The product of two polynomials is x^{3}-3x^{2 | vedclass

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Question

(A) Let the given polynomial be $P(x) = x^{3}-3x^{2}-x+3$ and the known factor be $g(x) = x+1$. To find the other polynomial $q(x)$,we divide $P(x)$ b

Vedclass · Accepted Answer

$x^{2}-4x+3$

Vedclass · Answer

(A) Let the given polynomial be $P(x) = x^{3}-3x^{2}-x+3$ and the known factor be $g(x) = x+1$. To find the other polynomial $q(x)$,we divide $P(x)$ by $g(x)$.Using polynomial long division:$1$. Divide $x^{3}$ by $x$ to get $x^{2}$.$2$. Multiply $x^{2}(x+1) = x^{3}+x^{2}$.$3$. Subtract $(x^{3}-3x^{2}-x+3) - (x^{3}+x^{2}) = -4x^{2}-x+3$.$4$. Divide $-4x^{2}$ by $x$ to get $-4x$.$5$. Multiply $-4x(x+1) = -4x^{2}-4x$.$6$. Subtract $(-4x^{2}-x+3) - (-4x^{2}-4x) = 3x+3$.$7$. Divide $3x$ by $x$ to get $3$.$8$. Multiply $3(x+1) = 3x+3$.$9$. Subtract $(3x+3) - (3x+3) = 0$.The quotient is $x^{2}-4x+3$.

Part $I$	Part $II$
$1.$ The graph of $p(x)=x^{2}-5x+6$	$a.$ Intersects the $X$-axis at one point.
$2.$ The graph of $p(x)=x^{2}-10x+25$	$b.$ Intersects the $X$-axis at zero points.
$3.$ The graph of $p(x)=x^{3}-4x$	$c.$ Intersects the $X$-axis at two points.
$4.$ The graph of $p(x)=x^{2}+4x+5$	$d.$ Intersects the $X$-axis at three points.

The product of two polynomials is $x^{3}-3x^{2}-x+3$ and one of the polynomials is $x+1$. Find the other polynomial.

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