Question

When x5 -5x4 +9x3 -6x2 -16x +13 is divided by X2 -3x +a the quotient and remainder are x3-2x2 +x+1 and -15x +11 find a

Answer 1

Answer:

2

Step-by-step explanation:

Given in the question that,

divisor = $x^5 -5x^4 +9x^3 - 6x^2 -16x + 13$

dividend = $x^2 -3x +a$

quotient = $x^3 - 2x^2 + x+1$

reminder  =  -15x +11

divisor = dividend (quotient) + remainder

$x^5 -5x^4 +9x^3 - 6x^2 -16x + 13$=$x^2 -3x +a$($x^3 - 2x^2 + x+1$) -15x +11

$x^5 -5x^4 +9x^3 - 6x^2 -16x + 13$ = ($x^5 -6x^4+2x^3a+6x^3-2x^2a-2x^2+xa -3x +a$) -15x + 11

$x^5 -5x^4 +9x^3 - 6x^2 -16x + 13$=$x^5 -6x^4+2x^3a+6x^3-2x^2a-2x^2+xa -3x +a -15x + 11$

Match the coefficient of both sides, we can see that

13 = 11+a

13-11 = a

a = 2