f(x)=13x^2 -15x-14
g(x)=15x^3+14x^2-15x+12
find f(3) × f(10) + f(-7) × g(9)
see
http://www.jiskha.com/display.cgi?id=1388190290
To find f(3), we substitute x = 3 into the function f(x) and simplify:
f(3) = 13(3)^2 - 15(3) - 14
= 13(9) - 45 - 14
= 117 - 45 - 14
= 58
To find f(10), we substitute x = 10 into the function f(x) and simplify:
f(10) = 13(10)^2 - 15(10) - 14
= 13(100) - 150 - 14
= 1300 - 150 - 14
= 1136
To find g(9), we substitute x = 9 into the function g(x) and simplify:
g(9) = 15(9)^3 + 14(9)^2 - 15(9) + 12
= 15(729) + 14(81) - 135 + 12
= 10935 + 1134 - 135 + 12
= 12046
Now, we can substitute the values we found back into the original expression:
f(3) × f(10) + f(-7) × g(9)
= 58 × 1136 + f(-7) × 12046
Next, we need to find f(-7) by substituting x = -7 into the function f(x):
f(-7) = 13(-7)^2 - 15(-7) - 14
= 13(49) + 105 - 14
= 637 + 105 - 14
= 728
Now we can substitute f(-7) and g(9) back into the expression:
f(3) × f(10) + f(-7) × g(9)
= 58 × 1136 + 728 × 12046
To get the final answer, we multiply the two terms and sum them up:
f(3) × f(10) + f(-7) × g(9)
= 65888 + 88166088
= 88131976
Therefore, f(3) × f(10) + f(-7) × g(9) equals 88,131,976.