Is this right?

[Stouffville]

Determine the value of ? such that when f(x) = x^4 +kx^3 - 3x -5 is divided by x-3 , the remainder is -10 ?
Here is the work that I have done
-10 = 3^4 + k(3)^3-3(3) -5
-10=81 + 9k -9 -5
-10 = 67 + 9k
-10-67 =9k
77=9k

 

[Dr.Peterson]

Determine the value of ? such that when f(x) = x^4 +kx^3 - 3x -5 is divided by x-3 , the remainder is -10 ?
Here is the work that I have done
-10 = 3^4 + k(3)^3-3(3) -5
-10=81 + 9k -9 -5
-10 = 67 + 9k
-10-67 =9k
77=9k

What is 3^3? And are all your signs right? I wonder if you copied the problem correctly.

 

[Stouffville]

What is 3^3? And are all your signs right? I wonder if you copied the problem correctly.

that means to the power of three

 

[Otis]

Hi Stouffville. Have you learned how to divide one polynomial by another (i.e., polynomial longhand division)?

 

[Stouffville]

Hi Stouffville. Have you learned how to divide one polynomial by another (i.e., polynomial longhand division)?

yes

 

[Otis]

If you divide (x^4+kx^3-3x-5) by (x-3), you will get a remainder. The remainder will be an expression containing symbol k. That expression equals -10.

 

[Stouffville]

but we know what the reainder is :
Determine the value of ? such that when f(x) = x^4 +kx^3 - 3x -5 is divided by x-3 , the remainder is -10 ?
Here is the work that I have done
-10 = 3^4 + k(3)^3-3(3) -5
-10=81 + 9k -9 -5
-10 = 67 + 9k
-10-67 =9k
77=9k

 

[Otis]

we know what the [remainder] is

We know its value, but we don't have an algebraic expression for it. (That's okay; I was suggesting another method.)

[3^3] means [three] to the power of three

Yes, and you've written that 3^3 equals 9, but it doesn't.

 

[Stouffville]

We know its value, but we don't have an algebraic expression for it. (I was suggesting another method.)


Yes, and you've written that 3^3 equals 9, but it doesn't.

sorry it = 27

 

[Otis]

sorry it = 81

No, the fourth power of three is 81 (3^4).

3^3 is something else.

3×3×3 = ?

 

[Stouffville]

27

 

[Otis]

Fix that mistake in your work, and you can solve for the correct value of k.

?

 

[Stouffville]

but we know what the reainder is :
Determine the value of ? such that when f(x) = x^4 +kx^3 - 3x -5 is divided by x-3 , the remainder is -10 ?
Here is the work that I have done
-10 = 3^4 + k(3)^3-3(3) -5
-10=81 + 27k -9 -5
-10 = 67 + 27k
-10-67 =27k
77=27k

77/27 = k

 

[Otis]

-10-67

Oops, I'd missed another mistake.

When you did the subtraction above, you wrote 77. Check your arithmetic.

 

[Stouffville]

Fix that mistake in your work, and you can solve for the correct value of k.

?

but we know what the reainder is :
Determine the value of ? such that when f(x) = x^4 +kx^3 - 3x -5 is divided by x-3 , the remainder is -10 ?
Here is the work that I have done
-10 = 3^4 + k(3)^3-3(3) -5
-10=81 + 27k -9 -5
-10 = 67 + 27k
-10-67 =27k
77=27k
77/27 = k

 

[Stouffville]

-77/27

 

[Otis]

-77/27 is correct.

PS: If we do the polynomial division, then we get (67+27k) for the remainder. That's just another way to obtain the equation -10=67+27k.

?

 

[Stouffville]

-77/27 is correct.

PS: If we do the polynomial division, then we get (67+27k) for the remainder. That's just another way to obtain the equation -10=67+27k.

?

for the remainder I got -157/8

 

[Otis]

for the remainder I got -157/8

67 + 27k = -10

67 + 27(-77/27) = -10

67 - 77 = -10

-10 = -10

The remainder is -10.

 

[Steven G]

You can do it the way you did or do the long division (or synthetic division). Personally I prefer your way.