8-1 A d d i n g an d Su b t r act i n g Po l y n o m i al s
Quick Review
A monomial is a number, a variable, or a product of a
number and one or more variables. A polynomial is a
monomial or the sum of two or more monomials. The
degree of a polynomial in one variable is the same as the
degree of the monomial with the greatest exponent. To add
two polynomials, add the like terms of the polynomials. To
subtract a polynomial, add the opposite of the polynomial.Ex a m p l e
What is the difference of 3x 3 - 7x2 + 5 and
2x2 - 9x - 1?
(3x3 — 7x2 + 5) - (2x2 - 9 x - l)
= 3x3 - 7x2 + 5 - 2x2 + 9x + 1
= 3x3 + ( —7x2 — 2x2) + 9 x + ( l + 5)
= 3x3 - 9x2 + 9x + 6Ex e r c i s e s
Write each polynomial in standard form. Then name each
polynomial based on its degree and number of terms.
6. 4r + 3 - 9 r 2 + 7r 7. 3 + b3 + b2
8. 3 + 8t2 9. n3 + 4n5 + n — n 3- 7 x 2 + 8 + 6x-7x 2 11. p V
Simplify. Write each answer in standard form. - (2v3 - y + 8 ) + (~ v3 + v - 3 )
- (6s4 + 7s2 + 7 ) + ( 8 s 4 - 1 1 s 2 + 9 s )
- (4hs + 3h+ l) - (—5h3 + 6h —2)
- ( 8 z 3 — 3 z 2 ~ 7 ) — ( z 3 — z 2 + 9 )
8-2 M ultiplying and Factoring
Quick Review
You can multiply a monomial and a polynomial using
the Distributive Property. You can factor a polynomial by
finding the greatest common factor (GCF) of the terms of
the polynomial.Ex a m p l e
What is the factored form of 10y4 — 12y3 + 4y2?
First find the GCF of the terms of the polynomial.
10j/4 = 2 • 5 • y • y • y • y
12 y3 = 2*2»3*y*y*y
4y2 = 2 • 2 • y • y
The GCF is 2 • y • y or 2y2.Then factor out the GCF.
10y4 - 12y3 + 4y2 = 2y2(5y2) + 2y2(-6y) + 2y2(2)
= 2y2(5y2-6y+2)Ex e r c i s e s
Simplify each product. Write in standard form.- 5fc(3 - 4k) 17. 4m[2m + 9m2 - 6)
- 6g2(g -8 ) 19. 3d(6d + d2)
- -2n2(5ra-9 + 4n2) 21. q(ll + 8q - 2q2)
Find the GCF of the terms of each polynomial. Then factor
the polynomial.- 12p4 + 16p3 + 8p 23. 3b4 - 9b2 + 6b
- 45c5 - 63c3 + 27c 25. 4g2 + 8g
- 314 - 613 - 9 1 + 12 27. 30h5 - 6h4 - 15 h3
- Reasoning The GCF of two numbers p and q is
5. Can you find the GCF of 6p and 6ql Explain
your answer.
5 3 6 Chapter 8 Ch ap t er Revi ew