Answer:

1) To solve for the roots of the polynomial y = x² - 3x + 2, we can set the equation equal to zero:

x² - 3x + 2 = 0

Factoring the equation, we get:

(x - 1)(x - 2) = 0

Setting each factor equal to zero, we find the roots:

x - 1 = 0 --> x = 1

x - 2 = 0 --> x = 2

Therefore, the roots of the polynomial are x = 1 and x = 2.

To graph the polynomial, we plot the points (1, 0) and (2, 0) on a coordinate plane and draw a parabolic curve passing through these points.

2) To solve for the roots of the polynomial f(x) = x¹ - 7x²³ - 12x² + 28x + 32, we set the equation equal to zero:

x¹ - 7x²³ - 12x² + 28x + 32 = 0

Unfortunately, this polynomial cannot be easily factored or solved algebraically. To find the roots, we can use numerical methods such as graphing or using a calculator.

To graph the polynomial, plot multiple points on a coordinate plane and connect them to form a curve.

3) To solve for the roots of the polynomial f(x) = x² + x³ - 7x² - x + 6, we set the equation equal to zero:

x² + x³ - 7x² - x + 6 = 0

Rearranging the terms, we get:

x³ - 6x² - x + 6 = 0

Again, this polynomial cannot be easily factored or solved algebraically. We can use numerical methods to find the roots.

To graph the polynomial, plot multiple points on a coordinate plane and connect them to form a curve.

4) To solve for the roots of the polynomial y = x^5 - 5x¹ - 5x³ + 25x² + 4x - 20, we set the equation equal to zero:

x^5 - 5x¹ - 5x³ + 25x² + 4x - 20 = 0

Similar to the previous polynomials, this equation cannot be easily factored or solved algebraically. Numerical methods can be used to find the roots.

To graph the polynomial, plot multiple points on a coordinate plane and connect them to form a curve.