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)
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)
3 answers
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.
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.
1 answer