Question

Should be added to x3-76 so that the resulting polynomial is divisible by x-4

Answer 1

Step-by-step explanation:

add 64 becoz adding 64 will cut out the -ve 64 and u will get the answer

Answer 2

Concept

The division algorithm is an equation that establishes a connection between the division's four components. In any division fact, the dividend value is always equal to the product of the divisor and the quotient added to the remainder. As a result, the basic division formula is: Dividend = (Divisor × Quotient) + Remainder. Divisibility means that a number can be divided evenly (with no remainder).

Given

Here, the dividend = x³ - 76

The divisor = x - 4

Find

We have to modify the dividend to make the remainder = 0.

Solution

Now, x³ - 76 =  x²(x - 4) + 4x(x - 4) + 16(x - 4) - 12

i.e. x³ - 76 + 12 = (x - 4)(x² + 4x + 16)

Then the remainder = 0 and the modified dividend = x³ - 76 + 12

So, we have to add 12 with the dividend.

Therefore, 12 should be added to x³ - 76 so that the resulting polynomial is divisible by x - 4.

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