
1, 2
Let h = -3598 - -7043/2. Let p = h - -78. Factor 0 + 0*b + p*b**3 + 0*b**2.
3*b**3/2
Let p(c) be the third derivative of 3*c**8/112 + 5*c**7/14 + 31*c**6/20 + 33*c**5/10 + 31*c**4/8 + 5*c**3/2 + 227*c**2. Let p(o) = 0. What is o?
-5, -1, -1/3
Let h(y) be the first derivative of 16 + 0*y**2 + 0*y + 5/4*y**4 - 1/6*y**6 + 1/5*y**5 + y**3. Factor h(r).
-r**2*(r - 3)*(r + 1)**2
Let x(u) be the second derivative of -1/3*u**4 + 32/3*u**3 - 10*u - 128*u**2 + 0. Factor x(s).
-4*(s - 8)**2
Suppose 5*u + 5*d = 6 - 11, -d - 7 = -u. Suppose -v + u - 9/4*v**2 - 1/4*v**4 + 3/2*v**3 = 0. Calculate v.
-1, 2, 3
Suppose 4*h = -4*a - 4, a + 2*h + 31 = 7*h. Let g(w) = -w**3 - 4*w**2 + 8*w - 1. Let z be g(a). Factor -4*i**2 - 2*i**3 + z*i - 23*i.
-2*i**2*(i + 2)
Let c be (25 + -26)*(5 - 38/6). Find q such that 4*q - 5/3*q**3 + c + q**2 = 0.
-1, -2/5, 2
Let f(c) = -16*c**2 + 18*c - 2. Let s be f(1). Let 3/7*r**3 + 0*r + 3/7*r**2 + s = 0. What is r?
-1, 0
Let z be ((-4)/6)/((-4)/(-12)) - 4. Let c be (-1)/(-6) + (-11)/z. Factor -1/2 + 5/2*i**2 - c*i.
(i - 1)*(5*i + 1)/2
Suppose -5*j + 3*m + 11 = 0, 21 = 3*j - m + 4*m. Let 6*t**j - 2*t**3 - 14*t**2 - 4*t**4 + 6*t**2 + t**5 - 2*t**3 = 0. Calculate t.
-2, 0, 2
Find v, given that -2/5*v**2 + 0 - 464/5*v = 0.
-232, 0
Let o(g) be the first derivative of 2*g**3/15 - 48*g**2/5 + 1152*g/5 - 31. Find h, given that o(h) = 0.
24
Let g(d) be the third derivative of -d**7/315 + 17*d**6/90 - 289*d**5/90 + 299*d**2 + d. Suppose g(o) = 0. Calculate o.
0, 17
Let l(j) = -122*j**2 - 214*j + 6. Let z(g) = -178*g**2 - 321*g + 9. Let c(h) = 7*l(h) - 5*z(h). Let c(d) = 0. What is d?
-3, 1/36
Let w(h) be the second derivative of 2*h**4 + 46*h**3/3 - 8*h**2 + 6*h + 21. Find q, given that w(q) = 0.
-4, 1/6
Let i(f) be the first derivative of -f**7/1050 + f**5/100 + f**4/60 - 13*f**2 + 34. Let k(r) be the second derivative of i(r). Suppose k(m) = 0. Calculate m.
-1, 0, 2
Let f(p) be the second derivative of -3*p**5/20 - p**4/2 + 15*p**3/2 - 84*p. Factor f(t).
-3*t*(t - 3)*(t + 5)
Suppose 18/7*f**3 - 10/7*f**2 - 2*f**5 + 10/7*f**4 + 0 - 4/7*f = 0. Calculate f.
-1, -2/7, 0, 1
Suppose -h - 11 = -14, -h + 7 = u. Let l(q) be the first derivative of 7 - 64*q**2 - 4/5*q**5 - 64*q - 32*q**3 - 8*q**u. Let l(r) = 0. Calculate r.
-2
Let a(t) = t**4 - 22*t**3 - 57*t**2 + 14*t + 61. Let v(y) = 2*y**4 - 66*y**3 - 168*y**2 + 40*y + 184. Let g(l) = -8*a(l) + 3*v(l). Solve g(b) = 0.
-8, -2, 1
Let z = 44 - -6. Let x = -199/4 + z. Factor 0*q**2 + 0 + 0*q + x*q**3 - 1/2*q**4 + 1/4*q**5.
q**3*(q - 1)**2/4
Let x(l) = -8*l**3 - 11*l**2 - 5*l. Let q(n) = -39*n**3 - 54*n**2 - 24*n. Let h(d) = -5*q(d) + 24*x(d). Factor h(i).
3*i**2*(i + 2)
Suppose -4*d + 10 = -2*b, -3*b + 5 = 2*d + 20. Suppose -j - j = d. Factor 0*u**2 + 1/2*u**4 + 1/2*u**5 + 0*u - u**3 + j.
u**3*(u - 1)*(u + 2)/2
Let a(d) be the third derivative of -2*d**7/105 - 5*d**6/6 - 72*d**5/5 - 352*d**4/3 - 1024*d**3/3 - 2*d**2 + 26*d. Suppose a(b) = 0. Calculate b.
-8, -1
Let p(a) be the second derivative of -14/9*a**3 - 1/18*a**4 - 49/3*a**2 - 15*a + 0. Determine r, given that p(r) = 0.
-7
Let x be -5 + (-6)/(24/(-28)). Factor x*d**2 - 6*d - 10*d + d**2 - 9 + 22*d.
3*(d - 1)*(d + 3)
Let k(n) be the third derivative of -n**2 + 3/140*n**5 + 9/56*n**4 + 7/6*n**3 + 0 + 0*n + 1/840*n**6. Let p(s) be the first derivative of k(s). Factor p(b).
3*(b + 3)**2/7
Let h(b) be the first derivative of -2*b**7/21 + 4*b**5/5 + 2*b**4/3 - 2*b**3 - 4*b**2 + 8*b + 15. Let q(s) be the first derivative of h(s). Factor q(u).
-4*(u - 2)*(u - 1)*(u + 1)**3
Let n be (2/(-8))/(7/4 + -2). Let b(q) = -4*q**2 + 60*q - 120. Let o(v) = -v + 1. Let u(a) = n*b(a) + 20*o(a). Factor u(s).
-4*(s - 5)**2
Let t(i) be the third derivative of i**8/1680 - i**7/1050 - i**6/200 + i**5/60 - i**4/60 - 2*i**2 + 1. Factor t(z).
z*(z - 1)**3*(z + 2)/5
Solve -5*h**4 + 31*h**2 - 26*h**2 - 3*h - 10*h**3 + 13*h = 0 for h.
-2, -1, 0, 1
Let x(r) = -r**3 + 10*r**2 - 14*r + 5. Let m(c) = c**3 - 2*c**2 + 1. Let t(g) = 3*m(g) + x(g). Factor t(z).
2*(z - 1)**2*(z + 4)
Let r(q) = 3*q**2 + q - 2. Let j be r(-1). Suppose 6*z + 13 - 13 = j. Factor -2/3*t**3 + 0 - 4/3*t**2 + z*t.
-2*t**2*(t + 2)/3
Find y, given that 12/7 + 3/7*y**3 + 6/7*y**2 - 3*y = 0.
-4, 1
Solve i**3 + 2/7 - 3/7*i - 3/7*i**2 - 3/7*i**4 = 0.
-2/3, 1
Let j(d) be the second derivative of d**7/42 + 4*d**6/15 + 4*d**5/5 + 92*d. Solve j(g) = 0 for g.
-4, 0
Let z(w) be the third derivative of w**7/1365 + w**6/156 + 7*w**5/390 + w**4/52 - 7*w**2 + w. Let z(s) = 0. What is s?
-3, -1, 0
Let t be (18/117)/(28/91). Suppose -t*x**2 - x + 0 + 1/2*x**3 = 0. What is x?
-1, 0, 2
Suppose 4*w - 4*x = 28, 4*x = x. Let l(r) be the second derivative of 0*r**3 - w*r + 0 + 0*r**5 + 0*r**2 + 0*r**4 + 1/294*r**7 + 1/210*r**6. Factor l(b).
b**4*(b + 1)/7
Let b be (1/((-70)/(-12)))/((-35)/2800*-24). Factor 0 + 0*p**3 - 4/7*p**2 + 0*p + b*p**4.
4*p**2*(p - 1)*(p + 1)/7
Solve 1/8*s**2 - 225/4*s + 50625/8 = 0.
225
Let x(s) be the first derivative of -s - 15/2*s**2 - 209/4*s**4 - 50/3*s**6 - 48*s**5 - 83/3*s**3 - 26. Let x(j) = 0. What is j?
-1, -1/2, -1/5
Determine t so that 21/2*t**3 - 15/2*t**2 + 0 - 3/2*t**5 - 9*t + 15/2*t**4 = 0.
-1, 0, 1, 6
Let c = 659/7 + -3253/35. Let a(u) be the second derivative of -c*u**2 + 0 + 1/10*u**4 - 7/15*u**3 - 5*u. Factor a(q).
2*(q - 3)*(3*q + 2)/5
Let x be (-2 + 3)*(-8)/40*-35. Suppose -25 + 39 = x*d. Factor -2/11*r + 2/11*r**d + 0.
2*r*(r - 1)/11
Let r(y) be the third derivative of y**6/720 - y**5/72 - y**4/18 + y**3/3 + 72*y**2 + 1. Factor r(c).
(c - 6)*(c - 1)*(c + 2)/6
Find u, given that -8*u - 72/5 - 2/5*u**2 = 0.
-18, -2
Let x(j) = -j. Let o be -65*(-14)/175 - 1/5. Let k(z) = -z**2 + 25*z - 225. Let i(a) = o*x(a) - k(a). Factor i(t).
(t - 15)**2
Let j be (1/1)/2*2. Let z = 1 + j. Factor -9*f - z + 16 + 4 - 3*f + 2*f**2.
2*(f - 3)**2
Suppose -5*p - 450 = 480. Let u = p - -1304/7. Let 0 + 2/7*m**2 + 2/7*m**5 - u*m**4 + 0*m - 2/7*m**3 = 0. Calculate m.
-1, 0, 1
Let y(c) be the first derivative of -4/9*c**3 + 27 - 5/9*c**2 + 0*c - 1/18*c**4. Find p, given that y(p) = 0.
-5, -1, 0
Let u be ((-6)/(1 + 5))/((-2)/4). Let s(f) be the first derivative of 1/6*f**3 - 1/16*f**4 + 0*f + 0*f**2 + u. Factor s(k).
-k**2*(k - 2)/4
Let o be (-13)/((-455)/(-10))*14/(-8). Factor 1/3 - o*v + 1/6*v**2.
(v - 2)*(v - 1)/6
Let t(q) be the first derivative of -3 - 3/16*q**4 + 0*q + 0*q**2 + 1/40*q**5 + 5/3*q**3 + 1/240*q**6. Let i(u) be the third derivative of t(u). Factor i(l).
3*(l - 1)*(l + 3)/2
Let r(a) be the second derivative of -a**4/126 - 8*a**3/21 - 23*a**2/21 - 3*a - 15. Solve r(f) = 0.
-23, -1
Let g(d) = -6*d**4 - 158*d**3 - 3198*d**2 - 3038*d + 4. Let y(n) = 2*n**4 - 2*n - 2. Let k(z) = g(z) + 2*y(z). Factor k(p).
-2*p*(p + 1)*(p + 39)**2
Let l(o) be the second derivative of o**4/12 + o**3 - 7*o**2/2 + o + 19. Factor l(d).
(d - 1)*(d + 7)
Let y(x) be the third derivative of x**5/12 - 115*x**4/24 + 55*x**3/3 + 28*x**2 + 6. Factor y(w).
5*(w - 22)*(w - 1)
Suppose 0 = 4*i - 8*i + 12*i. Solve i - 1/10*t**4 + 1/10*t**3 + 0*t + 0*t**2 = 0 for t.
0, 1
Let r = 12 + -1. Suppose 5 = -3*h + r. Solve 2/7*x**3 + 0*x + 0 - 2/7*x**h = 0.
0, 1
Let n(j) be the first derivative of -j**5/5 - 3*j**4/4 + 2*j**3/3 + 6*j**2 + 8*j - 18. Determine p, given that n(p) = 0.
-2, -1, 2
Suppose 11*t + 9 = 14*t. Let q(k) be the first derivative of 0*k + 0*k**2 - 1/15*k**t - 2. Determine u, given that q(u) = 0.
0
Let t(c) be the first derivative of -c**7/168 - c**6/24 - c**5/8 - 5*c**4/24 + 26*c**3/3 + 3. Let m(d) be the third derivative of t(d). Factor m(v).
-5*(v + 1)**3
Let w(o) be the second derivative of 1/220*o**5 - 17*o + 5/22*o**3 + 3/44*o**4 + 7/22*o**2 + 0. Factor w(g).
(g + 1)**2*(g + 7)/11
Let q(i) be the first derivative of i**3 + 39*i**2 + 75*i + 47. What is w in q(w) = 0?
-25, -1
Let f be 6/((-1)/3 - 100/(-30)). Let v(k) be the first derivative of 2/3*k**3 + 2*k**f + 2*k + 4. Factor v(j).
2*(j + 1)**2
Suppose -1 = 2*n - 4*w - 13, 0 = 3*n - 2*w - 26. Let m(z) = 4*z**2 + 24*z + 40. Let d(b) = -b**2 - 8*b - 13. Let x(j) = n*d(j) + 3*m(j). Factor x(h).
2*(h - 5)*(h + 1)
Let h(c) be the third derivative of c**7/105 + 47*c**6/30 + 496*c**5/5 + 16337*c**4/6 + 29791*c**3/3 - 2*c**2 + 167. What is b in h(b) = 0?
-31, -1
Fac