Algebra 1 Common Core Student Edition, Grade 8-9

^ G o t It? 3. Divide.

a. (q4 + q2 + q - 3 ) - (q ~ 1) b. (ft 3 -4h+ 12 ) -s- (ft + 3)

To divide polynom ials using long division, you m u st write th e divisor an d the dividend

in stan d ard form before you divide.

How can you
elim inate choices?
If the product of the
divisor and choice A
equals the dividend, then
choice A is correct. Here,
the product does not
equal the dividend, so
eliminate choice A.

P__ Problem 4 Reordering Terms and Dividing Polynomials

Multiple Choice What is (- lOx - 1 + 4x2) -f- ( - 3 + 2x)?

C£ ) 2 x — 2

2x — 2 —2x — 3

2x - 2

2 x - 3 ) 4 x 2 - l O x - 1

4x2 - 6x

—4 x - 1

—4 x + 6

CO 2x 2 + 2x ~ 3

D 2 x ~ 2 + 2 x + 2

You must rewrite - 1 0x - 1 + 4x 2 and

• 3 + 2x in standard form before you divide.

The answ er is 2x - 2 - 2x - 3. The correct answ er is B.

G o t It? 4. In parts (a) and (b), divide.

a. ( - 7 - 10y + 6y2) ^ (4 + 3y) b. (21a + 2+ 18a2) h- (5 + 6a)

c. Reasoning How can you check th e answ er to Problem 4? Show

your work.

Concept Sum m ary Dividing a Polynomial by a Polynomial

\

St e p 1 Arrange th e term s of th e dividend an d divisor in stan d ard form. If a term is

m issing from th e dividend, ad d th e term w ith a coefficient of 0.

St e p 2 Divide th e first term of th e dividend by the first term of th e divisor. This is the

first term of the quotient.

St e p 3 M ultiply the first term of th e q u o tien t by th e w hole divisor a n d place the

product under the dividend.

St e p 4 Subtract this p ro d u c t from the dividend.

St e p 5 Bring dow n th e next term.

R epeat Steps 2-5 as necessary until the degree of th e re m a in d er is less th a n th e degree

of the divisor.

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6 8 0 C h a p t e r 11 Rat io nal Expressions and Funct ions