Question

Which binomial expressions are factors of 5x3 8x2−7x−6?

a) x−2 x minus
b) 2 x−1 x minus
c) 1 x 1 x, 1 x 2

Answer 1

To find the factors of 5x^3 + 8x^2 - 7x - 6, we can test potential roots using the Rational Root Theorem and divide the polynomial by any binomial expression corresponding to a root that zeroes the polynomial.

Step-by-step explanation:

To determine which binomial expressions are factors of the polynomial 5x3 + 8x2 - 7x - 6, we can use either polynomial long division or synthetic division. Unfortunately, without doing actual calculations for each given option (a, b, c), it's impossible to determine which binomials are factors. But we can use the Rational Root Theorem to test possible binomial factors of the form (x - p/q), where p is a factor of the constant term (in this case, 6) and q is a factor of the leading coefficient (in this case, 5).

To apply the Rational Root Theorem, we note that potential roots are ±(1, 2, 3, 6) divided by ±(1, 5). We then test these potential roots in the polynomial until we find one that gives a value of zero. When a binomial expression such as (x - root) is a factor, we can divide the polynomial by this binomial to find the other factors.