Question

▶Polynomial 3x³ - 5x² + kx -2 and -x³ - x² +7x + k leave the same remainder when divided by x + 2. Find the value at k.​

Answer 1

Answer:

-12

Step-by-step explanation:

Substitute $x=-2$ to both polynomial to get remainder.

$3*(-8)-5*4-2k-2$

$=-24-20-2k-2$

$=-2k-46$

$-(-8)-4-14+k$

$=8-4-14+k$

$=k-10$

$-2k-46=k-10$

$3k=-36$

∴$k=-12$

Answer 2

$\huge\mathfrak{Bonjour!!}$

$\huge\bold\pink{Solution:-}$

☘ Answer:-

☞ k= -12.

☘ Step-by-step explanation:-

Let, p(x)= 3x³ - 5x² + kx -2,

and

q(x)= -x³ - x² + 7x + k

Now, put, x+2= 0

=> x= -2 in p(x) and q(x)

Now,

→ On substituting the value, -2 on p(x), we get,

p(-2) = 3(-2)³ -5(-2)² + k(-2) -2

= -24 -20 -2k -2

= -2k - 46

→ On substituting the value, -2 on q(x), we get,

q(-2) = -(-2)³ -(-2)² + 7(-2) + k

= 8 - 4 -14 + k

= -10 + k

Since, p(x) and q(x) leave the same remainder when divided by x+2,

Therefore,

-2k - 46 = k -10

=> -3k = 36

☞ K= -12.

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