Question

what must be SUBTRACTED from 4x^3+16x^2-x+5 to obtain a polynomial which is exactly divisiblr by x+5​

Answer 1

Question :-- what must be SUBTRACTED from 4x^3+16x^2-x+5 to obtain a polynomial which is exactly divisible by x+5 ?

Solution :--

The meaning of Exactly divisible , is Its Remainder will be Equal to Zero.

And if we Subtract the Remainder From the Polynomial we will get our Result.

So, let see Some Property First ..

→ Remainder Theorem :-- The remainder theorem states that when a polynomial, f(x), is divided by a linear polynomial , (x - a), the remainder of that division will be equivalent to f(a).

So, if Given Polynomial 4x³ + 16x² -x +5 is Exactly divisible by (x+5) , than f(-5) must be zero. or , if we put f(-5), we will get our Remainder .

Lets put ,

→ f(x) = 4x³ + 16x² -x +5

→ f(-5) = 4(-5)³ + 16(-5)² - (-5) + 5

→ f(-5) = 4 * (-125) + 16*25 + 10

→ f(-5) = (-500) + 400 + 10

→ f(-5) = (-500) + 410

→ f(-5) = (-90) .

So, our Remainder is (-90).

If we subtract this From given Polynomial , it will be Completely Divisible by (x+5).

Answer 2

Answer:

Explanation:

We Have :-

4x³ + 16x² - x + 5

To Find :-

What must be subtracted from 4x³ + 16x² - x + 5 to obtain a polynomial which is exactly divisible by x + 5​

Solution :-

f ( x ) = 4x³ + 16x² - x + 5

To be exactly divisible by x + 5 the remainder must be zero

x + 5 = 0

x = -5

Putting it in f ( x )

f ( -5 ) = 4 ( -5 )³ + 16 ( -5 )² - ( -5 ) + 5

         = 4 ( -125 ) + 16 ( 25 ) + 5 + 5

         = -500 + 400 + 10

         = -90

So to make 4x³ + 16x² - x + 5 exactly divisible by x + 5 we need to subtract ( -90 ) from it