Question

Expand the expression to a polynomial in standard form:
left parenthesis, x, minus, 6, right parenthesis, left parenthesis, minus, 3, x, squared, minus, 5, x, minus, 2, right parenthesis
(x−6)(−3x
2
−5x−2)
Answer

Answer 1

To expand the expression \((x - 6)(-3x^2 - 5x - 2)\), we can use the distributive property (also known as the FOIL method for binomials). Each term in the first polynomial will be multiplied by each term in the second polynomial.

1. Multiply \(x\) by each term in \(-3x^2 - 5x - 2\):
\[
x \cdot (-3x^2) = -3x^3
\]
\[
x \cdot (-5x) = -5x^2
\]
\[
x \cdot (-2) = -2x
\]

2. Now, multiply \(-6\) by each term in \(-3x^2 - 5x - 2\):
\[
-6 \cdot (-3x^2) = 18x^2
\]
\[
-6 \cdot (-5x) = 30x
\]
\[
-6 \cdot (-2) = 12
\]

3. Now, combine all the terms obtained from the multiplications:
\[
-3x^3 + (-5x^2) + (-2x) + 18x^2 + 30x + 12
\]

4. Combine like terms:
\[
-3x^3 + (-5x^2 + 18x^2) + (-2x + 30x) + 12
\]
\[
-3x^3 + 13x^2 + 28x + 12
\]

So, the expanded expression in standard form is:
\[
\boxed{-3x^3 + 13x^2 + 28x + 12}
\]