Question

when 6x3-7x2-23x=5x is divided by 3x-5, the quotient is 2x2 +bx-6. and the remainder is 5-2a. find the value of and b

Answer 1

Answer:

a = 20 & b = 1

Step-by-step explanation:

When 6x3-7x2-23x=5x is divided by 3x-5, the quotient is 2x2 +bx-6. and the remainder is 5-2a. find the value of and b

f(x) = 6x³ - 7x² -23x - 5

g(x) = (3x - 5)

q(x) = 2x² + bx - 6

r = 5 -2a

f(x) = g(x)q(x) + r

=> 6x³ - 7x² -23x - 5 = (3x -5)(2x² + bx - 6)  + 5 -2a

=>6x³ - 7x² -23x - 5 = 6x³ - (10-3b)x² -(5b +18)x + 30 + 5 - 2a

=> 6x³ - 7x² -23x - 5 = 6x³ - (10-3b)x² -(5b +18)x + 35 - 2a

Comparing

10-3b = 7

=> b = 1

5b +18 = 23 => b = 1

35 - 2a = -5

=> a = 20