2 - 2/13*h**w + 0 - 2/13*h.
-2*h*(h + 1)**2/13
Let j(u) = -u**2 - 12*u - 14. Let m be j(-7). Let v be (-2)/(-21)*(m + (-12)/4). Factor -v*n + 3/7*n**2 + 12/7.
3*(n - 2)**2/7
Let v = -2498/3 - -834. Factor 0 + 4/3*k - 2/3*k**4 - v*k**3 + 2/3*k**2.
-2*k*(k - 1)*(k + 1)*(k + 2)/3
Suppose -6*i + 15*i - 36 = 0. Suppose -6*t - i = -16. Suppose -4/9 - 2/9*v**3 + 4/9*v**t + 2/9*v = 0. What is v?
-1, 1, 2
Let a = -1072/3 + 11816/33. Solve 6/11*k - 2/11 + a*k**2 = 0.
-1, 1/4
Suppose -4*d = 4*l, 3 = -4*l - 5*d - 1. Suppose -g + l = -5. Let u**2 + 18*u**3 + u**2 - 8*u - 4 + 3*u**2 + g*u**4 = 0. Calculate u.
-1, -2/3, 2/3
Suppose -317*r = -285*r - 128. Factor 288/5*x + 72*x**3 - 15*x**r - 552/5*x**2 - 48/5.
-3*(x - 2)**2*(5*x - 2)**2/5
Let d(m) be the third derivative of m**6/120 - m**5/20 - 5*m**4/12 + 2*m**2 + 45*m. Solve d(o) = 0 for o.
-2, 0, 5
Let x(j) be the second derivative of -j**4/48 + j**3/8 - 86*j + 1. Find f such that x(f) = 0.
0, 3
Let n(u) be the first derivative of 64*u + 16 + 1/3*u**3 + 8*u**2. Factor n(v).
(v + 8)**2
Let v(m) be the second derivative of -m**4/8 + 36*m**3 - 3888*m**2 - 195*m. Factor v(b).
-3*(b - 72)**2/2
Suppose -2*h - 28*h + 180 = 0. Let k(s) be the second derivative of -1/24*s**3 + 0 - 3/80*s**5 - 4*s + 0*s**2 - 1/120*s**h - 1/16*s**4. Factor k(z).
-z*(z + 1)**3/4
Suppose -231*x + 36 - 39/2*x**2 = 0. What is x?
-12, 2/13
Suppose 5 = 5*c + 5*n - 5, -4*c + 2*n = 4. Let s(u) be the second derivative of 0*u**2 + 1/3*u**4 + 9*u + 4/3*u**3 + c. Let s(x) = 0. What is x?
-2, 0
Let l(b) = 5*b**2 + 11*b - 3. Let q(v) = -6*v**2 - 12*v + 3. Let t(j) = -5*l(j) - 4*q(j). Let u be t(-7). Factor 0*c - 2*c**2 + 0*c + 5*c**3 - u*c**3.
2*c**2*(c - 1)
Let z(a) be the first derivative of a**5 - 55*a**4/2 + 235*a**3 - 550*a**2 + 500*a + 145. Factor z(d).
5*(d - 10)**2*(d - 1)**2
Suppose -796 = -5*f + 9. Let n be (-2)/7 + f/49. Let 10*r - 12*r**3 - 4*r + 3*r**5 - 3*r**4 + 3*r**5 + 6*r**2 - n = 0. What is r?
-1, 1/2, 1
Let c(q) be the third derivative of q**6/80 + q**5/20 - 13*q**4/16 + 5*q**3/2 + 33*q**2. Factor c(d).
3*(d - 2)*(d - 1)*(d + 5)/2
Let s(j) be the third derivative of 0 + 0*j**3 - 13*j**2 + 1/660*j**6 - 1/330*j**5 + 0*j**4 + 0*j. Let s(y) = 0. What is y?
0, 1
Let x(i) = 2*i - 15. Let h be x(11). Suppose -5*b = -8 - h. Solve 1 + 13*w**4 - b*w**2 + 6 + 6*w**3 + 6*w**5 - 7 - 2*w = 0.
-1, -2/3, 0, 1/2
Let c(x) = 18*x**3 + 10*x**2 - 22*x + 12. Let j(a) = -a**3 + a**2 + a - 2. Let q(w) = c(w) + 6*j(w). Determine k so that q(k) = 0.
-2, 0, 2/3
Suppose 261/8*f + 15/4*f**3 + 24*f**2 - 3/2*f**4 - 3/8*f**5 + 27/2 = 0. Calculate f.
-3, -1, 4
Let b(k) be the second derivative of -k**6/120 - k**5/16 + 64*k. Factor b(s).
-s**3*(s + 5)/4
Let k be (-1)/4 + 198/24 + -4. Factor -4/21*c + 0*c**3 - 2/21*c**k + 2/7*c**2 + 0.
-2*c*(c - 1)**2*(c + 2)/21
Let u be 13 - 18/12*8/(-6). Suppose -16*g + u*g = -3. Suppose 10/3*c**2 + 2*c**g - 2/3 + 2/3*c = 0. Calculate c.
-1, 1/3
Factor -1/4*p**4 + 9/4 - 3/2*p + 3/2*p**3 - 2*p**2.
-(p - 3)**2*(p - 1)*(p + 1)/4
Factor -2/9*j**2 + 2/9*j + 40/9.
-2*(j - 5)*(j + 4)/9
Let f be 178/14 - ((-24)/21)/4. Let b = -11 + f. Factor -3*i + 3/2*i**b + 0.
3*i*(i - 2)/2
Let s be ((-2)/(-3))/(10/30). Suppose -2*g - 3*a = -2*a - 2, 0 = 3*g + 4*a + s. Solve -2*t**3 - t + 3*t + 0*t**2 + 4*t**2 - 2 - 2*t**g = 0.
-1, 1
Solve 8/5*r**2 + 0 - 12/5*r**3 + 8/5*r**4 - 2/5*r - 2/5*r**5 = 0.
0, 1
Let z be (-6)/(-5 - -2)*2. Suppose -2*v = -z*v. Factor 0*l**2 + 3*l + v*l**2 + 3*l**2.
3*l*(l + 1)
Let g = -13876 + 13880. Factor -16/7 + 16/7*t - 16/7*t**3 + 4/7*t**g + 12/7*t**2.
4*(t - 2)**2*(t - 1)*(t + 1)/7
Factor -144*b - 308*b**2 + 144*b**3 + 28 - 74 + 324*b**4 + 30.
4*(b - 1)*(b + 1)*(9*b + 2)**2
Let y be ((-4)/(-10))/((-8)/(-20)) + 3. Let m(a) be the first derivative of -y*a + 0*a**2 + 1/3*a**3 + 1. Solve m(k) = 0.
-2, 2
Let y(w) be the second derivative of 7/27*w**3 + 15*w + 1/9*w**2 + 5/18*w**4 + 4/135*w**6 + 0 + 13/90*w**5. Suppose y(g) = 0. What is g?
-1, -1/4
Suppose -33*d + 31*d + 20 = -4*s, 4*d + 4*s = -8. Let q(b) be the first derivative of 0*b + 1/2*b**4 + 2/3*b**3 - 8 - d*b**2. Determine i, given that q(i) = 0.
-2, 0, 1
Factor 5*j**4 + 296 + 725*j**2 + 266 - 1060*j - 115*j**3 - 192 - 155*j**2 + 310.
5*(j - 17)*(j - 2)**3
Factor 29*g**2 + 18*g**2 - 18 - 49*g**2 - 12*g.
-2*(g + 3)**2
Let j(o) = 104*o**3 + 156*o**2 - 528*o - 160. Let z(m) = 21*m**3 + 31*m**2 - 105*m - 32. Let c(a) = 5*j(a) - 24*z(a). Factor c(p).
4*(p - 2)*(p + 4)*(4*p + 1)
Let b(a) = -a**2 - 22*a - 15. Let u(f) = 20*f + 16. Let g(p) = 4*b(p) + 6*u(p). Factor g(s).
-4*(s - 9)*(s + 1)
Let y(r) be the second derivative of -2*r + 1/15*r**4 + 0 + 0*r**2 + 1/15*r**3 + 1/50*r**5. Factor y(u).
2*u*(u + 1)**2/5
Let s(l) = -3*l + 4. Let c be s(2). Let i be c + 112/60 + (-88)/(-210). Factor i*w**2 - 16/7*w + 32/7.
2*(w - 4)**2/7
Let w(f) be the second derivative of -5*f**8/336 + f**7/14 - f**6/12 + 20*f**2 + 48*f. Let o(h) be the first derivative of w(h). Let o(p) = 0. Calculate p.
0, 1, 2
Let y be 0/(1 - -3)*(-4)/12. Suppose 1/7*h**3 + y - 1/7*h**4 - 1/7*h + 1/7*h**2 = 0. What is h?
-1, 0, 1
Let b = 739/80 + -135/16. Factor -b*l + 2/5*l**2 - 6/5.
2*(l - 3)*(l + 1)/5
Let k(n) be the first derivative of 2*n**3 - 8/5*n**2 + 4/5*n**4 + 2/5*n - 32/25*n**5 + 14. Determine z so that k(z) = 0.
-1, 1/4, 1
Let x(f) be the third derivative of -1/32*f**4 + 0 - 3/80*f**6 + 0*f - 1/16*f**5 + 0*f**3 + 9*f**2. Find q such that x(q) = 0.
-1/2, -1/3, 0
Let r be 80 - (-16 - 496/(-32)). Determine f, given that -343/2*f**5 - 67*f**2 + 196*f**4 - 34*f + r*f**3 - 4 = 0.
-2/7, 1
Let t(z) = 27*z**2 + 69*z. Let d(s) = 5*s**2 + 14*s. Let j(u) = -33*d(u) + 6*t(u). Solve j(q) = 0 for q.
-16, 0
Let i(j) be the second derivative of j**4/54 + 26*j**3/27 - 3*j**2 + 71*j - 1. Factor i(n).
2*(n - 1)*(n + 27)/9
Suppose -2*b = 23 - 31. Suppose 6*n + b = 22. Factor 3/7*s**n + 0 + 0*s + 3/7*s**2.
3*s**2*(s + 1)/7
Let u be 4/(-1 - (-2 + -2 + 1)). Let c(r) = -21*r + 42. Let k be c(u). Determine i so that 4/7*i**3 + 8/7*i**4 - 16/7*i - 32/7*i**2 + k = 0.
-2, -1/2, 0, 2
Let f(q) be the second derivative of 6*q**2 - 17*q - 6/5*q**5 - 20/3*q**3 + 2/15*q**6 + 0 + 4*q**4. Factor f(k).
4*(k - 3)*(k - 1)**3
Let y(a) = a**3 + a**2. Let o(r) = 4*r**3 + 4*r**2 + 8*r + 12. Suppose -5 = -s + 2*s. Let f(w) = s*y(w) + o(w). Factor f(t).
-(t - 3)*(t + 2)**2
Factor -62/15*y + 4/15 - 32/15*y**2.
-2*(y + 2)*(16*y - 1)/15
Suppose 4*l + 20 = -2*n, 4*l + 17 = 3*n - 3. Let v(i) = -i**2 + 3. Let j be v(n). What is w in -j*w**2 + 2*w**3 + w**2 + 0*w**3 + 2*w**4 - 2*w = 0?
-1, 0, 1
Let b be 2 - (0 + -4 + 3). Suppose -2*o = -z - 6, o + z - 3 = -z. Let 4 - 5*f**2 + f**4 - 3*f**4 - 6*f + 6*f**b + o*f**2 = 0. What is f?
-1, 1, 2
Find q, given that -440*q + 5/3*q**4 - 40*q**3 + 830/3*q**2 + 605/3 = 0.
1, 11
Let j(h) be the third derivative of h**7/840 + h**6/96 + h**5/40 + 12*h**2 + 4*h. Suppose j(c) = 0. What is c?
-3, -2, 0
Suppose -3*x = -2*k - 1, -5*x = -0*k - 3*k - 3. Factor -7*n + 3*n + 4*n + 5*n**x.
5*n**3
Let l = -99 - -104. Factor 2*m - l*m**3 - 7*m**2 + 14*m**2 - 5*m + m**4.
m*(m - 3)*(m - 1)**2
Let t be -5 + 10 - (3 + -3)/1. Let w(m) be the third derivative of 1/60*m**t - 4*m**2 + 1/12*m**3 - 1/16*m**4 + 0*m + 0. Determine b, given that w(b) = 0.
1/2, 1
Let j be 0/(-1) + 4 - (16 + -17). Suppose 4*m - 1 - 1 = -2*l, -m + j = -l. Factor -1/2*i + 0 - 1/2*i**m.
-i*(i + 1)/2
Let 5*t**3 - 5*t + 2*t - 29*t**2 + 61*t**2 - 28*t**2 - 2*t**4 = 0. Calculate t.
-1, 0, 1/2, 3
Let g(f) = f**3 + 2*f**2 + 12*f + 24. Let t be g(-2). Factor 0*u + 4/3*u**3 + 4/3*u**2 + t.
4*u**2*(u + 1)/3
Suppose -5*z + 29 = 2*x - 4, 5*x = 5*z - 5. Let c be (280/225)/7 + x/18. What is h in -4/5*h**4 + 0*h - c*h**5 + 0*h**2 + 0 - 2/5*h**3 = 0?
-1, 0
Let c(u) be the first derivative of -1/24*u**3 - 6*u + 1/4*u**2 + 5 - 1/16*u**4. Let l(j) be the first derivative of c(j). Suppose l(d) = 0. Calculate d.
-1, 2/3
Suppose -n - 210 = -3*i, -3*i + 0*n + 4*n + 219 = 0. Let t = -21 + i. Factor -4*c**4 + 36*c**4 - t*c**3 + 3*c - 5*c + 18*c**2.
2*c*(c - 1)*(4*c - 1)**2
What is x in -34 + 2*x**2 - 8*x + 17 - 7 = 0?
-2, 6
Let v = -446 + 449. Let m(n) be the second derivative of -v*n + 0 - 1/5*n**2 + 1/30*n**4 + 0*n**3. Factor m(i).
2*(i - 1)*(i + 1)/5
Let a(b) be the third derivative