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

2. Lesson Quiz 2. (2a – 3)(a + 5) 1. 5jk(k – 2j) 5jk2 – 10j2k
Find each product.
1. 5jk(k – 2j)
5jk2 – 10j2k
2a2 + 7a –15

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. x4 –4x3 x2 5x3 5x Check It Out! Example 2b Find the product.
Multiply each term of one polynomial by each term of the other. Use a table to organize the products.
x –4x x2 5x
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
x4 + (–4x3 + 5x3) + (– 20x2 + x2) + (5x)
x4 + x3 – 19x2 + 5x

7. 2x4 -2x2 -5x3 +5x 3x2 -3 Check It Out! Example 2b Find the product.
Multiply each term of one polynomial by each term of the other. Use a table to organize the products.
x x
2x2
-5x 3
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.
2x4
+8x3
-2x2
-5x3
-20x2
+5x
3x2
+12x -3
2x4 + (- 5x3 + 8x3) + (3x2 -20x2 - 2x2) + (+12x +5x) -3
2x4 + 3x3 -19x2 +17x -3

8. Starting with 1. (6n+2)(-5n2 + 8n + 5)
Assignment
ALL Odd numbers
Starting with 1. (6n+2)(-5n2 + 8n + 5)
Need to see 1,3, 5 before you leave class today.
Due Wed/Thurs(whichever day I have you)
Quiz Tomorrow
Assignment
Odd numbers
Starting with 1. (x2 – 4x + 1)(x2 + 5x – 2)