Question

If C, equals, 2, x, minus, 5, x, squared, minus, 9C=2x−5x
2
−9 and D, equals, x, squared, plus, 9, x, commaD=x
2
+9x, find an expression that equals 3, C, plus, 2, D3C+2D in standard form.

Answer 1

Given the expressions for \( C \) and \( D \):

\[
C = 2x - 5x^2 - 9
\]
\[
D = x^2 + 9x
\]

We need to find \( 3C + 2D \).

First, we calculate \( 3C \):

\[
3C = 3(2x - 5x^2 - 9)
\]
\[
= 6x - 15x^2 - 27
\]

Next, we calculate \( 2D \):

\[
2D = 2(x^2 + 9x)
\]
\[
= 2x^2 + 18x
\]

Now we can add \( 3C \) and \( 2D \):

\[
3C + 2D = (6x - 15x^2 - 27) + (2x^2 + 18x)
\]

Now we combine like terms:

1. For \( x^2 \) terms:
\[
-15x^2 + 2x^2 = -13x^2
\]

2. For \( x \) terms:
\[
6x + 18x = 24x
\]

3. The constant term:
\[
-27
\]

Putting it all together, we have:

\[
3C + 2D = -13x^2 + 24x - 27
\]

Thus, the expression \( 3C + 2D \) in standard form is:

\[
-13x^2 + 24x - 27
\]