MATH SOLVE

2 months ago

Q:
# can someone please help me with equating coefficients?(x+4)(ax^2 + bx + c) = -2x^3 -7x^2 + 3x -4

Accepted Solution

A:

ANSWERa=-2,v=1,c=-1EXPLANATION[tex](x + 4)(a {x}^{2} + bx + c) = - 2 {x}^{3} - 7 {x}^{2} + 3x - 4[/tex]We expand the left hand side to get,[tex]a {x}^{3} + b {x}^{2} + cx + 4ax^{2} + 4bx + 4c = - 2 {x}^{3} - 7 {x}^{2} + 3x - 4[/tex]Simplify further to get:[tex]a {x}^{3} +(4a + b) {x}^{2} +( 4b + c)x + 4c = - 2 {x}^{3} - 7 {x}^{2} + 3x - 4[/tex]Comparing the coefficients of the cubic terms , we have[tex]a {x}^{3}=-2{x}^{3} [/tex][tex]a =- 2[/tex]Comparing the quadratic terms,[tex](4a + b) {x}^{2} = - 7 {x}^{2} [/tex][tex]4a + b = - 7[/tex][tex]4( - 2) + b = - 7[/tex][tex] - 8 + b = - 7[/tex][tex]b = - 7 + 8 = 1[/tex]Comparing the constant terms, [tex]4c = - 4[/tex][tex]c = - 1[/tex]