Question

1. match the polynomial with its factored form.

$x^3 - 1$ ______ a $(x + 1)^3$
$x^3 + 1$ ______ b $(x + 1)(x^2 - x + 1)$
c $(x - 1)^3$
d $(x - 1)(x^2 + x + 1)$

Explanation:

Step1: Factor $x^3 - 1$ (difference of cubes)

Use difference of cubes formula: $a^3 - b^3=(a-b)(a^2+ab+b^2)$.
Here $a=x$, $b=1$, so:
$$x^3 - 1=(x-1)(x^2+x+1)$$

Step2: Factor $x^3 + 1$ (sum of cubes)

Use sum of cubes formula: $a^3 + b^3=(a+b)(a^2-ab+b^2)$.
Here $a=x$, $b=1$, so:
$$x^3 + 1=(x+1)(x^2-x+1)$$

Answer:

$x^3 - 1$: D. $(x - 1)(x^2 + x + 1)$
$x^3 + 1$: B. $(x + 1)(x^2 - x + 1)$