Question

How to Write a Polynomial in Standard Form from the Product of Three Linear Factors

Answer 1

Explanation: I assume you are talking about three linear factors such as

(x-2)(x+5)(x-1). In this case, what I highly recommend you do is to expand this as if there were only two of the three factors and multiply by the third factor last.

Keeping with the example given, you would first expand (x-2)(x+5), which you can do by multiplying each part by each other giving you, x^2-2x+5x-10

Combining like terms will give you x^2+3x-10. Now you have to multiply by (x-1). To do this best, multiply each part of your expanded term by each part of (x-1). This looks like x(x^2+3x-10) and -1(x^2+3x-10). Doing this will give you x^3+3x^2-10x and -x^2-3x+10. Now add together these two terms and combine anything with equal powers of x.

x^3+3x^2-x^2-10x-3x+10

x^3+2x^2-13x+10

Answer 2

To write a polynomial in standard form from the product of three linear factors, multiply the factors together and simplify the expression.

Step-by-step explanation:

To write a polynomial in standard form from the product of three linear factors, you need to multiply the three factors together and then simplify the expression. Let's say the linear factors are (x - a), (x - b), and (x - c). To find the polynomial, you multiply these factors:

1. Multiply (x - a) and (x - b) to get x² - (a + b)x + ab
2. Multiply the result with (x - c) to get the polynomial in standard form