Easy Algebra Step-by-Step

130 Easy Algebra Step-by-Step

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^251 xx 4 =()xx ()x

?

)(x+

Check: ()x )()(xx+ =xxx^227272 x++ xxx− 1414 x − 51 xx− 4

Correct



Step 4. Write the factored form.

xx^251 xx (^4) ()xxx (^7) ()x+ 2
e. 3 x^2 + 5 x − 2
Step 1. Because the expression has the form ax^2 + bx + c, look for two bino-
mial factors.
3 x^2 + 5 x− 2 = ( )( )
Step 2. 3 x^2 is the fi rst term, so the fi rst terms in the two binomial factors
must be 3x and x.
3 x^2 + 5 x− 2 = ( 3 x )(x )
Step 3. −2 is the last term, and it is negative, so the last terms in the two
binomial factors have opposite signs with a product of –2. Try com-
binations using the factors of –2 and check with FOIL until the mid-
dle term is correct.
Tr y 35 xx^2555 x− 2 ?() 33 xx )()(xx+
Check: ()^32 x^2 ()x+^133 xxx^222 +^32233222 xx^233333 x^2
Wrong

Tr y 35 xx^2555 x− 2 ?() 33 xx+ )()(xx−
Check: () 31 x 1 ()x− 2 33 xxx^2262626 xx 2 33353 x− 2
Wrong

Tr y 35 xx^2555 x− 2 () 33 xx ()x
?
)(x+
Check: () 31 x (^1) ()x+ 2 33 xxx^222 + 66262 xx 2 33333 5 x − 2
Correct