Lesson 5: Mastery Check Solutions

Show What You Know

A student completed the following problem. They know that the solution contains an error because the check does not result in the original problem. Find the correct solution. Prove your solution is correct by checking your work.

$x + 2 3 x^{2} + 11 x + 22 3 x^{3} + 5 x^{2} + 0 x + 7 - (3 x^{3} + 6 x^{2}) 11 x^{2} + 0 x - (11 x + 22 x) 22 x + 7 - (22 x + 44) 51 + \frac{51}{x + 2}$

$x + 2 3 x^{2} - x + 2 3 x^{3} + 5 x^{2} + 0 x + 7 - (3 x^{3} + 6 x^{2}) - x^{2} + 0 x - (- x^{2} - 2 x) 2 x + 7 - (2 x + 4) 3 + \frac{3}{x + 2}$

Check

$(x + 2) (3 x^{2} - x + 2) + 3 3 x^{3} - x^{2} + 2 x + 6 x^{2} - 2 x + 4 + 3 3 x^{3} + 5 x + 7 ✓$

Note

The given problem shows the same error repeated. This student forgot to change all of the signs when they subtracted their expressions from the given dividend.

When checking your work, be sure the remainder is added in after you find the product of terms.

Explain the error in the given work from part A.

The student did not subtract both terms when dividing. This error happened 3 times and that is why the values are so much larger than the correct solution.

Note

Compare your correct work to that of the given student work that contains errors. You may want to circle where the errors occur to make comparisons before you explain the error.

Another student found when
$12 x^{4} y^{3} - 6 x^{3} y^{2} - 5 x y + 3$
is divided by 3xy the quotient is
$4 x^{3} y^{2} - 2 x^{2} y .$
Find the correct solution. Show your work.

$\frac{12 x^{4} y^{3}}{3 x y} - \frac{6 x^{3} y^{2}}{3 x y} - \frac{5 x y}{3 x y} + \frac{3}{3 x y} 4 x^{3} y^{2} - 2 x^{2} y - \frac{5}{3} + \frac{1}{x y}$

Note

The solution is missing the last two terms because the exponent rules were applied incorrectly.

Say What You Know

In your own words, talk about what you have learned using the objectives for this part of the lesson and your work on this page.

Note

Restate the objectives of the lesson in your own words. If you are unable to restate the lesson objectives, go back and reread the objectives and then explain them.

Simplify expressions by dividing a polynomial by a monomial.
Use long division to divide polynomials.
Write the remainder of a polynomial expression as a rational expression.