Precalculus Examples

$(2 x^{2} - 3 x + 4) \cdot (1 - x^{2})$

Step 1

Rewrite $1$ as $1^{2}$ .

$(2 x^{2} - 3 x + 4) \cdot (1^{2} - x^{2})$

Step 2

Factor.

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Step 2.1

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 1$ and $b = x$ .

$(2 x^{2} - 3 x + 4) \cdot ((1 + x) (1 - x))$

Step 2.2

Remove unnecessary parentheses.

$(2 x^{2} - 3 x + 4) \cdot (1 + x) (1 - x)$

Step 3

Since the polynomial can not be factored, it is a prime polynomial.

Prime