2a + 8 then add the next coeffcient, b
2a + b + 8 then multiply by 2 again
4a + 2b + 16 and add the next coefficient, 15
4a + 2b + 31 that's where i got that from. then set it equal to the 35
you do the same thing, jsut use the negative 3. you bring down the first coefficient, multiply the -3 add the next coefficient, multiply the -3, and continue that pattern until you reach the end. and then set it equal to zero, since they said it factors in, meaning it a a zero
you may want to consider looking into synthetic division if you haven't heard of it before online. it is a really nifty tool, and once learned, makes dividing factors into a function super fast
as i said we can check our work by substituting in x = 2 and x = - 3 to our new found function with our designated values for a and b. i'll do the grunt work to show you we are correct:
f(x) = 2x^3 +3x² - 4x + 15 plug in 2 for x
f(2) = 2(2)^3 +3(2)² - 4(2) + 15
f(2) = 16 + 12 - 8 + 15
f(2) = 35
f(x) = 2x^3 +3x² - 4x + 15 plug in -3 for x
f(-3) = 2(-3)^3 +3(-3)² - 4(-3) + 15
f(-3) = -54 + 27 + 12 + 15
f(-3) = 0