Question

The area of a rectangular classroom is given by the trinomial 10x2 + 3x – 4. What are the possible dimensions of the classroom? Use factoring.%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0A(5x – 4) and (2x + 1)%0D%0A(5 x – 4) and (2 x + 1)%0D%0A%0D%0A(5x – 4) and (2x – 1)%0D%0A(5 x – 4) and (2 x – 1)%0D%0A%0D%0A(5x + 4) and (2x – 1)%0D%0A(5 x + 4) and (2 x – 1)%0D%0A%0D%0A(5x + 4) and (2x + 1)

Answer 1

To factor the trinomial 10x^2 + 3x - 4, we want to find two binomials that multiply together to give us the trinomial.

First, find two numbers that multiply to give us -40 (the product of the first and last terms of the trinomial) and add up to 3 (the coefficient of the middle term). In this case, those numbers are 8 and -5.

Then, rewrite the middle term using these two numbers:
10x^2 + 8x - 5x - 4

Now, group the terms:
(10x^2 + 8x) - (5x + 4)

Factor out the greatest common factor from each group:
2x(5x + 4) - 1(5x + 4)

Now, notice that we have a common factor of (5x + 4) in both terms. We can factor it out:
(5x + 4)(2x - 1)

So the possible dimensions of the classroom are (5x + 4) and (2x - 1).