Easy Algebra Step-by-Step

Factoring Polynomials 129

b. x^2 − 9 x + 14

Step 1. Because the expression has the form ax^2 + bx + c, look for two bino-

mial factors.

x^2 − 9 x+ 14 = ( )( )

Step 2. x^2 is the fi rst term, so the fi rst terms in the two binomial factors must be x.

x^2 − 9 x+ 14 = (x )(x )

Step 3. 14 is the last term, and it is positive, so the last terms in the two

binomial factors have the same sign as −9, with a product of 14 and

a sum of −9. Try −7 and −2 and check with FOIL.

xx^2919 xx 4 =?()xx )()(xx−

Check: ()x )()(xx− =−xxx^2272 xx−− 2 xxx++ 1414 x − 91 xx+ 4

Correct



Step 4. Write the factored form.

xx^2919 xx 4 ()xxx 7 ()x− 2

c. x^2 + 5 x− 14

Step 1. Because the expression has the form ax^2 +bx+c, look for two bino-

mial factors.

x^2 + 5 x − 14 = ( )( )

Step 2. x^2 is the fi rst term, so the fi rst terms in the two binomial factors must be x.

x^2 + 5 x− 14 = (x )(x )

Step 3. −14 is the last term, and it is negative, so the last terms in the two

binomial factors have opposite signs with a product of −14 and a sum

of 5. Try combinations of factors of −14 and check with FOIL.

Tr y xx^2 + 515 xx 4 =()xx+ ()x

?

)(x−

Check: ()x+ )()(xx− =+xxx^22 + 7272 x− xxx 1414 =+x 51 xx − 4

Correct



Step 4. Write the factored form.

xx

(^2) + 551 xx 4 ()xxx 7 ()x− 2
d. x^2 − 5 x− 14
Step 1. Because the expression has the form ax^2 + bx + c, look for two bino-
mial factors.
x^2 − 5 x − 14 = ( )( )