Factoring using the quadratic formula
Factoring using the quadratic formula is the goal of this lesson. It is closely related to solving equations using the
quadratic formula
2 easy steps to follow when factoring using the quadratic formula:
Step #1:
Solve the quadratic equation to get x
_{1} and x
_{2}
Step #2
Uisng the answers found in step #1, the factorization form is a (x  x
_{1})(x  x
_{2})
Example #1:
Factor 4x
^{2} + 9x + 2 = 0 using the quadratic formula.
a = 4, b = 9, and c = 2
x = (b ± √(b
^{2}  4ac)) / 2a
x = (9 ± √(9
^{2}  4 × 4 × 2)) / 2 × 4
x = (9 ± √(81  4 × 4 × 2)) / 8
x = (9 ± √(81  4 × 8)) / 8
x = (9 ± √(81  32)) / 8
x = (9 ± √(49)) / 8
x = (9 ± 7 ) / 8
x
_{1} = (9 + 7 ) / 8
x
_{1} = (2 ) / 8
x
_{1} = 1/4
x
_{2} = (9  7 ) / 8
x
_{2} = (16 ) / 8
x
_{2} = 2
The factorization form is a (x  x
_{1})(x  x
_{2})
The factorization form is 4 (x  1/4)(x  2)
The factorization form is 4 (x + 1/4)(x + 2)
Now, use distributive property to simplify the expression by getting rid of fractions
4 (x + 1/4)(x + 2) = (4 × x + 4 × 1/4) (x + 2) = (4x + 1)(x + 2)
Example #2:
Factor x
^{2} + 2x  15 = 0 using the quadratic formula
a = 1, b = 2, and c = 15
x = (b ± √(b
^{2}  4ac)) / 2a
x = ( 2 ± √(2
^{2}  4 × 1 × 15)) / 2 × 1
x = (2 ± √(4  4 × 1 × 15)) / 2
x = (2 ± √(4  4 × 15)) / 2
x = (2 ± √(4 + 60)) / 2
x = (2 ± √(64)) / 2
x = (2 ± 8 ) / 2
x
_{1} = (2 + 8 ) / 2
x
_{1} = ( 6 ) / 2
x
_{1} = 3
x
_{2} = (2  8 ) / 2
x
_{2} = (10) / 2
x
_{2} = 5
The factorization form is a (x  x
_{1})(x  x
_{2})
The factorization form is 1 (x  3)(x  5)
The factorization form is 1 (x  3)(x + 5)
Now, use distributive property to simplify the expression
1 (x  3)(x + 5) = (1 × x + 1 × 3) (x + 2) = (x  3)(x + 5)
It is important to understand how to use the
quadratic formula before fatoring using the quadratic formula.

Feb 17, 19 12:04 PM
There is no rational number whose square is 2. An easy to follow proof by contraction.
Read More
New math lessons
Your email is safe with us. We will only use it to inform you about new math lessons.