Question

Factor the expression completely. -x^4-4x^2+21

Answer 1

Answer:

-(x^2-3)(x^2+7) Is the answer

Step-by-step explanation:

The first term is,  x4  its coefficient is  1 .

The middle term is,  +4x2  its coefficient is  4 .

The last term, "the constant", is  -21

Step-1 : Multiply the coefficient of the first term by the constant   1 • -21 = -21

Step-2 : Find two factors of  -21  whose sum equals the coefficient of the middle term, which is   4 .

     -21    +    1    =    -20

     -7    +    3    =    -4

     -3    +    7    =    4    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -3  and  7

                    x4 - 3x2 + 7x2 - 21

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

                   x2 • (x2-3)

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

                   7 • (x2-3)

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

                   -(x^2-3)(x^2+7)

            Which is the desired factorization

(Hope this helps can I pls have brainlist (crown) ☺️)