Long-Division LoaderTilewrights · polynomials and factoring

Loads under a long bracket-shaped roof: dividing polynomials.

Divide Polynomials

Dividing polynomials. In MathBound, the free Algebra I adventure game, Long-Division Loader asks these problems, and the only way past is to solve them.

Part of More topics: taught by some textbooks beyond the usual course.

Play this battle free

10 questions, no sign-up, nothing saved. Climbs from the basics to harder questions.

What you will practice

Divide by a Monomial. Divide a polynomial by a monomial by separating it into individual fractions.
Polynomial Long Division. Divide a polynomial by a binomial using long division with no remainder.

Worked examples

Made by the game’s own question engine. Try each one, then open its steps.

Example 1 · Divide by a Monomial

A

rectangle

has

area

12 x^{2} + 12 x

and

width

4 x .

Which

expression

gives

its

length?

$12 x + 12$
$3 x^{2} + 3 x$
$3 x + 12 x$
$3 x + 3$

Show the worked steps

$The$ $length$ $is$ $the$ $area$ $divided$ $by$ $the$ $width.$
$Divide$ $every$ $term$ $by$ $the$ $divisor,$ $separately.$
$That$ $gives$ $3 x + 3 .$

Answer: $3 x + 3$

Example 2 · Polynomial Long Division

What

goes

in

the

box?

(x - 1) \cdot □ = x^{2} - 6 x + 5

$x - 1$
$x - 5$
$x + 5$
$x - 6$

Show the worked steps

$The$ $missing$ $factor$ $is$ $x^{2} - 6 x + 5$ $divided$ $by$ $x - 1 .$
$Check:$ $(x - 1) (x - 5)$ $multiplies$ $back$ $to$ $x^{2} - 6 x + 5 .$

Answer: $x - 5$

Example 3 · Divide by a Monomial

What

goes

in

the

box?

3 x \cdot □ = 15 x^{3} - 15 x^{2} + 18 x

$5 x^{3} - 5 x^{2} + 6 x$
$5 x^{2} - 5 x + 6$
$15 x^{2} - 15 x + 18$
$5 x^{2} - 5 x + 18 x$

Show the worked steps

$The$ $missing$ $factor$ $is$ $the$ $product$ $divided$ $by$ $3 x .$
$Divide$ $every$ $term$ $by$ $the$ $divisor,$ $separately.$
$That$ $gives$ $5 x^{2} - 5 x + 6 .$

Answer: $5 x^{2} - 5 x + 6$

Where it is in your textbook

Textbook	Lessons
Big Ideas Math Algebra 1 (2022)	7.2
Glencoe Algebra 1	11-5
Math Nation Algebra 1 (Florida B.E.S.T.)	2.9
OpenStax Elementary Algebra 2e	6.6
Pearson Algebra 1 Common Core	11-3
SpringBoard Algebra 1	28

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