Question

the remainder when 2x3+5x2-6x+2 is divided by (x+2)​

Answer 1

Answer:

When 2x³ + 5x² – 6x + 2 is divided by (x + 2) the remainder is 16.

Step-by-step explanation:

Given polynomial = 2x³ + 5x² – 6x + 2

It is divided by = (x + 2)

Using remainder theorem,

$\longrightarrow$ g(x) = x + 2

$\longrightarrow$ x + 2 = 0

$\longrightarrow$ x = –2

Put value of x in the polynomial,

$\longrightarrow$ p(x) = 2x³ + 5x² – 6x + 2

$\longrightarrow$ p(–2) = 2(–2)³ + 5(–2)² – 6(–2) + 2

$\longrightarrow$ p(–2) = 2(–8) + 5(4) + 12 + 2

$\longrightarrow$ p(–2) = –18 + 20 + 14

$\longrightarrow$ p(–2) = 2 + 14

$\longrightarrow$ p(–2) = 16

Remainder is 16

Therefore, when 2x³ + 5x² – 6x + 2 is divided by (x + 2) the remainder is 16.

Answer 2

16

Step-by-step explanation:

QUESTION :-

Find the remainder when 2x³ + 5x² - 6x + 2 is divided by (x + 2).

SOLUTION :-

Polynomial,

p(x) = 2x³ + 5x² - 6x + 2

Using the remainder theorem,

divider,

g(x) = x + 2

=> x + 2 = 0

=> x = - 2

Now,

put the value of x in p(x),

=> p(x) = 2x³ + 5x² - 6x + 2

=> p(-2) = 2(-2)³ + 5(-2)² - 6(-2) + 2

= 2(-8) + 5(4) + 12 + 2

= - 16 + 20 + 12 + 2

= - 16 + 32

= 16

So,

When 2x³ + 5x² - 6x + 2 is divided by x-2, the remainder is 16 .

Hope it helps.