Question

factorise x4+x2-2 solve​

Answer 1

Solution:

We have to factorise - x⁴ + x² - 2

By splitting the middle term, we get,

= x⁴ - x² + 2x² - 2

= x²(x² - 1) + 2(x² - 1)

Taking x² - 1 as common, we get,

= (x² - 1)(x² + 2)

Using identity a² - b² = (a + b)(a - b), we get,

= (x + 1)(x - 1)(x² + 2) which is our required answer.

Answer:

• (x + 1)(x² + 2)(x - 1)

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Answer 2

Answer:

• $\left(x-1\right)\left(x+1\right)\left(x^{2}+2\right)$

Step-by-step Explanation :

Given that :

• x⁴ + x² - 2.

To Do :

• Factorize.

Factorizing the given equation :

⇝ x⁴ + x² - 2.

⇝ $x^{4}+x^{2}-2=0$

⇝ $\pm2,\pm1$

⇝ $x=1$

⇝ $x^{3}+x^{2}+2x+2=0$

⇝ $\pm2,\pm1$

⇝ $x=-1$

⇝ $x^{2}+2=0$

⇝ $x=\frac{0\pm\sqrt{0^{2}-4\times 1\times 2}}{2}$

⇝ $x=\frac{0\pm\sqrt{-8}}{2}$

⇝ $x^{2}+2$

⇝ $\bf\left(x-1\right)\left(x+1\right)\left(x^{2}+2\right)$

.°. The answer of the equation is $\bf\left(x-1\right)\left(x+1\right)\left(x^{2}+2\right)$.

Method used for solving it :

• To factor the expression, solve the equation where it equals to 0.

• By Rational Root Theorem, all rational roots of a polynomial are in the form p/q, where p divides the constant term -2 and q divides the leading coefficient 1. List all candidates p/q.

• Find one such root by trying out all the integer values, starting from the smallest by absolute value. If no integer roots are found, try out fractions.

• By Factor theorem, x-k is a factor of the polynomial for each root k. Divide x⁴ + x² - 2 by x-1 to get x³ + x² + 2x + 2. To factor the result, solve the equation where it equals to 0.

• By Rational Root Theorem, all rational roots of a polynomial are in the form p/q, where p divides the constant term 2 and q divides the leading coefficient 1. List all candidates p/q.

• Find one such root by trying out all the integer values, starting from the smallest by absolute value. If no integer roots are found, try out fractions.

• By Factor theorem, x-k is a factor of the polynomial for each root k. Divide x³ + x² + 2x + 2 by x+1 to get x² + 2. To factor the result, solve the equation where it equals to 0.

• All equations of the form ax² + bx + c = 0 can be solved using the quadratic formula: {-b±√(b² - 4ac)}/(2a). Substitute 1 for a, 0 for b, and 2 for c in the quadratic formula.

• Do the calculations.

• Polynomial x² + 2 is not factored since it does not have any rational roots.

• Rewrite the factored expression using the obtained roots.