To solve this problem you must apply the proccedure shown below:
1. If the function 
is shifted 
units left, this means that you must substitute the value of 
by 
to find 
, as following:
2. Now, expand the function:
3. Then, you have that is:
Therefore, the answer is:
<span> divide a polynomial p(x) by (x-3). Add and subtract the multiple of (x-3) that has the same highest-power term as p(x), then simplify to get a smaller-degree polynomial r(x) plus multiple of (x-3). </span>
<span>The multiple of (x-3) that has x^4 as its leading term is x^3(x-3) = x^4 - 3x^3. So write: </span>
<span>x^4 + 7 = x^4 + 7 + x^3(x - 3) - x^3(x - 3) </span>
<span>= x^4 + 7 + x^3(x - 3) - x^4 + 3x^3 </span>
<span>= x^3(x - 3) + 3x^3 + 7 </span>
<span>That makes r(x) = 3x^3 + 7. Do the same thing to reduce r(x) by adding/subtracting 3x^2(x - 3) = 3x^3 - 9x^2: </span>
<span>= x^3(x - 3) + 3x^3 + 7 + 3x^2(x - 3) - (3x^3 - 9x^2) </span>
<span>= x^3(x - 3) + 3x^2(x - 3) + 9x^2 + 7 </span>
<span>Again to reduce 9x^2 + 7: </span>
<span>= x^3(x - 3) + 3x^2(x - 3) + 9x^2 + 7 + 9x(x - 3) - (9x^2 - 27x) </span>
<span>= x^3(x - 3) + 3x^2(x - 3) + 9x(x - 3) + 27x + 7 </span>
<span>And finally write 27x + 7 as 27(x - 3) + 88; </span>
<span>x^4 + 7 = x^3(x - 3) + 3x^2(x - 3) + 9x(x - 3) + 27(x - 3) + 88 </span>
<span>Factor out (x - 3) in all but the +88 term: </span>
<span>x^4 + 7 = (x - 3)(x^3 + 3x^2 + 9x + 27) + 88 </span>
<span>That means that: </span>
<span>(x^4 + 7) / (x - 3) = x^3 + 3x^2 + 9x + 27 with a remainder of 88</span>
Answer:
3/8
Step-by-step explanation:
If there are three blue tickets out if 8, (which is 3 blue and 5 black put together), you'd have a 3/8 chance of pulling a blue ticket.
Answer:
The greatest common factor of the terms is 1.
Step-by-step explanation:
The terms have no variables in common, and the coefficients have no factors in common. The greatest common factor of the terms is 1.
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The discriminant is negative (40² -4(30)(51) = -4520), so any linear factors will be complex.
