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Chapter 0: Problem 89

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

Short Answer

Expert verified
The complete factorization of the given polynomial is \((y - 2)(x^{2} + 16)\).

Step by step solution

01

Rearrange the Polynomial

Rearrange the polynomial. The best practice typically is to order the terms in descending powers of the variable, \(x\). Let's take the polynomial and rearrange it as \(x^{2} y- 2x^{2} + 32 - 16y\).
02

Find Common Factors

Look for common factors in all terms. In the first and the second term we can take out a common factor of \(x^{2}\), and in the third and the fourth term a common factor of 16. This gives us: \(x^{2}(y - 2) + 16(2 - y)\).
03

Rearrange the terms and factor

Rearrange the terms in the brackets to be identical. By reversing the order in the second bracket we get: \(x^{2}(y - 2) + 16(y - 2)\). Now, we see that \((y - 2)\) is a common factor we can factor out. We get for the polynomial: \((y - 2)(x^{2} + 16)\).

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Most popular questions from this chapter

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