Question

x³-6x²+11x-6 ÷x-1 by factor theorm​

Answer 1

According to Factor theorem, if (x - a) is a polynomial factor f(x), then f(a) = 0

=$f(X)=X^{3}-6X^{2}+11X-6$

Let us check if (x - 1) is the factor of f(x),

Then,

=$F(1)=1^{3}-6(1)^{2}+11(1)-6$

=$1-6+11-6=0$

Therefore (x-1) is a factor of f(x)

Let us check for the other factors

Hence

$=F(X)=(X-1)(X^{2}-5X+6)\\\\=X^{2}-5X+6=X^{2}-2X-3X+6\\\\=X(X-2)-3(X-2)\\\\=F(X)=(X-1)(X-2)(X-3)$

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