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Chapter 0: Problem 124

Suppose that a polynomial contains four terms. Explain how to use factoring by grouping to factor the polynomial.

Short Answer

Expert verified
To factor a 4-term polynomial by grouping, firstly, group the polynomial in pairs. Then, factor out the common factor from each grouped term. Lastly, factor out the common binomial term from the expression.

Step by step solution

01

Group the Terms

Let's consider a general 4-term polynomial: \(ax + ay + bx + by\). Begin by grouping the terms in pairs: \((ax + ay) + (bx + by)\).
02

Factor Each Group

After grouping, factor out the common factor from each group. If \(ax + ay\) is the first group and \(bx + by\) is the second group, factor out the common factor 'a' out of the first group and 'b' out of the second group. The polynomial therefore becomes \(a(x + y) + b(x + y)\).
03

Factor out Common Binomial

Now, observe the resulting expression. It has a common factor \((x + y)\) in each term. Factor this out to give the factorized polynomial: \((a + b)(x + y)\).

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Most popular questions from this chapter

$$\text { Factor completely.}$$ $$2 x^{2}-7 x y^{2}+3 y^{4}$$

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