Question

Using remainder theoram,find the remainder when x⁴-3x³+2x²-4
is divided by x+2
please help me​

Answer 1

Remainder :

$\huge{\boxed{\tt{ 44}}}$

$\tt{ To \: find \: the \: Value \: of\: x \: \implies}$

$\tt{ x + 2 \implies 0}$

$\tt{ Transposing \: 2 \: gives\: x \implies 0 - 2}$

$\tt{ x \implies -2}$

So , we have found the value of (x)

The given polynomial is :

$\tt{ p(x) \implies {x}^{4} - {3x}^{3} + {2x}^{2} - 4}$

When we substitute the value of (x) ; we get :

$\tt{ p(-2) \implies {(-2)}^{4} - 3 \times {(-2)}^{3} + 2 \times {-2}^{2} - 4}$

$\tt{ p(-2) \implies 16 - 3 \times (-8) + 2 \times (4) - 4}$

$\tt{ p(-2) \implies 16 + 24 + 8 - 4}$

$\large{\boxed{\tt{ p(-2) \implies 44}}}$

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Remainder theorem :

In simple words using the remainder theorem if we divide the given polynomial p(x) with given g(x) ; if we get the remainder as 0 ; we can conclude that the given polynomial is a factor of g(x).