Rewrite 40 − 8x3 using a common factor.
a) 4x(10 − 2x2)
b) 4(10 − 2x3)
c) 8x(5 − x2)
d) 8(5 − 8x3)
c) 8x(5 - x^2)
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
d) one half times x times y times the quantity x squared plus 3 times y end quantity
Rewrite x4y2 − 3x3y3 using a common factor.
a) 3xy(x3y − x2y)
b) 3xy2(x2 − x2y)
c) x2y(xy − 3xy2)
d) x2y2(x2 − 3xy)
d) x2y2(x2 - 3xy)
Factor −6x2 + 18x.
a) 6x(−x + 3)
b) −6x(x + 3)
c) x(6x + 18)
d) 6(−x2 + 18x)
a) 6x(-x + 3)
Rewrite 7x + 49 using a common factor.
a) 7(x + 7)
b) 7(x + 49)
c) 7x(x + 7)
d) 7x(x + 49)
a) 7(x + 7)
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.
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).