SOLUTION: For the polynomial below, 3 is a zero. H(x)=x^3-7x^2 +11x+3 Express h(x) as a product of linear factors.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: For the polynomial below, 3 is a zero. H(x)=x^3-7x^2 +11x+3 Express h(x) as a product of linear factors.       Log On


   

Question 821628: For the polynomial below, 3 is a zero. H(x)=x^3-7x^2 +11x+3
Express h(x) as a product of linear factors.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Case level is important. Use either H or h, because each may name different functions. H is not taken as equal to h.

Synthetic division of H(x) using the zero of 3 (not shown here), gives x%5E2-4x-1, which has the zeros, 2%2Bsqrt%285%29 and 2-sqrt%285%29. In factored form, H%28x%29=%28x-3%29%28x-%282%2Bsqrt%285%29%29%29%28x-%282-sqrt%285%29%29%29
which you could simplify, carrying out the multiplications and groupings, to
H%28x%29=%28x-3%29%28%28x-2%29%5E2-5%29, but this is not linear factors. The best form of the answer is then highlight%28H%28x%29=%28x-3%29%28x-%282%2Bsqrt%285%29%29%29%28x-%282-sqrt%285%29%29%29%29