Final answer:
Since -2 is a zero of the polynomial h(x), one factor is (x + 2). After dividing h(x) by (x + 2), we get a quadratic equation that can be factored or solved using the quadratic formula. The solutions provide the remaining linear factors, expressing h(x) as a product of linear factors.
Step-by-step explanation:
If we're given that -2 is a zero of the polynomial h(x) = x3 – 4x2 + x + 26, we can use this information to help us factor the polynomial. To express h(x) as a product of linear factors, we need to find the other zeros of the polynomial.
Since -2 is a zero, we know that (x + 2) is a factor of h(x). We can perform polynomial long division or synthetic division to divide h(x) by (x + 2) to find the other factors.
Once we do the division, we'll be left with a quadratic equation, which can be factored further or solved using the quadratic formula. The quadratic formula is expressed as x = (-b ± √(b2 - 4ac)) / (2a), where a, b, and c are the coefficients of the quadratic equation of the form ax2 + bx + c = 0.
Finding these solutions gives us the remaining linear factors of h(x), and from there, we can express the original polynomial as a product of three linear factors.