If C, equals, 2, x, minus, 5, x, squared, minus, 9C=2x−5x

Question

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:

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