PRIME FACTORS A polynomial is prime if it cannot be factored using integer
coefficients. To factor a polynomial completely, write it as the product of
monomial and prime factors.
EXAMPLE
2
Factor Completely
Factor 4x3 20x2 24x completely.
Solution
4x3 20x2 24x 4x(x2 5x 6)
Factor out GCF.
4x(x 2)(x 3)
Monomial factor
Factor trinomial.
Prime factors
Factor Completely
Factor the expression completely.
7. 2n3 4n2 2n
10. x3 4x2 4x
8. 3x3 12x
9. 5m3 45m
11. 2x3 10x2 8x
12. 6p3 21p2 9p
FACTORING BY GROUPING Another use of the distributive property is in
factoring polynomials that have four terms. Sometimes you can factor the
polynomial by grouping the terms into two groups and factoring the greatest
common factor out of each term.
EXAMPLE
3
Factor by Grouping
Factor x3 2x2 9x 18 completely.
Solution
x3 2x2 9x 18 (x3 2x2) (9x 18)
Group terms.
x2(x 2) (9)(x 2)
Factor each group.
(x 2)(x 9)
Use distributive
property.
(x 2)(x 3)(x 3)
Factor difference of
two squares.
2
Factor by Grouping
Use grouping to factor the expression completely.
13. 2x3 8x2 3x 12 14. x3 5x2 4x 20
10.8
15. x3 4x2 9x 36
Factoring Cubic Polynomials
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