Explanation:
Factoring and multiplying polynomials are basically inverse operations. Factoring is the process of breaking down a polynomial expression into its constituent factors, while multiplying polynomials involves combining two or more polynomial expressions into one polynomial.
Let's take two polynomials, (x + 2) and (x - 3), and multiply them together:
(x + 2) * (x - 3)
To do this we can use the distributive property. Applying this property to our example, we get:
(x + 2) * (x - 3) = x * (x - 3) + 2 * (x - 3)
Now, we just simplify each term:
x * (x - 3) = x^2 - 3x
2 * (x - 3) = 2x - 6
Combining these simplified terms, we get:
(x + 2) * (x - 3) = x^2 - 3x + 2x - 6
(x + 2) * (x - 3) = x^2 - x - 6
Now, if we reverse the process and try to factor the polynomial x^2 - x - 6, we want to express it as a product of two or more simpler polynomials.
In this case, we can factor it as:
x^2 - x - 6 = (x - 3) * (x + 2)
Here we can see that factoring and multiplying polynomials are related operations. Factoring breaks down a polynomial into simpler factors, while multiplying polynomials combines factors to form a more complex polynomial. Hope this helped a bit :)