AI Math Solver
Resources
Questions
Pricing
Login
Register
Home
>
Questions
>
Factor the Expression Using Distributive Property: x² + 9x = x(? + 9)
Mathematics
Grade 7
Question Content
Use the distributive property in reverse (factoring) to complete the statement: x² + 9x = x(____ + 9)
Correct Answer
x
Detailed Solution Steps
1
Step 1: Recall factoring using the distributive property: ab + ac = a(b + c), where a is the greatest common factor (GCF) of ab and ac.
2
Step 2: Identify the GCF of x² and 9x, which is x.
3
Step 3: Divide each term by the GCF: x²÷x = x, 9x÷x = 9.
4
Step 4: Fill in the blank with x, so the factored form is x(x+9).
Knowledge Points Involved
1
Factoring Variable Terms with Exponents
When factoring terms with variable exponents, the GCF is the variable with the lowest exponent. For x² and 9x, the lowest exponent of x is 1, so the GCF is x. Factoring out x gives x(x+9).
2
Dividing Variable Terms with Exponents
When dividing variable terms with exponents, subtract the exponent in the denominator from the exponent in the numerator: x^m ÷ x^n = x^(m-n). For x²÷x, m=2, n=1, so x²÷x = x^(2-1) = x.
Loading solution...
