Question

Use synthetic division and the given factor

(X + 5) to completely factor the polynomial
Y = x^3 -31x+30

Answer 1

To factor the polynomial y = x^3 - 31x + 30 using synthetic division and the factor (x + 5), follow these steps.

Step-by-step explanation:

To factor the given polynomial using synthetic division and the factor (x + 5), follow these steps:

1. Arrange the terms of the polynomial in descending order of their exponents: y = x^3 - 31x + 30.
2. Set up synthetic division, dividing by the factor (x + 5).
3. Perform the synthetic division, bringing down the leading coefficient (1) and multiplying it by the factor (-5) to get -5. Add this result to the next term (-31) to get -26. Multiply this sum by the factor (-5) again to get 130. Subtract this result from the next term (30) to get 160.
4. The quotient from synthetic division gives the factors: x^2 - 26x + 160.
5. To completely factor the polynomial, set x^2 - 26x + 160 = 0 and solve for x using factoring, completing the square, or the quadratic formula.
6. The factors of the polynomial are (x + 5)(x - 2)(x - 28).