Easy Algebra Step-by-Step

132 Easy Algebra Step-by-Step

Solution

a. 4 x^2 − 11 x− 3

Step 1. Identify the coeffi cients a, b, and c and

then fi nd two factors of ac whose sum is b.

a = 4, b = −11, and c = − 3

ac = 4 ⋅ − 3 = − 12

Two factors of −12 that sum to −11 are −12 and 1.

Step 2. Rewrite 4x^2 − 11 x− 3, replacing the middle term, − 11 x, with − 12 x+ 1 x.

4 x^2 − 11 x− 3 = 4 x^2 − 12 x+ 1 x− 3

Step 3. Group the terms in pairs that will yield a common factor.

= ( 4 x^2 − 12 x) + ( 1 x − 3 )

Step 4. Factor the common factor 4x out of the fi rst term and simplify the

second term.

= 4 x(x − 3 ) + (x − 3 )

Step 5. Use the distributive property to factor (x− 3) from the expression.

= (x− 3 )( 4 x+ 1 )

Step 6. Write the factored form.

xx^2111113 =()xx 33 () 44 x+ 1

b. 9 x^2 − 12 x + 4

Step 1. Identify the coeffi cients a, b, and c and then fi nd two factors of ac

whose sum is b.

a= 9, b=−12, and c= 4

ac= 9. 4 = 36

Two factors of 36 that sum to −12 are −6 and −6.

Step 2. Rewrite 9x^2 − 12 x + 4, replacing the middle term, − 12 x, with − 6 x − 6 x.

9 x^2 − 12 x + 4 = 9 x^2 − 6 x − 6 x + 4

Step 3. Group the terms in pairs that will yield a common factor.

=()− −()−

Check sign

When you’re identifying coeffi cients

for ax^2 + bx + c, keep a − symbol

with the number that follows it.