Divide and verify the result for (3x to the power 2 - 11x -4) divided by (x -4) class 8
Answers
Step-by-step explanation:
We have to divide 30x
4
+11x
3
−82x
2
−12x+48 by 3x
2
+2x−4
10x
2
−3x−12
3x
2
+2x−4)
30x
4
+11x
3
−82x
2
−12x+48
30x
4
+20x
3
−40x
2
(−) (−) (+)
−9x
3
−42x
2
−12x+48
−9x
3
−6x
2
+12x
(+) (+) (−)
−36x
2
−24x+48
−36x
2
−24x+48
(+) (+) (−)
0
Now, to verify, use the formula,
Dividend = Divisor × Quotient + Reminder
=(3x
2
+2x−4)×(10x
2
−3x−12)+0
=30x
4
−9x
3
−36x
2
+20x
3
−6x
2
−24x−40x
2
+12x+48
=30x
4
+11x
3
−82x
2
−12x+48
If g(x) is a factor of f(x), then the remainder will be zero that is g(x) = 0. g(x) = x - 3 = 0 or x = 3 Remainder = f(3) Now, f(3) = (3)3 – 6(3)2 + 11 x 3 – 6 = 27 – 54 + 33 – 6 = 60 – 60 = 0 Therefore, g(x) is a factor of f(x).Read more on Sarthaks.com - https://www.sarthaks.com/607309/f-x-x-3-6x-2-11x-6-g-x-x-3