4.9 Review

Leanne Thompson

4.9 Review

Fill in the following chart.

Polynomial Type Coefficient(s) Leading Coefficient Constant Term Degree

a) $7x^3$

b) $4y^2 - 3y$

c) $5a^2 + 3a - 2b$

d) $6x^2 - 4y + 5z - 3$
Simplify the expressions.

a) $8x^2 - 3x + 4 + 6x^2 + 2x - 5$

b) $9y^5 - 2y^3 + 4y - 6 + 3y^3 + 5y - 2$

c) $(5x^3 + 2x^2 - 4x) + (3x^3 - x^2 + 5x)$

d) $(7y^4 - 2y^3 + 3y) - (3y^4 + 5y^3 - 2y)$

e) $(4a^2 - 3a + 7) + (2a^2 + 5a - 8)$

f) $(6m^3 - 4m^2 + 3) - (2m^3 + 5m^2 - 1)$
Multiply and simplify.

a) $3 + 2(4x - 6)$

b) $5m - 2(3m + 4n)$

c) $6(3x + 2) + 4(x - 5)$

d) $8(2a - 4b) - 3(4a + b)$

e) $7(3y - 1) + 5(2y + 3)$

f) $4(5x - 2y + 3) + 3(x + y - 6)$

g) $x(3x^2 - 4x + 5) - 2(2x^2 - 3x + 6)$

h) $2y(4y^2 - 5y + 2) + 3(3y^2 + y - 4)$
Determine the product.

a) $\left( 2x + 3 \right)\left( x + 5 \right)$

b) $\left( 3y + 4 \right)\left( 2y - 6 \right)$

c) $\left( x^2 + 4 \right)\left( x + 7 \right)$

d) $\left( 5a + 2 \right)\left( a - 3 \right)$

e) $\left( 3m + 7 \right)\left( 2m - 1 \right)$

f) $\left( 2p^2 + 3 \right)\left( p + 4 \right)$
a) A blanket is the shape of a triangle and has a base of (2n + 6) m and a height of (4n – 6) m. Write an expression to represent the area of the blanket in the form an²+ bn + c.
b) Find the area of the blanket given that x = 2.5.
A square with side lengths (2x + 6) ft and a rectangle with side lengths (4x – 1) ft and (x + 4) ft have equal areas. Determine the value of x. Write your answer as an exact value.
In the following exercises, factor the greatest common factor from each polynomial.

a) $7n - 42$

b) $14x{y}^{2} + 21{x}^{2}{y}^{2} - 35{y}^{3}$

c) $4{x}^{2} + 8x - 16$

d) $28p{q}^{2} + 42{p}^{2}{q}^{2} - 35{q}^{3}$

e) $5p^{2} - 25p + 30$

f) $9q^{2} + 15q - 18$

g) $-3x - 6$

h) $12{q}^{2} + 18q + 24$

i) $-4b + 16$

j) $15{x}^{3} - 12x$

k) $6{x}^{3} - 18{x}^{2} + 24x$

l) $10{m}^{2} - 50m + 20$
Factor each trinomial of the form ${x}^{2}+bx+c$ .

a) ${x}^{2}+4x+3$

b) ${x}^{2}-8x+12$

c) ${p}^{2}+5p-6$

d) ${y}^{2}-6y-7$

e) ${x}^{2}-12-11x$

f) $4y^2 + 16y - 48$
Factor where possible.

a) $36 - x^2$

b) $64 - y^2$

c) $100a^2 - 25b^2$

d) $121p^2 - 49q^2$

e) $49x^2 - 9z^2$

f) $144m^2 - 81n^2$
Factor.

a) $2x^{2} + 9x - 5$

b) $5x^{2} + 2x - 3$

c) $3x^{2} - 2x - 8$

d) $4x^{2} + 19x - 5$

e) $6x^{2} + 9x - 6$

f) $2x^{2} - 5x + 3$

g) $6 - 7x -20x^{2}$

h) $8x^{2} + 42x + 40$

Answers

1.

Polynomial	Type	Coefficient(s)	Leading Coefficient	Constant Term	Degree
a) $7x^3$	Monomial	$7$	$7$	$0$	$3$
b) $4y^2 - 3y$	Binomial	$4, -3$	$4$	$0$	$2$
c) $5a^2 + 3a - 2b$	Trinomial	$5, 3, -2$	$5$	$0$	$2$
d) $6x^2 - 4y + 5z - 3$	Polynomial	$6, -4, 5$	$6$	$-3$	$2$

2.

a) $14x^2 - x - 1$	b) $9y^5 + y^3 + 9y - 8$
c) $8x^3 + x^2 + x$	d) $4y^4 - 7y^3 + 5y$
e) $6a^2 + 2a - 1$	f) $4m^3 - 9m^2 + 4$

3.

a) $8x - 9$	b) $-m - 8n$
c) $22x - 8$	d) $4a - 35b$
e) $31y + 8$	f) $23x - 5y - 6$
g) $3x^3 - 8x^2 + 11x - 12$	h) $8y^3 - y^2 + 7y - 12$

4.

a) $2x^2 + 13x + 15$	b) $6y^2 - 10y - 24$
c) $x^3 + 7x^2 + 4x + 28$	d) $5a^2 - 13a - 6$
e) $6m^2 + 11m - 7$	f) $2p^3 + 8p^2 + 3p + 12$

5. a) 4n²+ 6n – 18
b) 22 m²

6. $\frac{-16}{9}$

7.

a) $7(n - 6)$	b) $7y^2(2x + 3x^2 - 5y)$
c) $4(x^2 + 2x - 4)$	d) $7q^2(4p + 6q^2 - 5q)$
e) $5(p^2 - 5p + 6)$	f) $3(3q^2 + 5q - 6)$
g) $-3(x + 2)$	h) $6(2q^2 + 3q + 4)$
i) $-4(b - 4)$	j) $3x(5x^2 - 4)$
k) $6x(x^2 - 3x + 4)$	l) $10(m^2 - 5m + 2)$

8.

a) $\left(x+1\right)\left(x+3\right)$	b) $\left(x-2\right)\left(x-6\right)$	c) $\left(p-1\right)\left(p+6\right)$
d) $\left(y+1\right)\left(y-7\right)$	e) $\left(x-12\right)\left(x+1\right)$	f) $4(y - 2)(y + 6)$

9.

a) $(6 - x)(6 + x)$	b) $(8 - y)(8 + y)$	c) $25(2a - b)(2a + b)$
d) $(11p - 7q)(11p + 7q)$	e) $(7x - 3z)(7x + 3z)$	f) $9(4m - 3n)(4m + 3n)$

10.

a) $(2x - 1)(x + 5)$	b) $(5x - 3)(x + 1)$	c) $(3x + 4)(x - 2)$	d) $(4x - 1)(x + 5)$
e) $(3x + 6)(2x - 1)$	f) $(2x - 3)(x - 1)$	g) $(3 + 4x)(2 - 5x)$	h) $2(4x + 5)(x + 4)$

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