Question

Factorise the expression x^4+4x^2+3

Answer 1

${x}^{4} + 4 {x}^{2} + 3 = 0$

x4-4x2+3

Final result :

(x + 1) • (x - 1) • (x2 - 3)

Step by step solution :

Step 1 :

Equation at the end of step 1 :

((x4) - 22x2) + 3

Step 2 :

Trying to factor by splitting the middle term

2.1 Factoring x4-4x2+3

The first term is, x4 its coefficient is 1 .

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

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 -4 .

-3 + -1 = -4 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