Ask a New Question
Menu

Given that the polynomial f (×)=6-×-×^2 is a factor of the polynomial g (×)=ax^3+5×^2+bx-18=0.find the values of the constants a and g.The remainder when g (x) is divided by x+2

1 answer

If (6-x-x^2) divides g(x), then that means that (3+x) and (x-2) are both factors of g(x)

g(x)/(x+3) has a remainder of -27a-3b+27
g(x)/(x-2) has a remainder of 8a+2b+2

Since those are both zero, we have

9a+b = 9
4a+b = -1
a=2, b=-9

g(x) = 2x^3+5x^2-9x-18 = (2x+3)(x-2)(x+3)
Similar Questions
  1. the polynomial y= x^3 + 9x^2 - 30x - 270 has an x-intercept at x=-9a) use the x-intercept to find a factor of the polynomial b)
    1. answers icon 1 answer
    1. answers icon 1 answer
  3. Drag and drop.To factor a ______, first factor each _______. Then find the ________ of the terms and ______ out of the
    1. answers icon 1 answer
  4. A polynomial with integer coefficients is of the form\[12x^4 + a_3 x^3 + a_2 x^2 + a_1 x + 24 = 0.\] If $r$ is a rational root
    1. answers icon 1 answer
more similar questions