6.3 Adding, Subtracting, and Multiplying Polynomialsmrkuhlthau.weebly.com/uploads/9/4/4/2/9442708/6.3.pdf · Multiplying Polynomials To multiply two polynomials, each term of the

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Homework Quiz: On a separate sheet of paper, turn in the following homework problems. SHOW ALL WORK with your answer!

Bonus:

13. 17.19.

21. 25.

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Classifying Polynomials by the Number of Terms

Number of Terms Name Example

1 Monomial x; x2; x3

2 Binomial x + 3; x2 ­ 4

3 Trinomial x2 + x + 1

4+ Polynomial x3 + x2 + x +1

Degree Type Standard Form

0 Constant f(x) = a0

1 Linear f(x) = a1x + a0

2 Quadratic f(x) = a2x2 + a1x + a0

3 Cubic f(x) = a3x3 + a2x2 + a1x + a0

4 Quartic f(x) = a4x4 + a3x3 + a2x2 + a1x + a0

Recall: Classifying Polynomials by the Degree

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6.3 Adding, Subtracting, and Multiplying Polynomials

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Adding or Subtracting Polynomials

To add or subtract polynomials, add or subtract the coefficients of like terms. You can use a vertical or horizontal format, whichever makes you

Ex.) (4x2 ­ 6x + 3) + (­2x2 + 8x ­ 5)

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Ex.) (3x3 + 2x2 ­ x ­ 7) + (x3 ­ 10x2 + 8)

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Ex.) (8x3 ­ 3x2 ­ 2x + 9) ­ (2x3 + 6x2 ­x + 1)

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Ex.) (­3x3 + x ­ 11) ­ (4x3 + x2 ­ x)

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Multiplying Polynomials

To multiply two polynomials, each term of the first polynomial must be multiplied by each term of the second polynomial, then add the products together. Consider (­x2 + 3) (x2 ­ 2x + 1)

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One Method

Ex.) (­x2 + 3) (x2 ­ 2x + 1)

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Another Method

Ex.) (­x2 + 3) (x2 ­ 2x + 1)

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1.) (x ­ 3) (2x ­ 4)

2.) (x ­ 2) (3x2 ­ 2x ­ 4)

3.) (x ­ 1) (x + 4) (x + 3)

4.) (x2 + x + 4) (2x2 ­ x + 1)

Try the following: Find the product.

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1.) (x ­ 3) (2x ­ 4)

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2.) (x ­ 2) (3x2 ­ 2x ­ 4)

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3.) (x ­ 1) (x + 4) (x + 3)

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4.) (x2 + x + 4) (2x2 ­ x + 1)

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Special Product Patterns

Sum and Difference Example(a + b) (a ­ b) = a2 ­ b2 (x + 3) (x ­ 3) = x2 ­ 9

Square of a Binomial(a + b)2 = a2 + 2ab + b2 (y + 4)2 = y2 + 8y + 16(a ­ b)2 = a2 ­ 2ab + b2 (3t ­ 2)2 = 9t4 ­ 12t2 + 4

Cube of a Binomial(a + b)3 = a3 + 3a2b + 3ab2 + b3 (x + 1)3 = x3 + 3x2 + 3x + 1(a ­ b)3 = a3 ­ 3a2b + 3ab2 ­ b3 (p ­ 2)3 = p3 ­ 6p2 + 12p ­ 8

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Complete the classwork sheet

Take out your student handbook and write down the homework:

pg. 341 #13­61 EOO (every other odd)if necessary, Finish Classwork (will be graded)