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Question Find the trinomial CC when F=2x2+6x−5F=2x^2+6x-5 and G=3x2+G=3x^2+, given C=G−3FC=G-3F.

Studdy Solution

STEP 1

Assumptions1. The formula for CC is C=G−3C = G -3 . =x+6x−5 =x^{} +6x -5
3. G=3xG =3x^{}

STEP 2

We need to substitute the given expressions for $$ and $G$ into the formula for $C$.
C=G−C = G -

STEP 3

Substitute the given expressions for $$ and $G$ into the formula.
C=3x2−3(2x2+6x−5)C =3x^{2} -3(2x^{2} +6x -5)

STEP 4

Now, we need to distribute the −3-3 across the terms in the parentheses.
C=3x2−3(2x2)−3(6x)−3(−)C =3x^{2} -3(2x^{2}) -3(6x) -3(-)

STEP 5

implify the equation.
C=3x2−x2−18x+15C =3x^{2} -x^{2} -18x +15

STEP 6

Combine like terms.
C=−3x2−18x+15C = -3x^{2} -18x +15So, the trinomial that represents CC when =2x2+6x−5 =2x^{2} +6x -5 and G=3x2G =3x^{2} is C=−3x2−18x+15C = -3x^{2} -18x +15.

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