PARCC Algebra I Arithmetic with Polynomials and Rational Expressions Practice

Arithmetic with Polynomials and Rational Expressions skills

Understand the relationship between zeros and factors of polynomials

Use polynomial identities to solve problems

Rewrite rational expressions

Standards basis

Common Core State Standards for Mathematics (CCSS-M) / PARCC Model Content Frameworks — national

How the PARCC reports it

PARCC was a multistate assessment system built around the Common Core-era PARCC mathematics model content frameworks rather than a separate proprietary standards set. Its math structure is organized by grade/course and aligned to CCSS-M content categories and model content frameworks.

Blueprint & weighting

No single published PARCC weighting table was located in the accessible sources used here.

Official sources

PARCC Assessment
Common Core State Standards Initiative

8 free questions · 0/0 correct

Practice playeasy

What is $C(5, 2)$ ?

$C(5,2) = \dfrac{5!}{2! \cdot 3!} = \dfrac{120}{2 \cdot 6} = 10$ .

Practice playmedium

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

Group: $p(x)=(x^3+3x^2)+(-x-3)=x^2(x+3)-(x+3)=(x+3)(x^2-1)=(x+3)(x+1)(x-1)$ . After factoring, set each linear factor equal to zero: $(x+3)=0 \Rightarrow x=-3$ ; $(x+1)=0 \Rightarrow x=-1$ ; $(x-1)=0 \Rightarrow x=1$ . The zeros are $-3$ , $-1$ , and $1$ .

Practice playeasy

Which expression is equivalent to $\dfrac{x^{2}-5x+6}{x^{2}-4}$ when $x \neq 2$ and $x \neq -2\textsf{?}$

Factor: $\dfrac{(x-2)(x-3)}{(x-2)(x+2)}=\dfrac{x-3}{x+2}$ for $x \neq \pm 2\textsf{.}$

Practice playeasy

What is $4!$ ?

$4! = 4 \times 3 \times 2 \times 1 = 24$ .

Practice playmedium

The polynomial function defined by $p(x)=x^3-7x+6$ has $(x-1)$ as one of its linear factors. What are all and only the zeros of $p$ ?

Since $(x-1)$ is a factor, dividing by $(x-1)$ gives $p(x)=(x-1)(x^2+x-6)=(x-1)(x+3)(x-2)$ . The zeros are the roots of the linear factors, so set each equal to zero: $(x-1)=0 \Rightarrow x=1$ ; $(x+3)=0 \Rightarrow x=-3$ ; $(x-2)=0 \Rightarrow x=2$ . The zeros are $1$ , $2$ , and $-3$ .

Practice playeasy

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

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

Practice playeasy

What is $C(4, 1)$ ?

$C(4,1) = \dfrac{4!}{1! \cdot 3!} = \dfrac{24}{1 \cdot 6} = 4$ .

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 $-2$ .