Example 1
Let's multiply the polynomial $$(3x^6 + 2x^5 + 5)$$ by the polynomial (5x + 2).
Step 1
Step 2
$$( 15x^7 + 10x^6 + 25x) + (6x^6 + 4x^5 + 10) = 15x^7 + 16x^6 + 4x^6 + 25x + 10 $$
$$( 15x^7 + 10x^6 + 25x) + (6x^6 + 4x^5 + 10) \\ = 15x^7 + 16x^6 + 4x^6 + 25x + 10 $$
Example 2
Let's multiply the polynomial$$(3x^6 + 2x^5 + 5)$$ by $$(4x^2 + x + 5)$$.
Step 1
Step 2
Add the resulting Polynomials.
$$ (12x^8 + 8x^7 + 20x^2) + (3x^7 + 2x^6 + 5x) + (15x7^6+ 10x^5 + 25) \\ = \boxed{ 12x^8 + 11x^7 + 17x^6 + 10x^5 + 20x^2 + 5x + 25} $$
$$ (12x^8 + 8x^7 + 20x^2) + (3x^7 + 2x^6 + 5x) + (15x7^6+ 10x^5 + 25) \\ = \boxed{ 12x^8 + 11x^7 + 17x^6 + 10x^5 + 20x^2 + 5x + 25} $$
Practice Problems
Problem 1
15x5 + 41x4 + 28x3 + 15x2 + 20x
Problem 2
6x13 + 4x12 + 12x8 + 27x7 + 6x6 + 20x 2 + 15x
