If f(x) = x + 10x² + 13x – 24 and x + 8 is a factor of f (x), then find all of the zeros of f (x) algebraically.

Step 1: Find the gradient/slope

Gradient and slope are interchangeable words. To find the gradient/slope we need to use two points that we know are on the line and the following formula: (y2 - y1) / (x2 - x1)

Point 1 = (0,1)

Point 2 = (3,13)

Gradient = (13 - 1) / (3 - 0)

Gradient = 12 / 3

Gradient = 4

Step 2: Find the y-intercept

We can use the slope-intercept form to find the y-intercept. To do so, we plug in the gradient and one of the points on the line. You can pick either point to plug in here!

Slope-intercept form: y = mx + b

-m is the gradient

-b is the y-intercept (that we are trying to find)

13 = 4(3) + b

13 = 12 + b

b = 1

Step 3: Put it all together in slope-intercept form

Now that we have the slope and y-intercept, all that's left to do is plug in the values.

y = mx + b

y = 4x + 1

y = 4x + 1

Hope this helps!!