Tejas S. answered • 06/01/15

Math, Physics & Chemistry Tutor - Alexandria, VA

Tara F.

asked • 06/01/15Determine the value of the constant k so that x-2 is a factor of the function g(x)=2x^4+kx^3+3x+4

More

Tejas S. answered • 06/01/15

Tutor

4
(2)
Math, Physics & Chemistry Tutor - Alexandria, VA

Since x-2 is a factor, g(2) = 0

g(2) = 2(2^4) + k(2^3) + 3(2) + 4 = 0

2(16) + k(8) + 6 + 4 = 0

42 + 8k = 0

k = -42/8

k = -5.25

Just a note to all students and tutors: PLZ, always check your answers; I've often found trivial calculation errors. Thankfully, Tutors can edit their Answers and several have made corrections. THX.

For example, last night I wrote comments on two answers (which differed, but now are the same -- THX) and voted to indicate the correct answer.

My comments:

And, checking: Does g(2) = 2*(2^4)+(-5.25)*(2^3)+3*(2)+4 = 0 ? Yes.

And, checking: Does g(2) =2*2^4+(-0.25)*2^3+3*(2)+4 = 0 ? No, it equals 40, so k ≠ -1/4.

p.s., Tutors cannot change Comments.

Michael J.

You should give the tutors a chance to catch their errors, rather than thinking they will just let it slide. In addition, you are right that we cannot change comments, but we can add a new comment that corrects the previous comment.

Report

06/03/15

David W.

tutor

My experience is (not verified with WyzAnt) that there is a small quota for comments that I may add per time period (or other).

Report

06/03/15

Michael J. answered • 06/01/15

Tutor

5
(5)
Effective High School STEM Tutor & CUNY Math Peer Leader

We can use synthetic division to determine the value of k. This method divides coefficient of the polynomial by the root of the factor. Also, the remainder must be zero. In the synthetic division, the last digit is the remainder.

The coefficients of the polynomial is: 2 k 0 3 4.

The root of the factor (x - 2) is 2. This is because if we set x-2 = 0, x is 2.

Set ups the division.

2 | 2 k 0 3 4

__________________________

Bring down the first coefficient of the polynomial below the line. Place a zero below the line under the polynomials last digit.

2 | 2 k 0 3 4

__________________________

__________________________

2 0

Multiply the root by the first digit under the line. This product will be the addend in the succeeding column.

2 | 2 k 0 3 4

4 -4

__________________________

2 0

4 -4

__________________________

2 0

Next, we need to go backwards. That is the reason why I inserted a -4 as the addend in the last column because 4 and -4 gets us zero. So if we multiply going forward, we must divide going backward. Divide the addend by the root and place under the line in the preceding column. Repeat this step.

2 | 2 k 0 3 4

4 - 5/2 -5 -4

______________________________

2 -5/4 -5/2 -2 0

4 - 5/2 -5 -4

______________________________

2 -5/4 -5/2 -2 0

Now we focus on the column that has k.

Write an equation since we know we have to add to get the sum of -5/4.

k + 4 = -5 / 4

Subtract 4 on both sides of equation.

k = (-5 / 4) - 4

k = (-5 / 4) - (16 / 4)

k = -21 /4

David W.

tutor

And, checking: Does g(2) =2*2^4+(-0.25)*2^3+3*(2)+4 = 0 ? No, it equals 40, so k ≠ -1/4.

Report

06/01/15

Michael J.

I checked my work. You will see that my solution will match Tejas'. We only had a different method of solving the problem.

Report

06/01/15

Andrew M.

Michael's answer is k = - 21/4 which is -5.25 which does work out as already shown above by Tejas S.

Report

06/02/15

David W.

tutor

Michael's answer now says k = -21/4, which is quite correct. THX. As you can see, I quoted his answer as "k=-1/4" and indicated "k ≠ -1/4."

Report

06/02/15

Ask a question for free

Get a free answer to a quick problem.

Most questions answered within 4 hours.

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.

David W.

06/01/15