- 7*i**4 = 0.
-1, -2/7, 0
Let s(n) be the third derivative of -n**8/112 + n**6/20 - n**4/8 - 22*n**2. Solve s(v) = 0.
-1, 0, 1
Suppose 3*y**2 + 20 + 9*y + 2*y**2 - 10*y + 21*y = 0. Calculate y.
-2
Let j be ((-8)/(-14))/(44/33)*1. Solve 9/7*x**2 - 6/7*x**3 + 0*x + 0 - j*x**4 = 0.
-3, 0, 1
Let d(a) be the first derivative of -a**5/60 - a**4/24 - 7*a**2/2 - 4. Let i(x) be the second derivative of d(x). Factor i(h).
-h*(h + 1)
Suppose -9*d**4 + 23*d**3 - 25*d**3 + 11*d**4 = 0. Calculate d.
0, 1
Let p(r) = r - 8. Let h = -22 + 30. Let s be p(h). Factor 0 + 0*u**3 + s*u - 3/4*u**4 + 3/4*u**2.
-3*u**2*(u - 1)*(u + 1)/4
Let 10/3*i**2 + 13/3*i + 144*i**5 + 24*i**4 - 2/3 - 55*i**3 = 0. Calculate i.
-2/3, -1/3, 1/4, 1/3
Let p(b) be the first derivative of -b**4/2 - 4*b**3/3 + b**2 + 4*b + 14. Suppose p(d) = 0. What is d?
-2, -1, 1
Let l(f) be the third derivative of f**6/420 - f**5/210 - f**4/21 + 4*f**3/21 - 25*f**2. Factor l(d).
2*(d - 2)*(d - 1)*(d + 2)/7
Suppose 4*h - 11 + 55 = 0. Let c = h - -13. Find f such that 2/3*f**c + 0*f + 0 = 0.
0
Let m = 60 + -16. Let o = m - 216/5. Factor o - 2/5*k**3 - 4/5*k**2 + 2/5*k.
-2*(k - 1)*(k + 1)*(k + 2)/5
Factor -7*g + g**3 + 115*g**2 + 0*g**3 - 4 - 117*g**2.
(g - 4)*(g + 1)**2
Suppose 9*h = 5*h. Let f(s) be the third derivative of -3*s**2 + 0*s - 1/60*s**4 - 1/840*s**8 + 0*s**3 + 1/150*s**6 + 0*s**5 + h + 0*s**7. Solve f(i) = 0 for i.
-1, 0, 1
Factor 0*w**2 - 8/3*w**3 + 20/9*w**4 + 0 + 0*w - 4/9*w**5.
-4*w**3*(w - 3)*(w - 2)/9
Find o, given that -300 + 66*o - 61*o - 3*o**2 + 55*o = 0.
10
Let s(u) be the first derivative of -u**4/4 - 2*u**3/3 + u**2/2 + 2*u - 1. Let s(a) = 0. What is a?
-2, -1, 1
Let c(n) be the first derivative of n**8/2016 - 23*n**7/5040 + n**6/72 - n**5/180 - n**4/18 - 2*n**3 - 5. Let a(m) be the third derivative of c(m). Factor a(d).
(d - 2)**2*(d - 1)*(5*d + 2)/6
Let l(x) be the first derivative of -2 - 3/8*x**4 - 1/8*x**2 - 1/24*x**6 - 1/5*x**5 + 0*x - 1/3*x**3. Determine y, given that l(y) = 0.
-1, 0
Suppose -3/7*t**4 - 18/7*t**3 - 12/7 - 36/7*t - 39/7*t**2 = 0. What is t?
-2, -1
Let p(j) be the second derivative of 0*j**3 + 0 + 1/20*j**5 + 2*j + 0*j**2 - 1/42*j**4 - 1/42*j**6. Factor p(x).
-x**2*(x - 1)*(5*x - 2)/7
Let q(h) = h**2 - 5*h - 6. Let o be q(6). Let p = 5 + -1. Find m, given that -1/4*m**5 + o*m + 0 + 0*m**3 - 1/4*m**p + 0*m**2 = 0.
-1, 0
Let o(x) be the first derivative of x**4/4 - 3*x**3/2 + 27*x**2/8 + x + 2. Let t(j) be the first derivative of o(j). Factor t(g).
3*(2*g - 3)**2/4
Let p(w) be the third derivative of -w**9/16632 - w**8/4620 - w**7/4620 - w**3/3 + 4*w**2. Let v(k) be the first derivative of p(k). Factor v(c).
-2*c**3*(c + 1)**2/11
Let o(b) be the first derivative of -1/6*b + 3 + 1/9*b**3 + 1/12*b**2. Factor o(g).
(g + 1)*(2*g - 1)/6
Factor 28*s**3 - 65 - 61*s - 183*s**2 + 17 - 21*s**2 + 285*s.
4*(s - 6)*(s - 1)*(7*s - 2)
Let d = 123/185 - -5/37. Let f = d - 18/35. Let -8/7*s - f*s**2 - 8/7 = 0. What is s?
-2
Let d(s) be the second derivative of 2*s**6/105 - 4*s**5/35 + 2*s**4/7 - 8*s**3/21 + 2*s**2/7 + 2*s. Factor d(u).
4*(u - 1)**4/7
Let j(f) be the second derivative of 3*f**4/14 + 10*f**3/7 + 25*f**2/7 + 11*f. Solve j(n) = 0.
-5/3
Suppose -14 = 2*x + 4*i, 3*x + i + 45 = 3*i. Let w = 17 + x. Let 7/3*m**w + 0 - 19/3*m**3 + 4/3*m + 8/3*m**2 = 0. Calculate m.
-2/7, 0, 1, 2
Let t = -398/35 + 88/7. Let l(i) be the first derivative of 1/2*i**6 + 2*i**3 - t*i**5 + 0*i**4 - 1 + 0*i - 3/2*i**2. Factor l(f).
3*f*(f - 1)**3*(f + 1)
Let r(t) be the first derivative of -1/3*t**3 - 1/4*t**4 + 1 + 1/2*t**2 + t. Factor r(p).
-(p - 1)*(p + 1)**2
Suppose -5*w + 9 = -11. Let v(h) be the third derivative of 0*h**w + 0*h**5 + 1/210*h**7 + 2*h**2 + 1/120*h**6 + 0 + 0*h**3 + 0*h. Determine q so that v(q) = 0.
-1, 0
Let v(k) be the first derivative of 0*k + 1/120*k**5 + 1/6*k**3 - 1/16*k**4 + 1 - 3/2*k**2. Let w(h) be the second derivative of v(h). Factor w(i).
(i - 2)*(i - 1)/2
Let m(b) be the second derivative of 9/2*b**2 - b**3 + 1/12*b**4 + 0 - 8*b. Solve m(q) = 0.
3
Let x(g) be the second derivative of -g**9/10584 + g**7/1470 - g**5/420 - 4*g**3/3 + g. Let b(f) be the second derivative of x(f). Factor b(z).
-2*z*(z - 1)**2*(z + 1)**2/7
Let q(p) = 2*p**4 - 12*p**3 + 16*p**2 - 8*p + 6. Let g(m) = 6*m**4 - 35*m**3 + 47*m**2 - 24*m + 17. Let n(u) = 4*g(u) - 11*q(u). Solve n(y) = 0.
1
Let o(l) be the first derivative of l**4/28 - 5*l**3/21 + 2*l**2/7 + 27. Suppose o(h) = 0. What is h?
0, 1, 4
Let p(z) be the first derivative of z**5/90 + 2*z**4/27 + 4*z**3/27 + 3*z + 2. Let v(g) be the first derivative of p(g). Let v(y) = 0. Calculate y.
-2, 0
Let y(n) be the first derivative of -5*n**4/4 + 5*n**2/2 + 3. Solve y(p) = 0 for p.
-1, 0, 1
Let f be 4/(-8) + 59/(-2). Let i be f/(-12)*(-12)/(-10). What is z in -5*z**4 - 9*z**4 + 18*z**2 - 1 - 10*z**3 - i + 10*z = 0?
-1, 2/7, 1
Let 1/4*c**5 + 1/2*c**3 + 1/2*c**2 + 1/4 - 3/4*c - 3/4*c**4 = 0. Calculate c.
-1, 1
Suppose -4*b = -0*b. Suppose -2*o = 3*l - 6, l - 2 = -b*o - 4*o. Factor 3*a**3 - a**4 + 6*a**2 - a**4 - 2*a**5 - a**3 - 4*a**l.
-2*a**2*(a - 1)*(a + 1)**2
Let g be 0/3*11/(-11). Factor 0*y**3 + g + 2*y**4 - 3/2*y**2 - 1/2*y.
y*(y - 1)*(2*y + 1)**2/2
Let z(l) be the third derivative of l**6/280 + l**5/70 - 9*l**2. What is t in z(t) = 0?
-2, 0
Suppose o - 10 = -2*w + 1, 0 = 3*o - 5*w. Suppose -o - 7 = -4*g. Factor -2*x + 5*x**2 + g*x**2 + 6*x - 2*x.
2*x*(4*x + 1)
Factor 10*s**2 + 4*s**3 + 2*s**4 - 6*s**2 - 6*s**2 + 2*s - 6*s**3.
2*s*(s - 1)**2*(s + 1)
Let d(y) be the second derivative of -1/42*y**7 + 0 - 1/6*y**6 - 1/3*y**4 - y + 0*y**2 - 2/5*y**5 + 0*y**3. Determine m so that d(m) = 0.
-2, -1, 0
Let m(r) be the first derivative of -r**6/180 + r**5/30 - 4*r**3/9 + r**2 - 1. Let n(q) be the second derivative of m(q). Suppose n(g) = 0. What is g?
-1, 2
Let a = 7 + -1. Let 6*i + 0*i**2 + 0*i**2 - a*i**2 + 2*i**3 - 2 = 0. What is i?
1
Factor -2/5*m**2 + 0*m + 2/5.
-2*(m - 1)*(m + 1)/5
Let c(h) = 3*h**3 - h**2 - 3*h + 1. Let y(g) = -4*g**3 + g**2 + 4*g - 1. Let o = -8 - -5. Let m(p) = o*c(p) - 2*y(p). Determine k so that m(k) = 0.
-1, 1
Let h = -5/8 - -31/24. Factor -2/3 + h*b**2 + 0*b.
2*(b - 1)*(b + 1)/3
Let 21/4*m - 3/4*m**4 + 15/4*m**3 - 27/4*m**2 - 3/2 = 0. What is m?
1, 2
Let a(s) be the first derivative of -1/10*s**4 - 4 + 0*s + 0*s**3 + 1/5*s**2. Suppose a(o) = 0. What is o?
-1, 0, 1
Let a(s) be the first derivative of s**5/25 - s**3/15 - 10. Factor a(q).
q**2*(q - 1)*(q + 1)/5
Find z, given that 0 - 2*z + 2/3*z**2 = 0.
0, 3
Factor 5*v**2 - 20*v + 817 - 817.
5*v*(v - 4)
Solve -5*k**2 + k**5 + 0 + 7*k**2 + 5*k**3 + 4*k**4 + 0 = 0 for k.
-2, -1, 0
Let i(k) = -k**3 - 2*k**2 + 2*k. Let o be i(-3). Factor -12*p**o + 4*p - 4*p**3 - 10*p**4 + 0*p - 2*p**2.
-2*p*(p + 1)**2*(5*p - 2)
Let r(x) be the third derivative of -x**2 + 0*x - 3/20*x**5 + 0 - 1/10*x**7 + 0*x**3 - 3/10*x**6 + 1/4*x**4. Factor r(w).
-3*w*(w + 1)**2*(7*w - 2)
Let a(t) be the second derivative of 1/18*t**4 - 1/9*t**3 + 0 + 0*t**2 + 3*t. Factor a(h).
2*h*(h - 1)/3
Suppose -27 + 39 = 6*q. Suppose -5*g + 2*i = 4, -3*g + i - 2 = g. What is y in 1/2*y**q + g + 1/2*y = 0?
-1, 0
Let k(u) be the first derivative of u**7/42 - u**6/10 + u**5/10 - 4*u + 4. Let w(c) be the first derivative of k(c). Suppose w(f) = 0. What is f?
0, 1, 2
Let c(k) = 5*k**2 - 25*k - 10. Let n(x) = x + 1. Let f(w) = c(w) + 15*n(w). Factor f(d).
5*(d - 1)**2
Suppose 5*c - 21 = -3*p, -5*p - 2*c + 2 = -7*p. Let 4/11*n - 4/11*n**3 + 2/11*n**4 + 0*n**p - 2/11 = 0. What is n?
-1, 1
Let x(u) be the third derivative of u**6/120 - u**5/10 + 5*u**4/24 - 21*u**2. Factor x(n).
n*(n - 5)*(n - 1)
Suppose t + t + 10*t**2 - 6*t**2 - 2*t**2 = 0. What is t?
-1, 0
Let g(k) be the first derivative of k**4/16 + 15*k**3/4 + 675*k**2/8 + 3375*k/4 - 14. Factor g(p).
(p + 15)**3/4
Let d(o) be the first derivative of -2*o**3/3 - 3*o**2 - 4*o + 7. Suppose d(j) = 0. Calculate j.
-2, -1
Let c = -88/9 - -433/36. Factor -3/4*p**4 - 1/2 - 15/4*p**2 - c*p - 11/4*p**3.
-(p + 1)**3*(3*p + 2)/4
Let i(d) be the third derivative of -1/630*d**7 + d**2 + 0*d**4 + 0 + 0*d**5 + 1/360*d**6 + 0*d**3 + 0*d. Solve i(b) = 0.
0, 1
Suppose 0 = -l - 6 + 9. Factor 0*u**2 + 1/4*u**l + 0 - 1/4*u.
u*(u - 1)*(u + 1)/4
Let d(j) be the third derivative of 0 +