IXL - Solve quadratic equations by factoring: leading coefficient 1 (Algebra 1 practice)

Solve for

Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.

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question

Solve for

Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.

key idea

To factor a quadratic of the form

write it as

(

)

(

)

where

and

solution

Step 1: Factor.

The

term is 7, so you need to find a pair of factors with a product of 7. The

term is 8, so you need to find a pair of factors with a sum of 8. Since the product is positive (7) and the sum is positive (8), you need both factors to be positive.

Make a list of the possible factor pairs with a product of 7, and then find the one with a sum of 8.

Factor pairs of c = 7	Sum of factor pairs
1 7 = 7	1 + 7 = 8

The factors 7 and 1 have a sum of 8. Use those numbers to factor

(

)

(

)

Step 2: Use the zero product property to solve.

According to the zero product property, if

(

)

(

)

then

must be 0 or

must be 0. Write the two equations and solve for

–

The solutions are

–

and

–

Looking for more? Try these:

Lesson: Factoring quadratic equations

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Teacher tools

Work it out

Not feeling ready yet? These can help:

Z.2Solve a quadratic equation using the zero product property

X.5Factor quadratics with leading coefficient 1

Lesson: Factoring quadratic equations

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