1. Multiplying Polynomials
6-2
Multiplying Polynomials
Warm Up
Lesson Presentation
Lesson Quiz
Holt Algebra 2

2. Warm Up Multiply. 1. x(x3) x4 2. 3x2(x5) 3x7 3. 2(5x3) 10x3 4. x(6x2)
5. xy(7x2)
7x3y
6. 3y2(–3y)
–9y3

3. Objectives
Multiply polynomials.

4. To multiply a polynomial by a monomial, use the Distributive Property and the Properties of Exponents.

5. Zero exponent, the answer is one and the base goes away.
Exponent Rules
When you multiply like bases, you add the exponents and the base stays the same.
When you divide like bases, you subtract the exponents and the base stays the same.
Power raised to a power, you multiply the powers and the base stays the same.
Zero exponent, the answer is one and the base goes away.
Negative exponent, send the base to the other side, and the exponent becomes positive.

6. Example 1: Multiplying a Monomial and a Polynomial
Find each product.
4x(y - 3x)
4xy –12x2
y x 4x
Distribute.
4xy
–12x2
Multiply.
B. fg(f4 + 2f3g – 3f2g2 )
f f3g – 3f2g2
f 5g
2f 4g2
– 3f 3g3 fg
Distribute.
Multiply.
f 5g + 2f 4g2 – 3f 3g3

7. Check It Out! Example 1
Find each product.
a. 3cd2(4c2d – 6cd + 14cd2)
3cd2(4c2d – 6cd + 14cd2)
3cd2  4c2d – 3cd2  6cd + 3cd2  14cd2
Distribute.
12c3d3 – 18c2d3 + 42c2d4
Multiply.
b. x2y(6y3 + y2 – 28y + 30)
x2y(6y3 + y2 – 28y + 30)
x2y  6y3 + x2y  y2 – x2y  28y + x2y  30
Distribute.
6x2y4 + x2y3 – 28x2y2 + 30x2y
Multiply.

8. Example 2B: Multiplying Polynomials
Find the product.
(-7y - 5)(y + 3)
Multiply each term of one polynomial by each term of the other. Use a table to organize the products. y
-7y -5
The top left corner is the first term in the product. Combine terms along diagonals to get the middle terms. The bottom right corner is the last term in the product.
-7y2
-21y
-5y
-15
-7y2 + (- 5y -21y ) + (-15)
-7y2 -26y - 15

9. Check It Out! Example 3
Mr. Silva manages a manufacturing plant. From 1990 through 2005 the number of units produced (in thousands) can be modeled by N(x) = 0.02x x + 3. The average cost per unit (in dollars) can be modeled by C(x) = –0.004x2 – 0.1x + 3. Write a polynomial T(x) that can be used to model the total costs.
Total cost is the product of the number of units and the cost per unit.
T(x) = N(x)  C(x)

10. Assignment Multiples of 3 (3,6,9,12,15,….)
(rest of paper- extra credit)
Page 1 5(2x+6y)
Page 2 (x-1)(2x-3)
Due Tuesday
Quiz Tomorrow
Assignment Odd problems
Even problems extra credit
Due Tuesday

11. Lesson Quiz 2. (2a3 – a + 3)(a2 + 3a – 5) 1. 5jk(k – 2j) 5jk2 – 10j2k
Find each product.
1. 5jk(k – 2j)
5jk2 – 10j2k
2a5 + 6a4 – 11a3 + 14a – 15

12. x4 –4x3 x2 5x3 5x –2x2 8x –2 Check It Out! Example 2b
Find the product.
(x2 – 4x + 1)(x2 + 5x – 2)
Multiply each term of one polynomial by each term of the other. Use a table to organize the products.
x –4x x2 5x –2
The top left corner is the first term in the product. Combine terms along diagonals to get the middle terms. The bottom right corner is the last term in the product. x4
–4x3 x2
5x3
–20x2 5x
–2x2 8x –2
x4 + (–4x3 + 5x3) + (–2x2 – 20x2 + x2) + (8x + 5x) – 2
x4 + x3 – 21x2 + 13x – 2