A 4th degree polynomial fuction has the form y=ax2+bx3+cx+cx+dx+e. A through the

Question

A 4th degree polynomial fuction has the form y=ax2+bx3+cx+cx+dx+e. A through the points (-2,90),(-1,-9),(2,-14),and (3,35) Write a system of equation that could be solved to find values of a,b,c,d and e Use your calculator to solve the system and write out the polynomial .(advice: check your answer uding the table function on your calculator.) Find the general solution to the system of equation below. Tell which variables are free variable.Use your calculator to the put the matrix in RREF. a - 2b+ c+ 3d - e=1 -3a + 6b-4c-9d+3e=-1 -a + 2b - 2c -4d -3e=3 a- 2b+ 2c +2d - 5e =1 Compare the determinant of this matrix using cofactor expansion You must show your work to receive credit 1 2 -3 8 0 4 7 5 1 0 0 2 1 -2 8 -3 Use Cramer's rule to solve this system for z Show me what you are doing ,but feel free to use your calculator to take the determinants x+2y-3z+8=4 4y+7z+5=1 x+2=2x_2y+8z_3=7.

Explanation / Answer

Eqns are : 1) 16a-8b+4c-2d+e=90; 2) a-b+c-d+e=19; 3) a+b+c+d+e=-9; 4) 16a+8b+4c+2d+e=-14; 5) 81a+27b+9c+3d+e=35. The solutions are : a=2, b=-4, c=1, d=-10, e=2. So the polynomial is 2x^4-4x^3+x^2-10x+2.

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