The area of a rectangular classroom is given by the trinomial 10x^2 + 3x – 4. What are the possible dimensions of the classroom? Use factoring.
1. (5x-4) and (2x+1)
2. (5x-4) and (2x-1)
3. (5x+4) and (2x-1)
4. (5x+4) and (2x+1)
The area of a rectangle is given by length times width, so in this case we want to factor the trinomial 10x^2 + 3x - 4 in order to find the possible dimensions of the classroom.
To factor the trinomial, we need to find two numbers that multiply to -40 (product of the constant term -4 and the coefficient of x^2 10) and add up to the coefficient of the middle term 3.
The numbers that satisfy this condition are 5 and -8. Therefore, the trinomial can be factored as:
10x^2 + 3x - 4 = (5x - 4)(2x + 1)
So the possible dimensions of the classroom are 5x - 4 and 2x + 1.
Therefore, the correct answer is 1. (5x-4) and (2x+1)
can you explain?
Of course!
To find the possible dimensions of the rectangular classroom, we need to factor the trinomial given, which is 10x^2 + 3x - 4. The area of a rectangle can be expressed as length times width, which corresponds to the given trinomial.
In order to factor the trinomial, we are looking for two binomials of the form (ax + b)(cx + d) that multiply to give the trinomial.
In the trinomial 10x^2 + 3x - 4, the leading coefficient is 10. To factor this trinomial, we first multiply the leading coefficient (10) by the constant term (-4), which gives -40.
Next, we need to find two numbers that multiply to -40 and add up to the coefficient of the middle term, which is 3. After some trial and error, we find that the numbers are 5 and -8, since 5 * -8 = -40 and 5 - 8 = 3.
Using these two numbers, we can then rewrite the trinomial as a product of two binomials:
10x^2 + 3x - 4 = (5x - 4)(2x + 1)
Therefore, the possible dimensions of the classroom are 5x - 4 and 2x + 1. This indicates that the length of the classroom could be represented as 5x - 4 and the width could be represented as 2x + 1.
I hope this helps clarify the reasoning behind the factoring process! Let me know if you have any more questions.