Given polynomial 
.
(a) To show that (x – 3) is a factor of f(x).
Factor theorem:
<em>A polynomial f(x) has a factor of (x – a), if and only if f(a) = 0.</em>
= 0
f(3) = 0
Hence (x – 3) is a factor of f(x).
(b) 
Here 
is common in first 2 terms and 2 is common in next 2 terms.
Now, (x – 3) is common in both terms.
and 
x = 3 and 
3 is the real root.
using quadratic formula solve and find the other roots.
These are complex roots.
Hence 3 is the only real root of the equation f(x) = 0.
The additive inverse property states that when you add a number and its opposite (rational numbers), the result is zero. The reason is that the inverse of a number is the opposite, so if you have a number and when do the opposite with it (add the opposite), the result will be zero. This applies to adding!!!
Hope This Helped =3
Check the solution of all options
First option
p + 2 1/2 = 5
p = 5 - 2 1/2
p = 5 - 5/2
p = 10/2 - 5/2
p = 5/2
p = 2 1/2
Second option
2 + p = 2 1/2
p = 2 1/2 - 2
p = 1/2
Third option
p - 2 1/2 = 5
p = 5 + 2 1/2
p = 7 1/2
Fourth option
4 - p = 2 1/2
-p = 2 1/2 - 4
-p = 5/2 - 4
-p = 5/2 - 8/2
-p = -3/2
p = 3/2
p = 1 1/2
The equation that has p = 2 1/2 as its solution is first option
We need to find the increasing function with constant slope.
Let us check each option one by one.
A) 6x -5y =10.
Let us solve it for y to get slope-intercept form
6x-5y =10.
-5y =-6x +10.
y =6/5 x-2.
<em>Slope is 6/5 positive, therefore, it's an increasing function.</em>
<em>A linear function always has a constant slope.</em>
<h3>Therefore, correct option is option A.</h3><h3>A. 6x -5y =10</h3>
All other options are incorrect.
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