Question

One factor of x4 + x² -20 is (x² +5), then the other factor is
​

Answer 1

Factor x^4 + x^2 - 20

Divide by x^2 + 5

Remainder = 0, Quotient = x^2 - 4

a^2 - b^2 = (a + b)(a - b)

x^2 - 4 = (x + 2) (x - 2)

So,

x^4 + x^2 - 20 = (x^2 + 5)(x + 2)(x - 2)

Hope this helps ;)

Answer 2

The other factor is (x² - 4).

Step-by-step explanation:

The expression is:

$x^{4}+x^{2}-20$

The equation is a quadratic equation in x².

One factor of the equation is (x² + 5).

Let the other factor be (x² + a).

Compute the product of the two factors and equate it to $x^{4}+x^{2}-20$ to compute the value of a as follows:

$(x^{2}+5)(x^{2}+a)=x^{4}+x^{2}-20\\(x^{2}+5)(x^{2}+a)=x^{4}+5x^{2}-4x^{2}-20\\(x^{2}+5)(x^{2}+a)=x^{2}(x^{2}+5)-4(x^{2}+5)\\(x^{2}+5)(x^{2}+a)=(x^{2}+5)(x^{2}-4)$

Thus, the value of a is -4.

Hence the other factor is (x² - 4).

Learn more:

https://brainly.in/question/1870001