1003032402
Level:
C
The polynomial \( 27+x^3 \) is equal to a product:
\( (3+x)\left(9-3x+x^2\right) \)
\( (3+x)^2(3-x) \)
\( (3-x)\left(9+3x+x^2\right) \)
\( (3+x)^3 \)
C
1003187313
Level:
C
Which of the given sets contains exactly all negative integers that satisfy the inequality \( \sqrt{(2x-8)^2} < 14 \)?
\( \{-2;-1\} \)
\( \{-3;-2;-1\} \)
\( \{-10;-9;-8;-7;-6;-5;-4;-3;-2;-1\} \)
\( \{-4;-3;-2;-1\} \)
1003187305
Level:
C
Which of the given numbers are the solutions of the equation \( \frac{|2x|-4}{1-|x|}+\frac{12}7=0 \)?
\( -8;8 \)
\( -\frac8{13};\frac8{13} \)
\( -\frac{20}{13};\frac{20}{13} \)
\( -20; 20 \)
1003187302
Level:
C
The equation \( \left| |2x-8|-4 \right|=4 \) has:
three real solutions
one real solution
four real solutions
two real solutions
1003187206
Level:
C
How many \( x \)-intercepts does the graph of \( f(x)=\left|-|2-x|- 2\right| \) have?
\( 0 \)
\( 2 \)
\( 1 \)
\( 4 \)
1003187205
Level:
C
Let \( f(x)=\left|3|2x-1|-9\right| \). The number of argument values \( x \) for which \( f(x)=2 \) is:
\( 4 \)
\( 2 \)
\( 3 \)
\( 1 \)
1003187204
Level:
C
The solution set of the equation \( \sqrt{x^2-2x+1}-2|x+3|+x+7=0 \) is:
\( \{-7\}\cup[1;+\infty) \)
\( \{-7\}\cup(1;+\infty) \)
\( [1;+\infty) \)
\( (1;+\infty) \)
1003187203
Level:
C
How many solutions does the equation \( \sqrt{x^2-4x+4}=|x| \) have?
\( 1 \)
\( 2 \)
\( 0 \)
\( 3 \)
1003187202
Level:
C
Which of following equalities is true for all real numbers \( x \)?
\( \sqrt{(x-3)^2} = |x-3| \)
\( |-x| = x \)
\( |x-1|=x-1 \)
\( \sqrt{x^2} = x \)
1003187410
Level:
C
How many integers are in the solution set of the given inequalities?
\[ \left|\sqrt{17}-2x\right| \leq 5 \text{ and } \left|2x-\sqrt{17}\right| \leq 5 \]
\( 5 \)
\( 4 \)
\( 6 \)
\( 7 \)