Find the quotient and remainder when ( 3X4+5x³-7x²+2x+2 ) is divided by ( x²+3x+1 ).
Answers
Answer:
3x²-x-7
Step-by-step explanation:
hope this helps
Answer:
The expression 3x^4+5x^3-7x^2+2x+23x
4
+5x
3
−7x
2
+2x+2 divided by x^2+3x+1x
2
+3x+1
TO FIND :
The quotient for the given expression by using Long Division Method.
SOLUTION :
Given that 3x^4+5x^3-7x^2+2x+23x
4
+5x
3
−7x
2
+2x+2 divided by x^2+3x+1x
2
+3x+1
Here by using the Long Division Method we have to find the quotient.
3x^2-4x+23x
2
−4x+2
_________________________
x^2+3x+1x
2
+3x+1 ) 3x^4+5x^3-7x^2+2x+23x
4
+5x
3
−7x
2
+2x+2
3x^4+9x^3+3x23x
4
+9x
3
+3x2
_(-)__(-)___(-)_________
-4x^3-10x^2+2x−4x
3
−10x
2
+2x
-4x^3-12x^2-4x−4x
3
−12x
2
−4x
___(+)___(+)___(+)______
2x^2+6x+22x
2
+6x+2
2x^2+6x+22x
2
+6x+2
__(-)___(-)___(-)_______
0
__________________
Therefore the quotient when the given expression 3x^4+5x^3-7x^2+2x+23x
4
+5x
3
−7x
2
+2x+2 divided by x^2+3x+1x
2
+3x+1 is 3x^2-4x+23x
2
−4x+2
∴ the quotient is 3x^2-4x+23x
2
−4x+2