Functions, Domain, Range, Interval Notation, Factoring

When factoring, it is good practice to always begin by:

• checking for a greatest common factor.

• applying the ac-method.

• applying the grouping technique.

• distributing all factors; using the FOIL strategy.

• decide if terms can be perfect squares or cubes.

Classify the given polynomial expressions by the degree and number of terms. 

• (a.)parabola trinomial,   (b.)five-nomial,   (c.)trinomial polynomial

• (a.)bidratic trinomial,   (b.)quartic binomial,   (c.)cubic quadrinomial

• (a.)parabola trinomial,   (b.)pentic binomial,   (c.)cubic quadrinomial

• (a.)quadratic trinomial,   (b.)quintic binomial,   (c.)cubic polynomial of 4 terms

• (a.)quadratic trinomial,   (b.)quintic binomial,   (c.)cubic fournomial

Which of the following sets contains numbers which are exclusively perfect squares? Select all that apply.

•  $\left\{0,\ 4,\ 16,\ 64,\ 196\right\}$  

•  $\left\{1,\ 9,\ 25,\ 49,\ 169,\ 225\right\}$  

•  $\left\{81,\ 100,\ 121,\ 144\right\}$  

•  $\left\{265,\ 298,\ 342\right\}$  

•  $\left\{256,\ 289,\ 324\right\}$  

Find the prime factorization of 72 & 32. Select 2 answers.

•  $2^5$  

•  $2^33^2$  

•  $2^6$  

•  $2^43^3$  

•  $2^43^2$  

Identify the choice which exclusively contains perfect cubes.

•  $216,\ 225,\ 343,\ 8,\ 684$  

•  $125,\ 8,\ 64,\ 349,\ 27,\ 927$  

•  $81,\ 225,\ 343,\ 981,\ 27$  

•  $512,\ 216,\ 125,\ 343,\ 729$  

Given: $a^3x^3\ ±\ b^3;$  identify the appropriate way to factor the given expression.

•  $\left(ax\ \pm\ b\right)\left(a^2x^2\ ∓\ abx\ +\ b^2\right)$  

•  $\ \left(ax\ \pm\ b\right)^3$  

•  $\left(a^2x^2\ +\ b\right)\left(ax\ -\ b\right)$  

•  $\left(ax\ \pm\ b\right)\left(ax^2\ ∓\ abx\ +\ b^2\right)$  

 $2\left|4x-5\right|-7\ge3$ ; which inequalities should be used to solve the given absolute value inequality. Try to use mental math. Look carefully.

•  $4x+5\ge5\ \ \&\ \ 4x+5\le-5$  

•  $8x-10\ge10\ \ \&\ \ 8x-10\ge-10$  

•  $4x-5\ge5\ \ \&\ \ 4x-5\le-5$  

Check all of the choices which apply to the given number line.

• $x<3$ OR $x>5$

• $\left(-\infty,\ 3\right)\cup\left(5,\ \infty\right)$

• $x\le2.9$ AND $x\ge5.1$

• $\left(-\infty,\ 3\right]\cup\left[5,\ \infty\right)$

• $\left(-\infty,\ 4\right)\cup\left(4,\ \infty\right)$

If the function  $f\left(x\right)$  is equal to  $-x^2+2x^3-x^5$ ,  find  $f\left(-2\right)$ .

• -70

• -52

• -50

• 20

• 12

Tags

CCSS.HSF.IF.A.2

Given  $g\left(x\right)=\frac{1}{x^2-4}$ , determine the domain based on what you know about basic arithmetic of real numbers.

•  $x\ne2;\ \left(-\infty,\ 2\right)\cup\left(2,\ \infty\right)$  

•  $x\ne0;\ \left(-\infty,\ 0\right)\cup\left(0,\ \infty\right)$  

•  $x\ne\pm2;\ \left(-\infty,-2\right)\cup\left(-2,\ 2\right)\cup\left(2,\ \infty\right)$  

•  $x\ne0,\ x\ne2;\ \left(-\infty,0\right)\cup\left(0,\ 2\right)\cup\left(2,\ \infty\right)$  

Tags

CCSS.HSA.APR.D.7

CCSS.HSF.IF.B.5