 - 116/5*y**3 - 16/5*y**5 = 0 for y.
-1, 1/2, 2, 4
Let i(b) be the first derivative of 4*b**7/525 + b**6/100 - b**5/150 - 9*b**2/2 - 6. Let r(t) be the second derivative of i(t). Solve r(k) = 0 for k.
-1, 0, 1/4
Let u(m) be the first derivative of 7*m**5 - 45*m**4/4 - 55*m**3 - 55*m**2/2 + 30*m - 41. Determine o, given that u(o) = 0.
-1, 2/7, 3
What is t in 2/9*t**3 + 2*t**2 + 10/3*t + 14/9 = 0?
-7, -1
Suppose 0 = -5*l + 18 + 7. Solve -23*n**l - 68*n**3 + 2*n**5 - 27*n**4 + 62*n**3 = 0 for n.
-1, -2/7, 0
Let f(j) = -2*j**3 - 2*j**2 + 2*j - 2. Let h(t) = 2 + 2*t**3 + t**3 - 7*t**2 - t + 8*t**2. Let g(y) = -5*f(y) - 4*h(y). Determine u so that g(u) = 0.
1
Let c = 5 - 2. Suppose 26 = c*q + q - 2*p, 0 = -q - 3*p - 11. Factor -6*j**2 + 7*j**4 - 3*j**5 + 4 + 3*j - q - j**4.
-3*j*(j - 1)**3*(j + 1)
Let x be 0 + -7 + -111 + 121. Let 5/2*q**2 - 5/2 - 5/4*q**x + 5/4*q = 0. What is q?
-1, 1, 2
Let a(c) = -c**2 + 9*c - 6. Let u = 32 + -24. Let x be a(u). Factor 5*z**5 + x*z - z - 10*z**3 + 4*z + 5 + 2*z**4 - 10*z**2 + 3*z**4.
5*(z - 1)**2*(z + 1)**3
Let a(y) = 2*y**2 + 2*y. Let u(d) = d**2 + 2*d + 1. Let w(h) = -2*a(h) + 2*u(h). Let w(x) = 0. What is x?
-1, 1
Let t(j) = -28*j**3 + 111*j**2 + 5*j - 1. Let f be t(4). Factor 0*o - 3/2*o**2 + 0 - 12*o**f.
-3*o**2*(8*o + 1)/2
Let y be (-299)/(-138) + (-2)/3. Let -3 - y*t + 3/2*t**2 = 0. Calculate t.
-1, 2
Suppose 11*h = 38*h - 81. Let g(o) be the first derivative of 1/4*o**4 + o + 4 - 1/3*o**h - 1/2*o**2. Factor g(l).
(l - 1)**2*(l + 1)
Let u(a) be the first derivative of -a**4 - 40*a**3/3 + 22*a**2 - 36. Solve u(j) = 0 for j.
-11, 0, 1
Let u(v) be the second derivative of 0*v**2 - 12*v + 0 - 1/36*v**4 - 1/6*v**3. Suppose u(l) = 0. What is l?
-3, 0
Suppose -10 = -5*y - 4*i, -5*y - i + 10 = -0*y. Let b(k) = k - 4. Let q be b(4). Factor -3 + 1 + 2*z - 2*z**3 - 4*z**y + q*z**3 + 6*z**2.
-2*(z - 1)**2*(z + 1)
Suppose -x + 2*w = 0, 5*x - 5*w = 2*x. Let o(c) be the second derivative of -1/42*c**4 + c + 0*c**2 - 1/70*c**5 + 2/21*c**3 + x. Factor o(q).
-2*q*(q - 1)*(q + 2)/7
Suppose -4*d - 227*c = -223*c + 4, -2*c = 5*d + 2. Find r such that 9/2*r**2 + 0 - 3/2*r**3 + d*r = 0.
0, 3
Let s(c) be the third derivative of -c**7/490 - 11*c**6/280 - 43*c**5/140 - 69*c**4/56 - 18*c**3/7 - c**2 + 38*c. Find h, given that s(h) = 0.
-4, -3, -1
Let f(v) be the second derivative of v**7/1680 + v**6/240 - 2*v**3/3 - 17*v. Let o(y) be the second derivative of f(y). Let o(k) = 0. What is k?
-3, 0
Let k(u) be the first derivative of 3*u**4/14 - 62*u**3/21 + 37*u**2/7 - 18*u/7 + 21. Factor k(m).
2*(m - 9)*(m - 1)*(3*m - 1)/7
Let a(w) be the third derivative of -w**7/1050 - w**6/600 + w**5/150 - 104*w**2. Suppose a(c) = 0. What is c?
-2, 0, 1
Let t(f) be the second derivative of -f**5/15 - f**4/3 - 2*f**3/3 + 7*f**2/2 + 5*f. Let s(z) be the first derivative of t(z). Factor s(a).
-4*(a + 1)**2
Let g be ((-14)/(-28))/(((-2)/(-9))/(72/81)). Suppose 0*s - 15 = 4*c - 3*s, s - 5 = 3*c. Determine q so that -1/2*q**g + 0 + c*q - 1/6*q**3 = 0.
-3, 0
Let u be -7 + -10 + 7 + 12. Factor 16/9*c + 2/9*c**3 + 8/9 + 10/9*c**u.
2*(c + 1)*(c + 2)**2/9
Let j(s) be the second derivative of -s**5/30 + 13*s**4/9 - 49*s**3/9 + 8*s**2 + 107*s. Factor j(x).
-2*(x - 24)*(x - 1)**2/3
Let o = -2007 + 2009. Factor -2/3*l**o + 2/3*l - 2/9 + 2/9*l**3.
2*(l - 1)**3/9
Let y(v) be the third derivative of -v**8/1344 - v**7/168 + v**6/60 + v**5/20 + 168*v**2. Find s, given that y(s) = 0.
-6, -1, 0, 2
Let o = 126 - 123. Suppose 4*u - 2 = o*u. Let 2*t - 4/3 - 2/3*t**u = 0. What is t?
1, 2
Let n(r) be the second derivative of r**6/105 - 9*r**5/70 + 13*r**4/42 + 15*r**3/7 - 50*r**2/7 + 2*r - 17. Factor n(z).
2*(z - 5)**2*(z - 1)*(z + 2)/7
Suppose 22*p**2 - 8/3*p - 2/3*p**4 - 88/3 - 16/3*p**3 = 0. Calculate p.
-11, -1, 2
Let v(d) = d**3 + d. Let t(p) = -14*p**3 - 40*p**2 - 109*p - 65. Let o(u) = -t(u) + 6*v(u). Let r(s) = -s**3 - s + 1. Let x(l) = -o(l) - 15*r(l). Factor x(h).
-5*(h + 2)**2*(h + 4)
Let m(r) be the first derivative of -r**4/12 + 33*r**3 - 9801*r**2/2 + 323433*r + 83. Suppose m(q) = 0. Calculate q.
99
Let b(w) = 0*w - 6*w + 38*w**2 - 5*w + 29 - 39*w**2. Let d be b(-13). Find g, given that -22/3*g**2 - 1/3*g**4 + 8*g + 8/3*g**3 - d = 0.
1, 3
Let j(h) = 2*h**3 + 15*h**2 + 9*h + 10. Let o be j(-7). Let s be (-3)/(3/o) - 546/147. Factor -2/7*g**4 + 2/7*g**3 + 2/7*g**2 - s*g + 0.
-2*g*(g - 1)**2*(g + 1)/7
Let b = 112 + -109. Suppose 1/3*x**b + 0*x**2 - 7/3*x - 2 = 0. Calculate x.
-2, -1, 3
Let q(j) be the second derivative of j**4/4 + 5*j**3 - 33*j**2/2 + 67*j. Solve q(u) = 0.
-11, 1
Suppose c - 4*d = -8, 4*d = -d + 15. Factor 5*q**2 - 5*q**c + 306*q**3 - 306*q**3.
-5*q**2*(q - 1)*(q + 1)
Suppose 39 = 3*q + 24. Let i be 24/q*1/2. What is t in i*t + 4/5*t**2 + 8/5 = 0?
-2, -1
Let y be (29 - 5/(-5))/(-1). Let c be 5/(y/9)*-4. What is m in m + 225*m**3 + c*m**2 - 228*m**3 - 4*m = 0?
0, 1
Factor -564*i + 48*i**3 - 61*i**3 + 5 - 1440*i**2 - 75*i**3 - 12*i**3 - 61.
-4*(i + 14)*(5*i + 1)**2
Suppose 12*w = 18*w. Let z(i) be the second derivative of 3*i + 1/96*i**4 + 0 + w*i**2 + 1/16*i**3. Factor z(v).
v*(v + 3)/8
Let a(g) be the first derivative of -g**3/12 + 37*g**2/8 - 9*g + 278. What is n in a(n) = 0?
1, 36
Let c(v) = -v**2 - 4*v + 8. Let k be 14/(-2) - -1*(-4)/(-2). Let s be c(k). Solve 1/2*h + 1/2*h**4 - 1/2*h**2 - 1/2*h**s + 0 = 0 for h.
-1, 0, 1
Let c = 1337/2 + -14703/22. Factor -c*f - 10/11*f**3 - 4/11 + 16/11*f**2.
-2*(f - 1)**2*(5*f + 2)/11
Let c(y) be the third derivative of y**5/12 - 5*y**4/2 + 50*y**3/3 + 89*y**2. Let c(t) = 0. What is t?
2, 10
Let a(o) be the first derivative of -o**3/15 + 61*o**2/5 - 3721*o/5 - 219. Solve a(u) = 0.
61
Let o be (1/16 - 729/(-2160))*(-3)/(-2). Factor -6*y + o*y**2 + 15.
3*(y - 5)**2/5
Find t such that 107*t**4 - 36*t**3 + 21*t**5 + 8*t**2 - 33*t**4 - 52*t**4 = 0.
-2, 0, 2/7, 2/3
Let w(k) be the first derivative of k**6/27 - 2*k**5/15 + k**4/9 - 49. Factor w(x).
2*x**3*(x - 2)*(x - 1)/9
Suppose -5*c = 3*u - 23 - 187, -3*u = -5*c + 210. Let g be (-2 - 30/(-7)) + (-12)/c. Determine h so that -4/11*h**g - 2/11*h + 0 - 2/11*h**3 = 0.
-1, 0
Let y(z) be the second derivative of 6*z**6/35 + 327*z**5/35 - 221*z**4/21 + 74*z**3/21 - 48*z. Solve y(d) = 0 for d.
-37, 0, 1/3
Suppose 8*m = 84 + 100. Suppose m*a = 19*a. Find w such that 16/5*w**2 + 0*w + a + 104/5*w**3 - 98/5*w**5 + 28*w**4 = 0.
-2/7, 0, 2
Let a(s) be the first derivative of -s**4/2 + 18*s**3 + 981. Find m such that a(m) = 0.
0, 27
Let w(k) = 8*k**3 + 43*k**2 + 57*k + 11. Let o(m) = 3*m**3 + 14*m**2 + 19*m + 4. Let q(j) = 11*o(j) - 4*w(j). Find v, given that q(v) = 0.
-1, 0, 19
Let r be (-35)/14*(-24)/20. Let l be (-4)/(-18) - (-142)/9. Factor -32*p**2 + l*p**2 + 8*p**2 - 4*p**r.
-4*p**2*(p + 2)
Let g(y) be the first derivative of 5*y**6/12 + 27*y**5/10 + 21*y**4/4 + 7*y**3/3 - 15*y**2/4 - 9*y/2 + 731. What is u in g(u) = 0?
-3, -1, 3/5
Factor 0 - 2/11*b**3 + 14/11*b + 12/11*b**2.
-2*b*(b - 7)*(b + 1)/11
Let o(m) be the second derivative of 0 + 15*m**2 - 25/6*m**3 - 23*m - 5/12*m**4. Factor o(b).
-5*(b - 1)*(b + 6)
Find l, given that 5/6*l**2 + 0 + 0*l - 2/3*l**3 - 1/6*l**4 = 0.
-5, 0, 1
Suppose 0 = 4*y - 61 - 15. Determine r so that r**3 - 2*r**2 - 19*r + y*r = 0.
0, 2
Let j = -20 - -21. Let x(u) = -u**3 - u**2 + 1. Let y(o) = 3*o**4 + 10*o**3 + 10*o**2 + 2. Let w(h) = j*y(h) - 2*x(h). Factor w(q).
3*q**2*(q + 2)**2
Let l(i) be the first derivative of 1/8*i**4 - 10 + 1/2*i**3 + 0*i + 1/2*i**2. Let l(x) = 0. What is x?
-2, -1, 0
Let k(b) = 4*b**4 + 25*b**3 - 23*b**2 + 33*b - 13. Let o(n) = 2*n**4 + 12*n**3 - 12*n**2 + 16*n - 6. Let m(w) = -6*k(w) + 13*o(w). Factor m(z).
2*z*(z - 1)**2*(z + 5)
Find c such that 432/5*c + 342/5*c**2 + 6/5*c**4 + 84/5*c**3 + 0 = 0.
-8, -3, 0
Let b(v) be the third derivative of v**8/1008 + v**7/105 + 11*v**6/360 + v**5/30 + 28*v**2 - 8. Factor b(x).
x**2*(x + 1)*(x + 2)*(x + 3)/3
Let u = 1251 + -1251. Solve 2/9*s**2 + 0*s + u + 2/9*s**3 = 0.
-1, 0
Let o(k) = -13*k**2 - 78*k + 77. Let z(s) = 9*s**2 + 52*s - 51. Let c(i) = -5*o(i) - 7*z(i). Factor c(y).
2*(y - 1)*(y + 14)
Let a(x) be the third derivative of 1/21*x**7 + 1/12*x**6 + 0 - 1/3*x**5 - 5/24*x**4 - 5/336*x**8 + 5/3*x**3 + 0*x - 27*x**2. Suppose a(c) = 0. What is c?
-1, 1, 2
Determine w