Question

Use the Factor Theorem to determine whether the first polynomial is a factor of the second polynomial. x - 5; 3x2 + 5x + 50 A) Yes B) No

Answer 1

it is not a factor because when you divide it by 5, the remainder is not 50.

Answer 2

notice, the factor or divisor is x-5, so we could just do a quick synthetic division on it for x - 5 = 0, x = 5, so, let's divide it by 5.


`\bf \cfrac{3x^2+5x+50}{x-5}\implies \begin{array}{llllll} 5&&3&5&50\\ &&&15&70\\ --&&--&--&--\\ &&3&20&\boxed{120}\impliedby remainder \end{array}`

now, notice the remainder, is NOT 0.