this is in long division... Plss... say .. solve
Answers
Required Solution:-
Question 1:
- (x³ + x² - 7x - 3) ÷ (x - 3)
Solution:
x - 3 ) x³ + x² - 7x - 3 ( x² + 4x + 5
x³ - 3x²
(-) (+)
-----------------------------
4x² - 7x - 3
4x² - 12x
(-) (+)
-----------------------------
5x - 3
5x - 15
(-) (+)
-----------------------------
12
Therefore,
- Q = x² + 4x + 5
- R = 12
Verification:
➡ Dividend = Divisor × Quotient + Remainder
Divisor × Quotient + Remainder
= (x - 3)(x² + 4x + 5) + 12
= x³ + 4x² + 5x - 3x² - 12x - 15 + 12
= x³ + x² - 7x - 3
= Dividend (Verified)
Question 2:
- (3x³ - 2x² + 7x - 5) ÷ (x + 3)
Solution:
x + 3 ) 3x³ - 2x² + 7x - 5 ( 3x² - 11x + 40
3x³ + 9x²
(-) (-)
------------------------------
-11x² + 7x
-11x² - 33x
(+) (+)
------------------------------
40x - 5
40x + 120
(-) (-)
------------------------------
-125
Therefore,
- Q = 3x² - 11x + 40
- R = -125
Verification:
➡ Dividend = Divisor × Quotient + Remainder
Divisor × Quotient + Remainder
= (x + 3)(3x² - 11x + 40) - 115
= 3x³ - 11x² + 40x + 9x² - 33x + 120 - 125
= 3x³ - 2x² + 7x - 5
= Dividend (Verified)