Algebraic Manipulation Worksheets With Answers - Craven Community College Page 8
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2916. A piece of cardboard 18 inches wide by 24 inches long is to have square pieces cut out of each corner
so that it can be made into a box. If the side of each square that will cut out is X inches by X inches, write
a polynomial that represents the volume of the box.
F
P
ACTORING
OLYNOMIALS
Using Common Factors
Factoring a polynomial means writing the polynomial as a product of two terms. To factor using common
factors, first find the greatest common factor (GCF) of the terms of the polynomial; then divide the GCF
into each term.
3
2
2
2
Example 1:
Factor
4X
Y
+ 12X
Y + 20XY
GCF = 4XY
3
2
2
2
4X
Y
+ 12X
Y + 20XY
Divide each term by 4XY
4XY
4XY(X2Y + 3X + 5Y)
Write answer as a product
Example 2:
Factor
3XZ – 4YZ – 3XA + 4YA
(3XZ – 4YZ) – (3XA – 4YA)
Group first two terms and
Second two terms together
Z(3X – 4Y) – A(3X – 4Y)
Factor GCF from each group
(3X – 4Y)(Z – A)
Factor (3X – 4Y) from each
term
Factoring Trinomials
Quadratic trinomials factor into the product of two binomials. Factoring trinomials is based on the FOIL
method of multiplication. Note that the first term of the trinomial is the product of the first terms of the
binomials. The last term of the trinomial is the product of the last terms of the binomials. The middle
term of the trinomial is the sum of the products of the two inner terms and the two outer terms.
To factor a quadratic trinomial, first list all possible factors for the first term and the last term. Write out
these choices as trial factors; then find the sum of the outer and inner products. Compare this sum to the
middle term to determine the correct factorization.
Example 1:
Factor X2 – 7X + 12
The last term has a positive sign; therefore both signs are alike. The sign on the
middle term is negative; therefore both signs are negative. The factors of X2 must
be X and X. The factors of 12 are -1, -12 or -2, -6 or -3, -4.
Trial factors
Sum outer and inner products
(X – 1)(X – 12)
-13X
(X – 2)(X – 6)
8X
(X – 3)(X – 4)
-7X
Therefore the answer is (X – 3)(X – 4)
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