BackClose

Select a Subject

Math

Question 5 of 18

beginning of content:

M:N:MC:4

Tags:
SAT

Exam

Learn more about this exam.

PSAT/NMSQT

Exam

Learn more about this exam.

PSAT 10

Exam

Learn more about this exam.

Calculator: Not Permitted
Passport to Advanced Math

Subscore

Learn more about Passport to Advanced Math.

If y equals x cubed plus 2 x plus 5 and z equals x squared plus 7 x plus 1 comma what is 2 y plus z in terms of x?

Select an Answer

3 x cubed plus 11 x plus 11

Correct Answer: 
No

2 x cubed plus x squared plus 9 x plus 6

Correct Answer: 
No

2 x cubed plus x squared plus 11 x plus 11

Correct Answer: 
Yes

2 x cubed plus 2 x squared plus 18 x plus 12

Correct Answer: 
No

View Correct Answer

Choice C is correct. Substituting the expressions equivalent to y and z into 2 y plus z results in the expression 2 left parenthesis x cubed plus 2 x plus 5 right parenthesis plus x squared plus 7 x plus 1. The student must apply the distributive property to multiply x cubed plus 2 x plus 5 by 2 and then combine the like terms in the expression.

Choice A is not the correct answer. This answer may result if a student correctly finds 2y in terms of x but does not pay careful attention to exponents when adding to x squared plus 7 x plus 1 and then combines the x cubed and x squared terms.

Choice B is not the correct answer. This answer may result if a student fails to distribute the 2 when multiplying 2 left parenthesis x cubed plus 2 x plus 5 right parenthesis.

Choice D is not the correct answer. This answer may result from a student finding 2 left parenthesis y plus z right parenthesis instead of 2 y plus z. 

Question Difficulty: 
medium
Objective: 

Students must substitute polynomials into an expression and then simplify the resulting expression by combining like terms.