First, we use the rational root theorem to determine any solutions of p(x). <span>= x3 + 4x2 + x − 6</span>
Factoring -6:
1
-1
2
-2
3
-3
6
-6
<span>x = 1 </span>
<span>p(1) = 1^3 + 4 * 1^2 + 1 - 6 = 6 - 6 = 0 </span>
<span>x = 1 is a solution. </span>
(x^3 + 4x^2 + x - 6) / (x - 1) =
x^3 / x = x^2
x^2 * (x - 1) = x^3 - x^2
x^3 + 4x^2 - x^3 + x^2 = 5x^2
5x^2 / x = 5x
5x * (x - 1) = 5x^2 - 5x
5x^2 + x - 5x^2 + 5x = 6x
6x / x = 6
6 * (x - 1) = 6x - 6
6x - 6 - 6x + 6 = 0
<span>(x - 1) * (x^2 + 5x + 6) </span>
x^2 + 5x + 6 factors to (x + 3) * (x + 2)
Factors:
<span>(x - 1) </span>
<span>(x + 2) </span>
<span>(x + 3) </span>
<span>roots: </span>
<span>x = 1 </span>
<span>x = -2 </span>
<span>x = -3</span>
I'm assuming you're trying to simplify the expression?
If so, start by combining like terms.
4x+56-57
becomes 4x-1
That is the furthest you can simplify. If it had an equals sign, it would be an equation, and you would solve for x algebraically. But, since there is no equals sign, it is just an expression, and you simplify it to the best of your ability.
Hope this helps!
Answer:
Step-by-step explanation:
In the graphs below. I'm feel like the person that asked this question didn't understand that the lines would be reallly tuff to see.. as they are less than one.. but the graph is going out to 42,000 :0
as you can see in the graphs, i've used the given formulas :P
Because 5 goes into 5 AND 35, you can divide the expression by 5, which results in 5(p+7q).