IXL - Factor quadratics completely (Algebra 1 practice)

Factor completely.

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Learn with an example

question

Factor completely.

key idea

To factor a quadratic of the form

write it as

where

and

Then factor by grouping.

solution

First factor out 2, the greatest common factor of

(

)

Next look at the quadratic inside the parentheses,

The product

is 6, so you need to find a pair of factors with a product of 6. The

term is 7, so you need to find a pair of factors with a sum of 7. Since the product is positive (6) and the sum is positive (7), you need both factors to be positive.

Make a list of the possible factor pairs with a product of 6, and then find the one with a sum of 7.

Factor pairs of a c = 6	Sum of factor pairs
1 6 = 6	1 + 6 = 7
2 3 = 6	2 + 3 = 5

The factors 1 and 6 have a sum of 7. So, replace the quadratic's

term with

and

and then factor by grouping.

(

)

(

)

Factor by grouping; the expressions in parentheses should match

[

(

)

(

)

]

Factor by grouping; the expressions in parentheses should match

(

)

(

)

Finally, check your work.

(

)

(

)

Apply the distributive property (FOIL)

(

)

Apply the distributive property (FOIL)

(

)

Yes,

(

)

(

)

Looking for more? Try these:

Lesson: Factoring expressions

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Teacher tools

Work it out

Not feeling ready yet? These can help:

X.5Factor quadratics with leading coefficient 1

X.3Factor out a monomial

Lesson: Factoring expressions

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