Question : Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:
x²+3x+1, 3x⁴+5x³–7x²+2x+2
Doubt by Ziya
Video Solution :
Text Solution :
Let
p(x) = 3x⁴+5x³–7x²+2x+2
g(x) = x²+3x+1
Dividing p(x) by g(x)
________________
x²+3x+1) 3x⁴+5x³–7x²+2x+2 ( 3x²-4x+2
3x⁴+9x³+3x²
- - -
---------------------------
-4x³-10x²+2x+2
-4x³-12x²-4x
+ + +
----------------------------
2x²+6x+2
2x²+6x+2
- - -
------------------------------
0
------------------------------
q(x) = 3x²-4x+2
r(x) = 0
∵ r(x) = 0
Hence, g(x) must be a factor of p(x).
OR
The first polynomial is a factor of second polynomial.