Question

finals review - u3 dec: december 18 at 11:59 pm grade: 34% arithmetic on polynomial question if c = x + 6 and d = 3x - 6 + 4x², find an expression that equals c + 3d in standard form. answer attempt 1 out of 2 submit answer

Explanation:

Step1: Substitute C and D into the expression

We know \( C = x + 6 \) and \( D = 4x^{2}+3x - 6 \). So we substitute these into \( C + 3D \):
\( C + 3D=(x + 6)+3(4x^{2}+3x - 6) \)

Step2: Distribute the 3 in 3D

Using the distributive property \( a(b + c + d)=ab+ac + ad \), we get:
\( (x + 6)+3\times4x^{2}+3\times3x+3\times(- 6)=(x + 6)+12x^{2}+9x - 18 \)

Step3: Combine like terms

First, combine the \( x \)-terms: \( x+9x = 10x \)
Then, combine the constant terms: \( 6-18=-12 \)
So the expression becomes \( 12x^{2}+10x - 12 \)

Answer:

\( 12x^{2}+10x - 12 \)