Question

Rewrite 40 − 8x3 using a common factor.

a) 4x(10 − 2x2)

b) 4(10 − 2x3)

c) 8x(5 − x2)

d) 8(5 − 8x3)

Answer 1

Rewrite one fourth times x cubed times y plus three fourths times x times y squared using a common factor.

a) one fourth times x times y times the quantity x squared plus 3 times y end quantity

b) one fourth times x cubed times y squared times the quantity y plus 3 times x end quantity

c) one half times x times y times the quantity 2 times x squared plus 6 times y end quantity

d) one half times x times y times the quantity x squared plus 3 times y end quantity

Answer 2

Rewrite x4y2 − 3x3y3 using a common factor.

a) 3xy(x3y − x2y)

b) 3xy2(x2 − x2y)

c) x2y(xy − 3xy2)

d) x2y2(x2 − 3xy)

Answer 3

Factor −6x2 + 18x.

a) 6x(−x + 3)

b) −6x(x + 3)

c) x(6x + 18)

d) 6(−x2 + 18x)

Answer 4

Rewrite 7x + 49 using a common factor.

a) 7(x + 7)

b) 7(x + 49)

c) 7x(x + 7)

d) 7x(x + 49)

Answer 5

You are given the expression 36x4y3 − 16x3y.


Part A: Find a common factor for the expression that has a coefficient other than 1 and that contains at least one variable.

Part B: Explain how you found the common factor.

Part C: Rewrite the expression using the common factor you found in Part A. Show every step of your work.

Answer 6

c) 8x(5 - x^2)

Answer 7

d) one half times x times y times the quantity x squared plus 3 times y end quantity

Answer 8

d) x2y2(x2 - 3xy)

Answer 9

a) 6x(-x + 3)

Answer 10

a) 7(x + 7)

Answer 11

Part A: The common factor for the expression is 4xy.

Part B: To find the common factor, we look for the highest power of each variable that appears in both terms. In this case, both terms have x to the power of 3 and y to the power of 1. Therefore, the common factor is 4xy.

Part C: To rewrite the expression using the common factor 4xy:

Step 1: Take out the common factor:
36x^4y^3 - 16x^3y = 4xy(9x^3y^2 - 4x^2)

Therefore, the rewritten expression using the common factor is 4xy(9x^3y^2 - 4x^2).