Question

2x^4 + 4x2 +4x -x3 - 7 by (x-1)

Answer 1

Answer:

4.2 Factoring x4 - 2x2 - 3

The first term is, x4 its coefficient is 1 .

The middle term is, -2x2 its coefficient is -2 .

The last term, "the constant", is -3

Step-1 : Multiply the coefficient of the first term by the constant 1 • -3 = -3

Step-2 : Find two factors of -3 whose sum equals the coefficient of the middle term, which is -2 .

-3 + 1 = -2 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -3 and 1

x4 - 3x2 + 1x2 - 3

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 :

1 • (x2-3)

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

(x2+1) • (x2-3)

Which is the desired factorization