find the quotient when p(x)=8x^4+22x^3+21x^2+9x divided by g(x)=2x^2+3x
Answers
The quotient is (4x² + 5x + 3)
Step-by-step explanation:
Method 1:
Given, p(x) = 8x⁴ + 22x³ + 21x² + 9x
g(x) = 2x² + 3x
∴ p(x) = 8x⁴ + 22x³ + 21x² + 9x
= 8x⁴ + 12x³ + 10x³ + 15x² + 6x² + 9x
= 4x² (2x² + 3x) + 5x (2x² + 3x) + 3 (2x² + 3x)
= (2x² + 3x) (4x² + 5x + 3)
∴ the required quotient is (4x² + 5x + 3).
Method 2:
2x² + 3x ) 8x⁴ + 22x³ + 21x² + 9x ( 4x² + 5x + 3
8x⁴ + 12x³
( - ) ( - )
------------------------------------
10x³ + 21x² + 9x
10x³ + 15x²
( - ) ( - )
----------------------------
6x² + 9x
6x² + 9x
( - ) ( - )
---------------
0
∴ the required quotient is (4x² + 5x + 3).