Question

the value of k for which (x+2)is a factor of (x+1)⁷+ (2x+k)³​

Answer 1

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K = 5

Answer 2

Answer:

Step-by-step explanation:

x+2 = 0

=x=-2

therefore,

(x+1)^7 + (2x+k)³=0

=( -2 +1)^7 + ( 2x-2 +k)³ =0

= -1 + (-4 +k)³ = 0

= -1 + (-4)³ + k³ - 3 x 4 x k ( k-4)=0

= -1 - 64 + k³ -12k² + 48k = 0

= k³ - 12k² +48k -65 =0

here, we can se k= 5 is a factor of this cubic polynomial.

so, k³ - 12k² + 48k - 65 / k-5

= k² - 7k +13

so, (k-5) (k² -7k + 13) = 0

b2-4ac = -4

hence one value of k is 5 and the other values are non real numbers.

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