Question

You are familiar with the following types of factoring:
•factoring out the Greatest Common Factor (GCF).
•factoring by grouping .
•factoring trinomials of the form x2 + bx + c and ax2 + bx + c.

As you know, you need to know the first two types of factoring listed above in order to be successful in factoring trinomials of the form ax^2 + bx + c.

Part 1:
In your own words, explain how a trinomial of the form 2x^2 + 13x + 15 can be turned into a four term polynomial suitable for factoring by grouping. Use complete sentences.

Part 2:
If you were an Algebra 1 instructor and were creat

Answer 1

PLease I need help, and please answer in complete sentance.

Answer 2

Part One
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I learned the "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)

Answer 3

Thank you!

Answer 4

The technique is not anything new but it is systematic and the name "bust the b" is cool.