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:
\( -8 \)
\( -16 \)
\( 4 \)
\( 6 \)
Polynomials and fractions
1003032505
Level:
C
Factoring the polynomial \( x^4+4 \) you get:
\( \left(x^2-2x+2\right)\left(x^2+2x+2\right) \)
\( \left(x^2+2\right)\left(x^2-(-2)\right) \)
\( \left( x+\sqrt2 \right)^4 \)
\( \left(x^2-\sqrt2x+2\right)\left(x^2+\sqrt2x+2\right) \)
1003032506
Level:
C
In a parallel circuit the total resistance \( R \) of three components with the resistances \( R_1 \), \( R_2 \), \( R_3 \) is given by the formula \( \frac1R=\frac1{R_1}+\frac1{R_2}+\frac1{R_3} \). Express \( R_1 \) from this formula.
\( R_1=\frac{RR_2R_3}{R_2R_3-R(R_2+R_3)} \)
\( R_1=\frac{R-R_2-R_3}{RR_2R_3} \)
\( R_1=R-\frac{R_2R_3}{R_2+R_3} \)
\( R_1=\frac{R_2R_3-R(R_2+R_3)}{RR_2R_3} \)
1003032507
Level:
C
Express \( v_1 \) from the formula \( v=\frac{v_1v_2(d_1+d_2 )}{d_1v_2+d_2v_1} \).
\( v_1=\frac{vd_1 v_2}{v_2d_1+v_2d_2-vd_2} \)
\( v_1=\frac{vv_2 d_1}{vd_2-v_2d_1-v_2d_2} \)
\( v_1=\frac{vv_2(d_1+d_2)}{d_1v_2+d_2 v} \)
\( v_1=\frac{v(d_1v_2+d_2 v_1 )}{v_2 (d_1+d_2 )} \)
1003032508
Level:
C
Find the term that does not contain \( x \) and \( y \) (constant term) in the expansion of \( (x+y)^4(\frac1x+\frac1y)^4 \).
\( 70 \)
\( 2 \)
\( 36 \)
\( 0 \)
2000002609
Level:
C
The equation \(x^3 +27=0\) can be solved by factoring. The expression on the left can be factored as:
\( (x+3)(x^2-3x+9) \)
\( (x+3)(x^2+3x+9) \)
\( (x+3)^3 \)
\( (x-3)(x^2+3x+9) \)
2010000802
Level:
C
The polynomial \( 2x^5-px^3+(p-1)x^2+2x-5 \) is divisible by the binomial \( x^2+1 \) if \( p \) is equal to:
\(-4\)
\(-8\)
\(4\)
\(8\)
2010000803
Level:
C
Factoring the polynomial \(-4x^4+24x^3-36x^2\) you get:
\( -4x^2(x-3)(x-3)\)
\( -4x^2(x+3)(x+3)\)
\( -4x^2(x+3)(x-3)\)
\( -4x^2(x^2+6x-9)\)
2010000804
Level:
C
Factoring the polynomial \(-3x^5-24x^4-48x^3\) you get:
\( -3x^3(x+4)(x+4)\)
\( -3x^3(x-4)(x-4)\)
\( 3x^3(4-x)(4-x)\)
\( 3x^3(x+4)(x-4)\)
2010000805
Level:
C
In a parallel circuit the total resistance \( R \) of three components with the resistances \( R_1 \), \( R_2 \), \( R_3 \) is given by the formula \( \frac1R=\frac1{R_1}+\frac1{R_2}+\frac1{R_3} \). Express \( R_2 \) from this formula.
\( R_2=\frac{RR_1R_3}{R_1R_3-R(R_1+R_3)} \)
\( R_2=\frac{R-R_1-R_3}{RR_1R_3} \)
\( R_2=R-\frac{R_1R_3}{R_1+R_3} \)
\( R_2=\frac{R_1R_3-R(R_1+R_3)}{RR_1R_3} \)