Find the polynomial f(x) of degree 3 has the following zeros
9, 0, -7

Answer:

x³ - 2x² - 63x

Step-by-step explanation:

Zeroes = 9 , 0 , -7

Factors = (x - 9) x (x + 7)

Polynomial = x (x - 9)(x + 7)

Polynomial = x (x² -2x - 63)

= x³ - 2x² - 63x

Final answer:

To find the polynomial f(x) of degree 3 with zeros 9, 0, and -7, we can use the zero-product property. The polynomial can be written as f(x) = (x-9)(x-0)(x+7), which simplifies to f(x) = (x-9)(x)(x+7). Expanding the expression and multiplying the remaining factors, we obtain f(x) = x^3 - 2x^2 - 63x.

Explanation:

To find the polynomial f(x) of degree 3 with the given zeros 9, 0, and -7, we can use the zero-product property. This property states that if a polynomial has a zero a, then (x-a) is a factor of the polynomial. Therefore, the polynomial can be written as:

f(x) = (x-9)(x-0)(x+7)

Simplifying further, we get:

f(x) = (x-9)(x)(x+7)

Expanding this expression, we have:

f(x) = (x^2 - 9x)(x+7)

Finally, multiplying the remaining factors, we obtain the polynomial:

f(x) = x^3 + 7x^2 - 9x^2 - 63x

= x^3 - 2x^2 - 63x

Learn more about Finding Polynomial with Given Zeros here:

brainly.com/question/34347327

#SPJ11