Which binomial expressions are factors of 5x^3+8x^2-7x-6

x - 1 and x + 2

Step-by-step explanation:

By the factor theorem if (x - a) is a factor then f(a) = 0.

Try x - 1:_

f(1) =  5(1)^3 + 8(1)^2 - 7 - 6

= 5 + 8 - 7 - 7

= 0  so x - 1 is a factor

We can find the other factors by long division:-

            5x^2  + 13x + 6

x - 1 )    5x^3  + 8x^2  -  7x  -  6

           5x^3  -   5x^2

                        13x^2  -   7x

                         13x^2  -  13x

                                       6x - 6

                                        6x - 6

    5x^2  + 13x + 6   = (5x + 3)(x + 2)                          

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2   is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of   numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes.     our only condition is that it passes through the point (-2,5)