Question

Drag each term to the correct location on the expression. Each term can be used more than once, but not all terms will be used.

Completely factor this quadratic expression:
4x²2² +12x-72.
3
x² 2 4 4x 1 8
Reset
90
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+6)

Answer 1

The completely factored form of the quadratic expression 4x^2 + 12x - 72 is (x + 6) * 4(x - 3).

To completely factor the quadratic expression 4x^2 + 12x - 72, we can follow these steps:

Step 1: Find the product of the coefficient of the quadratic term (4) and the constant term (-72). In this case, the product is -288.

Step 2: Look for two numbers whose product is the same as the result obtained in Step 1 (-288) and whose sum is equal to the coefficient of the linear term (12). In this case, the numbers are 24 and -12.

Step 3: Rewrite the middle term (12x) using the two numbers found in Step 2:

4x^2 + 24x - 12x - 72

Step 4: Group the terms:

(4x^2 + 24x) - (12x + 72)

Step 5: Factor out the greatest common factor from each group:

4x(x + 6) - 12(x + 6)

Step 6: Notice that we have a common factor of (x + 6) in both terms. Factor it out:

(x + 6)(4x - 12)

Step 7: Simplify further by factoring out 4 from the second term:

(x + 6) * 4(x - 3)

The completely factored form of the quadratic expression 4x^2 + 12x - 72 is (x + 6) * 4(x - 3).