Need answer and steps for part c and d.
In this question, you will determine a cubic polynomial which passes through the points (1,14), (-1,-2), (2,31), and (-2,-13) by solving linear equations. Let a general cubic be p(x) = ax^3 + bx^2 + cx + d.
(a) Enter the linear equation which is obtained by setting p(1) = 14. The constant term should be on the right-hand side.
a + b + c + d = 14
(b) Determine the linear equations obtained from each of the other points. Enter the resulting linear system (for all four points) in the form of an augmented matrix below. The rows should be in the same order as the corresponding points are listed above (So, for example, the first row corresponds to the equation you gave in part (a).) To enter a matrix, click on the 3x3 grid of squares below. Next, select the exact size of the matrix you want. Then change the entries in the matrix to the entries of your answer. If you need to start over, then click on the trash can.
1 1 1 1 | 14
1 -1 1 -1 | -2
8 4 2 1 | 31
-8 -4 2 -1 | -13
(c) Use G-J elimination on this matrix and enter the result in reduced row echelon form.
1 0 0 0 | 3
0 1 0 0 | -1
0 0 1 0 | 2
0 0 0 1 | 4
(d) Hence give the formula for the cubic polynomial.
