When x^4 + 2x^3 + 8x^2 + 12x + 18 is divided by x^2 + 5, the remainder comes out to be px + q. Find p and q.
Answers
Answer:
p = 2, q = 3
Step-by-step explanation:
Let, f(x) = x⁴ + 2x³ + 8x² + 12x + 18 and g(x) = x² + 5.
Long Division Method:
x² + 5) x⁴ + 2x³ + 8x² + 12x + 18 (x² + 2x + 3
x⁴ - 5x²
-------------------------------------
2x³ + 3x² + 12x
2x³ + 10x
-----------------------------------------
3x² + 2x + 18
3x² + 15
------------------------------------------
2x + 3
Remainder = 2x + 3.
On comparing the remainder with px + q, we get
p = 2, q = 3.
Hope it helps!
Let us divide x⁴ + 2x³ + 8x² +12x +18 by x²+5. The division process is as follows:
x²+5 )x⁴ + 2x³ + 8x² +12x +18(x²+2x+3
x⁴ +5x²
(-) (-)
-------------------------
2x³+3x²+12x +18
2x³ +10x
(-) (-)
---------------------------
3x² +2x+18
3x² +15
(-) (-)
---------------------------
2x + 3
We get the Remainder = 2x + 3
Remainder given= px+q
px+q = 2x + 3
p= 2 , q= 3
[Comparing coefficient of x and constant terms both sides]
Hence, the value of p is 2 & value of q is 3.
HOPE THIS WILL HELP YOU...