chapter 5 5.5 – multiplying and dividing a polynomial by a constant
TRANSCRIPT
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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(2x2 + x + 4) b) 9x ÷ 3
a) When dealing with negative constants, you switch the signs of all the algebra tiles.
–2(2x2 + x + 4) = (–2×2)x2 + (–2)x + (–2×4)= –4x2 – 2x – 8
b)
39x
3x
9x ÷ 3 = (9 ÷ 3)x = 3x
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TRY IT
Divide:
(5x2 + 10x + 20) ÷ (–5)
(5x2 + 10x + 20) ÷ (–5) = (5 ÷ –5)x2 + (10 ÷ –5)x + (20 ÷ –5)
= –1x2 + (–2)x + (–4)
= –x2 – 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)= 8c2
b) (2c)(–4c)
(2 × –4)(c × c)= –8c2
c) –4c(2c – 3)
(–4 × 2)(c × c) + (–4)(–3)c= –8c2 + 12c
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TRY IT
Multiply:
–2x(–3x + 4)
–2x(–3x + 4) = (–2x)(–3x) + (–2x)(4)
= 6x2 – 8x
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(–6 ÷ 3)(w2 ÷ 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