On this step, (x + 2) is the common factor of the expression.

[ (x + 2) ]  ( 4x - 9 ) =

( x + 2 )  ( 4x - 9)