Question

on dividing a polynomial px by x^2 -4 quotient and remainder are found to be x and 3 respectively the polynomial px is ​

Answer 1

p (x) = x³ - 4x + 3

Step-by-step explanation:

We have to find the polynomial p (x), which is divided by (x² - 4).

Then, dividend = p (x),

divisor = (x² - 4),

quotient = x and

remainder = 3.

We know that,

dividend = divisor × quotient + remainder

i.e., p (x) = (x² - 4) × x + 3

= (x² × x) - (4 × x) + 3

= x³ - 4x + 3

Therefore p (x) = x³ - 4x + 3

Note: To solve this type of problems, find the dividend, divisor, quotient and remainder. Then use the 'dividend = divisor × quotient + remainder' formula to find the unknown one.

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