Daniel M. answered • 05/23/20
Degree in Engineering & Mathematics with 10 Years Tutoring Experience
Define a cubic polynomial: 2x3+3x2+4x+1
Define a binomial: (2x3+3x)
(Used only one variable "x" in each)
To multiply these two, we basically need to multiply each term of the polynomial with the binomial, and then add all those results together for the final answer.
Write it vertically for the Vertical Method:
2x3+3x2+4x+1
x (2x3+3x)
First step is 2x3 * (2x3+3x) = 4x6+6x4
Write this at the bottom:
2x3+3x2+4x+1
x (2x3+3x)
4x6+6x4
Second step is 3x2 * (2x3+3x) = 6x5+9x3
Write this at the bottom:
2x3+3x2+4x+1
x (2x3+3x)
4x6+6x4
6x5+9x3
Third step is 4x * (2x3+3x) = 8x4+12x2
Write this at the bottom:
2x3+3x2+4x+1
x (2x3+3x)
4x6+6x4
6x5+9x3
8x4+12x2
Fourth step is 1 * (2x3+3x) = 2x3+3x
Write this at the bottom:
2x3+3x2+4x+1
x (2x3+3x)
4x6+6x4
6x5+9x3
8x4+12x2
2x3+3x
Now, add those 4 new binomials for the final answer:
4x6+6x4
6x5+9x3
8x4+12x2
+ 2x3+3x
4x6+6x5+8x4+6x4+9x3+2x3+3x
Simplify by combining variables with same exponent:
4x6+6x5+14x4+11x3+3x
That's the answer. Hope this helps. :)
