Think$ I *S ft S' '• *• ,
Is th e sum o r
difference of tw o
polynomials always
a polynom ial?
Yes. The set o f
p o lyn o m ia ls is dosed
under addition and
subtraction, which means
that adding or subtracting
polynomials always gives
you another polynomial.Recall th at subtraction m ean s to ad d the opposite. So w h en you su b tract a polynom ial,
change each of th e term s to its opposite. Then ad d th e coefficients.Pr o b l em 5 Su b t r a c t i n g Po l y n o m i a l s
What is a simpler form of (jc3 — 3 x 2 + 5x) - (7 x 3 + 5x2 - 12)?Method 1 Subtract vertically.
x 3 - 3x2 + 5x
-(7x3 + 5x^2 - 1 2 )x3 - 3x2 + 5x
—7 x 3 - 5 x 2 12Line up like terms.Then add the opposite o f each term in
th e polyn o m ia l being subtracted.-6 x 3 — 8x2 + 5x + 12Method 2 Subtract horizontally.
( x 3 - 3x2 + 5x) - (7 x 3 + 5x2 - 12)= x 3 - 3x2 + 5x - 7x3 - 5x2 + 12 Write the opposite of each term in the polynomial being subtracted.( x 3 - 7x3) + ( - 3 x 2 - 5x2) + 5x + 12 Group like terms.
= -6 x 3 - 8x2 + 5x + 12 Simplify.Got It? 5. W hat is a sim pler form of ( - 4 m 3 — m + 9 ) - ( 4 m 2 + m - 1 2 ) 'Lesso n Ch eck
Do y o u k n o w H OW?
Find the degree of each monomial.- — 7 x 4 2. 8y2z 3
Simplify each sum or difference.- (5r3 + 8) + (6r3 + 3)
- (x2 — 2 ) - ( 3x + 5)
MATHEMATICAL
Do y o u UN DERSTAN D? PRACTICES
@ Vocabulary Nam e each polynom ial b ase d on its degree
an d n u m b e r of term s.r n f t p r m s- 5x2 + 2x + 1 6. 3z - 2
- Compare and Contrast How are th e processes of
adding m onom ials an d adding polynom ials alike?
How are the processes different?
8*^ Practice and Problem-Solving Exercises
wA P ra c tic e Find the degree of each monomial.
8. 3x 9. 8a3- -7y3z 13. -3
MATHEMATICAL
PRACTICES
20
12 w4
^ See Problem 1.- 2b8c2
15.0
PowerAlgebra.com I Lesso n 8-1 Adding and Subtracting Polynomials^489