College Board Test 4, Math 4 #25 (the explanation link that you previously made does not work):
f(x) = 2x^3 + 6 x^2 + 4x
g(x) = x^2 + 3x + 2
The polynomials f(x) and g(x) are defined above. Which of the following polynomials is divisible by 2x + 3?
A) h(x) = f(x) + g(x)
B) p(x) = f(x) + 3 g(x)
C) r(x) = 2 f(x) + 3 g(x)
D) s(x) = 3 f(x) + 2 g(x)
Hi! On q8 page 149 (polynomials), what is happening in D? Why is it true?
Hi Mike! In SAT official test 1, Q 29 (in the math calculator section), how do you solve this problem? I don’t quite understand the explanation/concepts mentioned in the book.
29)For a polynomial p(x), the value of p(3) is -2. Which of the following must be true about p(x)?
A) x-5 is a factor of p(x).
B) x-2 is a factor of p(x).
C) x+2 is a factor of p(x).
D) The remainder when p(x) is divided by x-3 is -2.
(Also what does PWN stand for?)
A question on polynomials practice question #10 (p. 149 in PWN the SAT Math Guide): I understand how to solve using polynomial long division but can you explain your shortcut from the answer explanation? How would we know to plug in -3?
Could you further explain your explanation of Practice Question #4 in PWN the SAT Math Guide “Polynomials” chapter (p. 148). In your long division confirmation of the answer (explanation p. 326), how do you know to divide by 9x + 1?
Hi, I don’t get these types of problems & would really like an explanation for their solution. (x- 3)(x – d) = x^2 – 2dx + m. I don’t know how to find the value of dm because I can’t isolate d without getting a fraction. Please help );
This may be a little advanced for the SAT, but complex numbers sometimes show up –as do cubic polynomials– so hopefully you can address this for me! TIA!
Which of the following could be the full set of complex roots of a cubic polynomial with real coefficients?
A. { 0, 1, i}
B. {1, i, 2i}
C. {2, i}
D. {3, 2 + i, 2 – i}
PWN p. 151 #8 question
In PWN the SAT Math Guide (4th Ed, first printing p. 151), Polynomials chapter question #8, you explain the answer by graphing on calculator. Could you explain the answer to this question without graphing, in particular, why A, C and D are true and why B is false? Many thanks!
f(x) = x^3 – cx^2 + 4x – 4c
In the function f above, c is a constant. How many x-intercepts does the function have?
Can you show how to solve this through logic/algebra? TIA!!
Hi Mike, Can you work the solution for Test 7, Section 3, #13? Thanks!
PSAT #2, Section 3, #16
PSAT #1, Section 3, #17
Hi Mike,
Can you give me some help with question 10 in the Polynomials section of PWN (pg 149)? I plug in x=-3, per your suggestion, and I get 41 as the answer on the left-hand side of the equation and 3(-3) – 13 + a on the right. That means 41 = -22 + a, or a = 63. What am I missing? Thanks!
Hi Mike. How would you do practise test 8, section 3 question 11? Can you explain the whole polynomials to an odd/even degree etc. The collegeboard answer was a little confusing
Thank you!
I’m not sure you are answering questions about Practice Test 6 yet. If so, would you please work # 12 in section 3 of that test?
