Add and Subtract Polynomials

Adding and subtracting polynomials. In MathBound, the free Algebra I adventure game, Tile Sorter asks these problems, and the only way past is to solve them.

Part of Polynomials and Factoring: chapter 8 of the standard course.

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

What you will practice

Identify and Classify. Classify a polynomial as a monomial,binomial,or trinomial based on the number of terms.
Evaluate Polynomials. Evaluate a polynomial for a given positive integer value.
Add/Subtract Monomials. Add or subtract monomials by combining like terms (identical variable parts).
Add/Subtract Polynomials. Add two polynomials by combining their corresponding like terms.

Worked examples

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

Example 1 · Identify and Classify

Which

of

these

is

NOT

a

monomial ?

$- 2 x^{4}$
$- 8$
$- 2 x^{4} - 1$
$- 5 x^{3}$

Show the worked steps

$A$ $monomial$ $has$ $one$ $term,$ $a$ $binomial$ $two$ $and$ $a$ $trinomial$ $three;$ $terms$ $are$ $separated$ $by$ $+$ $and$ $-$ $signs.$
$- 2 x^{4} - 1$ $has$ $2$ $terms,$ $so$ $it$ $is$ $a$ $binomial,$ $not$ $a$ $monomial .$

Answer: $- 2 x^{4} - 1$

Example 2 · Evaluate Polynomials

If

p (x) = - 5 x^{2} - 4 x - 8,

what

is

p (6)?

$- 164$
$- 196$
$- 212$
$- 92$

Show the worked steps

$p (6)$ $means:$ $put$ $6$ $in$ $place$ $of$ $every$ $x .$
$(6)^{2} = 36 .$
$- 5 (36) - 24 - 8 = - 212 .$

Answer: $- 212$

Example 3 · Add/Subtract Monomials

Simplify:

7 x^{2} - 3 x^{2} - 6 x - 5 x

$4 x^{2} - 11 x$
$4 x^{4} - 11 x^{2}$
$- 7 x^{2}$
$- 7 x^{3}$

Show the worked steps

$Only$ $like$ $terms$ $combine:$ $the$ $x^{2}$ $terms$ $together,$ $the$ $x$ $terms$ $together.$
$7 + (- 3) = 4$ $and$ $- 6 + (- 5) = - 11 .$

Answer: $4 x^{2} - 11 x$

Where it is in your textbook

Textbook	Lessons
Standard course	8.1
Big Ideas Math Algebra 1	7.1
Big Ideas Math Algebra 1 (2022)	7.1
Carnegie Learning Algebra I	M5 2.1
CPM Core Connections Algebra	3.2.1, 8.1.1
CPS Skyline Algebra	3.5, 6.1-6.2
enVision Algebra 1	7-1
enVision Algebra 1 (2024)	7-1
Eureka Math Algebra I (EngageNY)	1.8-1.9
Glencoe Algebra 1	8-1
HMH Into Algebra 1	15.2, 16.1, 16.2, 20.2
Holt McDougal Larson Algebra 1	8.1
Illustrative Mathematics Algebra 1	6.3-6.4
Illustrative Mathematics Algebra 1 (v.360)	7.3-7.4
Math Nation Algebra 1 (Florida B.E.S.T.)	2.4, 2.5, 2.8
Open Up NC Math 1 (MVP)	7.2
OpenStax Elementary Algebra 2e	6.1
Pearson Algebra 1 Common Core	8-1
Reveal Algebra 1	10-1
SpringBoard Algebra 1	24

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