Factoring Quadratics Worksheet With Answers Page 2
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1
2Factoring Quadratics
Remember to check your answer by multiplying to compare.
(x - 3)(x - 9)
2
x
- 3x - 9x + 27
2
2
x
- 12x + 27
original: x
- 12x + 27
Factoring Quadratic Trinomials with Leading Coefficient Other Than 1:
1. Multiply the leading coefficient and the constant together,
.
2. List all possible factors of the result from step one.
3. Determine which factors, p and q, will add together to give the middle coefficient, b.
Note:
If no factors can be found, a different form of factoring must be used.
4. Write as ( x + p)( x + q).
5. Since we had to multiply by a in step 1, we now need to undo that by dividing p and q by a.
6. If a does not divide into p and q evenly, clear the fraction in that factor.
7. This will give your factored form.
8. Check your answer by multiplying to compare to the original trinomial.
2
Example: 2x
+ 17x + 26
Step 1) Multiply a & c.
2 26 = 52
Step 2) Factors of
.
1, 52
-1, -52
2, 26
-2, -26
4, 13
-4, -13
Step 3) Sum of the factors equals middle term.
1 + 52 = 53
-1 - 52 = -53
2 + 26 = 28
-2 - 26 = -28
4 + 13 = 17
-4 - 13 = -17
Step 4) Write as (x + p) ( x + q).
( x + 4)(x + 13)
Step 5) Divide p and q by a.
( x + 2)( x +
)
Step 6) Clear fraction left in step 5.
( x + 2 ) [ 2 ( x +
) ] = ( x + 2) ( 2x + 13)
Step 7) Factored form.
(x + 2)(2x + 13)
Step 8) Remember to check your answer by multiplying.
2
2
(x + 2)(2x + 13) =
2x
+ 13x + 4x + 26 = original: 2x
+ 17x + 26
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