Remainder Theorem & Evaluation
According to the Remainder Theorem, if a polynomial f(x) is divided by (x - k), what value does the remainder equal?
f(k)
True or False: Synthetic division can only be directly used when dividing by a linear factor of the form (x - k).
True
What is the first term of the quotient when you divide
2x^2 + 5x + 3
by x + 1
2x
What do you call an expression consisting of variables, coefficients, and non-negative integer exponents, such as
x^3 - 4x + 7
polynomial
What popular app uses a white ghost on a yellow background as its logo?
Snapchat
If you divide f(x) by (x - 4) and get a remainder of 0, what does this tell you about (x - 4)?
(x - 4) is a factor of f(x) (or x = 4 is a zero/root)
Use synthetic division to divide (x^2 - 9x + 20) by (x - 5). What is the result?
x - 4
What is the quotient when (x^2 + 7x + 12) is divided by (x + 3) using long division?
x + 4
When dividing polynomials, what must you insert as a placeholder if a term of a specific degree (like x^2 ) is missing from the dividend?
0 (or 0x^2 / a placeholder zero)
Which high school musical instrument features 88 keys and belongs to both the percussion and string families?
a piano?
Use the Remainder Theorem to evaluate f(x) = x^3 - 4x^2 + 2x + 5 at x = 2 .
1 (Since 2^3 - 4(2)^2 + 2(2) + 5 = 8 - 16 + 4 + 5 = 1 )
If the bottom row of a synthetic division problem shows the numbers 2 \quad -3 \quad 4 \quad \quad 0 , what degree polynomial is the quotient?
degree 2 (or a quadratic polynomial, 2x^2 - 3x + 4 )
Divide (3x^3 + 4x^2 + x + 2) by (x + 1) . What is the quotient and remainder?
3x^2 + x with a remainder of 2 (or 3x^2 + x + \frac{2}{x + 1} )
In the rational expression \frac{P(x)}{D(x)} , what are the formal math terms for the top expression P(x) and the bottom expression D(x)
numerator (or dividend) and denominator (or divisor)
What standard standardized test score scale goes from 400 to 1600 for college admissions?
SAT
Use synthetic division and the Remainder Theorem to evaluate f(x) = 2x^4 - 3x^2 + 5x - 8 at k = -1 .
-14
Use synthetic division to divide (x^3 - 2x^2 - 5x + 6) by (x - 3).
x^2 + x - 2
When using long division to divide a polynomial by (2x - 1), why can't you directly set up simple synthetic division without modifying the coefficient?
the leading coefficient of the divisor is not 1
To perform synthetic division by a binomial factor of the form (x - k) , what value of k do you place in the division box for (x - 3)?
3
In the movie Mean Girls, on what day of the week do the "Plastics" wear pink?
Wednesday
If f(-3) = 0 for a polynomial f(x), what is the remainder when f(x) is divided by (x + 3)?
0
Divide (x^4 - 16) by (x - 2) using synthetic division.
x^3 + 2x^2 + 4x + 8
Divide (2x^3 - 5x^2 + 3x + 7) by (x - 2) using long division. Express the result as a quotient plus a rational expression.
2x^2 - x + 1 + \frac{9}{x - 2}
How should you write the final answer when a polynomial division problem leaves a remainder R(x) with a divisor D(x)?
\text{Quotient} + \frac{R(x)}{D(x)}
What element on the periodic table has the chemical symbol Na?
Sodium