QuestionAugust 25, 2025

For the polynomial below, 3 is a zero. f(x)=x^3-7x^2+13x-3 Express f(x) as a product of linear factors.

For the polynomial below, 3 is a zero. f(x)=x^3-7x^2+13x-3 Express f(x) as a product of linear factors.
For the polynomial below, 3 is a zero. f(x)=x^3-7x^2+13x-3 Express f(x) as a product of linear factors.

Solution
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Answer

f(x) = (x - 3)(x - 1)(x - 3) Explanation 1. Use the Factor Theorem Since 3 is a zero, (x - 3) is a factor of f(x). 2. Perform Polynomial Division Divide f(x) by (x - 3) using synthetic division or long division to find the quotient polynomial. 3. Factor the Quotient Polynomial Factor the resulting quadratic polynomial from the division.

Explanation

1. Use the Factor Theorem<br /> Since 3 is a zero, $(x - 3)$ is a factor of $f(x)$.<br />2. Perform Polynomial Division<br /> Divide $f(x)$ by $(x - 3)$ using synthetic division or long division to find the quotient polynomial.<br />3. Factor the Quotient Polynomial<br /> Factor the resulting quadratic polynomial from the division.
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