IXL - Solve quadratic equations by factoring: other leading coefficients (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 product

–

so you need to find a pair of factors with a product of

–

The

term is 19, so you need to find a pair of factors with a sum of 19. Since the product is negative

(

–

you need one factor to be negative and one factor to be positive.

Make a list of the possible factor pairs with a product of

–

and then find the one with a sum of 19.

Factor pairs of a c = – 42	Sum of factor pairs
1 – 42 = – 42	1 + – 42 = – 41
– 1 42 = – 42	– 1 + 42 = 41
2 – 21 = – 42	2 + – 21 = – 19
– 2 21 = – 42	– 2 + 21 = 19
3 – 14 = – 42	3 + – 14 = – 11
– 3 14 = – 42	– 3 + 14 = 11
6 – 7 = – 42	6 + – 7 = – 1
– 6 7 = – 42	– 6 + 7 = 1

The factors 21 and

–

have a sum of 19. So, replace the quadratic's

term with

and

–

and then factor by grouping.

–

(

–

)

(

–

)

Factor by grouping; the expressions in parentheses should match

(

)

(

–

)

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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Work it out

Not feeling ready yet? These can help:

X.6Factor quadratics with other leading coefficients

Solve quadratic equations by factoring: leading coefficient 1

X.3Factor out a monomial

Lesson: Factoring quadratic equations

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