Question

examine whether x+2 is a factor of x³+3x²+5x+6 and of 2x+4​

Answer 1

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SOLUTION:-

• The zero of x+2 is -2. Let p(x) = x³+3x²+5x+6 and s(x) = 2x+4.

Then,

$\rm{p( - 2) = ( { - 2})^{3} + 3( { - 2)}^{2} + 5( - 2) + 6}$

$\rm{ = - 8 + 12 - 10 + 6}$

$\rm{ = 0}$

So, By the factor theorem, x+2 is a factor of x³ +3x²+5x+6.

Again,

• $\rm{s( - 2) = 2( - 2) + 4 = 0}$

So, x+2 is a factor of 2x+4. In fact, you can check this without applying the factor theorem, since 2x+4=2(x+2).

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Answer 2

Given- $x^3+3x^2+5x+6$ and of $2x+4$

The zero of $x+2$ is $-2$. Let p(x) = $x^3+3x^2+5x+6$ and $s(x) = 2x+4$

Then,

$P(-2)=(-2)^3+3(-2)^2+5(-2)+6$

$=-8+12-10+6$

$=0$

Both are the factor

So, By the factor theorem, $x+2$ is a factor of $x^3 +3x^2+5x+6$

Again,

$s(-2)=2(-2)+4=0$

So, $x+2$ is a factor of $2x+4$. In fact, you can check this without applying the factor theorem, since $2x+4=2(x+2)$.

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