Question

find k, if x51+2x60+3x+k is divisible by x+1

Answer 1

I guss you're qurstion is this way,
${x}^{51} + 2 {x}^{60} + 3x + k$
Let this polynomial be equal to p(x).



The given factor is x+1
Then by factor theorem,

$p( - 1) = 0$

This gives us,

$p( - 1) = {( - 1)}^{51} + 2 {( - 1)}^{60} + 3( - 1) + k = 0 \\ p( - 1) = - 1 + 2 - 3 + k = 0 \\ p( - 1) = - 2 + k = 0$

Therefore, k= 2.

Answer 2

Answer:

2

Step-by-step explanation:

x⁵¹+2x⁶⁰+3x+k

Polynomial = x+1

x+1 =0

x= -1

p(-1) = x⁵¹+2x⁶⁰+3x+k

= (-1)⁵¹ + 2(-1)⁶⁰ + 3×(-1) +k

= -1 + 2×1 +(-3) + k

= -1+2-3+k

= -2+k

-2+k = 0

k = 2