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Step 7Factoring polynomials by grouping
Sometimes you will get four or more terms, that look something like this:
2x^2 + 6x^3 + 5x^7 + 15x^8
There is no common coefficient, and factoring out x^2 doesn't help much. This is where you would use grouping to factor.
Grouping means factoring out the GCF of only two terms of the equation. You can see that 2x^2 + 6x^3 and 5x^7 + 15x^8 both can have a GCF taken out. Do so.
2x^2 (1 + 3x) + 5x^7 (1 + 3x)
Note that there is a common factor, 1+3x. This equation can be rephrased to (2x^2 + 5x^7) (1 + 3x). There's your answer.
Note that (2x^2 + 5x^7) (1 + 3x) can be factored further by factoring out an x^2 from the first binomial: x^2 (2 + 5x^5) (1 + 3x).
2x^2 + 6x^3 + 5x^7 + 15x^8
There is no common coefficient, and factoring out x^2 doesn't help much. This is where you would use grouping to factor.
Grouping means factoring out the GCF of only two terms of the equation. You can see that 2x^2 + 6x^3 and 5x^7 + 15x^8 both can have a GCF taken out. Do so.
2x^2 (1 + 3x) + 5x^7 (1 + 3x)
Note that there is a common factor, 1+3x. This equation can be rephrased to (2x^2 + 5x^7) (1 + 3x). There's your answer.
Note that (2x^2 + 5x^7) (1 + 3x) can be factored further by factoring out an x^2 from the first binomial: x^2 (2 + 5x^5) (1 + 3x).
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