using synthetic subsititution to evaluate the polynomial functuion for the given value of x.
h(x)= -8x^3+14x-35; x=4
homepage.smc.edu/kennedy_john/syntheticexamples.pdf
look at the examples. It is too complicated to do here.
h(4) = -8(4^3) + 15(4) - 35 = .....
To evaluate the polynomial function h(x) = -8x^3 + 14x - 35 for the given value of x = 4 using synthetic substitution, follow these steps:
Step 1: Write down the coefficients of the polynomial in descending order.
The coefficients for -8x^3 + 14x - 35 are -8, 0, 14, -35.
Step 2: Start with the given value x = 4. Write it down on the left side.
4 | -8 0 14 -35
Step 3: Bring down the first coefficient (-8) directly below the line.
4 | -8 0 14 -35
-8
Step 4: Multiply the number just brought down (-8) by the given value (4) and write the result below the next coefficient (0). Then add the result to the next coefficient.
4 | -8 -32 14 -35
-8
Step 5: Repeat the previous step for each subsequent coefficient, bringing the result from the previous step down and adding it to the next coefficient.
4 | -8 -32 14 -35
-8 0
------
-32 -128
-32 -128
-------
-114
Step 6: The number at the bottom of the final column (-114) is the remainder. It represents the value of the polynomial function h(x) when x = 4 using synthetic substitution.
Therefore, h(4) = -114.