SOLUTION: Given that (x-2)^2 is a factor of the polynomial a(x^3) + b(x^2) + 7x + 4, find a and b and the other factor. Thank you.

Question 157666: Given that (x-2)^2 is a factor of the polynomial a(x^3) + b(x^2) + 7x + 4, find a and b and the other factor. Thank you.
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
(x-2)^2
=x^2-4x+4 we have to divide this into the number below:
a(x^3) + b(x^2) + 7x + 4
The last number of the quotient has to be 1 so that when it is multiplied by +4 the result is 4. There can be no remainder.
The 1st number when multiplied by 4 has to equal 11 so that when it is subtracted from 7 it equals -4. 4z=11...z=11/4=2.75
==========___________2.75x+1___________
x^2-4x+4 /2.75x^3-10x^2+7x+4
==========2.75x^3-11x^2+11x
_______________________________
====================x^2-4x+4
====================x^2-4x+4
_______________________________
==========================0
.
.
So a=2.75, b=-10 and the other factor is 2.75x+1
.
Ed
RELATED QUESTIONS
Given polynomial and a factor, find the other factors. x^3-7x^2+7x-15;factor... (answered by josgarithmetic)

given that x=3+i is a root of p(x)=3x^4+ax^3+34x^2+bx-20 find the value of a and b if... (answered by greenestamps)

Factor the polynomial p(x) = 2x^3-9x^2+7x+6 given the fact that x=2 is a root of the... (answered by jsmallt9)

1)consider the polynomial p(x)=x^3+ax^2+bx-12 given that (x+3)and (x-4)are factors of... (answered by Edwin McCravy)

Which of the following is NOT a factor of (x^4-x^3-7x^2+x+6)? A. x-1? B. x-2 C. x+1 D. (answered by Boreal)

The polynomial x^4 + 3x^2 + a. where a is a constant, is denoted by p(x). It is given... (answered by greenestamps)

A polynomial P is given. P(x) = x^4 + 18x^2 + 81 (a) Factor P into linear and... (answered by MathLover1)

Factor the polynomial below completely, given that the binomial following it is a factor... (answered by RAY100)

A polynomial P is given a.) Factor P into linear and irreducible quadratic factors with... (answered by stanbon)