Question

question 9
rewrite each of the following polynomial expressions in factored form. (make sure it is completely factored!)

$4w^2 - 12w - 40 = \square$

$-3w^2 + 12w + 15 = \square$

question help: video

Explanation:

Step1: Factor out GCF for \(4w^2 - 12w - 40\)

The greatest common factor (GCF) of \(4w^2\), \(-12w\), and \(-40\) is 4. Factor out 4:
\(4(w^2 - 3w - 10)\)

Step2: Factor the quadratic \(w^2 - 3w - 10\)

Find two numbers that multiply to \(-10\) and add to \(-3\). The numbers are \(-5\) and \(2\). So:
\(w^2 - 3w - 10 = (w - 5)(w + 2)\)

Thus, \(4w^2 - 12w - 40 = 4(w - 5)(w + 2)\)

Step3: Factor out GCF for \(-3w^2 + 12w + 15\)

The GCF of \(-3w^2\), \(12w\), and \(15\) is \(-3\). Factor out \(-3\):
\(-3(w^2 - 4w - 5)\)

Step4: Factor the quadratic \(w^2 - 4w - 5\)

Find two numbers that multiply to \(-5\) and add to \(-4\). The numbers are \(-5\) and \(1\). So:
\(w^2 - 4w - 5 = (w - 5)(w + 1)\)

Thus, \(-3w^2 + 12w + 15 = -3(w - 5)(w + 1)\)

Answer:

For \(4w^2 - 12w - 40\): \(4(w - 5)(w + 2)\)
For \(-3w^2 + 12w + 15\): \(-3(w - 5)(w + 1)\)