DC CAPE Algebra I Arithmetic with Polynomials and Rational Expressions. Practice it free.

This domain covers arithmetic operations with polynomials and rational expressions. This Algebra I reporting domain maps to 7 practice skills and 8 representative questions from the playable bank.

Algebra IArithmetic with Polynomials and Rational Expressions7 mapped skills

What the test measures

Arithmetic with Polynomials and Rational Expressions skills

perform arithmetic operations on polynomials
understand the relationship between zeros and factors of polynomials
use polynomial identities to solve problems
rewrite rational expressions

Standards basis

Common Core State Standards (CCSS-M) — District of Columbia

How the DC CAPE reports it

DC CAPE math continues DC’s PARCC-era alignment to the Common Core State Standards and uses the same general development/review approach described by OSSE. The page says DC Math follows the same rigorous development and review process and measures the knowledge and skills that matter most for DC students, while also explicitly tying the assessments to CCSS.

Blueprint & weighting

DC CAPE uses the PARCC-derived / Common Core-based framework (by grade domains structure).

Official sources

OSSE DC CAPE
OSSE DC CAPE page content on CCSS and test specifications

Practice by skill

Topics mapped to this domain

Try it now

8 free questions · 0/0 correct

Practice playeasy

What is $C(6, 3)$ ?

$C(6,3) = \dfrac{6!}{3!\,(6-3)!} = 20$ .

Practice playmedium

What are all and only the zeros of the polynomial defined by $p(x)=x^3+4x^2+4x$ ?

Factor out $x$ : $p(x)=x(x^2+4x+4)=x(x+2)^2$ . Set each factor equal to zero: $x=0 \Rightarrow x=0$ ; $(x+2)^2=0$ , so $(x+2)=0 \Rightarrow x=-2$ . The zero $-2$ has multiplicity $2$ , so the zeros are $0$ , $-2$ , and $-2$ .

Practice playmedium

Which expression is equivalent to $\dfrac{2x^{3}-2x}{2x^{2}-2x}$ when $x \neq 0$ and $x \neq 1\textsf{?}$

Factor: $\dfrac{2x(x-1)(x+1)}{2x(x-1)}=x+1$ for $x \neq 0$ and $x \neq 1\textsf{.}$

Practice playeasy

Which expression is equivalent to $(2yz)(5y)(4)\textsf{?}$

Multiply the coefficients: $2 \cdot 5 \cdot 4 = 40\textsf{.}$ Add the exponents on $y$ : $y^{1+1} = y^{2}\textsf{.}$ The factor $z$ appears once, so the product is $40y^{2}z\textsf{.}$

Practice playmedium

Simplify: $(2x^2 + 7x + 1) + (-x^2 + 2x - 4)\textsf{.}$

Combine $x^2$ terms: $2x^2 - x^2 = x^2\textsf{.}$ Combine $x$ terms: $7x + 2x = 9x\textsf{.}$ Combine constants: $1 - 4 = -3\textsf{.}$ Result: $x^2 + 9x - 3\textsf{.}$