Algebra 1 Common Core Student Edition, Grade 8-9

Multiplying

and Fact o ring

Common Core State Standards

A -AP R.A .1 Understand that polynomials form a

system analogous to the integers, namely, they are

closed under the operations of addition, subtraction, and

multiplication; add, subtract, and multiply polynomials.

MP 1, MP 2, MP 3, MP 4

Objectives To m ultiply a m o nom ial by a polynom ial

To factor a m onom ial from a polynom ial

If Get t i n g Read y!

Sketch a diagram.

A diagram can help

you understand all

th e p a rts o f th is

problem.

« x C

............._................~................................................... 10 ft

Yo u se t a si d e p a r t o f a r e c t a n g u l a r p l o t o f

land f o r a garden and seed t he r est of t he

M

** *" W

-j

plot with grass, as shown. Grass seed costs ;* H |

$.03 per square foot. Write an expression

1 f o r t h e t o t al co st o f t h e seed. Sup p o se you

1 buy $ 5 0 w o r t h o f seed. How w ide can t h e

i* a m*

45 ft

1 sect i o n o f g r ass b e? Ex p l ai n yo u r r easo n in g.

*

1-------x f t-------

PRACTI CES ^ s s e n ^ ' a l U n d e r s t a n d i n g You can use th e Distributive P roperty to m ultiply a

m onom ial by a polynom ial. x x x \

For example, consider the p ro d u ct 2x(3x + 1).

2x(3x + 1) = 2x(3x) + 2x(l)

= 6x2 + 2x

You can show w hy the m ultiplication m akes sense using

th e area m odel at th e right.

Pl an

What should I

keep in mind when

multiplying?

Remember to distribute

-x 3 to a/l o f the terms.

Also remember to add

the exponents instead o f

multiplying them.

Multiplying a Monomial and a Trinomial

Multiple Choice W hat is a sim p le r fo rm o f -x 3 (9 x 4 - 2x 3 + 7)?

(3D - 9 x 7 - 2x3 + 7

GD — 9x7 + 2x6 - 7x3

GD -9x12 + 2x9 - 7x3

GD 9x7 - 2 x 6 + 7 x 3

• x 3(9x4 - 2X3 + 7) = - x 3(9x4) - x3(-2 x 3) - x3(7) Use the D istrib u tive Property.

= —9x3+4+ 2x3+3 - 7x3

= —9x7 + 2x6 - 7x3

Multiply coefficients and

add exponents.

Simplify.

The correct answ er is D.

G ot It? 1. W hat is a sim pler form of 5«(3«3 — n2 + 8)?

492 Chapter 8 Polynomials and Factoring

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