
-2, 0, 1
Let u(t) be the first derivative of -t**6/60 + t**4/24 + 5*t + 4. Let s(b) be the first derivative of u(b). Let s(n) = 0. What is n?
-1, 0, 1
Let p be 452/(-8) - (-4)/8. Let a be (-2)/8 - 42/p. Factor a*c**2 - 1/2*c + 0.
c*(c - 1)/2
Let y(c) be the second derivative of -c**6/135 + 2*c**5/45 - 5*c**4/54 + 2*c**3/27 + 20*c. Factor y(v).
-2*v*(v - 2)*(v - 1)**2/9
Let g(k) = -k**2 - k + 1. Let j(h) = -3*h + 3. Let q(r) = 3*g(r) - j(r). Factor q(u).
-3*u**2
Suppose 6 = -2*q - 6. Let a = q - -10. Factor a*z - 11*z**2 + 2 + z**2 - 4*z**2 + 8*z**3.
2*(z - 1)**2*(4*z + 1)
Let r = 4 - 2. Factor -g**2 - 7*g + 2 + 3*g**3 + g**2 - 4 - 2*g**r.
(g - 2)*(g + 1)*(3*g + 1)
Let k = 86 - 84. Let i(j) be the second derivative of 0*j**k + 2*j + 0 - 1/6*j**4 - 2/3*j**3. Factor i(b).
-2*b*(b + 2)
Let k(g) = g**2. Let c(t) = 2 + 22*t - 3 - 27*t. Let w(i) = -c(i) + 4*k(i). Determine f so that w(f) = 0.
-1, -1/4
Let q(t) be the second derivative of t**7/210 - t**6/25 + 7*t**5/50 - 4*t**4/15 + 3*t**3/10 - t**2/5 - 7*t. Determine z so that q(z) = 0.
1, 2
Let b(p) = 8*p**3 - 4. Let a(m) = m**4 + m**3 - m**2 + m - 1. Let w(r) = 4*a(r) - b(r). Factor w(h).
4*h*(h - 1)**2*(h + 1)
Suppose -2/7*s + 1/7*s**2 + 1/7 = 0. Calculate s.
1
Let s(l) be the third derivative of -l**2 + 1/14*l**3 - 1/784*l**8 + 0*l + 0 - 3/490*l**7 + 1/70*l**5 - 1/140*l**6 + 3/56*l**4. Factor s(w).
-3*(w - 1)*(w + 1)**4/7
Determine f, given that -12/13*f**4 - 4/13 - 32/13*f**2 - 2/13*f**5 - 18/13*f - 28/13*f**3 = 0.
-2, -1
Let k = -19 + 26. Determine l so that -k + 3*l - 1 + 6 - 1 + 6*l**2 = 0.
-1, 1/2
Let v be ((-4)/(-8))/(2/40). Let x = v + -5. Factor -4*u - 7*u**3 - 14*u**4 + 4*u**x + 2 + 15*u**3 - 4*u**2 + 8*u**3.
2*(u - 1)**4*(2*u + 1)
Suppose 0*y - 2/3*y**3 + 0*y**4 + 0*y**2 + 0 + 2/3*y**5 = 0. What is y?
-1, 0, 1
Let j(m) be the first derivative of 3*m**4/8 + m**3 - 3*m**2/4 - 3*m + 3. Factor j(f).
3*(f - 1)*(f + 1)*(f + 2)/2
Let f(z) be the second derivative of 6*z**6/5 + 39*z**5/5 + 7*z**4/3 - 38*z**3/3 + 8*z**2 + 6*z - 2. Factor f(j).
4*(j + 1)*(j + 4)*(3*j - 1)**2
Let c = -1827 - -2577. Determine w, given that 1810*w**3 - 38*w + 14 + 1900*w**4 + 2 + c*w**5 + 222*w + 828*w**2 = 0.
-1, -2/5, -1/3
Determine k, given that 0 + 3/2*k - 3*k**2 = 0.
0, 1/2
Let o = 3 + 5. Let p be 22/o + 2/8. Suppose 7*z**4 + 6*z**3 + p*z**5 + 0*z**4 - z**5 - z**4 + 2*z**2 = 0. Calculate z.
-1, 0
Let n = -14/195 - -92/195. Factor 0 + 4/5*z**2 + 2/5*z + n*z**3.
2*z*(z + 1)**2/5
Let j(k) = 4*k. Let y(f) = -f**2 + f. Let z = 4 - 6. Let a(p) = z*y(p) + j(p). Solve a(n) = 0 for n.
-1, 0
Let j(w) be the first derivative of -1/4*w**4 + 1/10*w**5 + 1/2*w**2 + 1 + 0*w**3 - 1/2*w. Factor j(l).
(l - 1)**3*(l + 1)/2
Let g(y) = -y**2 - 6*y + 1. Let n be g(-6). Let k be n + -3 + 18/8. Factor k*w**2 - 1/4*w**3 + 0 + 1/4*w - 1/4*w**4.
-w*(w - 1)*(w + 1)**2/4
Let 2/5*c**4 - 8/5*c - 2*c**3 + 0 + 16/5*c**2 = 0. Calculate c.
0, 1, 2
Determine w, given that -4 + 34/9*w + 2/9*w**2 = 0.
-18, 1
Let l = 1/261 + 1561/1305. Factor -6/5*j - 3*j**2 + 0 - l*j**3.
-3*j*(j + 2)*(2*j + 1)/5
Let g(l) = -5*l**4 + 30*l**3 - 58*l**2 + 50*l - 15. Let d(y) = -60*y**4 + 360*y**3 - 695*y**2 + 600*y - 180. Let x(v) = 2*d(v) - 25*g(v). Factor x(n).
5*(n - 3)*(n - 1)**3
Factor -16/5*m**2 - 20 + 16*m.
-4*(2*m - 5)**2/5
Let t(u) be the third derivative of u**5/60 + u**4/24 - 8*u**2. Determine f, given that t(f) = 0.
-1, 0
Let o = -13 - -19. Let b(j) be the third derivative of 0*j**5 + 1/1344*j**8 - j**2 + 0 - 1/240*j**o + 1/96*j**4 + 0*j**7 + 0*j**3 + 0*j. Factor b(w).
w*(w - 1)**2*(w + 1)**2/4
Let k = 30/23 - 224/207. Factor 0 + k*x**2 - 2/9*x.
2*x*(x - 1)/9
Determine j so that 216*j**2 + 2*j**3 - 5*j**3 - 252*j**2 + 33*j + 12*j**4 - 6 = 0.
-2, 1/4, 1
Let q = 11 + -6. Suppose -6*z**q - 3*z**3 + 0*z**4 - 12*z**2 - 12*z**4 - 3*z + 3*z**5 - 15*z**3 = 0. Calculate z.
-1, 0
Let o(g) be the third derivative of 1/30*g**5 + 0 - 1/3*g**4 + 0*g + 4/3*g**3 - 3*g**2. Let o(f) = 0. Calculate f.
2
Suppose -16 = -a - 3*a. Suppose -l + 2*l = -1, 0 = -a*n + 4*l + 16. Find z, given that -2*z**n + z**4 - 2*z**2 + z**4 + 2*z + 0*z**2 = 0.
-1, 0, 1
Suppose 1 = 3*w - 2*k, 4*w + 2*k - 17 = w. Factor -12/7 - 9/7*f**2 - 36/7*f + 15/7*f**w.
3*(f - 2)*(f + 1)*(5*f + 2)/7
Let -1/2 + 1/2*s**4 - 2*s**2 - 7/4*s + 1/4*s**5 - 1/2*s**3 = 0. Calculate s.
-1, 2
Let o(s) be the third derivative of 0*s + 1/132*s**4 - 2/33*s**3 + 1/330*s**5 - 3*s**2 + 0. Factor o(u).
2*(u - 1)*(u + 2)/11
Factor 1/5*k**2 - 1/5 - 1/5*k + 1/5*k**3.
(k - 1)*(k + 1)**2/5
Factor -4*x + 4*x**2 - 4*x**2 - 4*x**2.
-4*x*(x + 1)
Let f(y) be the first derivative of y**3/6 - 5*y**2/8 + y/2 - 12. Find w such that f(w) = 0.
1/2, 2
Let c = 7 + -4. Let n(s) be the second derivative of 1/3*s**2 - s - 1/36*s**4 + 1/18*s**c + 0. Let n(i) = 0. Calculate i.
-1, 2
Let j be (-2)/(-8)*(-1 - -1). Let c(x) be the second derivative of 0*x**3 + 0*x**2 + 1/10*x**5 - 1/12*x**4 + j - 1/30*x**6 + 2*x. Let c(r) = 0. Calculate r.
0, 1
Let k be (0 - 4) + 28/6. Factor -2/3*x**2 - k*x + 4/3.
-2*(x - 1)*(x + 2)/3
Let r(h) be the third derivative of 0*h**3 + 1/280*h**8 + 0*h + 2/525*h**7 - 1/75*h**6 - 1/75*h**5 + h**2 + 1/60*h**4 + 0. Determine y so that r(y) = 0.
-1, 0, 1/3, 1
Let z = 799/3 - 10358/39. Let x = -1/13 + z. Factor -4/3 - x*i**4 - 10/3*i**3 - 14/3*i - 6*i**2.
-2*(i + 1)**3*(i + 2)/3
Let c(w) = w**3 - w**2 + 1. Let q be c(3). Suppose q = 2*p + 13. Factor 0 - 4/11*v**p + 0*v**4 + 0*v**2 + 2/11*v + 2/11*v**5.
2*v*(v - 1)**2*(v + 1)**2/11
Suppose -4 = -3*b + f + 15, 4*b - 26 = f. Suppose 0 = -2*q + b - 3. Let 0*o - 2/3*o**3 + 0 - 2/3*o**q = 0. What is o?
-1, 0
Let u(s) be the second derivative of 1/16*s**4 + 4*s - 1/40*s**6 + 0 + 1/16*s**5 - 1/24*s**3 - 1/42*s**7 + 0*s**2. Suppose u(d) = 0. Calculate d.
-1, 0, 1/4, 1
Let j(k) be the second derivative of -2*k + 0 - 1/4*k**4 - 3*k**2 - 3/2*k**3. Factor j(p).
-3*(p + 1)*(p + 2)
Let n(a) = -a**2 + 5*a - 2. Let v be n(3). Let r**2 - v - 3*r + 3 + 3 = 0. Calculate r.
1, 2
Let z(b) = b**4 - 10*b**2 - 8*b + 9. Let s(t) = 3*t**2 + 3*t - 3. Let l(y) = 8*s(y) + 3*z(y). Factor l(j).
3*(j - 1)**2*(j + 1)**2
Let u(i) be the second derivative of 0*i**3 + 0 - 2*i + 1/54*i**4 + 0*i**2 + 1/90*i**5. Find d, given that u(d) = 0.
-1, 0
Let a(r) = 2*r**2 + 3*r + 1. Suppose 7*s - 3 = 6*s. Let b(p) = -p**2 - p - 1. Let o(z) = s*a(z) + 3*b(z). Find l such that o(l) = 0.
-2, 0
Let a(b) be the second derivative of -11*b**4/6 + 23*b**3/3 - 2*b**2 + 8*b. Solve a(h) = 0.
1/11, 2
Let p be (68/(-595))/((-2)/7). Factor -2/5*n - 2/5*n**5 + 4/5*n**3 - p + 4/5*n**2 - 2/5*n**4.
-2*(n - 1)**2*(n + 1)**3/5
Let u(n) be the first derivative of -2*n**3 - 7*n**2/2 + 5. Let i(v) = -3*v**2 - 4*v. Let w(c) = 5*i(c) - 2*u(c). Factor w(p).
-3*p*(p + 2)
Let n(g) be the second derivative of 0*g**3 + 2/21*g**4 + 1/7*g**6 + 8/35*g**5 - g + 0 + 0*g**2. Factor n(x).
2*x**2*(3*x + 2)*(5*x + 2)/7
Let p be 69/21 + 4/(-14). Let q(t) be the first derivative of 0*t - 1 + 0*t**2 + 1/12*t**p. Factor q(n).
n**2/4
Let k = 894561/7 - 127447. Let t = 348 - k. Determine p so that 6/7*p**2 + 10/7*p + t = 0.
-1, -2/3
Let x(p) be the first derivative of -6*p**5/35 - p**4/14 + 4*p**3/21 + 29. Let x(l) = 0. Calculate l.
-1, 0, 2/3
Determine i so that 5 + 8*i**3 - 6*i**4 - 18*i**3 + 0*i**4 + i**4 + 10*i = 0.
-1, 1
Let g(a) be the third derivative of a**9/544320 - a**8/90720 + a**5/15 + 9*a**2. Let s(h) be the third derivative of g(h). Factor s(f).
f**2*(f - 2)/9
Let o(f) be the second derivative of -f**7/147 - 2*f**6/105 + 28*f. Factor o(n).
-2*n**4*(n + 2)/7
Let c(i) = 5*i**3 + 15*i**2 + 14*i. Let x(t) = 55*t**3 + 165*t**2 + 155*t. Let o(r) = 45*c(r) - 4*x(r). Factor o(s).
5*s*(s + 1)*(s + 2)
Let v = 275 + -275. Factor -6/5*p + v - 3/5*p**3 + 9/5*p**2.
-3*p*(p - 2)*(p - 1)/5
Let o(n) be the third derivative of 1/120*n**6 + 0 + 3*n**2 - 1/210*n**7 + 1/1008*n**8 + 0*n + 0*n**4 + 0*n**3 - 1/180*n**5. Solve o(d) = 0 for d.
0, 1
Factor 11*x**3 + 8*x**2 - 15*x**3 - 16 - 28*x**2 - 32*x.
-4*(x + 1)*(x + 2)**2
Let t(g) = -4*g**2 + 4*g - 6. Let w(s) = s**2 + 3*s + 6*s - 13 - 10*s**2. Let i(d) = -13*t(d) + 6*w(d). Suppose i(x) = 0. What is x?
0, 1
Let j(p) = -2*p**3. Let s be j(-1). Let l be (-12)/(-8) - (-1)/s. Factor -4/5 + 6/5*d - 2/5*d**l.
-2*(d - 2)*(d - 1)/5
