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Chapter 5 5.5 – MULTIPLYING AND DIVIDING A POLYNOMIAL BY A CONSTANT

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MULTIPLICATION What does this multiplication statement actually mean? How could you describe it in words? We have two groups of 3x = 6x

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MULTIPLICATION When we multiply or divide by a constant (i.e. a number, not a variable), then we just need to multiply/divide it by the coefficient(s). For example: or

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MULTIPLICATION

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EXAMPLE Multiply or divide: a) –2(2x 2 + x + 4)b) 9x ÷ 3 a) When dealing with negative constants, you switch the signs of all the algebra tiles. –2(2x 2 + x + 4) = (–2×2)x 2 + (–2)x + (–2×4) = –4x 2 – 2x – 8 b) 3 9x 3x 9x ÷ 3 = (9 ÷ 3)x = 3x

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TRY IT Divide: (5x 2 + 10x + 20) ÷ (–5) (5x 2 + 10x + 20) ÷ (–5) = (5 ÷ –5)x 2 + (10 ÷ –5)x + (20 ÷ –5) = –1x 2 + (–2)x + (–4) = –x 2 – 2x – 4

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EXAMPLE Divide:

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Independent Practice PG. 246-248 # 5, 8, 9, 14, 15, 16, 18, 20, 22, 23, 24

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Chapter 5 5.6 – MULTIPLYING AND DIVIDING A POLYNOMIAL BY A MONOMIAL

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EXAMPLE Multiply: a) (2c)(4c)b) (2c)(–4c)c) –4c(2c – 3) a) (2c)(4c) (2 × 4)(c × c) = 8c 2 b) (2c)(–4c) (2 × –4)(c × c) = –8c 2 c) –4c(2c – 3) (–4 × 2)(c × c) + (–4)(–3)c = –8c 2 + 12c

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TRY IT Multiply: –2x(–3x + 4) –2x(–3x + 4) = (–2x)(–3x) + (–2x)(4) = 6x 2 – 8x

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(–6 ÷ 3)(w 2 ÷ w) + (9 ÷ 3)(w ÷ w) = –2w + 3 Put the numerator down below, lining up with the denominator. Put the denominator in the top part

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TRY IT Sketch algebra tiles to represent the quotient, and then divide:

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Independent Practice PG. 4, 12, 14, 16, 19, 20, 21, 22, 23, 25.

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UNIT PROBLEM

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