IXL - Factor quadratics with other leading coefficients (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

Look at the given quadratic:

The product

is 20, so you need to find a pair of factors with a product of 20. The

term is 9, so you need to find a pair of factors with a sum of 9. Since the product is positive (20) and the sum is positive (9), you need both factors to be positive.

Make a list of the possible factor pairs with a product of 20, and then find the one with a sum of 9.

Factor pairs of a c = 20	Sum of factor pairs
1 20 = 20	1 + 20 = 21
2 10 = 20	2 + 10 = 12
4 5 = 20	4 + 5 = 9

The factors 4 and 5 have a sum of 9. 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)

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.4Factor quadratics using algebra tiles

X.5Factor quadratics with leading coefficient 1

W.8Multiply two binomials

X.3Factor out a monomial

Lesson: Factoring expressions

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