Question

Find the reminder (without division) 8 x square + 5 x + 1 is divisible by x minus 10

Answer 1

Answer :

Given:

$8 {x}^{2} + 5x + 1$

Divided by

$(x - 10)$

Required to find:

Find the remainder without performing actual division.

Solution:

To solve this problem we should have some idea about what is meant by remainder theorem.

Remainder theorem !

This remainder theorem simply states that for any given polynomial expression that is p (x) when divided by (x-a) . we can find it's remainder without performing actual division only just makes some changes that is sending the a to the right side we get the value of x and by substitution it in the place of x in p (x).

Example: p (x) when divided by (x-1)

let x-1 = 0

then x = 1

Here this states that when we substitute this 1 in place of x we can get the remainder without long division.

Now let's coming to the question!

we were asked to find the remainder when (x-10) divided with 8x^2 + 5x + 1 .

p (x) = 8x^2 + 5x + 1

So, let x - 10 = 0

x = 10

Now substitute this x Value in p (x)

Hence we get

$p(x) = 8 {x}^{2} + 5x + 1 \\ p(10) = 8(10 {)}^{2} + 5(10) + 1 \\ = 8(100) + 50 + 1 \\ = 800 + 50 + 1 \\ = 851$

Therefore,

The remainder is 851.

Answer 2

Given : 8x² +5x + 1 is divided by x - 10

To Find : Remainder

Solution:

Using remainder theorem :

if polynomial   p(x)  is divided by x - m

then remainder is p(m)

and if p(m) = 0 then (x - m) is a factor

p(x) = 8x² +5x + 1

divided by x - 10

Hence m = 10

so remainder =p(10)

p(10) =8(10)² +5(10) + 1  = 851

Verification by division

                          8x   + 85    

   x - 10    _|      8x² +5x + 1   |_

                         8x² - 80x

                       _______

                                  85x + 1

                                  85x - 850

                                 __________

                                            851

Verified that remainder is 851

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