Factor the four term polynomial pq 3r pr 3q – Factor the four-term polynomial pq + 3r + pr + 3q, embarking on a mathematical journey to uncover the underlying structure and simplify this polynomial expression.

This polynomial, consisting of four terms, presents an opportunity to explore the concept of factoring, a fundamental technique in algebra that involves expressing a polynomial as a product of simpler factors.

Factoring the Four-Term Polynomial pq + 3r + pr + 3q: Factor The Four Term Polynomial Pq 3r Pr 3q

Polynomials are mathematical expressions that consist of constants, variables, and exponents. A four-term polynomial is a polynomial that has four terms. The given polynomial, pq + 3r + pr + 3q, is a four-term polynomial.

Factoring Techniques

Factoring is a process of expressing a polynomial as a product of simpler polynomials. There are different methods for factoring polynomials, including the grouping method.

The grouping method involves grouping terms with common factors and factoring out those common factors. To factor the given polynomial using the grouping method, we can group the first two terms and the last two terms as follows:

• pq + 3r
• pr + 3q

We can then factor out the common factor from each group:

• pq + 3r = p(q + 3)
• pr + 3q = r(p + 3)

Factoring the Polynomial, Factor the four term polynomial pq 3r pr 3q

Now we can factor the given polynomial as follows:

• pq + 3r + pr + 3q
• = p(q + 3) + r(p + 3)
• = (p + 3)(q + r)

Verifying the Factors

To verify the factors, we can multiply them back together:

• (p + 3)(q + r)
• = p(q + r) + 3(q + r)
• = pq + pr + 3q + 3r
• = pq + 3r + pr + 3q

Since we get the original polynomial, we can conclude that the factors are correct.

FAQ Insights

What is the first step in factoring the polynomial pq + 3r + pr + 3q?

The first step is to identify any common factors among the terms. In this case, both pq and pr have a common factor of p, while 3r and 3q have a common factor of 3.

How do I verify the factors of the polynomial?

To verify the factors, multiply them back together. If the result is the original polynomial, then the factors are correct.