Question

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Answer 1

Answer:

(x + 1)(x - 1)(x² + 9)

Step-by-step explanation:

Factorise the following:

$\longrightarrow$ x⁴ + 8x² - 9

$\sf x^4 = {(x^2)}^{2}:$

$\longrightarrow$ $\sf {(x^2)}^{2} + 8x^2 - 9$

The factors of -9 that sum to 8 are 9 and -1.

So,

$\longrightarrow$ $\sf {(x^2)}^{2} + (9 - 1)x^2 - 9$

$\longrightarrow$ $\sf {(x^2)}^{2} + 9x^2 - x^2 - 9$

$\longrightarrow$ x²(x² + 9) - 1(x² + 9)

$\longrightarrow$ (x² - 1)(x² + 9)

x² - 1 = x² - 1²:

(x² - 1²)(x² + 9)

Factor the difference of two squares.

x² - 1² = (x + 1)(x - 1):

$\longrightarrow$ (x + 1)(x - 1)(x² + 9)