Question

f(x) = x4+2x-13x2-12x+21 is divisible by x2-4x+3 .find r(x).

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Answer 1

2x-3

Step-by-step explanation:

Given : Dividend = x^{4} +2x^{3} -13x^{2} -12x+21x

4

+2x

3

−13x

2

−12x+21

Divisor = x^{2} - 4x+3x

2

−4x+3

Solution :

Since we know that :

Dividend = divisor * quotient +remainderDividend=divisor∗quotient+remainder

x^{4} +2x^{3} -13x^{2} -12x+21 = (x^{2} - 4x+3)*x^{2} + (6x^{3}-16x^{2}-12x+21)x

4

+2x

3

−13x

2

−12x+21=(x

2

−4x+3)∗x

2

+(6x

3

−16x

2

−12x+21)

x^{4} +2x^{3} -13x^{2} -12x+21 = (x^{2} - 4x+3)*(x^{2}+6x) + (8x^{2}-30x+21)x

4

+2x

3

−13x

2

−12x+21=(x

2

−4x+3)∗(x

2

+6x)+(8x

2

−30x+21)

x^{4} +2x^{3} -13x^{2} -12x+21 = (x^{2} - 4x+3)*(x^{2}+6x+8) + (2x-3)x

4

+2x

3

−13x

2

−12x+21=(x

2

−4x+3)∗(x

2

+6x+8)+(2x−3)

Since the remainder is 2x-3

So, 2x-3 must be subtracted from x^{4} +2x^{3} -13x^{2} -12x+21x

4

+2x

3

−13x

2

−12x+21 so that the resulting polynomial is exactly divisible by x^{2} - 4x+3x

2

−4x+3

Answer 2

Answer:

2x-3 is the value of r(X)

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