Go t I t? 3. Geom etry A rectangular prism has volume 60x3 + 34x2 + 4x. What
expressions can represent the dimensions of the prism? Use factoring.Here is a summary of what to remember as you factor polynomials.
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Su m m ar y Fact oring Polynomials- Factor out the greatest common factor (G C F ).
- If the polynomial has two terms or three terms, look for a difference of two squares,
a perfect-square trinomial, or a pair of binomial factors. - If the polynomial has four or more terms, group terms and factor to find common
binomial factors. - As a final check, make sure there are no common factors other than 1.
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Lesso n Ch eck
Do y o u k n o w H OW?Factor each expression.
- 20r3 + 8r2 + 15r+6
- 6d3 + 3d2- 10d-5
- 24x3 + 60x2 + 36x + 90
- A rectangular prism has a volume of
36x3 + 36x2 + 8x. What expressions can represent
the dimensions of the prism? Use factoring.
1~ ^^MATHEMATICAL
Do y o u UN DERSTAND? {Sf PRACTICES
0 Vocabulary Tell whether you would factor the^
polynomial by grouping. Explain your answer.- x2 - 6x + 9
- 4w2 + 23w + 15
- 24t3 — 42t2 — 28f + 49
(§j^^8. R e a s o n i n g Can you factor the polynomial
6<y3 + 2q2 + 12 q - 3 by grouping? Explain.Pr act i ce an d Pr o b l em - So l v i n g Ex er ci ses
1 ^ 1 P ra c tic e. M A T H E M A T I C A L
I P R A C T I C E S
Find the GCF of the first two terms and the GCF of the last two terms for
each polynomial.- 10g3 - 25g2 + 4g - 10
See Problem 1.- 2 z 3 + 6 z 2 + 3z + 9
- 2 ^ 4 - 1 2 r 2 — 5 r — 3 0
Factor each expression.- 15q3 + 40q2 + 3q + 8
- llw 3 — 9w2 + llie — 9
- 20n3 + 24v2 - 25v - 30
c
- 6p3 + 3p2 + 2p + 1
- 14y3 + 8y2 + ly + 4
- 8m3 + 12m2 — 2m — 3
- 18h3 + 45h2 - 8 h - 2 0
- 14z — 35z + 16z — 40
- 12k 3 - 27fc2 - 40fc + 90
- 12y 3 + 4 y 2 - 9y - 3
Lesson Factoring by G rouping ] 531