Chapter 5

5.5 – MULTIPLYING AND DIVIDING A

POLYNOMIAL BY A CONSTANT

MULTIPLICATION

What does this multiplication statement actually mean? How could you describe it in words?

We have two groups of 3x

= 6x

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

MULTIPLICATION

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

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

EXAMPLE

Divide:

Independent Practice

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

23, 24

Chapter 5

5.6 – MULTIPLYING AND DIVIDING A

POLYNOMIAL BY A MONOMIAL

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

TRY IT

Multiply:

–2x(–3x + 4)

–2x(–3x + 4) = (–2x)(–3x) + (–2x)(4)

= 6x2 – 8x

(–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

TRY IT

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

Independent Practice

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

25.

UNIT PROBLEM