Question

x⁴ + 5x² - 36 = 0 solve the equation by reducing them to a quadratic equation ​

Answer 1

Answer:

2.1 Factoring x4-5x2-36

The first term is, x4 its coefficient is 1 .

The middle term is, -5x2 its coefficient is -5 .

The last term, "the constant", is -36

Step-1 : Multiply the coefficient of the first term by the constant 1 • -36 = -36

Step-2 : Find two factors of -36 whose sum equals the coefficient of the middle term, which is -5 .

-36 + 1 = -35

-18 + 2 = -16

-12 + 3 = -9

-9 + 4 = -5 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -9 and 4

x4 - 9x2 + 4x2 - 36

Step-4 : Add up the first 2 terms, pulling out like factors :

x2 • (x2-9)

Add up the last 2 terms, pulling out common factors :

4 • (x2-9)

Step-5 : Add up the four terms of step 4 :

(x2+4) • (x2-9)

Which is the desired factorization