Use synthetic division to find P(-3) for P(X)= x^4 - 2x^3 - 4x + 4
So I know how to do synthetic division and all, but I'm still somehow not coming up with the correct answer! Below is my work so far. Please help me interpret it so that I can get the correct answer. Thank you!
-3 | 1 -2 -4 4
| -3 15 -33
--------------------
| 1 -5 11 -29
I am being told that the answer is 151, but what about the 11 and the -29?
You have a very common mistake.
Notice there is no x^2 term, so you need a 0 as a placeholder
correction:
-3 | 1 -2 0 -4 4
.....| -3 15 -45 147
--------------------
.....| 1 -5 15 -49 151
hard to line up the columns , isn't it ?
Haha yeah it was, I wasn't sure if the spaces would register.
Thank you for this!!
thanks
Well, it seems like you're really close! But let's not get ahead of ourselves. The answer you mentioned, 151, is actually not correct. Don't worry, I won't clown around with the answer. Let's take a look at your synthetic division:
-3 │ 1 -2 -4 4
│________
3 -3 21
______________
-1 17
In the bottom row, we have the coefficients of the quotient polynomial. So, the equation we get is:
P(x) = x^3 - x^2 + 21x - 1
Now, you need to find P(-3). To do that, substitute -3 into the equation:
P(-3) = (-3)^3 - (-3)^2 + 21(-3) - 1
Let's simplify it:
P(-3) = -27 - 9 - 63 - 1
Now, let's do the math:
P(-3) = -100
So, the correct answer is -100. I apologize if this answer isn't as hilarious as you were hoping for, but sometimes math just doesn't bring out my jester side.
To find P(-3) using synthetic division, you should divide each term of the polynomial P(x) by x - (-3), which gives you x + 3. Here is how to interpret your synthetic division:
-3 | 1 -2 -4 4
| -3 15 -33
---------------------
| 1 -5 11 -29
The numbers in the bottom row of the synthetic division represent the coefficients of the resulting polynomial. In this case, the bottom row is 1 -5 11 -29, which corresponds to the polynomial P(x) = x^3 - 5x^2 + 11x - 29, which is the quotient of dividing P(x) by x + 3.
However, to find P(-3), you need to evaluate the polynomial P(x) = x^4 - 2x^3 - 4x + 4 at x = -3. Plugging in -3 into P(x), you get:
P(-3) = (-3)^4 - 2(-3)^3 - 4(-3) + 4
= 81 + 54 + 12 + 4
= 151
Therefore, the correct answer is 151, not the coefficients from the synthetic division. The coefficients from synthetic division only represent the result of dividing the polynomial by x + 3.