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
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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)