hey here's a question

the remainder obtained on dividing a polynomial p(x) by(x-1) is -5 and the qoutient is 3(x)3-(x)2-x-4. find p(x)

We know that,

Dividend = Divisor × Quotient + Remainder

 Here, the dividend is polynomial p(x) which we have to calculate, quotient is 3x³ - x² - x - 4, divisor is (x - 1) and remainder is -5.

So, p(x) = (x - 1) × (3x³ - x² - x - 4) + (-5)

= 3x⁴ - x³ - x² - 4x - 3x³ + x² + x + 4 - 5 

= 3x⁴ - 4x³ - 3x  - 1

Hence, p(x) = 3x⁴ - 4x³ - 3x  - 1, is the required polynomial.