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McGraw Hill Integrated II, 2012 View details

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Exercise 75 Page 84

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

Prime

Practice makes perfect

We want to factor the given polynomial. Note that it has three terms. x^2+5x+25 First, notice that there is no greatest common factor. There are two additional common factoring techniques for binomials.

Perfect Square Trinomials
General Trinomials

Since neither term is a square, the polynomial is not a perfect square trinomial. Furthermore, it cannot be factored by finding a pair of integers whose product is a* c, which here is 1* 25, and whose sum is b, which in the example is 5. Therefore, the given polynomial cannot be factored: it is prime.

Extra

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	Grouping

Subchapter links

1 Adding and Subtracting Polynomials p.81

2 Multiplying a Polynomial by a Monomial p.81

3 Multiplying Polynomials p.81

4 Special Products p.82

5 Using the Distributive Property p.82

6 Solving x^2+bx+c=0 p.83

7 Solving ax^2+bx+c=0 p.83

8 Differences of Squares p.84

9 Perfect Squares p.84

10 Roots and Zeros p.85

Exercise 75 Page 84

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