2010004406
Level:
A
Factor the expression: \(5ab-ac+15bd-3cd\).
\( (5b-c)(a+3d)\)
\( (c-5b)(a+3d)\)
\( (5b-c)(a-3d)\)
\( (c-5b)(a-3d) \)
Polynomials and fractions
2010004405
Level:
A
Factor the expression: \(3xy-ty-12xz+4tz\).
\( (3x-t)(y-4z)\)
\( (t-3x)(y-4z)\)
\( (3x-t)(4z-y)\)
\( (t-3x)(y+4z) \)
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 \(Y\).
\(10ab^2\)
\(20ab^3\)
\(20ab^2\)
\(20ab\)
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 \(B\).
\(12x^3y\)
\(24xy\)
\(24x^2y\)
\(24x^3y\)
2010004402
Level:
A
From the given expressions choose the one, that by substituting for \( \mbox{*} \) into a trinomial
\[ 9- \mbox{*} +16a^2b^4\]
makes possible to express the trinomial as a square of a difference, i.e. \( (A-B)^2\).
\(24ab^2\)
\(12ab^2\)
\(144ab^2\)
\(48ab^2\)
2010004401
Level:
A
From the given expressions choose the one, that by substituting for \( \mbox{*} \) into a trinomial
\[ 25x^4y^2 + \mbox{*} +4\]
makes possible to express the trinomial as a square of a sum, i.e. \( (A+B)^2\).
\(20x^2y\)
\(10x^2y\)
\(100x^2y\)
\(40x^2y\)
2000006102
Level:
A
Simplify: \(2(4y^2-2y+5)+2y^2-(3y^2+5y-1)\)
\(7y^2-9y+11\)
\(7y^2+y+11\)
\(7y^2-9y+9\)
\(7y^2+y+9\)
2000006101
Level:
A
Simplify: \(3(3x^2-5x+1)-2x^2-(4x^2+2x-5)\)
\(3x^2-17x+8\)
\(3x^2-13x+8\)
\(3x^2-17x-2\)
\(3x^2-13x+2\)
2010001306
Level:
C
Factor the following polynomial.
\[
x^{8} - 1
\]
\(\left (x - 1\right )\left (x + 1\right )\left (x^{2} + 1\right )\left (x^{4} + 1\right )\)
\(\left (x - 1\right )^2\left (x + 1\right )^2\left (x^{2} + 1\right )^2\)
\(\left (x - 1\right )\left (x + 1\right )\left (x^{3} + 1\right )^2\)
\(\left (x - 1\right )^2\left (x + 1\right )^2\left (x^{4} + 1\right )\)
2010001305
Level:
B
Factor the following polynomial expression.
\[
36b^{2}c^{2} - 9a^{2}b^{2} - 36c^{2}d^{2} + 9a^{2}d^{2}
\]
\(9\left (b - d\right )\left (b + d\right )\left (2c + a\right )\left (2c - a\right )\)
\(\left (b^2 + d^2\right )\left (36c^2 + 9a^2\right )\)
\(9\left (a - d\right )\left (a + d\right )\left (2b + c\right )\left (2b - c\right )\)
\(\left (a^2 + d^2\right )\left (36b^2 + 9c^2\right )\)