What is the simplified form of (4t^2-5t+3)/(2t^2-t+1)?
There is no common factor between the numerator and denominator that can be canceled out, so this expression cannot be simplified.
(4t^2-5t+3)/(2t^2-t+1)?
There is no common factor between the numerator and denominator that can be canceled out, so this expression cannot be simplified.
A box has a volume given by the trinomial 2x^3-16x^2-40x
To factor the trinomial 2x^3 - 16x^2 - 40x, we can begin by factoring out the greatest common factor, 2x:
2x(x^2 - 8x - 20)
Next, we can factor the quadratic expression x^2 - 8x - 20 using either factoring by grouping, completing the square, or the quadratic formula. Here, we will use factoring by grouping:
2x(x^2 - 10x + 2x - 20)
2x((x^2 - 10x) + (2x - 20))
2x(x(x - 10) + 2(x - 10))
2x(x - 10)(x + 2)
Therefore, the factored form of the trinomial 2x^3 - 16x^2 - 40x is:
2x(x - 10)(x + 2)
This means that the box has dimensions of (x - 10) by (x + 2) by 2x.
5d^-6 x d^12
To simplify 5d^-6 × d^12, we can use the rule of exponents that states that when we multiply two powers with the same base, we should add their exponents. That is:
5d^-6 × d^12 = 5 × d^-6+12
To simplify further, we need to add the exponents of d:
5 × d^(12-6) = 5 × d^6
Therefore, 5d^-6 × d^12 simplifies to 5d^6.
(-2x^3+13x^2-19x+6)/(-2x+3)
We can use long division to simplify (-2x^3 + 13x^2 - 19x + 6) / (-2x + 3):
```
x^2 - 5x + 12
---------------------
-2x + 3 | -2x^3 + 13x^2 - 19x + 6
| +2x^3 - 3x^2
|--------------
10x^2 - 19x
-10x^2 + 15x
--------------
-4x + 6
+4x - 6
-------
0
```
Therefore, (-2x^3 + 13x^2 - 19x + 6) / (-2x + 3) simplifies to x^2 - 5x + 12.