Synthetic Substitution and Synthetic Division
True or false: If you get a remainder of zero when performing synthetic division, that means that that value of x would be an x-intercept or factor.
True
The graph touches the x-axis at that value, but does not cross it. So, if y is negative, it will stay negative. If y is positive, it will stay positive.
List the factors of the leading coefficient (q) and the constant last term (p) in the polynomial 4x2 + x + 10
Factors of q = 1, 2, 4
What is the quotient or answer when you divide x2 + 3x - 4 by x - 1? (I am not asking for the remainder or final number you get. Your answer should have x's in it)
1x + 4 or x + 4
True or false: I drove to school today
False
When you evaluate the function x2 + x - 12 for x = 3, the answer is 0. That means (x + 3) is a factor of the this function.
False, (x - 3) would be the factor
What happens on a graph at a triple root/triple x-intercept?
The curve flattens out slightly at that x-intercept, but still cross the x-axis into either the positives or negatives.
List the factors of the leading coefficient (q) and the constant last term (p) in the polynomial 12x2 - x + 24
Factors of p = 1, 2, 3, 4, 6, 8, 12, 24
Factors of q = 1, 2, 3, 4, 6, 12
What is the quotient or answer when you divide x3 - 3x2 - 10x by x - 5? (I am not asking for the remainder or final number you get. Your answer should have x's in it)
x2 + 2x
Which of these fruits is actually a berry by the botanical definition
a) Strawberry
b) Banana
c) Blackberry
d) Cherry
c) Banana
Divide 2x3 - x2 - 27x + 36 by x - 3 to determine if it is a factor or not
It is a factor, you get 0.
It is negative. The two x-intercepts are 4 and -1. If x = 0 which is between these values, then y = (-4)(1) which will be negative.
Given that (qx-p) is a factor of the polynomial 2x3 + 17x2 + 27x - 18, use the rational root theorem to list all of the possible rational x-intercepts (meaning list all the values of p/q)
+- 1, 1/2, 2, 3, 3/2, 6, 9, 9/2, 18 (This includes the repeats which are 2/2 = 1, 6/2 = 3, and 18/2 = 9)
What is the quotient or answer when you divide x4 - 9x3 + 11x2 + 21x by x - 7 (I am not asking for the remainder or final number you get. Your answer should have x's in it)
x3 - 2x2 - 3x
If you take any number between 1 and 100, multiply it by 100, subtract that answer from your starting number, then add all of the digits in this final number together, you will always get 18
True
Divide 2x3 - x2 - 27x + 36 by x + 4 to determine if it is a factor or not
It is, you get 0.
Perform a sign test to determine whether the function y = -x2(x + 2) is positive or negative between the two x-intercepts.
The function will be negative. The x-intercepts are 0 (double root) and -2. When x = -1, y = -(-1)2(-1 + 2) = -(1)(1) = -1
Use the rational root theorem and synthetic division to find ONE factor of the polynomial y = 6x2 + 5x - 4
Using the rational root theorem, the possible x-intercepts p/q = +- 1, 1/2, 1/3, 1/6, 2, 2/3, 4, 4/3
Of these, synthetic division will yield that the two correct factors are (2x - 1) and (3x + 4), which are x-intercepts of 1/2 and -4/3
Use synthetic division to fill in the blank (x + 3)(_______) = x3 + 2x2 - 13x + 10. You will get a remainder when you divide, include that in your answer as a fraction.
x2 - x - 10 + (40/x+3)
Which of these pop artists would I say is my least favorite:
a) Dua Lipa
b) Taylor Swift
c) Charli xcx
d) Chappell Roan
If x = 5, what is the value of the function y = -x6 + 2x5 - 4x4 + x3 + 10x + 11701
1
It is not possible. A cubic function will always cross the x-axis at some point. This is not true of quadratic or quartic functions.
Use the rational root theorem and synthetic division to find ONE x-intercept of the polynomial y = 2x3 + 17x2 + 27x - 18.
What is the quotient AND remainder when you divide x4 - 9x3 + 11x2 + 21x by x + 2
x3 - 11x2 + 33x - 45 With a remainder of 90
How many siblings do I have?
2 (older and younger brother)