Question

X2-5X+6 is a factor of X3-5X2+ax+6 find the numbers a and b?

Answer 1

If $x^2 -5x + 6$ is a factor of the polynomial, then the remainder must be 0.

Hence, Refer to The Attachment.

As, the remainder is $x(a-6) + 6$, it must be equal to 0.

So,

$x(a - 6) + 6 = 0 \\ x(a - 6) = - 6 \\ x(a - 6) = - 6 + 0x$

In this, the coefficient of x in L.H.S. must be equal to the coefficient of x in R.H.S.

Hence,

$a - 6 = 0 \\ a = 6$

Hope it Helps.

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