erivative of -u**7/3780 + u**6/1080 - u**4/8 - 3*u**2. Let t(z) be the second derivative of f(z). Find p such that t(p) = 0.
0, 1
Let f(w) be the second derivative of -w**7/280 + w**6/180 + w**5/120 + w**3/3 - 2*w. Let l(v) be the second derivative of f(v). Find n, given that l(n) = 0.
-1/3, 0, 1
Let j = 2 + 8. Let a(g) = g - j*g + 0*g + 4 - g**2 - 3. Let q(m) = -2*m**2 - 10*m. Let d(p) = -4*a(p) + 3*q(p). Factor d(c).
-2*(c - 2)*(c - 1)
Let c = -35/3049 - -879337/106715. Let i = c + -52/7. Factor 0 + 0*t + i*t**3 + 2/5*t**4 + 0*t**2.
2*t**3*(t + 2)/5
Let m(y) be the first derivative of -2*y**3/27 + 4*y**2/9 - 8*y/9 + 3. Suppose m(q) = 0. Calculate q.
2
Let d(f) be the third derivative of -f**5/180 - f**4/72 - 7*f**2. Factor d(j).
-j*(j + 1)/3
Let d(a) be the third derivative of a**7/420 + a**6/60 + a**5/20 + a**4/12 + a**3/12 + 23*a**2. Factor d(x).
(x + 1)**4/2
Let g(x) be the third derivative of 0*x**3 + 0*x**7 - x**2 + 0*x + 1/150*x**6 - 1/840*x**8 + 0*x**5 + 0 - 1/60*x**4. Factor g(w).
-2*w*(w - 1)**2*(w + 1)**2/5
Suppose -t + 1 = 3*j, 0 = 4*j - 4*t + 4. Suppose j = -2*q - 3*q + 10. Determine c, given that 0*c**3 + 1/4*c**q - 1/4*c**4 + 0*c + 0 = 0.
-1, 0, 1
Factor 2/3*w**2 - 10/3*w + 8/3.
2*(w - 4)*(w - 1)/3
Let j = -489/2 + 247. What is f in -1 - 1/2*f - 3/2*f**4 + j*f**2 + 1/2*f**3 = 0?
-1, -2/3, 1
Let n(p) be the second derivative of p**3 + 7/4*p**4 + 0 + 0*p**2 - 7/10*p**6 + 3*p - 3/10*p**5. Factor n(u).
-3*u*(u - 1)*(u + 1)*(7*u + 2)
Let h(o) be the first derivative of o**6/75 + 3*o**5/50 + o**4/10 + o**3/15 + 3*o**2/2 + 2. Let r(y) be the second derivative of h(y). Factor r(w).
2*(w + 1)**2*(4*w + 1)/5
Let w be (-582)/(-20) - 10/(-25). Let a = 30 - w. Factor a - 1/2*h**2 - 1/2*h**3 + 1/2*h.
-(h - 1)*(h + 1)**2/2
Let s = -12 + 17. Let t(d) be the second derivative of 0 - 1/42*d**4 + 1/7*d**2 - 2*d - 1/70*d**s + 1/21*d**3. Factor t(h).
-2*(h - 1)*(h + 1)**2/7
Let r(m) = -8*m**2 + 30*m + 52. Let u(y) = -3*y**2 + 10*y + 17. Let l(k) = 2*r(k) - 7*u(k). Factor l(w).
5*(w - 3)*(w + 1)
Factor 73*h**2 + 45*h + 192*h**3 + 71*h**2 - 9*h + 3.
3*(4*h + 1)**3
Suppose 2*p = 3*c + 4, -5*c = -c + 2*p - 4. Suppose -2*m + 8 = c, -5*m + 11 = 4*x - 17. Let 0*y**4 + 0 + 0*y**x + 0*y - 1/4*y**3 + 1/4*y**5 = 0. Calculate y.
-1, 0, 1
Suppose -3*t + 4 = -8. Factor q**3 + 3*q**t - 3*q**3 - q**4.
2*q**3*(q - 1)
Let n(m) = -m**2 + 17*m - 13. Let c be n(16). Let b(h) be the first derivative of 3/10*h**4 + 0*h + 4/15*h**c - 3 + 0*h**2. Find s, given that b(s) = 0.
-2/3, 0
Let n be 2 + 15/((-270)/12). Factor -4/3*s**3 + 0 + n*s**2 + 0*s.
-4*s**2*(s - 1)/3
Let y(m) = 8*m - 13. Let x be y(2). Let 0*w + 0 - 1/2*w**x + 1/2*w**4 + 0*w**2 = 0. What is w?
0, 1
Let m = -118/5 + 24. Factor -1/5*f**2 + 0 - m*f + 1/5*f**3.
f*(f - 2)*(f + 1)/5
Find f, given that 0 - 4/9*f + 2/9*f**4 + 0*f**3 - 2/3*f**2 = 0.
-1, 0, 2
Let v(n) be the first derivative of -n**4 - 8*n**3 - 10*n**2 - 32. Suppose v(a) = 0. Calculate a.
-5, -1, 0
Let p = 324 - 970/3. Solve -p*u**3 + 2/3*u**2 + 2/3*u - 2/3 = 0.
-1, 1
Factor 0 + 8/3*v**5 - 2/3*v**4 + 0*v**3 + 0*v + 0*v**2.
2*v**4*(4*v - 1)/3
Let m(z) be the first derivative of -z**5/150 - z**4/30 - z**3/15 - z**2 - 3. Let b(t) be the second derivative of m(t). Factor b(n).
-2*(n + 1)**2/5
Let j(k) = k**2 - k + 1. Let x(y) = 12*y**5 - 8*y**4 - 16*y**3 + 24*y**2 - 12*y + 16. Let b(r) = -16*j(r) + x(r). Let b(s) = 0. What is s?
-1, -1/3, 0, 1
Let b(u) = u**2 - 5*u + 3. Let d(t) = t - 1. Let i(k) = b(k) + 3*d(k). Suppose i(j) = 0. Calculate j.
0, 2
Factor -2/7*h**5 - 44/7*h**3 - 18/7*h - 48/7*h**2 + 0 - 16/7*h**4.
-2*h*(h + 1)**2*(h + 3)**2/7
Suppose -2 - 4 = -2*t. Suppose s - 4 = -t*s, 4*i - 21 = 3*s. Factor -i*h**4 + 0*h**5 + 4 - 2 + 4*h**3 + 4*h**2 - 6*h + 2*h**5.
2*(h - 1)**4*(h + 1)
Let x(r) be the first derivative of 7 + 1/2*r**4 + 0*r + 1/6*r**6 + 0*r**2 + 3/5*r**5 + 0*r**3. Suppose x(s) = 0. Calculate s.
-2, -1, 0
Let i(x) be the third derivative of 0*x + 1/9*x**3 + 1/9*x**4 + 1/30*x**5 + 0 + 4*x**2. Suppose i(g) = 0. Calculate g.
-1, -1/3
Let r = -3/70 + 9/10. Find x such that r*x + 0 + 2/7*x**2 = 0.
-3, 0
Let a(o) be the third derivative of o**6/120 + o**5/30 + o**4/24 + 8*o**2. Factor a(r).
r*(r + 1)**2
Let m(o) = -o - 12. Suppose 0 = h + c - 4*c, -4*h + 5*c = 28. Let w be m(h). Factor w - 1/5*b - 1/5*b**2.
-b*(b + 1)/5
Suppose -17 = -r - 3*q, r - 3*q - 18 - 5 = 0. Suppose -m + r = 4*m. Factor 0*n - 2/3*n**m - 4/3*n**3 + 0 - 2/3*n**2.
-2*n**2*(n + 1)**2/3
Suppose -5*g + 3*x = -82, -g - x + 13 = 3. Let k(n) = -7*n**2 - 9*n + 7. Let c(q) = 34*q**2 + 44*q - 34. Let i(m) = g*k(m) + 3*c(m). Let i(h) = 0. What is h?
-2, 1/2
Factor 6/5*p**2 + 0 + 0*p**3 - 6/5*p**4 + 3/5*p**5 - 3/5*p.
3*p*(p - 1)**3*(p + 1)/5
Let h(n) be the third derivative of 1/30*n**6 - 1/105*n**7 + 0*n**4 + 0 + 0*n + n**2 + 0*n**3 - 1/30*n**5. Solve h(z) = 0.
0, 1
Let h be (2 - (1 - 0)) + 1. Suppose -4 + u**4 + 8*u - u**h - 1 - 3*u**3 - 2*u**3 + u**5 + 1 = 0. What is u?
-2, 1
Let k(j) be the second derivative of 27*j**5/40 + 11*j**4/8 - 4*j**3 - 3*j**2 + 12*j. Factor k(c).
3*(c - 1)*(c + 2)*(9*c + 2)/2
Find y such that -4*y**2 - 339 + 339 + 5*y**2 = 0.
0
Solve -2/5 - 1/5*t + 2/5*t**2 + 1/5*t**3 = 0.
-2, -1, 1
Let q(x) be the first derivative of -x**6/540 - x**5/270 + 2*x**2 + 1. Let j(m) be the second derivative of q(m). Suppose j(p) = 0. Calculate p.
-1, 0
Let g(i) = 2*i**3 + 3*i**2 - 5*i. Let n(t) = -7*t**2 - 7*t**2 + 24*t - 10*t**3 + 0*t**2. Let r(q) = 14*g(q) + 3*n(q). Factor r(b).
-2*b*(b - 1)*(b + 1)
Let h(f) = -3*f**3 + 21*f**2 + 24*f + 6. Let r(x) = -x**3 + x**2 - 1. Let d(m) = h(m) - 6*r(m). Factor d(v).
3*(v + 1)*(v + 2)**2
Let h(a) be the first derivative of 1/2*a**2 + 0*a - 4 + 1/9*a**3. Factor h(g).
g*(g + 3)/3
Suppose 0 = 3*k - s - 18, 0 = 3*k + 3*s + 2*s. Solve 0*v + 1/2*v**2 + 2*v**3 - 1/2*v**4 + 0 - 2*v**k = 0.
-1, -1/4, 0, 1
Let u be -3 + 3 + 0 + 0. Let k = 92/273 - 2/39. Suppose u + 6/7*o**3 + 0*o + k*o**4 + 4/7*o**2 = 0. Calculate o.
-2, -1, 0
Let d be ((-2)/28)/((-48)/32). Let c(q) be the second derivative of -q - d*q**4 + 0*q**2 - 1/70*q**5 - 1/21*q**3 + 0. Let c(z) = 0. Calculate z.
-1, 0
Suppose -2*s = 5*r + 2*s - 16, 5*r + 5*s - 20 = 0. Let d be (-1 + 1 + r)/(-1). Find h, given that 4*h**3 + 0*h**2 - 2*h**4 - 2*h**2 + d*h**2 = 0.
0, 1
Let t(n) be the second derivative of 0*n**2 + 2/21*n**3 - 1/14*n**4 + n + 0 + 1/70*n**5. Factor t(v).
2*v*(v - 2)*(v - 1)/7
Let g(n) = n**2 + 3*n - 2. Let u be g(-4). Suppose -9*z + 11*z - 6 = 0. Factor 0*m**z - 4/7*m**u + 2/7*m**4 + 2/7 + 0*m.
2*(m - 1)**2*(m + 1)**2/7
Suppose 0 = v - 0*v - 11. Suppose 0*q = q - 4*f + 2, 0 = -3*q - 5*f + v. Find u such that 7*u + 16*u**3 + 5*u**2 + 6*u**4 - 3*u + 9*u**q = 0.
-1, -2/3, 0
Factor 12 - 5*t - 2*t**2 + 21*t + 6*t**2.
4*(t + 1)*(t + 3)
Factor 12*v + 26*v**2 - 17*v**2 + 11*v**2 - 8.
4*(v + 1)*(5*v - 2)
Let g(y) be the third derivative of 1/20*y**5 + 0 - 1/2*y**3 + 4*y**2 - 1/180*y**6 + 0*y - 1/6*y**4. Let w(x) be the first derivative of g(x). Factor w(j).
-2*(j - 2)*(j - 1)
Let g(n) be the first derivative of n**5/20 - n**4/8 - n**3 - 3*n**2 - 5. Let f(w) be the second derivative of g(w). Factor f(q).
3*(q - 2)*(q + 1)
Let d(z) be the first derivative of -z**3/5 - 9*z**2/10 + 3. Factor d(j).
-3*j*(j + 3)/5
Let b(x) = -11*x**2 + 20*x - 12. Let a(z) = -7*z + 2*z**2 + 1 + z**2 + 3 + z**2. Let h(l) = -8*a(l) - 3*b(l). Factor h(n).
(n - 2)**2
Let y(i) be the second derivative of -i**6/300 + i**4/60 - i**2/2 + 3*i. Let v(c) be the first derivative of y(c). Suppose v(p) = 0. Calculate p.
-1, 0, 1
Suppose 0*p = p - 3. Let -y**2 + y**2 - y**2 - y**p = 0. What is y?
-1, 0
Let i(u) = 8*u**3 - 6*u**2 + 4*u. Let h(j) = -j**4 - j**3 - j. Let x(m) = 4*h(m) + 2*i(m). Factor x(n).
-4*n*(n - 1)**3
Let s(h) be the third derivative of h**8/40320 + h**7/5040 - h**5/20 + 9*h**2. Let a(f) be the third derivative of s(f). Let a(j) = 0. What is j?
-2, 0
Let k(d) be the second derivative of -d**5/25 + 2*d**4/5 + 2*d**3/15 - 12*d**2/5 - 20*d. Factor k(o).
-4*(o - 6)*(o - 1)*(o + 1)/5
Let h(m) be the third derivative of -7*m**6/40 - 3*m**5/5 + m**4/2 - m**2 + 18. Determine g so that h(g) = 0.
-2, 0, 2/7
Let f(g) be the first derivative of -4*g**6/57 + 2*g**5/95 + 4*g**4/19 - 4*g**3/57 - 4*g**2/19 + 2*g/19 