 1)
Let y(r) be the second derivative of r**7/98 - r**6/140 - 3*r**5/140 - 3*r**2 - 4*r. Let s(o) be the first derivative of y(o). Find u such that s(u) = 0.
-3/5, 0, 1
Let t be ((-1532)/(-36))/((-8)/24). Let h = t + 129. Let -2/9*p**4 - 2/9*p**2 - 16/3*p - 32/9 + h*p**3 = 0. Calculate p.
-1, 4
Let f(r) = -32*r - 1533. Let p be f(-48). Determine v, given that 2/13*v + 0 - 2/13*v**2 + 2/13*v**4 - 2/13*v**p = 0.
-1, 0, 1
Let n = 39254/5 - 7850. Determine i, given that -2/5*i**2 - 2/5 + n*i = 0.
1
Let o(h) = -h**2 - 7*h - 3. Let y(t) = 6*t + 4. Let p be 0 - (2 + (-7)/1). Let u be 10/25 - (-13)/p. Let q(c) = u*y(c) + 2*o(c). Let q(v) = 0. What is v?
-1, 3
Let s = -5267/10 - -528. Suppose -18/5 - 1/10*k**2 + 1/10*k**4 + 24/5*k - s*k**3 + 1/10*k**5 = 0. Calculate k.
-3, 1, 2
Suppose 2 = -l, -6*z + l + 28 = -5*z. Factor 15*t**4 - 48*t**3 + 75*t**5 + 12*t**2 - 26*t + z*t.
3*t**2*(t + 1)*(5*t - 2)**2
Suppose 33*u - 5*u - 17 = 67. Factor 0 + 2/5*b**2 - 4/15*b - 2/15*b**4 + 0*b**u.
-2*b*(b - 1)**2*(b + 2)/15
Let b be (-25)/(-15) - (-125)/(-300). Determine c, given that -1/4*c**3 - b*c - 1/2 - c**2 = 0.
-2, -1
Let q(s) be the first derivative of s**5/5 + s**4/6 - 4*s**3/3 + s**2/2 - 1. Let t(j) be the second derivative of q(j). Factor t(b).
4*(b + 1)*(3*b - 2)
Let i be (-6)/(-7)*((-240)/54 + 6). Factor 1/3*x**2 + i*x + 1.
(x + 1)*(x + 3)/3
Let y(t) = -t**2 + 11*t - 15. Let j be y(2). Let c(i) be the first derivative of -2/5*i**2 - 3 - 3/20*i**4 + 1/5*i**5 - 4/5*i**j + 0*i. Solve c(k) = 0 for k.
-1, -2/5, 0, 2
Suppose -5*m - 35 = -j - m, 5*j + 4*m = 55. Let i = 22 - j. Factor n - n**3 - i*n**4 + 4*n**3 + 6*n**3 - 5*n**2 - 16*n**5 + 18*n**5.
n*(n - 1)**3*(2*n - 1)
Let v(r) be the first derivative of 5/6*r**6 + 0*r**2 + 10/3*r**3 + 4*r**5 + 0*r + 23 + 25/4*r**4. Factor v(m).
5*m**2*(m + 1)**2*(m + 2)
Let n be 4 - 10/(60/18). Let p be (7 + n/(-1))/3. Factor 0 + 1/5*s**3 + 1/5*s**p + 0*s.
s**2*(s + 1)/5
Factor 104/5*t + 36/5*t**2 + 64/5.
4*(t + 2)*(9*t + 8)/5
Let n(v) be the first derivative of 5*v**5/2 - 5*v**4/8 - 71*v**3/6 + 69*v**2/4 - 9*v - 71. Find a such that n(a) = 0.
-2, 3/5, 1
Let a = 3 + -4. Let q(f) = -3*f**2 + 4. Let z(d) = 5*d**2 + 3*d + 2. Let x be z(-1). Let i(w) = 1. Let r(j) = a*q(j) + x*i(j). Find y, given that r(y) = 0.
0
Let a(v) = -20*v - 30. Let c be a(-3). Let r be 185/c - 15/10. Factor r*j - 8/3*j**2 + 4/3.
-2*(j - 2)*(4*j + 1)/3
Let d(a) be the first derivative of -a**6/20 - 9*a**5/40 + a**4/2 - 3*a - 13. Let x(v) be the first derivative of d(v). Find u, given that x(u) = 0.
-4, 0, 1
What is k in -15*k**2 + 144 + 4*k**3 - 15*k**2 - 4*k - 44*k + 10*k**2 = 0?
-3, 2, 6
Let m(u) = -u**3 + u**2 + u. Let n be m(2). Let f be 3 + (3 + n - 1). Solve -104/3*p - 4394/9*p**f - 16/9 - 676/3*p**2 = 0.
-2/13
Let n = -788 + 792. Let a(l) be the second derivative of 0 - 5*l + n*l**2 - 1/3*l**4 + 2/3*l**3. Suppose a(r) = 0. Calculate r.
-1, 2
Suppose -153*b = -481*b + 656. Let -2/17*c + 4/17*c**b - 4/17 + 2/17*c**3 = 0. What is c?
-2, -1, 1
Let j(r) be the first derivative of -5*r**4/4 + 5*r**2/2 + 68. Suppose j(c) = 0. Calculate c.
-1, 0, 1
Let c = -45 + 57. Factor 13*b + 0*b + 4*b - c - b - 4*b**2.
-4*(b - 3)*(b - 1)
Factor -392/17 + 336/17*k + 54/17*k**2 + 2/17*k**3.
2*(k - 1)*(k + 14)**2/17
Let g = 5/2252 - -3373/2252. Determine l so that 1/2*l**2 + 1/2*l**5 + 0 + g*l**3 + 0*l + 3/2*l**4 = 0.
-1, 0
Suppose 47*h + 828 - 1000 = 4*h. Find i such that -3*i**2 + 25/3*i**h + 0 - 14/3*i + i**5 + 9*i**3 = 0.
-7, -1, 0, 2/3
Let j be 752/9 - (-36)/81. Let s be j/(-175)*10*1/(-4). Let -13/5*o**3 - s*o**4 + 0 - 9/5*o**2 - 2/5*o = 0. What is o?
-1, -2/3, -1/2, 0
Suppose -v - x + 4*x = -2, -2*x + 2 = v. Suppose 104 + 52 = v*w. Solve 78 + 4*o**2 - 4*o**3 - w = 0.
0, 1
Let u = -3721/5 - -859552/1155. Let z(r) be the third derivative of -r**2 + 0 + 0*r + 0*r**3 - 1/165*r**6 + 0*r**4 - u*r**7 - 2/165*r**5. Factor z(o).
-2*o**2*(o + 2)**2/11
Let c(x) be the first derivative of 5*x + 0*x**3 - 3/20*x**5 + 0*x**2 - 6 - 1/4*x**4. Let r(g) be the first derivative of c(g). Determine u so that r(u) = 0.
-1, 0
Let u = 347/9 - 691/18. Suppose 1/3*c**3 - u*c - 1/6*c**4 - 1/6*c**5 + 1/3*c**2 - 1/6 = 0. Calculate c.
-1, 1
Let h(g) = -g**3 + 1. Let y = -33 - -13. Let s(t) = -16*t**3 + 4*t**2 + 20. Let r(q) = y*h(q) + s(q). Let r(p) = 0. What is p?
-1, 0
Suppose 6/19*m**2 - 10/19*m**3 + 2/19*m**4 - 8/19 + 10/19*m = 0. What is m?
-1, 1, 4
Let r(j) be the third derivative of j**6/120 + j**5/6 - 11*j**4/24 + 4*j**2. Determine c, given that r(c) = 0.
-11, 0, 1
Let g be 3120/100 + 22 + -53. Suppose -4*y = -5*y + 3. Factor -1/5*u**4 - g*u**y + 0*u + 0*u**2 + 0.
-u**3*(u + 1)/5
Let c be 15 - (8 + 1) - 6. Determine p so that -1/2*p**3 + 0*p**2 + c + 1/2*p = 0.
-1, 0, 1
Let r(j) be the first derivative of 0*j**4 + 0*j - j**3 + 7 + 3/5*j**5 + 0*j**2. Factor r(q).
3*q**2*(q - 1)*(q + 1)
Let h(m) = -5*m**2 - 5*m + 22. Let v(f) = -4*f**2 - 6*f + 22. Let a(u) = 3*h(u) - 4*v(u). Determine b so that a(b) = 0.
-11, 2
Let h be 30/(-9)*3/(-1). Let y be 4/(-10) + h/25. Factor 12 + y*f**2 - f - 2*f**2 - f - 8.
-2*(f - 1)*(f + 2)
Let f(y) = -y**3 + 2*y**2 + 4*y - 3. Let l be f(3). Suppose l = -i, -2*i - i = -3*g + 6. Factor -1 + 2 - 4*v + v**g + 3 + 0*v**2.
(v - 2)**2
Let k = 3698/55 - 722/11. Suppose k + 14/5*u**2 - 32/5*u = 0. What is u?
2/7, 2
Let g(c) be the second derivative of c**7/147 + 4*c**6/105 + 3*c**5/35 + 2*c**4/21 + c**3/21 + 710*c. Factor g(n).
2*n*(n + 1)**4/7
Let z(c) be the second derivative of -c**6/240 + c**5/120 + c**4/24 + 3*c**2 + 11*c. Let b(u) be the first derivative of z(u). Let b(g) = 0. What is g?
-1, 0, 2
Let g(z) be the second derivative of -z**4/4 - 127*z**3/18 - 7*z**2/3 - 2*z + 282. Factor g(r).
-(r + 14)*(9*r + 1)/3
Let m(n) be the first derivative of n**4/14 - 4*n**2/7 + 203. Find y such that m(y) = 0.
-2, 0, 2
Suppose -39 - 13 = -4*b. Factor -4*v**2 - 5*v**4 + 2*v**5 + 11*v**3 + 9*v**4 - b*v**3.
2*v**2*(v - 1)*(v + 1)*(v + 2)
Let u be ((-130)/(-42) - 3)/((-108)/(-21)). Let o(b) be the third derivative of 4*b**2 - 1/270*b**5 + 0*b + 0 + u*b**4 - 1/27*b**3. Find c such that o(c) = 0.
1
Find o such that 3/7*o**5 + 0 + 33/7*o**2 + 3/7*o**4 - 12/7*o - 27/7*o**3 = 0.
-4, 0, 1
Let u be -8 - -11 - ((-6 - 1) + 6). Suppose -7/5*f**2 + 6/5*f**3 + 7/5*f**u - 2/5*f + 0 - 4/5*f**5 = 0. What is f?
-1, -1/4, 0, 1, 2
Let p(a) be the second derivative of a**3/6 + 5*a**2/2 + 3*a. Let y be p(-3). Solve -28*z**3 - 40*z**y - 47 - 30*z**4 - 22*z**3 + 45 - 7*z**5 - 15*z = 0.
-1, -2/7
Let l(j) = -7*j**2 + 8*j - 1. Let i(b) = 20*b**2 - 24*b + 4. Let q = -9 + 1. Let h(c) = q*l(c) - 3*i(c). Let h(r) = 0. Calculate r.
1
Let s = -3 - 5. Let j be (-3)/12 - 34/s. Factor b**5 + j*b**4 + b - 2*b - 3*b**4 + b**4 - 2*b**2.
b*(b - 1)*(b + 1)**3
Solve -304/5*n**2 + 0 - 2/5*n = 0.
-1/152, 0
Let d(q) be the third derivative of q**7/42 + 11*q**6/24 + 3*q**5 + 15*q**4/2 - 360*q**2. Factor d(w).
5*w*(w + 2)*(w + 3)*(w + 6)
Let m(g) = 6*g**3 + 24*g**2 - 3*g - 3. Let k(r) = r**4 - 5*r**3 - 22*r**2 + 2*r + 2. Let o(t) = -3*k(t) - 2*m(t). Factor o(d).
-3*d**2*(d - 3)*(d + 2)
What is l in -32/5*l + 48/5 + 8/5*l**3 - 28/5*l**2 + 4/5*l**4 = 0?
-3, -2, 1, 2
Let f(m) be the first derivative of 0*m - 2/15*m**3 + m**2 - 14. Determine n, given that f(n) = 0.
0, 5
Let f(v) = -100*v**3 + 230*v**2 + 265*v - 1055. Let c(m) = -9*m**3 + 21*m**2 + 24*m - 96. Let a(l) = 45*c(l) - 4*f(l). Factor a(q).
-5*(q - 5)*(q - 2)*(q + 2)
Let y be 12/42 - (-26)/7. Suppose -5*d + 2*d - y*f + 8 = 0, -3*d + f + 13 = 0. Factor -40*g**2 - 8*g**4 - 2*g**4 - 8*g - 46*g**3 - 4*g**d.
-2*g*(g + 1)*(g + 2)*(7*g + 2)
Let s be 12/42*(-7)/(-3)*6. Factor 2*u**5 - 2*u**5 - 15*u**s + 64*u**2 - 4*u**5 + 192 - 48*u**3 + 256*u - 13*u**4.
-4*(u - 2)*(u + 2)**3*(u + 3)
Let i = 547 + -543. Let p(w) be the second derivative of -2*w**2 + 4*w + 2/3*w**3 + 0 + 2/3*w**i. Factor p(t).
4*(t + 1)*(2*t - 1)
Factor 0*h - 2/15*h**4 + 0 + 2/5*h**3 - 4/15*h**2.
-2*h**2*(h - 2)*(h - 1)/15
Factor 85*p**3 - 23*p**2 - 239*p**2 - 14*p**2 + 55 + 54*p + 85*p**3 - 3*p**4.
-(p - 55)*(p - 1)**2*(3*p + 1)
Suppose 160*p - 6 = 157*p. Factor 5*s - p*s - 14*s**2 - 18*s**2 + 35*s**2.
3*s*(s + 1)
Let t(q) = -q**2 - 16*q + 59. Let s be t(-19). Let v(p) be the first derivative of 1/30*p**5