Practice using both the horizontal and vertical methods when multiplying the polynomials below. Click the tabs to reveal the next problem. Click the Answer button to check your solution.
Problem 1
Problem 2
Problem 3
(x + 1)(x\(\small\mathsf{ ^2 }\) + 2x + 2)
SOLUTION:
Here, the horizontal method works best for smaller multiplications.
x • x\(\small\mathsf{ ^2 }\) + x • 2x + x • 2 + x\(\small\mathsf{ ^2 }\) + 2x + 2
x\(\small\mathsf{ ^3 }\) + 2x\(\small\mathsf{ ^2 }\) + 2x + x\(\small\mathsf{ ^2 }\) + 2x + 2
x\(\small\mathsf{ ^3 }\) + 3x\(\small\mathsf{ ^2 }\) + 4x + 2
(x\(\small\mathsf{ ^2 }\) + 3x + 4)(x\(\small\mathsf{ ^2 }\) + 2x + 1)
SOLUTION:
Vertical is more organized for problems like this.
| x\(\small\mathsf{ ^2 }\) | + 3x | + 4 | ||
| x\(\small\mathsf{ ^2 }\) | + 2x | + 1 | ||
| x\(\small\mathsf{ ^2 }\) | + 3x | + 4 | ||
| 2x\(\small\mathsf{ ^3 }\) | + 6x\(\small\mathsf{ ^2 }\) | + 8x | ||
| x\(\small\mathsf{ ^4 }\) | + 3x\(\small\mathsf{ ^3 }\) | + 4x\(\small\mathsf{ ^2 }\) | ||
| x\(\small\mathsf{ ^4 }\) | + 5x\(\small\mathsf{ ^3 }\) | + 11x\(\small\mathsf{ ^2 }\) | + 11x | + 4 |
(3x\(\small\mathsf{ ^2 }\) – 9x + 5)(2x\(\small\mathsf{ ^2 }\) + 4x – 7)
SOLUTION:
Vertical is more organized for problems like this.
| 3x\(\small\mathsf{ ^2 }\) | – 9x | + 5 | ||
| 2x\(\small\mathsf{ ^2 }\) | + 4x | – 7 | ||
| –21x\(\small\mathsf{ ^2 }\) | + 63x | – 35 | ||
| 12x\(\small\mathsf{ ^3 }\) | – 36x\(\small\mathsf{ ^2 }\) | + 20x | ||
| 6x\(\small\mathsf{ ^4 }\) | – 18x\(\small\mathsf{ ^3 }\) | + 10x\(\small\mathsf{ ^2 }\) | ||
| 6x\(\small\mathsf{ ^4 }\) | – 6x\(\small\mathsf{ ^3 }\) | – 47x\(\small\mathsf{ ^2 }\) | + 83x | – 35 |
