QuestionAugust 25, 2025

For the polynomial below. -1 is a zero. h(x)=x^3-4x^2+x+6 Express h(x) as a product of linear factors.

For the polynomial below. -1 is a zero. h(x)=x^3-4x^2+x+6 Express h(x) as a product of linear factors.
For the polynomial below. -1 is a zero. h(x)=x^3-4x^2+x+6 Express h(x) as a product of linear factors.

Solution
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Answer

h(x) = (x + 1)(x - 2)(x - 3) Explanation 1. Use the Factor Theorem Since -1 is a zero, (x + 1) is a factor of h(x). 2. Perform Polynomial Division Divide h(x) by (x + 1) using synthetic division or long division to find the quotient. 3. Simplify the Quotient After division, the quotient is x^2 - 5x + 6. 4. Factor the Quadratic Factor x^2 - 5x + 6 into (x - 2)(x - 3).

Explanation

1. Use the Factor Theorem<br /> Since $-1$ is a zero, $(x + 1)$ is a factor of $h(x)$.<br /><br />2. Perform Polynomial Division<br /> Divide $h(x)$ by $(x + 1)$ using synthetic division or long division to find the quotient.<br /><br />3. Simplify the Quotient<br /> After division, the quotient is $x^2 - 5x + 6$.<br /><br />4. Factor the Quadratic<br /> Factor $x^2 - 5x + 6$ into $(x - 2)(x - 3)$.
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