Question

If h(x) = 6x² + 28x – 27, use synthetic division to find h(-3).

Answer 1

To find h(-3) for h(x), one should use synthetic division with the coefficients of the polynomial and the value x=-3. The steps involve bringing down the leading coefficient, multiplying and adding sequentially, resulting in h(-3) = -57.

Step-by-step explanation:

To find h(-3) for the function h(x) = 6x² + 28x – 27, we can use synthetic division. Synthetic division is a simplified form of polynomial division when dividing by a linear factor, and it's particularly useful for evaluating polynomials at a given point.

Here are the steps for synthetic division to find h(-3):

1. 
   
3. Write down the coefficients of h(x): 6, 28, and -27.
4. 
   
6. Write the zero of the linear divisor, which in this case is -3 (since we're finding h(-3)).
7. 
   
9. Bring down the 6 as the initial coefficient of the result.
10. 
    
12. Multiply -3 by 6, which gives -18. Add this to 28 to get 10.
13. 
    
15. Multiply -3 by 10 to get -30, and add this to -27, resulting in -57.

Now the bottom row, 6 and 10, represent the coefficients of the resulting polynomial, and -57 is the remainder which equals h(-3).

So, h(-3) = -57, which is the value of the polynomial h(x) when x is -3.