13.if ( c = g - 3f ), find the trinomial that represents ( c ) when ( f = 2x^{2}+6x - 5 ) and ( g = 3x^{2}+4…
13.if ( c = g - 3f ), find the trinomial that represents ( c ) when ( f = 2x^{2}+6x - 5 ) and ( g = 3x^{2}+4 ).
Answer
Explanation:
Step1: Substitute (F) and (G) into the formula
Given (C = G-3F), (F = 2x^{2}+6x - 5), (G=3x^{2}+4). Then (C=(3x^{2}+4)-3(2x^{2}+6x - 5))
Step2: Expand the expression
Use the distributive property (a(b + c+d)=ab+ac + ad). So (C = 3x^{2}+4-(6x^{2}+18x-15)=3x^{2}+4 - 6x^{2}-18x + 15)
Step3: Combine like - terms
Combine the (x^{2}) terms: (3x^{2}-6x^{2}=-3x^{2}), the constant terms: (4 + 15=19). So (C=-3x^{2}-18x + 19)
Answer:
(-3x^{2}-18x + 19)