Multiplying a Trinomial and a Binomial
W h at is a s im p le r fo rm o f (3x2 + x — 5)(2x - 7)?
M ultiply by arranging th e polynom ials vertically as shown.
How should you align
the polynomials? 3x2 + x -^5
Write the polynomials 2 x — 7
so that like terms are ------------------------------------
vertically aligned. —2 1 x 2 — 7x + 35 Multiply by-7.
6X3 + 2x2 — lOx Multiply by 2x.
6X3 - 19x2 - 17x + 35 Add like terms.The p ro d u c t is 6x3 - 19x2 - 17x + 35.0 Got It? 5. a. W hat is a sim pler form of (2x2 - 3x + l)(x - 3)?
b. Reasoning How can you use th e Distributive P roperty to find the
pro d u ct of a trinom ial an d a binom ial?9 Lesso n Ch eck
Do y o u k n o w H OW?
Simplify each product.- (x + 3)(x + 6)
- (2x - 5)(x + 3)
- (x + 2)(x2 + 3x - 4)
- A rectangle has length x + 5 an d w idth x - 3. W hat
is the area of the rectangle? W rite your answ er as a
polynom ial in stan d ard form.
_. ._______________________ _____________MATHEMATICAL
Do y o u UN DERSTAN D? PRACTICES- Reasoning Explain how to use th e FOIL m eth o d to
find th e p ro d u c t of two binom ials. - C o m p a r e a n d C o n t r a s t Simplify (3x + 8)(x + 1)
using a table, th e Distributive Property, a n d th e FOIL
m ethod. W hich m eth o d is m ost efficient? Explain. - W riting How is th e degree of th e p ro d u c t of two
polynom ials p(x) a n d q{x) related to the degrees of
p(x) and q(x)l
Pr act i ce an d Pr o b l em - So l v i n g Ex er ci ses
O Practice Simplify each product using the Distributive Property.
>8r
8. (x + 7)(x + 4 ) 9. [y — 3)(y + 8)- ( c - 1 0 )(c -5 ) 12. ( 2 r - 3 ) ( r + 1)
Simplify each product using a table.- (x + 5)(x — 4)
- [2h — 7)(h + 9)
15. (a - 1 )( a - 11)
18. (x — 8)(3x + 1)
MATHEMATICAL
PRACTICES49 See Problem 1.- [m + 6)(m - 7)
- (2x + 7)(3x — 4)
49 See Problem 2.- {w - 2)(w + 6)
- (3p + 4)(2p + 5)
| L e s s o n 8 - 3 M u l t i p l y i n g B i n o m i a l s 501