Problem 89 - Algebra and Trigonometry

Question

Factor completely, or state that the polynomial is prime. $$x^{2} y-16 y+32-2 x^{2}$$

Step-by-Step Solution

Answer

The completely factored form of the polynomial is \((x^{2}+16)(y-2)\)

Step 1: Rearrange term

Rearrange the terms in a way that simplifies the expression. Giving: \(x^{2} y - 2 x^{2} + 16 y - 32\)

Step 2: Group similar terms

Group the patterned terms together: \(\{x^{2} y - 2 x^{2}\} + \{16 y - 32\}\)

Step 3: Factor out

Factor out any common terms within the grouped terms: \(x^{2}(y - 2) + 16(y - 2)\)

Step 4: Check and Re-group

Since \(y - 2\) is a term that is common in both groupings, regrouping and factoring it would give: \((x^{2}+16)(y-2)\)