Question

Factor the four-term polynomial. pq - 2r + pr - 2q

a) (p - 2)(q + r)
b) (p - r)(q + 2)
c) (p + 2)(q - r)
d) None of the above

Answer 1

To factor the four-term polynomial pq - 2r + pr - 2q, we group the terms to find common factors, which are p and -2, and then factor out the common term (q + r), resulting in the factored form (q + r)(p - 2).

Step-by-step explanation:

To factor the four-term polynomial pq - 2r + pr - 2q, we should look for common factors in pairs of terms. First, we notice that p is a common factor in pq and pr, and -2 is a common factor in -2r and -2q. After factoring the polynomial by grouping, we get:

(pq - 2r) + (pr - 2q) = p(q + r) - 2(r + q).

Because (q + r) is a common term, we can factor it out:

p(q + r) - 2(r + q) = (q + r)(p - 2).

So, the factored form of the polynomial pq - 2r + pr - 2q is (q + r)(p - 2), which corresponds to option a) (p - 2)(q + r).