Applying Combined Exponents Rules: Factoring Out the Greatest Common Factor (GCF)

Extract the common factor:

$4x^3+8x^4=$

First, we use the power law to multiply terms with identical bases:

$a^m\cdot a^n=a^{m+n}$It is necessary to keep in mind that:

$x^4=x^3\cdot x$Next, we return to the problem and extract the greatest common factor for the numbers separately and for the letters separately,

For the numbers, the greatest common factor is

$4$and for the letters it is:

$x^3$and therefore for the extraction

$4x^3$outside the parenthesis

We obtain the expression:

$4x^3+8x^4=4x^3(1+2x)$To determine what the expression inside the parentheses is, we use the power law, our knowledge of the multiplication table, and the answer to the question: "How many times do we multiply the common factor that we took out of the parenthesis to obtain each of the terms of the original expression that we factored?

Therefore, the correct answer is: a.

It is always recommended to review again and check that you get each and every one of the terms of the expression that is factored when opening the parentheses (through the distributive property), this can be done in the margin, on a piece of scrap paper, or by marking the factor we removed and each and every one of the terms inside the parenthesis, etc.

$$$4x^3(1+2x)$

Solve the following by removing a common factor:

$6x^6-9x^4=0$

First, we take out the smallest power

$6x^6-9x^4=$

$6x^4\left(x^2-1.5\right)=0$

If possible, we reduce the numbers by a common factor

Finally, we will compare the two sections with: $0$

$6x^4=0$

We divide by: $6x^3$

$x=0$

$x^2-1.5=0$

$x^2=1.5$

$x=\pm\sqrt{\frac{3}{2}}$

$x=0,x=\pm\sqrt{\frac{3}{2}}$

Factor the following expression:

$2a^5+8a^6+4a^3$

$a^3(25a^2+8a^3+4)$