Question

If C=G-4F, find the trinomial that represents C when F=2x^(2)+6x-5 and G=3x^(2)+4

Answer 1

To find the polynomial for C given that C=G-4F and the expressions for F and G, simply perform substitution and simplification. The resulting polynomial is C = -5x^2 - 24x + 24.

Step-by-step explanation:

The question relates to finding the polynomial that represents C when given that C=G-4F and given expressions for F and G. Since F=2x^2+6x-5 and G=3x^2+4, we substitute these into the equation for C.

So, we compute C by following these steps:

1. First, multiply F by 4: 4F = 4(2x^2 + 6x - 5) = 8x^2 + 24x - 20.
2. Then, substitute F and G into the original equation for C: C = G - 4F = (3x^2 + 4) - (8x^2 + 24x - 20).
3. Lastly, simplify the expression for C to get the final polynomial: C = -5x^2 - 24x + 24.