Question

If x+2 is the factor of x³+4x-bx⁴, then what is the value of b?

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Given :-

x+2 is the factor of x³+4x-bx⁴

To find :-

What is the value of b?

Solution :-

Given polynomial is x³+4x-bx⁴

Let P(x) = x³+4x-bx⁴

=>P(x) = -bx⁴+x³+4x

Given factor = x+2

We know that

By Factor Theorem,

If x-a is a factor of P(x) then P(a) = 0

If x+2 is a factor of -bx⁴+x³+4x then P(-2) = 0

=> -b(-2)⁴+(-2)³+4(-2) = 0

=> -b(16)+(-8)+(-8) = 0

=> -16b-8-8 = 0

=> -16b-16 = 0

=> -16(b+1) = 0

=> b+1 = 0/-16

=> b+1 = 0

=> b = -1

Therefore, b = -1

Answer:-

The value of b for the given problem is -1

Used Theorem:-

Factor Theorem :-

Let P(x) be a polynomial of the degree greater than or equal to 1 and x-a is another linear polynomial if x-a is a factor of P (x) then P(a) = 0 vice-versa.