Most Missed SAT Math Question on May 2024 Digital SAT exam
Vložit
- čas přidán 20. 05. 2024
- The most missed math question on May 2024 SAT exam!!
34z^14+bz^7+70
In the given expression, b is a positive integer. If qz^7+r is a factor of the expression, where q and r are positive integers, what is the greatest possible value of b?
SUBSCRIBE NOW! And give us a thumbs up if you liked this video and want to receive exclusive DSAT videos.
Have a SAT video request?:
submit your request here: forms.gle/Wu5ZLs9n8Z1ypjqm9
CHECK OUT our Super Awesome SAT Math Video Course:
www.epicexamprep.com/
Learn more about Exam Prep Int Center (EPIC) Prep: www.epicexamprep.com/
Get more tips and tricks by following us!
www.instragram.com/epicexamprep
/ epicexamprep
Interested in taking private tutoring or group classes from a SAT exam prep expert? Check out www.epicexamprep.com/
Watch the rest of the DSAT playlist: • Digital SAT - Math
It's easier to solve the problem by factoring by grouping: Multiply 34 and 70 to get 2380. When you factor, you must find two numbers whose product is 2380 and sum is b. The two numbers that do this while maximizing b are 1 and 2380; therefore, b is 2380 + 1 = 2381.
This is what I eventually did too. I kept dividing 2380 by different numbers to check the sums of the quotient and the divisor. I finally realized that 2380 and 1 give the largest sum.
Also, if they were to ask for the lowest value of b all you have to do is factor like this: make the z^7 equal to x and the espression becomes 34x^2 + bx +70. Therefore, factor it like this (34x+70) (x+1). This will give you the smallest possible value of b which is 104. For the largest value of b switch the 70 and the 1. So, it's really about factoring and placing the factors of the c value in either the first or second patentheses based on how small or big they want the value of b.
Thank you for your comment and insight into the problem. Your approach to finding the smallest and largest values of b by factoring the polynomial using substitution is indeed a useful method! You can substitute x=z^7 into the polynomial 34x^2+bx+70... This helps us convert the original polynomial into a more manageable quadratic form. When we let x=z^7, the z^14 = (z^7)^2=x^2 .... so rewriting the polynomial in terms of x: 34(z^7)^2 + b(z^7)+70 -> 34x^2+bx+70....After the substitution, I want to factor 34x^2+bx+70 so that one of the factors is in the form (qz^7+r).... And then from there I am looking for two binomials that multiply to give 34x^2+bx+70...The factor pairs of the "c" value constant term are: (1,70),(2,35), (5,14), (7,10).....Then test the pairs....for example (34x+70)(x+1) = 34x^2+104x+70...here b=104 (SMALLEST value of b)....the other possibility is (34x+1)(x+70) = 34x^2+2381x+70 .... Where we can also see the correct answer, 2381 for the GREATEST value of b....There are multiple ways to solve, so use the method that comes most natural to you =)
How did we factor 34x²+bx+70 into two factors (34x+70) and (x+1)? Wouldn't the final expression then be 34x²+ 71x+70?
The smallest possible value of b would actually be 103 made up of 35+68. cuz 34*70 = 2380 and 35*68 also equals 2380. Using 34 and 70 in the front and back won’t ensure the smallest value.
Initially, i wanna thank you for making such a benificial videos, afterward i would say to those people who checks the comments before watching the video, guys honestly this is the only source that i see solves approximately the same questions as the SAT
Dont be lazy just checkout all the videos she has posted, believe in me u will all definietly face the same questions on the SAT.
Wow! Thank you for such a sweet comment! =) ... We do try to get questions that are most similar to what you will potentially see on the exam. Thank you again! =)
One can set q = 1 or q = 34 to get the same maximal value of b.
Why are we able to assume that z^7 + c is a factor? Shouldn't we express it as pz^7 + c? What is making the coefficient of z^7 1?
Great question!
Why Assume z^7 + c Instead of pz^7 + c?
The choice to express P(z) as z^7 + c simplifies the problem. If we tried pz^7 + c instead, it would introduce another variable p, making the factorization more complex without necessarily providing more useful information. The key is that we are looking for factors that simplify the polynomial, and z^7 + c is a common simplifying assumption that aligns with the degree of the polynomial we have.
By assuming z^7 + c as a factor, we streamline the factorization process and find the maximum value of b efficiently. The key is to simplify while ensuring all terms match the original polynomial's structure. It aligns with the structure and coefficients of the original polynomial, ensuring that we correctly factorize and solve for b.....I hope this makes sense!! =) =)
@@epicexamprep If you make the simplification of (z^7 + c) as a factor, then the overall equation becomes (qz^7 + r)(z^7 + c)(p) = 34z^14 + bz^7 +70. The second unknown (p) is required. This question is trying to make sure you know that the possible values for p and q are factors of 34 and the possible values of r and c are factors of 70. You must then realize the greatest value of b is to maximize one of each to get the largest product (largest factor of 34 is 34 and largest factor of 70 is 70. Using 34 *70 will make the second product 1 * 1). Because of this, p does equal 1 (34 * 1=34), but you have to justify it.
Lol. Glad I didn't get this one on my exam. There was one I haven't seen people discuss that was super hard involving sum of the solutions though.
I cover these ones in the June Predictions video (sum of solutions and product of solutions)...around the 29:16 mark. czcams.com/video/K8oMsv-dBLY/video.html
Hope it helps. =)
Does any body knows where can I find similar questions to practice from??
Hello! I cover more factoring problems in the June SAT Exam Prediction video: czcams.com/video/K8oMsv-dBLY/video.html
Alternatively, another great resource is the collegeboard question bank: satsuitequestionbank.collegeboard.org/
Look in "Advanced Math" (Equivalent Expressions)