Question

using factor method divide the following polynomial by binomial x^4+3x^2-10 by x^2+5​

Answer 1

x⁴+3x²-10

=----------------

x²+5

x⁴+(5-2)x²-10

=----------------------

x²+5

x⁴+5x²-2x²-10

=-----------------------

x²+5

x²(x²+5)-2(x²+5)

=--------------------------------

x²+5

(x²+5) (x²-2)

=--------------------------

(x²+5)

=(x²-2)

Answer 2

Answer:

The correct answer is (x²-2)

Step-by-step explanation:

Given polynomial P(x) =  x⁴+3x²-10

                             g(x) = x² + 5  

here we need to divide P(x) by g(x)

first simplify p(x) or write it as product of factors

P(x) =  x⁴+3x²-10  

       = x⁴ + (5x² - 2x²) - 10                [ 3x² = 5x² - 2x² ]

       = x⁴ + 5x² - 2x² - 10  

       = x² ( x²+ 5) - 2( x²+5)

       = (x²-2) (x²+5)

now divide p(x) by g(x)

⇒  $\frac{p(x)}{g(x)}$ =  $\frac{(x^{2} - 2) (x^{2} +5) }{ (x^{2} +5)}$

           =  (x²-2)