2010004403
Level:
A
Suppose that a trinomial
\[9x^4+24x^3y+B^2\]
could be expressed as a square of sum, i.e. \( (A+B)^2\). Find the product \(A\) times \(B\).
\(12x^3y\)
\(24xy\)
\(24x^2y\)
\(24x^3y\)
Polynomials and fractions
2010004404
Level:
A
Suppose that a trinomial
\[25a^2b^2+20ab^2+Y^2\]
could be expressed as a square of sum, i.e. \( (X+Y)^2\). Find the product \(X\) times \(Y\).
\(10ab^2\)
\(20ab^3\)
\(20ab^2\)
\(20ab\)
1003032301
Level:
A
The polynomial \( 2x^2\left(x^2+3\right)+x^2+3 \) equals:
\( \left(2x^2+1\right)\left(x^2+3\right) \)
\( 2x^2\left(x^2+3\right) \)
\( 4x^2\left(x^2+3\right) \)
\( 2x^2\left(x^2+3\right)^2 \)
1003032302
Level:
A
The relationship between the time \( t \), the travelling distance \( s \) and the average speed \( v \) is expressed by the formula \( s = v\cdot t \). If the speed doubles, then the time to travel the same distance
will decrease by half.
will decrease by \( 2 \) hours.
will double.
will increase by \( 2 \) hours.
1003032304
Level:
A
Reducing the rational expression \( \frac{13ab^2(c-d)}{39a^2b(c-d)^2} \) to lowest terms we get:
\( \frac{b}{3a(c-d)} \)
\( \frac{3b}{a(c-d)} \)
\( \frac{a}{3b(c-d)} \)
\( 3ab(c-d) \)
1003032305
Level:
A
Simplifying the rational expressions \( \frac{(x-y)^2(p+q)^3}{2(x-y)(p+q)^4} \) we get:
\( \frac{x-y}{2(p+q)} \)
\( \frac{p+q}{2(x-y)} \)
\( 2(x-y)(p+q) \)
\( 2(x+y)(p-q) \)
1003032306
Level:
A
The product \( \left(2x^2y+3xy^2\right)(x-y-4) \) equals:
\( 2x^3y+x^2y^2-3xy^3-8x^2y-12xy^2 \)
\( 2x^3y+2x^2y^2-3xy^3-8x^2y-12xy^2 \)
\( 2x^3y+3x^2y^2-3x^2y^2-8x^2y-12xy^2 \)
\( 2x^3y-x^2y^2+3xy^3-8x^2y+12xy^2 \)
1003032307
Level:
A
The sum of the polynomials \( -x^3 y^2+6xy+5xy^4 \) and \( x^3-4xy^4+y^2 x^3+2xy \) is:
\( x^3+xy^4+8xy \)
\( -y^2+8xy+xy^4+y^2 x^3 \)
\( -x^3 y^2+8xy+xy^4+y^2 x^3+3x \)
\( x^3+xy^4+8x^2 y^2 \)
1003032308
Level:
A
Consider polynomials \( p(x)=(m-2)x^3+3mx^2-x+m \) and \( q(x)=x^3+m^2x^2+x+3 \).
Polynomials \( p \) and \( q \) are different for every \( m \).
Polynomials \( p \) and \( q \) are equal for \( m=3 \).
Polynomials \( p \) and \( q \) are equal for \( m=-3 \).
Polynomials \( p \) and \( q \) are equal for \( m=3 \) and for \( m=0 \).
2000006101
Level:
A
Simplify: \(3(3x^2-5x+1)-2x^2-(4x^2+2x-5)\)
\(3x^2-17x+8\)
\(3x^2-13x+8\)
\(3x^2-17x-2\)
\(3x^2-13x+2\)