Use the factor theorem and synthetic division to determine whethe...

Question

Use the factor theorem and synthetic division to determine whether the second polynomial is a factor of the first. See Example 1. 4x^2+2x+54; x-4

Accepted Answer

Hey, everyone here we are asked to perform factor theorem in synthetic division to identify whether X minus five is a factor or not of our given function F of X is equal to five X squared plus nine X plus 60. Here we have two answer, choice options, answer A yes or answer choice B no. So here, the first step is to recall the factor theorem which states that if X minus A is a factor of our function F of X, then we know that F of A is equal to zero. So here we are asked to verify X minus five. And so from X minus five, we see that our value for A is positive five. And so we really want to find that or verify that F of five is equal to zero. So to verify this statement, we need to perform synthetic division. So first setting up for synthetic division, we draw a vertical line and then a horizontal line which passes through it into the left of the vertical line. We place the value for A which is five to the right of the vertical line. We place all of the coefficients from our given function starting with the highest power of X. Well, here we see the highest power is X squared, so its coefficient is five, then moving on to the coefficient of X, we have nine and lastly the coefficient of X to the zero of power or in other words, just the constant value here is 60. So now we have finished setting up for synthetic division so we can begin the process. And so the first step is to just bring down the first coefficient which is five and rewrite it underneath the horizontal line, we then take this value of five and multiply it by the value of A which is also five. And now simplifying this product, we get 25 then we take this product and add it to the coefficient in the second column. So we have nine plus 25 which gives us 34. We then repeat this process one more time. Now taking 34 multiplying it by five. This gives us 170 we then add 170 to our last coefficient which is 60. So 60 plus 170 gives us 230. And now from this last value of after performing synthetic division that we obtained here, this gives us our value for F +05. So we see F of five is equal to 230. Well, here clear five is not equal to zero. So that tells us that our factor of X minus five is not a factor of F of X. So X minus five is not a factor of F of X since F of five is not equal to zero. Therefore, our answer is no. And we are left with answer choice. B the answer no. Where again, X minus five is not a factor of our given function F of X. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Use the factor theorem and synthetic division to determine whether the second polynomial is a factor of the first. See Example 1. 4x^2+2x+54; x-4

Key Concepts

Factor Theorem

Synthetic Division

Polynomials