Remainder theorem and factor theorem: If f(x) + x^6 – 5x^4 – 10x^2 + k...

[jenny15]

Remainder theorem and factor theorem: If f(x) + x^6 – 5x^4 – 10x^2 + k...

I was given 2 problems to solve for home work, but don't quite know how to solve them. The teacher gave easy problems in school and left these two for home work. Please give me a hand as it is due for today..

1. If f (x) + x⁶ – 5x⁴ – 10x² + k, find the value of k for which x - 1 is a factor of f (x). When k has this value, find another factor of f (x), of the form x + a, when a is a constant.

2. Find the value of a and b if f (x) = ax³ + bx² +12 is exactly divisible by both (x + 1) and (x - 2). With these values a and b. solve the equation f (x) = 0

I need to show full working... Please help me..

 

[Deleted member 4993]

I was given 2 problems to solve for home work, but don't quite know how to solve them. The teacher gave easy problems in school and left these two for home work. Please give me a hand as it is due for today..

1. If f(x) + x^⁶ – 5x^⁴ – 10x^² +k, find the value of k for which x-1 is a factor of f(x). When k has this value, find another factor of f(x), of the form x+a, when a is a constant.

1. Find the value of a and b if f(x) = ax^3 + bx^2 +12 is exactly divisible by both (x+1) and (x-2). With these values a and b. solve the equation f(x) = 0

I need to show full working... Please help me..

Hint:

If (x-1) is a factor of f(x), what can you say about value of f(1)?

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

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[Steven G]

I was given 2 problems to solve for home work, but don't quite know how to solve them. The teacher gave easy problems in school and left these two for home work. Please give me a hand as it is due for today..

1. If f(x) + x^⁶ – 5x^⁴ – 10x^² +k, find the value of k for which x-1 is a factor of f(x). When k has this value, find another factor of f(x), of the form x+a, when a is a constant.

1. Find the value of a and b if f(x) = ax^3 + bx^2 +12 is exactly divisible by both (x+1) and (x-2). With these values a and b. solve the equation f(x) = 0

I need to show full working... Please help me..

As always Subhotosh's hint is right on target. Given the 2nd part of question 1 I would use synthetic division to do this problem.
Show us your attempt for the 2nd question and someone here will guide you.