Question

Divide polynomial 4xcube +3xsquare - 12-5 by x-1​ explaining by quotient and remainder​

Answer 1

Answer:

Given⤵

➡4x³+3x²-12x-5 and x-1

To find ⤵

➡Quotient and remainder by dividing polynomial 4x²+3x²-12x-5 by x-1

Solution ⤵

x-1) 4x³+3x²-12x-5(4x²+7x-5

4x³-4x²

- +

________

× 7x²-12x

7x²-7x

- +

__________

× -5x -5

-5x+5

+ -

_________

× -10

✅Hence, quotient is 4x²+7x-5 and remainder is -10.

Verification ⤵

➡ Dividend = Divisor×Quotient+Remainder

➡4x³+3x²-12x-5= (x-1) ×(4x²+7x-5) +(-10)

➡4x³+3x²-12x-5= x(4x²+7x-5) -1(4x²+7x-5) -10)

➡4x³+3x²-12x-5= 4x³+7x²-5x-4x²-7x+5-10

➡4x³+3x²-12x-5= 4x³+7x²-4x²-5x-7x+5-10

➡4x³+3x²-12x-5= 4x³+3x²-12x-5

LHS= RHS

✔Extra points ⤵

✡ Dividend = Divisor×Quotient+Remainder

Hope this is helpful to you!