Question

If one factor of x^4 + x^2 - 20 is x^2 + 5, its other factor is

Answer 1

Answer:

The other factor is x² - 4

Explaination:-

Given:-

↦ p(x) = x^4 + x^2 -20

↦ g(x) = x² + 5

If one Factor is x² + 5

Then,

To find:-

The other factor of p(x)

Solution:-

By using Division Algorithm ,

$\begin{array}{c|c|c} \tt{ x^2 + 5 }& \tt{x^4 + x^2 - 20} & \sf x^2 - 4 \\ & \sf x^4 + 5x^2 \: \: \: \: \: \: \: \: \: \: & \\ & \underline{ \sf \bf{ ( - ) \: ( - ) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } }& \\ & \rm - 4 {x}^{2} - 20 & \\ & \sf - 4 {x}^{2} - 20 & \\& \sf \underline{( + ) \ \: ( + ) \: \: \: \: \: \: \: \: } & \\ &0& \end{array}$

$\therefore{q(x) = x² - 4}$

$\therefore{The \:Other \:Factor \:of \p(x) \:is \:x² -4}$

As, The p(x) is also divisible by q(x).

so, we can say that q(x) is also a factor of p(x).