To find the width of the field, we need to divide the area trinomial by the length of the rectangle.
\( \frac{t^2 - 4t - 45}{t + 5} \)
This can be simplified using polynomial division or by factoring the trinomial.
\( t^2 - 4t - 45 = (t - 9)(t + 5) \)
Therefore, the width of the field is \( t - 9 \).
So, the correct answer is: t - 9
A)
The area of a rectangular field is given by the trinomial t^2 – 4t – 45. The length of the
rectangle is t + 5. What is the expression for the width of the field?
(1 point)
t – 9
t – 5
t – 11
t – 7
3 answers
Factor 2g^3-g^2-8g+4
To factor the polynomial 2g^3 - g^2 - 8g + 4, we can first group the terms:
2g^3 - g^2 - 8g + 4
Now, let's factor by grouping:
2g^3 - g^2 - 8g + 4
= 2g^2(g) - g^2(1) - 4g(2) + 4(1)
= g^2(2g - 1) - 4(2g - 1)
= (2g - 1)(g^2 - 4)
Therefore, the factored form of the polynomial 2g^3 - g^2 - 8g + 4 is:
(2g - 1)(g^2 - 4)
2g^3 - g^2 - 8g + 4
Now, let's factor by grouping:
2g^3 - g^2 - 8g + 4
= 2g^2(g) - g^2(1) - 4g(2) + 4(1)
= g^2(2g - 1) - 4(2g - 1)
= (2g - 1)(g^2 - 4)
Therefore, the factored form of the polynomial 2g^3 - g^2 - 8g + 4 is:
(2g - 1)(g^2 - 4)