0 - 1/4*r**2 + a*r = 0.
0
Suppose 6*i = 21 + 9. Let h(o) be the first derivative of 1/2*o**6 - 8*o**3 + 0*o**2 + 9*o**4 - 18/5*o**i + 0*o + 4. Factor h(s).
3*s**2*(s - 2)**3
Let s be 0*(-1 - 0)/4. Solve 0*k**2 + s*k**4 + 3/2*k**5 + 0 - 3*k**3 + 3/2*k = 0.
-1, 0, 1
Suppose 7*l = 4*l. Let i(z) be the third derivative of -2*z**2 - 1/60*z**6 + 0 + l*z + 0*z**3 + 0*z**4 + 0*z**5. Solve i(f) = 0.
0
Suppose 5*a - a - b = 18, -5*a - 4*b + 33 = 0. Suppose a*p = -0*p. Factor 1/3*v**4 + p*v**3 + 0 - 1/3*v**2 + 0*v.
v**2*(v - 1)*(v + 1)/3
Let d(g) be the third derivative of -g**7/420 + g**6/100 - g**5/150 - 12*g**2. Factor d(i).
-i**2*(i - 2)*(5*i - 2)/10
Let r = -4 + 7. Let p(f) be the third derivative of 0*f - 1/120*f**5 + 1/240*f**6 + 1/420*f**7 - 1/672*f**8 + 0*f**r + 0*f**4 + 0 - 2*f**2. Factor p(b).
-b**2*(b - 1)**2*(b + 1)/2
Let i(g) be the second derivative of g**5/12 + 5*g**4/36 - 13*g. Solve i(p) = 0 for p.
-1, 0
Suppose 4*b - 8 = 4. Factor -3*q**b - q + 0*q**3 - q**4 - 3*q**2 + 0*q**3.
-q*(q + 1)**3
Let l(n) be the third derivative of -n**6/360 + n**5/60 - n**4/24 + n**3/18 + n**2. What is c in l(c) = 0?
1
Let d(j) be the second derivative of -j**7/105 + j**6/30 - j**5/30 - 2*j**2 + j. Let c(r) be the first derivative of d(r). Factor c(x).
-2*x**2*(x - 1)**2
Let y(o) = 2*o**3 + 17*o**2 - 7*o + 11. Let m(k) = -k**3 - 9*k**2 + 4*k - 6. Let t be (9/(-4))/(39/(-104)). Let d(j) = t*y(j) + 11*m(j). Factor d(p).
p*(p + 1)*(p + 2)
Let l(z) be the third derivative of z**7/840 - z**6/480 - z**5/80 + 5*z**4/96 - z**3/12 + z**2 + 4. Factor l(q).
(q - 1)**3*(q + 2)/4
Let w(f) = f**2 + f. Let g be w(-2). Let v(j) = -4*j**3 - j**2 - 2*j - 1. Let m be v(-1). Factor 2 + m*p + 6*p**2 - p**2 - 1 + g*p**3.
(p + 1)**2*(2*p + 1)
Let u = -790 + 47401/60. Let i(z) be the third derivative of 0*z**4 + 0*z**3 + 2*z**2 + u*z**6 + 0 + 1/15*z**5 + 0*z. Factor i(b).
2*b**2*(b + 2)
Let f(m) be the second derivative of m**7/189 - m**6/45 + m**5/30 - m**4/54 + 17*m. Factor f(u).
2*u**2*(u - 1)**3/9
Let t be (-54)/4*(-8)/12. Let q = t + -9. What is z in -6/5*z**4 + 2*z**3 + q + 6/5*z**2 - 2/5*z - 8/5*z**5 = 0?
-1, 0, 1/4, 1
Suppose 37 = -h - 19. Let q be (-9)/(-6)*h/(-105). Factor 0*f + 0 + 14/5*f**3 + q*f**2.
2*f**2*(7*f + 2)/5
Let d(j) be the third derivative of -j**5/330 - 5*j**4/132 - 22*j**2. Factor d(o).
-2*o*(o + 5)/11
Let t(x) be the third derivative of x**7/1785 - 7*x**6/1020 + 11*x**5/510 - 5*x**4/204 - 16*x**2. Factor t(p).
2*p*(p - 5)*(p - 1)**2/17
Let g(u) = 3*u**3 + 18*u**2 - 27*u + 15. Let p(k) be the first derivative of k**4/4 + 3*k**3 - 13*k**2/2 + 7*k - 3. Let x(h) = 4*g(h) - 9*p(h). Factor x(y).
3*(y - 1)**3
Let m(l) be the second derivative of 1/120*l**5 + 0*l**4 + 0 - 3*l + 0*l**3 - 3/2*l**2. Let r(u) be the first derivative of m(u). Factor r(p).
p**2/2
Factor 8/9*d**3 - 10/9*d - 4/9 + 8/9*d**4 - 4/9*d**2 + 2/9*d**5.
2*(d - 1)*(d + 1)**3*(d + 2)/9
Let p be (-3)/((9/2)/(-3)). Factor -7*v + v**3 + 5*v + 3*v + 2*v**p.
v*(v + 1)**2
Let s = -22/35 - -271/420. Let x(j) be the third derivative of 0*j - s*j**6 + 0 + j**2 + 1/3*j**3 + 1/12*j**4 - 1/30*j**5. Factor x(z).
-2*(z - 1)*(z + 1)**2
Let x(f) = -f + 3. Let n be x(1). Let c(d) be the second derivative of 1/4*d**n - d + 0 - 1/12*d**4 - 1/12*d**3. Factor c(o).
-(o + 1)*(2*o - 1)/2
Let w(u) = u**2 + 3*u - 2. Let t = 5 - 4. Suppose -4*x + t = 9. Let j(d) = -4*d**2 - 13*d + 8. Let i(m) = x*j(m) - 9*w(m). Factor i(f).
-(f - 1)*(f + 2)
Let v be (-16)/(-4 + 2) - -2. Suppose -4*n - 12 - v = -2*g, -5*g + 19 = -n. Factor -s**4 - 3*s**g + s**5 + 0*s**5 + 2*s**3 + s**2.
s**2*(s - 1)**2*(s + 1)
Let w(h) be the third derivative of -h**8/336 - 2*h**7/105 - h**6/40 - 50*h**2. Suppose w(c) = 0. What is c?
-3, -1, 0
Suppose -3 = 5*r + 7. Let k be (14/35)/(r/(-10)). Determine v so that 7/3*v - 2/3 - 5/3*v**k = 0.
2/5, 1
Let p be (-4)/3*3/(-2). Let l be 1/(-4) - (-3)/12. Factor a**p + 2 + 9*a + l + 9*a**2 + 0*a.
(2*a + 1)*(5*a + 2)
Let a be (-15252)/14 - (5 - 6). Let l = 1091 + a. Determine o so that -l - 12/7*o - 2/7*o**2 = 0.
-3
Let o(v) = 4*v**5 - v**4 + v**3 - 4*v**2. Let b(i) = 0*i**2 + 2*i**2 + 2*i**5 - 4*i**5. Let z(l) = 5*b(l) + 2*o(l). Determine k, given that z(k) = 0.
-1, 0, 1
Suppose -21 = -7*u - 7. Let j(w) be the second derivative of -2*w + 0 + 0*w**3 - 1/30*w**4 + 1/5*w**u. Factor j(t).
-2*(t - 1)*(t + 1)/5
Let p(q) = 3*q**2 - 8*q + 9. Let f(b) = -15*b**2 + 39*b - 45. Let n(m) = 4*f(m) + 21*p(m). Factor n(d).
3*(d - 3)*(d - 1)
Let b(j) = -3*j**2 + 3*j + 2. Suppose -3*m + 9 + 90 = 0. Let d(k) = -24*k**2 + 24*k + 15. Let i(l) = m*b(l) - 4*d(l). Solve i(v) = 0 for v.
-1, 2
Let q(a) be the first derivative of -5*a**6/2 - 18*a**5/5 - 3*a**4/4 + 55. Factor q(f).
-3*f**3*(f + 1)*(5*f + 1)
Suppose -x + 4*x = 0. Let t = x + 3. What is b in 8 + b + b**5 - 2*b**t - 8 = 0?
-1, 0, 1
Let s(f) be the third derivative of 5*f**2 + 0*f**3 - 1/210*f**5 + 0*f**4 + 0 + 0*f - 1/420*f**6. Suppose s(g) = 0. What is g?
-1, 0
Let y be (-6)/(-10) + (-28)/(-20). Suppose w + 10 = -3*z, y*z = 4*w - 0*z - 16. Let 0 + w*u**3 + 4/7*u**2 + 16/7*u**4 + 0*u + 6/7*u**5 = 0. Calculate u.
-1, -2/3, 0
Determine h so that -9 + 20 + 21 + 1000*h**2 + 588*h**4 + 1316*h**3 + 304*h = 0.
-1, -2/3, -2/7
Let m be 9/6*(-104)/(-273). Find y such that 2/7*y**2 + 8/7*y**3 - m*y - 1/7 - 1/7*y**4 - 4/7*y**5 = 0.
-1, -1/4, 1
Let a(r) = 5*r**4 - 10*r**3 - 15*r**2 + 5. Let c(h) = h**3 + h**2 - 1. Let d(i) = a(i) + 5*c(i). Factor d(x).
5*x**2*(x - 2)*(x + 1)
Let n(v) = -v**2 + v + 1. Suppose 12*a = 9*a + 18. Let t(d) = 10*d**2 - 6*d - 10. Let p(b) = a*n(b) + t(b). What is i in p(i) = 0?
-1, 1
Let d(l) be the third derivative of l**9/15120 - l**8/3360 + l**7/2520 - l**4/24 + l**2. Let a(z) be the second derivative of d(z). Factor a(t).
t**2*(t - 1)**2
Let l(r) be the second derivative of 5/21*r**7 + 4*r + 0*r**2 - 2/3*r**4 + 4/3*r**3 + 0 - 3/2*r**5 - 2/15*r**6. Find n such that l(n) = 0.
-1, 0, 2/5, 2
Factor -2/9*f + 0*f**3 + 0 - 4/9*f**2 + 4/9*f**4 + 2/9*f**5.
2*f*(f - 1)*(f + 1)**3/9
Determine u so that -14*u - 250/7*u**5 + 1150/7*u**4 + 6/7 + 572/7*u**2 - 1380/7*u**3 = 0.
1/5, 1, 3
Suppose -2*m + 2*m**3 + 3*m**2 - 7*m**5 + 3*m**3 - 3*m**4 - 4*m**3 + 8*m**5 = 0. What is m?
-1, 0, 1, 2
Let g = 9 + -15. Let f(z) = z**3 + 5*z**2 - 8*z - 9. Let h be f(g). Let -6*n**2 - 2*n - 2*n**4 - 3*n**4 - 6*n**3 + h*n**4 = 0. Calculate n.
-1, 0
Let g(k) = -k + 8. Let c be g(8). Factor 0*y - 2*y**2 + 4*y + c*y.
-2*y*(y - 2)
Let r(i) be the second derivative of -i**7/21 + i**6/15 + i**5/5 - i**4/3 - i**3/3 + i**2 - 2*i. Factor r(q).
-2*(q - 1)**3*(q + 1)**2
Solve 6/7 + 9/7*w + 3/7*w**2 = 0.
-2, -1
Find l such that 0*l + 5/3*l**3 - l**4 - 2/3*l**2 + 0 = 0.
0, 2/3, 1
Let u = -6 - -12. Let y(r) = -15*r**2 + 6*r. Let f(t) = -16*t**2 + 6*t. Let i(x) = u*f(x) - 5*y(x). Solve i(k) = 0.
0, 2/7
Let w be (0 + -1)/((-5)/15). Let g(h) be the first derivative of 1 + 0*h + 11/3*h**w - 4*h**4 - h**2 + 7/5*h**5. Factor g(n).
n*(n - 1)**2*(7*n - 2)
Suppose -2*n - 4*y + 46 = 0, -y + 19 = -n + 2*n. Let -n + 15 + 4*l**2 + 4*l**3 = 0. Calculate l.
-1, 0
Let y = 182 - 2364/13. Factor 0*b**3 + 6/13*b**4 + 0 - 8/13*b**2 - y*b**5 + 0*b.
-2*b**2*(b - 2)**2*(b + 1)/13
Let x(t) be the first derivative of -1/2*t**3 + 3/2*t**2 + 3/10*t**5 - 3/4*t**4 + 0*t + 6. Determine z, given that x(z) = 0.
-1, 0, 1, 2
Let j(f) be the second derivative of -f**5/20 - f**4/3 - 5*f**3/6 - f**2 + 3*f. Suppose j(d) = 0. Calculate d.
-2, -1
What is s in -21/2*s**3 + 39*s**2 + 12*s + 0 = 0?
-2/7, 0, 4
Determine u, given that 0*u**2 + 0*u - 4/9*u**3 - 2/9*u**4 + 2/9*u**5 + 0 = 0.
-1, 0, 2
Let l(r) be the third derivative of -1/30*r**6 - 1/5*r**5 + 0*r + 0*r**3 + 0*r**4 + 0 - 9*r**2. Solve l(o) = 0.
-3, 0
Let o = -9 + 2. Let c = -7 - o. Solve 0*h - 4/5*h**3 - 2/5*h**4 - 2/5*h**2 + c = 0.
-1, 0
Let f(w) = -7*w + 101. Let b be f(14). Factor -2/7*d**b + 5/7*d**2 + 3/7*d + 0.
-d*(d - 3)*(2*d + 1)/7
Let h(u) = -u. Suppose -2*z = -5*z + 3. Let m(r) = 3*r**2. Let g(o) = z*m(o) + 3*h(o). Factor g(f).
3*f*(f - 1)
Let d(t) be the first derivative of -1/60*t**6 - 1/24*t**4 + 0*t**3 - 1 + 2*t - 1/20*t**5 + 0*t**2. Let p(h) be the first derivative of d(h). Factor p(b).
-b**2*(b + 1)**2/2
Let k be -1 + (-51)/(-6) + -2 + -1. What is j in k*j + 0*j**2 - 3