1003032504
Level:
B
Factoring the polynomial \( -4x^4+26x^3-12x^2 \) you get:
\( -2x^2(x-6)(2x-1) \)
\( 2x^2(x+1)(2x-1) \)
\( -2x^2(x+6)(2x+1) \)
\( 2x^2(x-6)(2x+1) \)
Polynomials and Rational Expressions
1003032503
Level:
C
The polynomial \( 3x^5+px^3-(p-1)x^2+5x-9 \) is divisible by the binomial \( x^2-1 \) if \( p \) is equal to:
\( -8 \)
\( -16 \)
\( 4 \)
\( 6 \)
1003032502
Level:
C
Let the polynomial \( (x-2)^5-(x+2)^5 \) be expressed in the form \( a_5x^5+a_4x^4+a_3x^3+a_2x^2+a_1x+a_0 \). Give the sum of \( a_5+a_4+a_3+a_2+a_1 \).
\( -180 \)
\( -244 \)
\( -242 \)
\( -212 \)
1003032501
Level:
B
The product \( (x+y)\left(x^2+y^2\right)\left(x^3+y^3\right) \) equals:
\( x^6+x^5y+x^4y^2+2x^3y^3+x^2y^4+xy^5+y^6 \)
\( x^6-x^5y+x^4y^2-2x^3y^3+x^2y^4-xy^5+y^6 \)
\( (x+y)^6 \)
\( x^6+y^6 \)
1003032404
Level:
C
Simplifying the rational expression \( \frac{x^6-y^6}{x^2-y^2} \) we get:
\( \left(x^2-xy+y^2\right)\left(x^2+xy+y^2\right) \)
\( x^4-y^4 \)
\( x^3 - y^3 \)
\( \left(x^2-2xy+y^2\right)\left(x^2+2xy+y^2\right) \)
1003032403
Level:
C
Reducing the rational expression \( \frac{4m^2-4mn+n^2}{8m^3-n^3} \) we get:
\( \frac{2m-n}{4m^2+2mn+n^2} \)
\( \frac{m-4mn+1}{2m-n} \)
\( \frac{2m-n}{4m^2-4mn+n^2} \)
\( \frac{2m-n}{4m^2+4mn+n^2} \)
1003032402
Level:
C
The polynomial \( 27+x^3 \) is equal to a product:
\( (3+x)\left(9-3x+x^2\right) \)
\( (3+x)^2(3-x) \)
\( (3-x)\left(9+3x+x^2\right) \)
\( (3+x)^3 \)
1003032401
Level:
B
Factoring the polynomial \( 625x^4-1 \) we get:
\( \left( 25x^2+1\right)(5x-1)(5x+1) \)
\( (5x-1)(5x+1)^2 \)
\( (5x-1)^4 \)
\( \left( 25x^2+1\right)(5x-1)^2 \)
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 \( m=0 \).
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:
\( x^3+xy^4+8xy \)
\( -y^2+8xy+xy^4+y^2 x^3 \)
\( -x^3 y^2+8xy+xy^4+y^2 x^3+3x \)
\( x^3+xy^4+8x^2 y^2 \)