If P(x) = 12x3 + 11x2 - 9x + 10 and
Q(x) = 4x2 – 3x + 2, find
P(x) + Q(x)

12x^3+15x^2-12x+12

Step-by-step explanation:

P(x) = 12x^3 + 11x^2 - 9x + 10

Q(x) = 4x^2 – 3x + 2

P(x) + Q(x) = 12x^3 + 11x^2 - 9x + 10+ 4x^2 – 3x + 2

Combine like terms

                 =12x^3+11x^2+4x^2-9x-3x+10+2

                  =12x^3+15x^2-12x+12

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0

answer: the resulting cross section is a rectangle. solution: a plane parallel to the base of a triangular prism will intersect a cross section that is the same shape as its bases. so the cross section is a triangle.

step-by-step explanation: