If (x + 2)(3x^2 - x + 8) = Ax^3 + Bx^2 + Cx + D, what is the value of A + 2B + 3C + 4D?
+9674 Expand out.
\(\quad(x + 2)(3x^2 - x + 8)\\ = x(3x^2 - x + 8) + 2(3x^2 - x + 8)\\ = 3x^3 - x^2 + 8x + 6x^2 - 2x + 16\\ = 3x^3 + 5x^2 + 6x + 16\)
Now you can compare the coefficients of \(3x^3 + 5x^2 + 6x + 16\) and \(Ax^3 + Bx^2 + Cx + D\) to find A, B, C, D. Then just calculate A + 2B + 3C + 4D.
+9674 Expand out.
\(\quad(x + 2)(3x^2 - x + 8)\\ = x(3x^2 - x + 8) + 2(3x^2 - x + 8)\\ = 3x^3 - x^2 + 8x + 6x^2 - 2x + 16\\ = 3x^3 + 5x^2 + 6x + 16\)
Now you can compare the coefficients of \(3x^3 + 5x^2 + 6x + 16\) and \(Ax^3 + Bx^2 + Cx + D\) to find A, B, C, D. Then just calculate A + 2B + 3C + 4D.
