Question

Use the Distributive Property to rewrite the polynomial (x+6)(3x−2)
.(1 point)
x2
+
x
+

Answer 1

To apply the Distributive Property to the expression \((x + 6)(3x - 2)\), we will distribute each term in the first polynomial to each term in the second polynomial.

1. First, distribute \(x\):
- \(x \cdot 3x = 3x^2\)
- \(x \cdot (-2) = -2x\)

2. Next, distribute \(6\):
- \(6 \cdot 3x = 18x\)
- \(6 \cdot (-2) = -12\)

Now, combine all the results:
\[
3x^2 - 2x + 18x - 12
\]

Combine like terms:
\[
3x^2 + ( -2x + 18x) - 12 = 3x^2 + 16x - 12
\]

So the rewritten polynomial is:
\[
3x^2 + 16x - 12
\]

Thus, filled out it is:
\(x^2\) = \(3\),
\(x\) = \(16\),
last term = \(-12\).