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McGraw Hill Integrated II, 2012 View details

9. Perfect Squares

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Exercise 33 Page 69

Is there a greatest common factor? What other factoring technique could be used according to the number of terms?

Prime

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We want to factor the given polynomial. Note that it has four terms. g^2+2g-3h^2+4hFirst, notice that there is no greatest common factor. There is one additional common factoring technique for quadrinomials.

Grouping

Let's take the greatest common factor from each group.

g^2 + 2g-3h^2+4h

FactorOut

Factor out g

g(g+2) - 3h^2 + 4h

FactorOut

Factor out - h

g(g+2)-h(3h-4)

Notice that there is no common factor in both terms. Therefore, we cannot use factoring by grouping. The given polynomial cannot be factored, so it is prime.

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Factoring Techniques

There are different factoring techniques to apply according to the number of terms the polynomial has.

Number of Terms	Factoring Technique
Any number	Greatest Common Factor (GCF)
Two	Difference of Two Squares, Sum of Two Cubes, or Difference of Two Cubes
Three	Perfect Square Trinomials, or General Trinomials
Four or More	Factoring by Grouping

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Exercises p.68-71

Exercise 33 Page 69

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