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General Information
Related Benchmark: MAFS.912.A-APR.1.1
Reporting Category: Algebra: Arithmetic with Polynomials & Rational Expressions
Type: GRID: Graphic Response Item Display
Difficulty: N/A
Question:

Roxanne wants to test the idea that polynomials are closed under addition. Her work and explanation are shown.

Drag an expression and phrases to the boxes to complete the statement.

Add begin mathsize 12px style 3 x to the power of 4 minus 7 x cubed plus 12 x minus 9 end style to ____________________. The sum is closed because  ______________ are ________________ and by definition the sum is a polynomial.

Answer Options:
begin mathsize 12px style 5 x squared minus left parenthesis 2 x right parenthesis cubed plus left parenthesis 4 x right parenthesis to the power of negative 1 end exponent end style

begin mathsize 12px style negative 8 x to the power of negative 2 end exponent minus left parenthesis 3 x right parenthesis cubed minus 12 x to the power of 6 plus 7 end style

begin mathsize 12px style left parenthesis 2 x right parenthesis cubed plus 2.1 x squared minus 11 end style

the variables

the coefficients

integers

real numbers

the exponents

whole numbers

Possible Answer:
Add begin mathsize 12px style 3 x to the power of 4 minus 7 x cubed plus 12 x minus 9 end style to begin mathsize 12px style left parenthesis 2 x right parenthesis cubed plus 2.1 x squared minus 11 end style. the sum is closed because the exponents are whole numbers and by definition the sum is a polynomial.