Introduction
When factoring a polynomial that has 4 terms, the objective is to change the sum and difference of many terms into the product of 2 polynomials. To do this, we will do the grouping method, which requires us to take the GCF (Greatest Common Factor) 3 times.
4x2 + 8x + 5x + 10
First, we put the terms into two pairs such that each pair has a GCF
This may require you to rearrange the 4 terms so that each pair has a something in common.
(4x2 + 8x) + (5x + 10)
4x(x + 2) + 5(x + 2)
We then take the GCF out of each pair of terms.
The expression that is left in each set of parentheses should look exactly the same, as that will be our GCF in the next step.
(x + 2)(4x + 5)
Check your answer by FOIL-ing or re-multiplying these two binomials together until you get the original polynomial back again. This confirms you factored it correctly.
Here’s a link to a video walking you through this method:
Practice Problems: Now you try!
- x2 + 5x + 8x + 10
- x2 + 3x + xy + 3y
- w2 + 4w + 3wz + 12z
- 3x2 – 4x + 6x – 8
- 4a2 + b + 2ab + 2a
- x3– x2 – 8x + 8
Hint: try rearranging the terms
(x + 5)(x + 8)
(x + 3)(x + y)
(w + 4)(w + 3z)
(3x – 4)(x + 2)
(2a + 1)(2a + b)
(x – 1)(x2– 8)
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