A polynomial function is defined as
f(x)=x4+ax3+2x2+bx−6 f(x) = x^4 + ax^3 + 2x^2 + bx - 6 f(x)=x4+ax3+2x2+bx−6where aaa and bbb are constants.
When f(x)f(x)f(x) is divided by (x−1)(x - 1)(x−1), the remainder is −10-10−10. Show that a+b=−7a + b = -7a+b=−7.
When f(x)f(x)f(x) is divided by (x+2)(x + 2)(x+2), the remainder is 222. Find the value of aaa and the value of bbb.
