Questions: Factor Completely 9 x^2 + 90 x a. 9 x(x+10) b. 9(x^2+10) c. (9 x+10)(x+7) d. (x+10)(9 x+7)

Transcript text: Factor Completely \[ 9 x^{2}+90 x \] a. $9 x(x+10)$ b. $9\left(x^{2}+10\right)$ c. $(9 x+10)(x+7)$ d. $(x+10)(9 x+7)$

Solution

Solution Steps

To factor the given expression $9x^2 + 90x$ completely, we need to find the greatest common factor (GCF) of the terms. The GCF of $9x^2$ and $90x$ is $9x$. We can then factor out $9x$ from each term.

Solution Approach

Identify the greatest common factor (GCF) of the terms in the expression.
Factor out the GCF from the expression.

Step 1: Identify the Expression

We start with the expression: \[ 9x^2 + 90x \]

Step 2: Find the Greatest Common Factor (GCF)

The GCF of the terms $9x^2$ and $90x$ is $9x$.

Step 3: Factor Out the GCF

We factor out $9x$ from the expression: \[ 9x^2 + 90x = 9x(x + 10) \]

Final Answer

The completely factored form of the expression is: \[ \boxed{9x(x + 10)} \]

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