39 - 12*m**2. Solve y(c) = 0 for c.
-1, 1
Suppose 3/2*n - 3/4*n**2 + 0 = 0. Calculate n.
0, 2
Let k(s) be the second derivative of 2*s**6/3 + s**5 - 35*s**4/12 + 5*s**3/3 + 14*s. Find r, given that k(r) = 0.
-2, 0, 1/2
Let u(h) be the second derivative of 4/9*h**3 + 13/30*h**5 + 0*h**2 - 2/3*h**4 + 0 + h + 1/63*h**7 - 2/15*h**6. Factor u(l).
2*l*(l - 2)**2*(l - 1)**2/3
Let q(z) be the second derivative of -1/12*z**3 + 0 + 0*z**2 + 2*z - 1/5*z**5 + 11/48*z**4 + 7/120*z**6. Factor q(t).
t*(t - 1)**2*(7*t - 2)/4
Let w = 24301/2034 - 215/18. Let d = w - -2705/2373. Factor 2/7*h**5 + 2/7*h + 8/7*h**2 + 12/7*h**3 + d*h**4 + 0.
2*h*(h + 1)**4/7
Let i(o) be the third derivative of -o**6/600 + o**5/150 + o**4/120 - o**3/15 + 8*o**2. What is n in i(n) = 0?
-1, 1, 2
Let u = -10 - -14. Determine r so that 4/3*r**2 - 2/3*r + 0 + 14/3*r**3 + 8/3*r**u = 0.
-1, 0, 1/4
Let o be 135/(-18)*1*-2. Suppose 0 = -o*z + 16*z - 4. Factor 5/3*u**5 + 0 + 0*u**3 + 2/3*u**z + 0*u + 0*u**2.
u**4*(5*u + 2)/3
Suppose 0 = -5*u + 3*u + 20. Let t be (1*8/2)/u. Factor -2/5*z**4 + t*z - 6/5*z**2 + 0 + 6/5*z**3.
-2*z*(z - 1)**3/5
Let c(i) be the third derivative of -i**2 - 1/112*i**8 - 1/8*i**6 + 0*i**4 + 0*i**3 + 0*i - 2/35*i**7 - 1/10*i**5 + 0. Let c(l) = 0. What is l?
-2, -1, 0
Let g = -24 - -24. Factor 4/9*j**3 + 0 + g*j**2 - 2/9*j**4 + 0*j.
-2*j**3*(j - 2)/9
Suppose 0 = -2*z + 3*z - 2. Let g be (3/(-4))/(z/(-8)). Factor 12*l + 4*l**3 - 12*l**2 - g*l**4 + 11*l**3 - 12*l**2.
-3*l*(l - 2)**2*(l - 1)
Suppose 5*y - 15 = 3*o, -y + o + 3 = 5*o. Factor -2*x**3 + 4*x**3 - x**y + x**2 - 2*x**3.
-x**2*(x - 1)
Factor 2/3*s - 5/9 - 1/9*s**2.
-(s - 5)*(s - 1)/9
Let i(g) be the second derivative of -g**6/240 - g**5/80 + g**3 + 2*g. Let s(m) be the second derivative of i(m). Factor s(p).
-3*p*(p + 1)/2
Let l(m) be the third derivative of 1/60*m**4 - 7/150*m**5 + 0*m + 1/20*m**6 + 0*m**3 + 0 - 3/175*m**7 + 2*m**2. Factor l(f).
-2*f*(f - 1)*(3*f - 1)**2/5
Let z(c) be the second derivative of c**5/5 + c**4/3 - 6*c**3 - 18*c**2 + c + 17. Determine q so that z(q) = 0.
-3, -1, 3
Suppose 0*m = -6*m + 2*m. Let u(d) be the first derivative of -1/6*d**2 - 2/9*d**3 + 2 + m*d - 1/12*d**4. What is w in u(w) = 0?
-1, 0
Let x(l) be the first derivative of 6 - 2/5*l**5 + 0*l + 0*l**3 + 0*l**2 + 0*l**4 + 1/3*l**6. Factor x(d).
2*d**4*(d - 1)
Let n(u) = -43*u**4 + 25*u**3 - 17*u**2 + 11*u. Let l(c) = 21*c**4 - 12*c**3 + 9*c**2 - 6*c. Let m(w) = 11*l(w) + 6*n(w). Factor m(q).
-3*q**2*(3*q - 1)**2
Let t be -1*2 + 1 + 1. Let d(q) = q**2 + q + 3. Let x be d(0). Factor -1/2*f**2 + 1/2*f**4 - 1/2*f**x + t + 1/2*f**5 + 0*f.
f**2*(f - 1)*(f + 1)**2/2
Let s(j) = j**3 - 9*j**2 - 4*j. Let i(x) = x**3 - 8*x**2 - 3*x. Let a(b) = -6*i(b) + 5*s(b). Factor a(w).
-w*(w - 2)*(w - 1)
Let s(q) be the third derivative of q**9/3024 - q**7/420 + q**5/120 + q**3/3 - 2*q**2. Let j(w) be the first derivative of s(w). Find n such that j(n) = 0.
-1, 0, 1
Let o = -244 + 509/2. Solve 3 - 21/2*f - 3*f**3 + o*f**2 = 0 for f.
1/2, 1, 2
Let t(p) be the third derivative of -p**8/1008 + p**6/360 + 9*p**2. Factor t(s).
-s**3*(s - 1)*(s + 1)/3
Let b(a) be the first derivative of -a**7/105 + a**5/30 - a**2/2 + 2. Let j(z) be the second derivative of b(z). Factor j(o).
-2*o**2*(o - 1)*(o + 1)
Factor -4*r + 0*r**2 + 7*r**2 - r**2 - 2*r**3.
-2*r*(r - 2)*(r - 1)
Let m(t) be the first derivative of 3 - 1/2*t**4 + 1/5*t**5 - t + 0*t**3 + t**2. Find y such that m(y) = 0.
-1, 1
Let x(l) = -39*l**2 + 336*l - 75. Let f(a) = -8*a**2 + 67*a - 15. Let p(h) = -21*f(h) + 4*x(h). Factor p(j).
3*(j - 5)*(4*j - 1)
Let p(i) = 8*i**5 - 20*i**4 + 24*i**3 - 10*i**2. Let f(b) = b**5 + b**4 - b**2. Let d(s) = -2*f(s) + p(s). Determine m, given that d(m) = 0.
0, 2/3, 1, 2
Let s(k) = -k**3 + k + 2. Let y be s(-1). Let r = 1/15 - -7/45. Factor 0*u + 2/9*u**y - r.
2*(u - 1)*(u + 1)/9
Let n(v) = -8*v**4 + 5*v**3 + 2*v**2 - 2*v + 3. Let m(r) = -105*r**4 + 65*r**3 + 25*r**2 - 25*r + 40. Let y(a) = 3*m(a) - 40*n(a). Factor y(j).
5*j*(j - 1)**2*(j + 1)
Suppose 2 = 2*a - a. Factor 2*l**3 - a*l - 9 - 2 - 2*l**2 + 13.
2*(l - 1)**2*(l + 1)
Let v(r) = -r - r + 3*r**2 + 4*r + 1 + 0*r. Let j(k) = 4*k**2 + 3*k + 2. Let g(t) = 2*j(t) - 3*v(t). Factor g(q).
-(q - 1)*(q + 1)
Let a(d) = -9*d - 1. Let l be a(-1). Suppose 0 = 4*r + 3*n - 39, -3*n = -3*r - 0*n + 3. Solve 10*z**5 - l*z**2 + 8*z**2 - 4*z**3 + r*z**4 = 0.
-1, 0, 2/5
Suppose 6 - 15 = -3*n. Factor -2*u**5 + 2*u**3 - 30*u**3 - n*u**2 - 13*u**2 + 4*u**3 - 12*u**4.
-2*u**2*(u + 2)**3
Suppose 4*w + 32 = -0*b + 3*b, 2*w = -3*b + 2. Suppose 4/3*c**2 - 13/3*c**3 + 4/3*c + 0 + 5/3*c**b = 0. Calculate c.
-2/5, 0, 1, 2
Let z(t) be the third derivative of t**6/180 - 2*t**5/45 + 5*t**4/36 - 2*t**3/9 + 3*t**2. What is l in z(l) = 0?
1, 2
Let y(c) be the first derivative of -4*c**3/21 - 18*c**2/7 + 40*c/7 - 26. Factor y(o).
-4*(o - 1)*(o + 10)/7
Suppose -3*s = 3*p + 12, 0 = 4*p + 4*s - 3*s + 4. Let -2/9*d**2 + 0 + p*d = 0. What is d?
0
Let i(m) be the third derivative of m**8/336 - m**7/210 - m**6/30 + m**5/15 + 12*m**2. Factor i(h).
h**2*(h - 2)*(h - 1)*(h + 2)
Let x(s) be the third derivative of -s**7/1260 + s**6/180 + s**4/12 - 4*s**2. Let t(n) be the second derivative of x(n). Factor t(l).
-2*l*(l - 2)
Let t(w) be the second derivative of 2*w**6/105 + w**5/35 - 29*w. Factor t(q).
4*q**3*(q + 1)/7
Let r(h) = -4*h - 8. Let y(g) = g**2 - 3*g - 10. Let j(u) = -3*r(u) + 2*y(u). What is p in j(p) = 0?
-2, -1
Let c(y) be the third derivative of -y**6/360 - y**5/60 - y**4/24 - 2*y**3/3 - y**2. Let u(m) be the first derivative of c(m). Factor u(j).
-(j + 1)**2
Suppose 4*p = -0*p - 0*p. Factor p - 1/2*n + 1/2*n**2.
n*(n - 1)/2
Let p(w) be the second derivative of 0 + 0*w**2 - 2*w**4 - 1/10*w**6 - 4*w + 2*w**3 + 3/4*w**5. Suppose p(i) = 0. What is i?
0, 1, 2
Factor -2062*v**2 - 3*v**5 + 2062*v**2 - 3*v**4.
-3*v**4*(v + 1)
Let n(b) be the third derivative of b**9/5040 - b**8/1120 + b**7/840 + 5*b**4/24 - 3*b**2. Let d(l) be the second derivative of n(l). Factor d(j).
3*j**2*(j - 1)**2
Let c be (-1)/2 - 12/(-42). Let l = 2/7 - c. Suppose -1/2*g + 0 - l*g**3 + g**2 = 0. What is g?
0, 1
Let f(m) = 44*m**3 - 40*m**2 + 44*m + 24. Let n(i) = 9*i**3 - 8*i**2 + 9*i + 5. Let h(j) = -5*f(j) + 24*n(j). Factor h(b).
-4*b*(b - 1)**2
Let o(v) be the third derivative of 0*v**3 + 9/112*v**8 + 1/10*v**5 + 0 - 3*v**2 - 1/8*v**6 - 3/35*v**7 + 0*v + 0*v**4. Find j such that o(j) = 0.
-2/3, 0, 1/3, 1
Let j(r) be the second derivative of -r**4/36 - 5*r**3/9 - 25*r**2/6 - 6*r. Factor j(q).
-(q + 5)**2/3
Let q(z) be the first derivative of 2*z**5/65 + z**4/13 - 2*z**3/39 - 2*z**2/13 - 12. Solve q(w) = 0.
-2, -1, 0, 1
Let p(u) = u**2 - 4*u - 2. Let s be p(5). Factor 0 + 2*w**2 + 21/2*w**4 + 0*w - 9/2*w**5 - 8*w**s.
-w**2*(w - 1)*(3*w - 2)**2/2
Suppose -4*a + 2 = -j + 4, 0 = -5*j + 2*a + 100. Let m = 22 - j. Factor -4/7*k**3 + 0*k - 2/7*k**4 + m + 0*k**2.
-2*k**3*(k + 2)/7
Let -9/5*o - 12/5*o**2 + 0 = 0. What is o?
-3/4, 0
Factor -1/11*s**4 + 4/11*s**3 + 4/11 - 4/11*s - 3/11*s**2.
-(s - 2)**2*(s - 1)*(s + 1)/11
Suppose 0 = -207*s + 228*s. Factor s - 1/5*i**2 + 0*i.
-i**2/5
Let j(b) = b**2 + 8*b + 13. Let t be j(-6). Let i be ((-10)/(-105))/(t/3). Let -i*c**5 + 2/7 - 10/7*c + 10/7*c**4 + 20/7*c**2 - 20/7*c**3 = 0. Calculate c.
1
Let a(r) = -r**2 - 24*r - 44. Let k be a(-22). Let y(o) be the second derivative of 1/10*o**5 + 0 + 0*o**4 + k*o**2 - 1/3*o**3 - o. Suppose y(m) = 0. What is m?
-1, 0, 1
Let d = -3 - -3. Suppose -2*x - 3 = -5*x, -5*m = 2*x - 12. Factor 4*a - 3*a**2 + a**2 + d - m.
-2*(a - 1)**2
Let b(d) be the third derivative of -2*d**7/735 + d**5/35 + d**4/21 - 8*d**2. Let b(o) = 0. What is o?
-1, 0, 2
Suppose -5*z + 59 - 9 = 0. Suppose 5*c = 3*c + z. Let 0*x - 5*x**2 - 8*x**5 + 5*x**4 - 2*x + x**c + 9*x**3 + 0*x**5 = 0. Calculate x.
-1, -2/7, 0, 1
Let h = -32/19 - -44/19. Let y = 122/133 - h. Solve -2/7*s**3 + 2/7*s - y + 2/7*s**2 = 0.
-1, 1
Let l(n) = -n**2 - 1. Let f(o) = 2*o**2 + o + 2. Let g(p) = 2*f(p) + 3*l(p). Factor g(u).
(u + 1)**2
Factor 15/7*i - 6/7 - 12/7*i**2 + 3/7*i**3.
3*(i - 2)*(i - 1)**2/7
Let y(u) be the third derivative of u**6/30 + 2*u**5/5 + 2*u**4 + 16*u**3/3 + 6*u**2. Factor y(a).
4*(a + 2)**3
Let z(t) be the first derivative of -t**5/15 - t**