Question

Factor the Trinomial 12r^2 + 7rs - 10s

a) (3r + 5)(4r - 2s)
b) (4r - 2s)(3r + 5)
c) (2r + 5)(6r - 2s)
d) (6r - 2s)(2r + 5)

Answer 1

The trinomial 12r² + 7rs - 10s is factored by finding two numbers that multiply to -120 and add up to 7, leading to the factorization of (2r - 2s)(6r + 5s). Thus, the correct answer is option (d) (6r - 2s)(2r + 5).

Step-by-step explanation:

To factor the trinomial 12r² + 7rs - 10s, we look for two numbers that multiply to give the product of the coefficient of r² (which is 12) and the constant term (which is -10), and add up to the coefficient of the middle term rs (which is 7).

These two numbers are 10 and -12. We can decompose the middle term, 7rs, using these two numbers:

12r² + 10rs - 12rs - 10s

Next, we group the terms:

(12r² + 10rs) - (12rs + 10s)

Then, we factor by grouping:

2r(6r + 5s) - 2s(6r + 5s)

Finally, we factor out the common binomial factor:

(2r - 2s)(6r + 5s)

Comparing with the provided options, the correct factorization of the trinomial is (d) (6r - 2s)(2r + 5).