How do I factor 2x^2-16x-66
To factorize the quadratic expression 2x^2 - 16x - 66, you can follow these steps:
Step 1: Check for the greatest common factor (GCF)
In this case, there is no common factor other than 2, so we can proceed to the next step.
Step 2: Multiply the coefficient of the x^2 term and the constant term
The product of the coefficient of the x^2 term (2) and the constant term (-66) is -132.
Step 3: Find two numbers that multiply to give the product from step 2 (the middle term coefficient)
We need to find two numbers that add up to -16 (the coefficient of the x term) and multiply to -132.
The two numbers are -6 and 22. (-6 + 22 = 16 and -6 * 22 = -132)
Step 4: Rewrite the middle term (-16x) using the two numbers found in step 3
Replace the -16x in the original expression with -6x and +22x to get:
2x^2 - 6x + 22x - 66
Step 5: Group the terms and factor by grouping
Now, you can group the terms and factor by grouping:
(2x^2 - 6x) + (22x - 66)
Factor out the common factors from each group:
2x(x - 3) + 22(x - 3)
Step 6: Factor out the common binomial factor
Notice that both groups have a common factor of (x - 3). Factor it out to get the final factored form:
(x - 3)(2x + 22)
Therefore, the factored form of the expression 2x^2 - 16x - 66 is (x - 3)(2x + 22).
To factor the quadratic expression 2x^2 - 16x - 66, follow these steps:
Step 1: Ensure the quadratic expression is in the form ax^2 + bx + c, where a, b, and c are the coefficients of the quadratic terms.
In this case, the expression is already in the correct form.
Step 2: Find the two numbers that multiply to give ac (the product of the coefficient of x^2 and the constant term c) and add up to give b (the coefficient of x).
In this case, a = 2, b = -16, and c = -66.
ac = (2)(-66) = -132
To find two numbers that multiply to -132 and add up to -16, we can start by listing all the factor pairs of 132:
1, 132
2, 66
3, 44
4, 33
6, 22
...
After analyzing these factor pairs, we find that the numbers -22 and 6 multiply to -132 and add up to -16.
Step 3: Rewrite the middle term (-16x in this case) using the two numbers found in step 2.
The expression becomes: 2x^2 - 22x + 6x - 66
Step 4: Group the terms in pairs.
(2x^2 - 22x) + (6x - 66)
Step 5: Factor out the greatest common factor from each group.
2x(x - 11) + 6(x - 11)
Step 6: Factor out the common binomial factor (x - 11) from both groups.
(x - 11)(2x + 6)
Step 7: Simplify the expression if necessary.
Final factored form: (x - 11)(2x + 6)