Monomials can be broken down into their component parts. This is what we call factoring monomials. This can be extended into factoring polynomials. What is done is that we look for a factor of each part of the polynomial. We find a factor that is common to each term. Then we divide out this common factor and place it in front of the remainder of the terms of the polynomial.

Example 1:
Find the greatest common factor of 3x^2 + 24x + 9, divide it out, and rewrite the polynomial as a multiplication problem using the factors you found. Look at each term of this polynomial. Is there a common factor that will divide evenly into all three terms? Hopefully you recognize that 3 divides into all three terms. Therefore, the answer is 3(x^2 +8x + 3).

Example 2:
Factor the polynomial 2n^3 + 6n^2 + 10n into the product of its greatest monomial factor and another trinomial. In this problem the greatest common factor is 2n. Therefore the answer is 2n(n^2 +3n + 5).

Now you try by completing the following problems:
1) 6x^2 + 9x - 21
2) 4r^5 - 16r^3 + 20r^2
3) 10y^2 + 25y^3 - 5y

Common Monomial FactorExample 1:

Find the greatest common factor of 3x^2 + 24x + 9, divide it out, and rewrite the polynomial as a multiplication problem using the factors you found. Look at each term of this polynomial. Is there a common factor that will divide evenly into all three terms? Hopefully you recognize that 3 divides into all three terms. Therefore, the answer is 3(x^2 +8x + 3).

Example 2:

Factor the polynomial 2n^3 + 6n^2 + 10n into the product of its greatest monomial factor and another trinomial. In this problem the greatest common factor is 2n. Therefore the answer is 2n(n^2 +3n + 5).

Now you try by completing the following problems:

1) 6x^2 + 9x - 21

2) 4r^5 - 16r^3 + 20r^2

3) 10y^2 + 25y^3 - 5y

ANSWERS

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General Trinomial Factoring