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Question

1. Jerry subtracted two polynomials and his incorrect solution is shown below. Explain the error(s) and enter the correct solution.

(x³ + 2x² - x) - (3x³ - 3x² + 2x - 4) =

-2x³ - x² + x + 4

2. Paula multiplied two polynomials as shown below. Explain the error(s) and enter the correct solution.

(x² - 3x + 2)(x + 1) =

x³ - 3x + 2x + x² - 3x + 2 =

x³ + x² - 4x + 2

Answer 1

Until you get comfortable with multiplying in-line, use the old grade school method of subtracting and multiplying:

1. Jerry subtracted two polynomials and his incorrect solution is shown below. Explain the error(s) and enter the correct solution.

(x³ + 2x² - x) - (3x³ - 3x² + 2x - 4) =

-2x³ - x² + x + 4

= = = = =

(x³ + 2x² - x)

- (3x³ - 3x² + 2x - 4) =

x³ + 2x² - x

3x³ - 3x² + 2x - 4

---------------------------- (SUSBTRACT)

-2x³ + 5x² - 3x + 4

2. Paula multiplied two polynomials as shown below. Explain the error(s) and enter the correct solution.

(x² - 3x + 2)(x + 1) =

x³ - 3x + 2x + x² - 3x + 2 =

x³ + x² - 4x + 2

= = = = = = = =

x²  - 3x + 2

x + 1

----------------------- MULTIPLY

x²  - 3x + 2

x³ - 3x² + 2x

------------------------------

x³ - 2x² - x + 2

Answer 2

It appears that Jerry did not remember to distribute the -1 before trying to combine like terms:

(x^3+2x^2-x) - (3x^3-3x^2+2x-4) = x^3+2x^2-x - 3x^3+3x^2-2x+4 = -2x^3+5x^2-3x+4

It appears that Paula did not distribute the x through the (x^2-3x+2) factor correctly:

(x^2-3x+2)(x+1) = x^3-3x^2+2x + x^2-3x+2 = x^3-2x^2-x+2