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8-3 Study Guide and Intervention: Multiplying Polynomials

1. The document provides examples and exercises for multiplying polynomials using the distributive property and FOIL (First, Outer, Inner, Last) method. 2. It shows how to multiply binomials by distributing the first term of one binomial to each term of the other binomial. 3. Students are given practice multiplying various polynomials, including binomials, trinomials, and polynomials with variables like x, y, n, etc. They are to find the products of the polynomial expressions.

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992 views2 pages

8-3 Study Guide and Intervention: Multiplying Polynomials

1. The document provides examples and exercises for multiplying polynomials using the distributive property and FOIL (First, Outer, Inner, Last) method. 2. It shows how to multiply binomials by distributing the first term of one binomial to each term of the other binomial. 3. Students are given practice multiplying various polynomials, including binomials, trinomials, and polynomials with variables like x, y, n, etc. They are to find the products of the polynomial expressions.

Uploaded by

bd6cpynwmp
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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NAME _____________________________________________ DATE ____________________________ PERIOD _____________

8-3 Study Guide and Intervention


Multiplying Polynomials
Multiply Binomials To multiply two binomials, you can apply the Distributive Property twice. A useful way to keep
track of terms in the product is to use the FOIL method as illustrated in Example 2.

Example 1: Find (x + 3)(x – 4). Example 2: Find (x – 2)(x + 5) using the FOIL method.
Horizontal Method (x – 2)(x + 5)
(x + 3)(x – 4) First Outer Inner Last

= x(x – 4) + 3(x – 4) = (x)(x) + (x)(5) + (–2)(x) + (–2)(5)


= (x)(x) + x(–4) + 3(x)+ 3(–4) = 𝑥 2 + 5x + (–2x) – 10
= 𝑥 2 – 4x + 3x – 12 = 𝑥 2 + 3x – 10
= 𝑥 2 – x – 12 The product is 𝑥 2 + 3x – 10.

Vertical Method
x+ 3
(×) x– 4
– 4x – 12
𝑥 2 + 3x
𝑥 2 – x – 12
The product is 𝑥 2 – x – 12.

Exercises
Find each product.
1. (x + 2)(x + 3) 2. (x – 4)(x + 1) 3. (x – 6)(x – 2)
𝟐 𝟐
𝒙 + 5x + 6 𝒙 – 3x – 4 𝒙𝟐 – 8x + 12

4. ( p – 4)( p + 2) 5. ( y + 5)( y + 2) 6. (2x – 1)(x + 5)


𝟐 𝟐
𝒑 – 2p – 8 𝒚 + 7y + 10 2𝒙𝟐 + 9x – 5

7. (3n – 4)(3n – 4) 8. (8m – 2)(8m + 2) 9. (k + 4)(5k – 1)


𝟐 𝟐
9𝒏 – 24n + 16 64𝒎 – 4 5𝒌𝟐 + 19k – 4

10. (3x + 1)(4x + 3) 11. (x – 8)(–3x + 1) 12. (5t + 4)(2t – 6)


12𝒙𝟐 + 13x + 3 –3𝒙𝟐 + 25x – 8 10𝒕𝟐 – 22t – 24

13. (5m – 3n)(4m – 2n) 14. (a – 3b)(2a – 5b) 15. (8x – 5)(8x + 5)
𝟐 𝟐 𝟐 𝟐
20𝒎 – 22mn + 6𝒏 2𝒂 – 11ab + 15𝒃 64𝒙𝟐 – 25

16. (2n – 4)(2n + 5) 17. (4m – 3)(5m – 5) 18. (7g – 4)(7g + 4)


4𝒏𝟐 + 2n – 20 20𝒎𝟐 – 35m + 15 49𝒈𝟐 – 16

Chapter 8 18 Glencoe Algebra 1


NAME _____________________________________________ DATE ____________________________ PERIOD _____________

8-3 Study Guide and Intervention (continued)


Multiplying Polynomials
Multiply Polynomials The Distributive Property can be used to multiply any two polynomials.

Example: Find (3x + 2)(2𝒙𝟐 – 4x + 5).


(3x + 2)(2𝑥 2 – 4x + 5)
= 3x(2𝑥 2 – 4x + 5) + 2(2𝑥 2 – 4x + 5) Distributive Property
= 6𝑥 3 – 12𝑥 2 + 15x + 4𝑥 2 – 8x + 10 Distributive Property
3 2
= 6𝑥 – 8𝑥 + 7x + 10 Combine like terms.
3 2
The product is 6𝑥 – 8𝑥 + 7x + 10.

Exercises
Find each product.
1. (x + 2)(𝑥 2 – 2x + 1) 2. (x + 3)(2𝑥 2 + x – 3)
𝒙𝟑 – 3x + 2 2𝒙𝟑 + 7𝒙𝟐 – 9

3. (2x – 1)(𝑥 2 – x + 2) 4. (p – 3)(𝑝2 – 4p + 2)


2𝒙𝟑 – 3𝒙𝟐 + 5x – 2 𝒑𝟑 – 7𝒑𝟐 + 14p – 6

5. (3k + 2)(𝑘 2 + k – 4) 6. (2t + 1)(10𝑡 2 – 2t – 4)


3𝒌𝟑 + 5𝒌𝟐 – 10k – 8 20𝒕𝟑 + 6𝒕𝟐 – 10t – 4

7. (3n – 4)(𝑛2 + 5n – 4) 8. (8x – 2)(3𝑥 2 + 2x – 1)


3𝒏𝟑 + 11𝒏𝟐 – 32n + 16 24𝒙𝟑 + 10𝒙𝟐 – 12x + 2

9. (2a + 4)(2𝑎2 – 8a + 3) 10. (3x – 4)(2𝑥 2 + 3x + 3)


4𝒂𝟑 – 8𝒂𝟐 – 26a + 12 6𝒙𝟑 + 𝒙𝟐 – 3x – 12

11. (𝑛2 + 2n – 1)(𝑛2 + n + 2) 12. (𝑡 2 + 4t – 1)(2𝑡 2 – t – 3)


𝒏𝟒 + 3𝒏𝟑 + 3𝒏𝟐 + 3n – 2 2𝒕𝟒 + 7𝒕𝟑 – 9𝒕𝟐 – 11t + 3

13. (𝑦 2 – 5y + 3)(2𝑦 2 + 7y – 4) 14. (3𝑏 2 – 2b + 1)(2𝑏 2 – 3b – 4)


2𝒚𝟒 – 3𝒚𝟑 – 33𝒚𝟐 + 41y –12 6𝒃𝟒 – 13𝒃𝟑 – 4𝒃𝟐 + 5b – 4

Chapter 8 19 Glencoe Algebra 1

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