nd derivative of h**6/40 + 3*h**5/80 - h**4/16 - h**3/8 - 6*h. Suppose a(k) = 0. Calculate k.
-1, 0, 1
Suppose -6 = -2*g - g. Suppose 14 - g = 4*v. Factor -3/4*h**2 + 1/4*h**4 + 0 + 0*h**v + 1/2*h.
h*(h - 1)**2*(h + 2)/4
Let v(g) be the third derivative of -g**5/120 + g**4/12 - g**3/3 + 9*g**2. Find u such that v(u) = 0.
2
Let a = -42/5 + 388/45. Solve 2/9*x - 4/9 + a*x**2 = 0 for x.
-2, 1
Let i(y) = y**3 + 21*y**2 - 2*y - 40. Let l be i(-21). Suppose 0 - 1/2*j**3 - 9/2*j - 3*j**l = 0. What is j?
-3, 0
Let w(m) = -20*m**2 - 15*m + 50. Let i(n) = 3*n**2 + 2*n - 7. Let s(q) = -15*i(q) - 2*w(q). Let s(x) = 0. What is x?
-1, 1
Let v(r) be the second derivative of -r**6/45 + r**5/15 + r**4/18 - 2*r**3/9 - 3*r. Solve v(p) = 0 for p.
-1, 0, 1, 2
Solve 120*n**2 + 7*n + 118*n**2 - n**3 - 236*n**2 + 4 = 0 for n.
-1, 4
Suppose -2*d + d + 3 = 0. Let y(r) = -2*r**3 - r**2 + 1. Let c be y(-1). Find l, given that d - 6 - c*l**3 - 4*l**2 - 2*l + 3 = 0.
-1, 0
Solve -1/8*z**4 + 0 + 1/8*z**2 - 1/4*z**3 + 1/4*z = 0.
-2, -1, 0, 1
Let l = -132 - -134. Factor -3/5*b**l - 4/5 + 8/5*b.
-(b - 2)*(3*b - 2)/5
Find b, given that -3*b**2 + 2*b + b**2 + 0*b = 0.
0, 1
Let c be (-6 + 2)/(49/(-21)*3). Factor 0 - c*m**3 + 6/7*m**5 + 0*m - 2/7*m**4 + 0*m**2.
2*m**3*(m - 1)*(3*m + 2)/7
Let j(r) be the third derivative of r**5/12 - 25*r**4/24 + 5*r**3 - 11*r**2. Suppose j(b) = 0. Calculate b.
2, 3
Suppose 5*v = -4*l + 6 + 13, 2*v - 7 = -l. Let f = 14/11 + -12/11. Solve 4/11*t**2 + 2/11*t**v + f*t + 0 = 0.
-1, 0
Let r(p) be the first derivative of -p**8/1680 - p**7/210 - p**6/120 + p**5/30 + p**4/6 + p**3 + 3. Let n(c) be the third derivative of r(c). Factor n(v).
-(v - 1)*(v + 1)*(v + 2)**2
Let p be (-1 + -3)*(-14)/(-176). Let l = 2/11 - p. Determine w, given that l*w**2 - 1/2*w**3 + 0 + 0*w = 0.
0, 1
Let y(x) = x - 1. Let a be (-1)/(-2) + 15/10. Let w be y(a). Factor 3 - 5 - m**2 + w + 2*m.
-(m - 1)**2
Suppose 2*q = -5*w - 10, 4*q - 16 - 8 = w. Suppose -q*i = -15 + 5. Factor 2*v**2 + 2/3*v**3 + 2/3 + i*v.
2*(v + 1)**3/3
Suppose -z + 5 = 3. Suppose -3*t + 4 = -z. Find q such that 5*q + 7*q**2 + 0*q - t + 0 = 0.
-1, 2/7
Let f(o) be the second derivative of 2*o**7/63 - 2*o**6/45 - 11*o**5/60 + 5*o**4/9 - 11*o**3/18 + o**2/3 + 11*o. Solve f(r) = 0.
-2, 1/2, 1
Factor -5*k**3 + k**3 - 4*k + 4*k**2 - 5*k**2 + 9*k**2.
-4*k*(k - 1)**2
Factor -t**3 + 1/3*t + 5/3*t**4 + 0 - 1/3*t**2 - 2/3*t**5.
-t*(t - 1)**3*(2*t + 1)/3
Let m = -2201/32760 + 8/117. Let k(b) be the third derivative of 1/240*b**5 + 0*b**3 + m*b**7 + 1/240*b**6 + 0 + 0*b**4 + 0*b - 3*b**2. Factor k(r).
r**2*(r + 1)**2/4
Factor -3/2*t**2 + 1/2*t**3 + 0 + 1/2*t**5 - t + 3/2*t**4.
t*(t - 1)*(t + 1)**2*(t + 2)/2
Let s(j) be the third derivative of j**8/13440 + j**7/1120 - j**6/120 - j**5/10 - 5*j**2. Let y(k) be the third derivative of s(k). Find z such that y(z) = 0.
-4, 1
Let l(k) = -k + 13. Let r be l(7). Let f(n) be the third derivative of 0*n**r + n**2 + 0*n**4 + 0*n + 0*n**3 + 0 - 1/210*n**7 + 1/60*n**5. Factor f(a).
-a**2*(a - 1)*(a + 1)
Let m(b) be the third derivative of -b**7/840 - b**6/240 + b**4/24 + 2*b**2. Let o(u) be the second derivative of m(u). Let o(j) = 0. Calculate j.
-1, 0
Let f be 8/6*(-1 + (-25)/(-10)). Let a = 452/9 - 50. Factor 0*r - a + 2/9*r**f.
2*(r - 1)*(r + 1)/9
Let a(i) be the first derivative of -i**5/10 + i**4/8 + i**3/3 + 12. Suppose a(p) = 0. Calculate p.
-1, 0, 2
Let b = 35/66 + 3/22. Factor -2/3*c**3 + 2/3 - 2/3*c**2 + b*c.
-2*(c - 1)*(c + 1)**2/3
Let x be (-8)/(-48)*(-16)/(-3). Factor -x*z - 2/3*z**2 + 2/9*z**4 + 8/9 + 4/9*z**3.
2*(z - 1)**2*(z + 2)**2/9
Let c(v) be the first derivative of v**6/6 - 7*v**4/4 - 2*v**3 + 48. Determine o, given that c(o) = 0.
-2, -1, 0, 3
Suppose -3*k + 13 = 1. Solve -53*j**2 + 3*j**5 + j - j**3 - 4*j**4 + 2*j**k - 3*j**3 + 55*j**2 = 0.
-1, -1/3, 0, 1
Suppose -17 = 4*r + x - 45, r - 4*x + 10 = 0. Determine g so that -3*g**3 + 11 - 14 + r*g**3 + 9*g - 9*g**2 = 0.
1
Let p(n) = 6*n**2 - 5*n + 2. Let m be p(3). Determine y so that -m*y + y**2 - 3*y**2 + 39*y = 0.
-1, 0
Let q(g) be the third derivative of 1/54*g**3 + 1/540*g**5 + 0 - 1/108*g**4 + 6*g**2 + 0*g. Factor q(x).
(x - 1)**2/9
Let y = 46 + -14. Factor -7*u + 28*u**2 - 48*u**4 - y*u**3 - u + 60*u**4.
4*u*(u - 1)**2*(3*u - 2)
Suppose 2*a - 2 = 0, -4*o = 2*a - 5 - 5. Let d be (9 - 4)*o/15. Factor 0*j + d*j**4 + 0*j**2 + 2/3*j**3 + 0.
2*j**3*(j + 1)/3
Let k be ((8 - 5) + 1)/7. Determine y, given that 0*y**2 - k*y + 4/7*y**3 - 2/7 + 2/7*y**4 = 0.
-1, 1
Determine r, given that -2 + 6*r - 5*r**4 + 4 - 1 - 6*r**3 + 4*r**2 = 0.
-1, -1/5, 1
Let k(t) = -3*t**2 + 2*t - 1. Let w(p) = -p**2. Let i = 3 + -4. Let o(x) = i*k(x) + 2*w(x). Factor o(l).
(l - 1)**2
Let v(k) be the first derivative of -k**5/20 + k**4/16 + k**3/12 - k**2/8 + 4. Determine n, given that v(n) = 0.
-1, 0, 1
Let q(k) be the first derivative of -1/25*k**5 + 1/5*k**3 - 4 + 0*k**4 - 1/5*k**2 + 0*k. Find a, given that q(a) = 0.
-2, 0, 1
Let h(u) be the first derivative of 2*u**3/33 - 2*u**2/11 - 6*u/11 - 14. Factor h(g).
2*(g - 3)*(g + 1)/11
Find b, given that -1/9 + 2/9*b - 1/9*b**2 = 0.
1
Determine v so that -123*v**2 - 93*v**2 + 47*v**2 + 4*v**2 + 5*v**3 - 6655 + 1815*v = 0.
11
Let r be 3/9 - -1*(-3 + 3). Suppose r*n**2 - 1/3*n + 0 = 0. What is n?
0, 1
Let y(t) = t + 4. Let d(p) = p - 3. Let h be d(3). Let v be y(h). Find j, given that 1/5*j + 1/5*j**v + 3/5*j**3 + 3/5*j**2 + 0 = 0.
-1, 0
Suppose 6*g**3 + 12*g - 8*g**2 - 10*g**3 + 0*g**3 = 0. What is g?
-3, 0, 1
Let w(r) = -11*r**2 - 4*r + 8. Let i(g) = -4*g**2 - g + 3. Let j(v) = -17*i(v) + 6*w(v). Let a(c) = c + 1. Let t(f) = 3*a(f) + j(f). Factor t(b).
2*b*(b - 2)
Suppose s = 5*p - s - 11, -5*s - 11 = 4*p. Suppose -n = -3 - p. Factor -q + q**5 + 2*q**2 - 5*q**n + 0*q + 3*q**4 + 0*q**5.
q*(q - 1)**3*(q + 1)
Let o be (-50 + 52)*(-1)/(-12). Determine l, given that o*l**2 + 0 + 1/6*l = 0.
-1, 0
Let -10*o**3 - 2/3*o + 0 - 14/3*o**2 - 8/3*o**5 - 26/3*o**4 = 0. What is o?
-1, -1/4, 0
Let f(z) be the third derivative of z**6/180 - 2*z**5/45 + z**4/9 - 2*z**3/3 - 6*z**2. Let a(j) be the first derivative of f(j). Suppose a(s) = 0. Calculate s.
2/3, 2
Find s such that 0*s + 6/7*s**4 + 0 + 2/7*s**5 + 6/7*s**3 + 2/7*s**2 = 0.
-1, 0
Suppose 7*g - 33 = -4*g. Suppose -1/4*v + 1/4*v**g - 1/4*v**2 + 1/4 = 0. Calculate v.
-1, 1
Let o be 3/(-108)*(-3 - -1). Let l(v) be the second derivative of 0 + 1/60*v**5 + 1/18*v**3 + 0*v**2 - v - o*v**4. Find x such that l(x) = 0.
0, 1
Let h(a) = -4*a**4 - 34*a**3 - 10*a**2 + 10*a + 10. Let u(o) = -o**3 + o**2 - o - 1. Let v(r) = h(r) + 10*u(r). Factor v(s).
-4*s**3*(s + 11)
Let o(n) be the third derivative of -1/28*n**4 + 2*n**2 - 1/140*n**5 + 0 + 0*n + 0*n**3. Factor o(h).
-3*h*(h + 2)/7
Factor 1/3*x**2 + 4/3*x + 1.
(x + 1)*(x + 3)/3
Let r = -69 - -69. Factor -2/7*c + r - 8/7*c**2.
-2*c*(4*c + 1)/7
Let t(y) be the first derivative of y**4 - 4. Suppose t(c) = 0. Calculate c.
0
Let i(g) = -30*g**5 - 155*g**4 - 385*g**3 - 265*g**2 + 25. Let d(r) = 5*r**5 + 26*r**4 + 64*r**3 + 44*r**2 - 4. Let w(z) = 25*d(z) + 4*i(z). Solve w(c) = 0.
-2, 0
Let b(r) be the second derivative of -r**7/84 + r**6/60 + 3*r. Find p, given that b(p) = 0.
0, 1
Suppose 7 = -w + 21. Let h = w - 12. Factor -3/5 - 6/5*d - 3/5*d**h.
-3*(d + 1)**2/5
Let b(z) be the second derivative of 0 + 3*z + 0*z**5 - 1/12*z**4 + 1/4*z**2 + 0*z**3 + 1/60*z**6. Let b(k) = 0. Calculate k.
-1, 1
Let t(i) = 10*i**5 + 10*i**4 - 21*i**3 - 10*i**2 + 11*i - 11. Let z(f) = 2*f**5 + 2*f**4 - 4*f**3 - 2*f**2 + 2*f - 2. Let r(o) = 2*t(o) - 11*z(o). Factor r(s).
-2*s**2*(s - 1)*(s + 1)**2
Let h = 6/13 - -8/39. Let g(c) = -2*c - 20. Let f be g(-10). Let 0 + f*y + h*y**3 - 2/3*y**2 = 0. What is y?
0, 1
Let w(d) = 10*d**3 + 2*d**2 - 2*d - 2. Let p(o) be the second derivative of o**5/20 + o**4/12 + o**3/6 - o**2/2 - 5*o. Let h(v) = -4*p(v) + w(v). Factor h(q).
2*(q - 1)*(q + 1)*(3*q - 1)
Let t(d) be the third derivative of -d**5/90 - d**4/36 + d**2. Factor t(r).
-2*r*(r + 1)/3
Suppose -68/3*z**3 + 8*z**2 - 32/3 + 20/3*z**4 + 80/3*z = 0. What is z?
-1, 2/5, 2
Let b(x) = -4*x**4 - 10*x**3 - 6*x**2 - 2*x. Let r(v) = 16*v**4 + 39*v**3 + 23*v**2 + 9*v. Let j(c) = 9*b(c) + 2*r(c). Factor j(f).
-4*f**2*(f + 1)*(f + 2)
Let p(z) = z**2 - z - 10. Let r