Examine the validity of the statement: (x+3) | vedclass

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(A) To check if $(x+3)$ is a factor of $p(x) = x^{3}+6x^{2}+5x-12$,we use the Factor Theorem.According to the Factor Theorem,$(x-a)$ is a factor of $p

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(A) To check if $(x+3)$ is a factor of $p(x) = x^{3}+6x^{2}+5x-12$,we use the Factor Theorem.According to the Factor Theorem,$(x-a)$ is a factor of $p(x)$ if $p(a) = 0$.Here,$x+3 = x-(-3)$,so we need to evaluate $p(-3)$.$p(-3) = (-3)^{3} + 6(-3)^{2} + 5(-3) - 12$$p(-3) = -27 + 6(9) - 15 - 12$$p(-3) = -27 + 54 - 15 - 12$$p(-3) = 54 - 54 = 0$.Since $p(-3) = 0$,$(x+3)$ is indeed a factor of the given polynomial.Therefore,the statement is True.

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.

Examine the validity of the statement: $(x+3)$ is a factor of $x^{3}+6x^{2}+5x-12$.

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