A greatest common factor is the largest product of numbers and letters shared by every term. For a two-term expression, take out that factor, then divide both terms by it to find what belongs inside the parentheses. Desmos can check your result at chosen values, but one numerical match does not prove two expressions are equivalent for every value.
Hints
- Hint 1
The greatest common factor must divide both terms. Look at the coefficients and the powers of and : what number divides and , and what letters appear in each term?
- Hint 2
Factoring reverses distribution. After you take out , each term left inside the parentheses must multiply by to restore an original term. What do you get when you divide each term by ?
Step-by-step
Factor out what both terms share
Step 1Find the shared factor
The numbers and share . The smallest power of in both terms is , and the smallest power of is . So the greatest common factor, the largest factor shared by both terms, is .
- Step 2
Find what remains in each term
Divide each term by the entire to find what goes inside the parentheses:
Dividing reverses multiplication: multiplying each result by restores its original term. Don't divide by alone; that would leave out the shared letters.
- Step 3
Set up a numerical check
Choose and for a quick check. Type those values and the original expression into Desmos. It shows . This gives you a number to compare with your factored expression, though one match alone won't prove equivalence.
- Step 4
Write and check the factored expression
Put the two results from dividing inside parentheses after :
Type into Desmos; it also shows . The check agrees, and dividing both original terms by shows why the expressions match for every and . The equivalent expression is . Choice D.