7)**2/11
Suppose 3*d - 10*g = -11*g + 7, -2*d - 2 = 2*g. Let c(u) be the first derivative of -2/27*u**3 + 0*u - 1/15*u**5 + 0*u**2 + 8 - 5/36*u**d. Factor c(p).
-p**2*(p + 1)*(3*p + 2)/9
Suppose -v + 5*y = 18, -3*y = -0*v + 5*v - 22. Factor -20/7*z - 12/7 - 8/7*z**v.
-4*(z + 1)*(2*z + 3)/7
Determine t, given that -64/3*t**2 + 4 - 4*t**3 + 26/3*t - 14/3*t**5 + 52/3*t**4 = 0.
-1, -2/7, 1, 3
Suppose 0 = -13*f + 43 + 48. Let 12*d - 15*d + f*d + 2*d**2 = 0. Calculate d.
-2, 0
Suppose -5*y = -4 - 11. What is x in 2*x**2 + y*x**2 - 2*x**2 + 3*x = 0?
-1, 0
Suppose 3*k + 4*s - 8 = 16, 5*s - 21 = -3*k. Let g be 22/k - 1/(-6). Suppose 3*u**5 - 3*u**2 + 0*u**g - 3*u**2 + 6*u**4 - 3*u**3 = 0. Calculate u.
-2, -1, 0, 1
Suppose -3*l = 4*m + l, 0 = -4*m + 2*l + 6. Solve -w**2 + m - 4*w - 4*w + 1 - 18 = 0.
-4
Let j(p) = 3*p**2 + p. Let w(r) = 14*r**2 + 93*r + 160. Let z(k) = 3*j(k) - w(k). Factor z(x).
-5*(x + 2)*(x + 16)
Suppose -54*m + 312 = 24*m. Let l(j) be the second derivative of 0 + 11*j - 1/3*j**m + 0*j**3 + 2*j**2. Factor l(u).
-4*(u - 1)*(u + 1)
Suppose 10*p + 15 + 15 = 0. Let s be p/12 - 6*(-12)/32. Solve -4/11*w - 2/11*w**s - 2/11 = 0.
-1
Suppose 12 = 14*k - 19*k + 4*a, 4*a = -3*k + 12. Let 1/4*j**2 - 1/4 + k*j = 0. Calculate j.
-1, 1
Suppose -4*l + 3*l - 16 = 0. Let v be (4/(-3))/(l/36). Suppose m**5 - 2*m**v - 2*m**4 + 5*m**3 - 2*m**3 = 0. What is m?
0, 1
Let s(v) be the second derivative of -v**7/14 + 13*v**6/5 - 189*v**5/5 + 539*v**4/2 - 1715*v**3/2 - 3*v + 8. Factor s(d).
-3*d*(d - 7)**3*(d - 5)
Let b(q) be the first derivative of q**4/20 + 16*q**3/15 + 9*q**2/2 - 162*q/5 + 1037. Factor b(j).
(j - 2)*(j + 9)**2/5
Factor -31*h - 10*h + 48 + 4*h**3 + 38*h - 4*h**2 - 29*h.
4*(h - 2)**2*(h + 3)
Let v(b) be the first derivative of 1/16*b**4 + 0*b**3 + 1/24*b**6 + 32 + 0*b**2 + 1/10*b**5 + 0*b. Solve v(n) = 0.
-1, 0
Let p = -239 - -19121/80. Let z(d) be the third derivative of 0 - 3*d**2 - 1/480*d**6 + p*d**5 - 1/32*d**4 + 1/24*d**3 + 0*d. Determine y so that z(y) = 0.
1
Let a(f) = 3*f + 29. Let q be a(-5). Let j = 18 - q. Find m, given that 6/7*m**j + 0*m + 0 - 6/7*m**3 + 2/7*m**2 - 2/7*m**5 = 0.
0, 1
Let b(x) = -54*x**2 + 130*x**2 + 3*x**3 - 64*x**2. Let n(l) = -l**3 - l**3 + 13*l**2 + 6*l**3. Let k(q) = -7*b(q) + 6*n(q). Factor k(z).
3*z**2*(z - 2)
Let -99/4*w - 3/4*w**4 + 33/4*w**2 + 15/4*w**3 + 27/2 = 0. Calculate w.
-3, 1, 6
Let l(v) be the second derivative of -v**4/30 + 50*v**3/3 - 3125*v**2 - 326*v. Let l(j) = 0. What is j?
125
Let p be (120/(-90))/(16/(-36)). Let y(o) be the second derivative of 1/2*o**p + 3/4*o**2 - 3*o + 1/8*o**4 + 0. Suppose y(i) = 0. What is i?
-1
Let d(r) be the third derivative of r**8/181440 - r**7/11340 + r**6/1620 - r**5/30 - r**2. Let q(o) be the third derivative of d(o). Solve q(x) = 0.
2
Let q(s) = -24*s**2 + 166*s - 646. Let l(h) = 5*h**2 - 33*h + 132. Let j(x) = 14*l(x) + 3*q(x). Factor j(k).
-2*(k - 15)*(k - 3)
Let f(l) be the first derivative of -6*l**2 + 343/40*l**6 + 4 - 3*l - 147/10*l**5 - 20*l**3 - 63/2*l**4. Let b(z) be the first derivative of f(z). Factor b(y).
3*(y - 2)*(7*y + 2)**3/4
Let x be 171/(-1 + 20/8). Suppose -75 = -3*w + x. Determine n, given that w + 4*n**2 - 5*n - 3*n - 59 = 0.
1
Let q(p) be the first derivative of -p**3/2 + 12*p**2 - 59. Suppose q(z) = 0. What is z?
0, 16
Let m be (-1 - (-3 - -3))*0. Let k(l) be the second derivative of 1/40*l**5 + 9*l + 1/12*l**4 + 1/12*l**3 + m*l**2 + 0. Factor k(r).
r*(r + 1)**2/2
Factor -1/4*s**4 + 19/4*s**2 + 15 - 1/2*s**3 + 17*s.
-(s - 5)*(s + 2)**2*(s + 3)/4
Let m(j) be the third derivative of -169*j**7/1155 + 26*j**6/33 - 4*j**5/15 - 40*j**4/11 - 48*j**3/11 + 17*j**2. Factor m(t).
-2*(t - 2)**2*(13*t + 6)**2/11
Let c(a) be the first derivative of -2/3*a - a**2 + 8/9*a**3 + 22. What is n in c(n) = 0?
-1/4, 1
Let l be (-28)/8*(-1)/7*20. Let j be -4 - ((-84)/l - -4). Let -2/5*u**2 + j*u**4 + 0 + 0*u + 0*u**3 = 0. What is u?
-1, 0, 1
Let q(i) be the third derivative of -2/105*i**7 + 2/3*i**5 + 0*i + 7/60*i**6 + 0 + i**4 - 1/168*i**8 + 32*i**2 + 0*i**3. Solve q(h) = 0 for h.
-2, -1, 0, 3
Suppose 3*o + 28 = 10*o. Suppose -2*l = -w + 4, 0 = -2*w + 5*l + o + 4. Find h such that -w - 2*h**4 - 2*h**3 + h - 2 + 4*h**2 + h**5 + 4 = 0.
-1, 1, 2
Let j(b) = b**4 - 5*b**3 - 3*b**2 - 3*b + 3. Let r be 0 + -1 + 3 - 3. Let k(a) = a**3 + a**2 + a - 1. Let t(n) = r*j(n) - 3*k(n). Suppose t(v) = 0. What is v?
0, 2
Let c(q) be the first derivative of -245*q**6/51 - 896*q**5/85 + 60*q**4/17 + 128*q**3/51 - 16*q**2/17 - 212. Find z, given that c(z) = 0.
-2, -2/5, 0, 2/7
Factor -3/5*z**3 + 0 + 0*z - 99/5*z**2.
-3*z**2*(z + 33)/5
Let v be (-8 - (-28 - -6)) + -9 + 0 + -5. Find u, given that 8/3*u**3 + v - 8/3*u - 4/3*u**2 + 4/3*u**4 = 0.
-2, -1, 0, 1
Suppose -8*h + 1 - 25 = 0. Let p be 6 + (h - 2) - -3. Factor -2/5*f**p - 4/5*f**2 + 1/5*f + f**3 + 0.
-f*(f - 1)**2*(2*f - 1)/5
Let f be (40/(-560))/((-60)/(-602)*1). Let i = -1/20 - f. Suppose i + q**2 + 5/3*q = 0. Calculate q.
-1, -2/3
Let n = -18427 + 18430. Determine y so that 0*y**2 - 1/4*y**5 + 1/2*y**4 + 0*y + 0 + 0*y**n = 0.
0, 2
Let b(s) = -123*s**3 + 99*s**2 + 288*s + 48. Let x(f) = 31*f**3 - 25*f**2 - 72*f - 12. Let w(o) = 2*b(o) + 9*x(o). Determine k, given that w(k) = 0.
-1, -2/11, 2
Let q(s) = -s**3 + 4*s**2 + 2*s - 12. Let x be q(4). Let k(v) = 15*v**2 - 20*v - 11. Let c(h) = 16*h**2 - 20*h - 12. Let p(o) = x*k(o) + 3*c(o). Factor p(n).
-4*(n - 2)*(3*n + 1)
Factor 2/3*w**2 - 8/3*w + 0.
2*w*(w - 4)/3
Let j be (2 + 7)*1/3. Let t(g) = -4*g**3 + 24*g**2 + 4*g + 4. Let k(u) = -u**3 + 5*u**2 + u + 1. Let l(x) = j*t(x) - 14*k(x). Factor l(b).
2*(b - 1)*(b + 1)**2
Let g = -27 + 30. Factor 0*m**3 - g*m**3 - 4*m - 2*m + 9*m**2.
-3*m*(m - 2)*(m - 1)
Factor 5/2*d - 1/3*d**3 + 2/3 - 3/4*d**2.
-(d - 2)*(d + 4)*(4*d + 1)/12
Find h such that -15 - 13*h + 0*h**2 + 8*h - 3*h**2 - 13*h = 0.
-5, -1
Determine p, given that -14/5*p**2 + 48/5*p - 2/5*p**5 - 46/5*p**3 + 32/5 - 18/5*p**4 = 0.
-4, -1, 1
Suppose -4*s + 12 = 4*w, -12*s = -11*s. Let x(p) be the first derivative of -5 + 0*p**2 + 0*p + 0*p**4 + 1/5*p**5 - 1/3*p**w. Suppose x(m) = 0. What is m?
-1, 0, 1
Factor 5*i**2 - 22*i**2 + 8*i**2 - 75*i + 6*i**2.
-3*i*(i + 25)
Let a(p) be the third derivative of 1/100*p**5 + 0*p + 0*p**3 - 17*p**2 + 0 - 1/40*p**4. Let a(o) = 0. What is o?
0, 1
Suppose 0 = 3*q + 3, 2*x + q + 0*q - 5 = 0. Suppose 0 = x*g - g - 6. What is y in 0*y - 18*y**g - 2*y + 20*y**3 - 4 + 4*y**2 = 0?
-2, -1, 1
Factor 40*z - 13*z**2 - 11*z - 6 - 11*z**2 - 9*z**2.
-(3*z - 1)*(11*z - 6)
Suppose -65 = -3*w - 2*d, 0*w + 3*w - 4*d = 59. Let c be 5 + (-7)/w - 8/2. Suppose -1/3*h**3 + 0 + 1/2*h**5 - c*h**4 + 2/3*h**2 - 1/6*h = 0. Calculate h.
-1, 0, 1/3, 1
Suppose 0 = -4*r + 2*q + 16, 2*r - 2*q - 4 = 2. Suppose -5*k + 10 = 4*j - 3*k, -12 = -r*j - 2*k. Factor 2/5*y**4 + 18/5*y**2 + 4/5 - 14/5*y - j*y**3.
2*(y - 2)*(y - 1)**3/5
Let x(t) be the third derivative of -t**5/140 - 3*t**4/28 - t**2 + 13*t. Solve x(h) = 0 for h.
-6, 0
Let a(m) be the second derivative of m**6/6 + m**5 + 5*m**4/3 + 8*m + 5. Factor a(j).
5*j**2*(j + 2)**2
Let n(q) be the second derivative of -q**7/315 - 2*q**6/75 - q**5/30 + 123*q. Determine c, given that n(c) = 0.
-5, -1, 0
Let r be -16*(-4)/((-8)/5). Let p be (4 - (-148)/r)/((-1)/(-5)). Factor 6*z - p*z**2 - 9/2.
-3*(z - 3)*(z - 1)/2
Let h(j) be the third derivative of -j**6/24 - 5*j**5/4 - 15*j**4 - 280*j**3/3 - 277*j**2. Find a, given that h(a) = 0.
-7, -4
Let t(h) be the second derivative of h**7/126 + 7*h**6/270 - 4*h**5/15 - 29*h**4/27 + 32*h**2/9 - 13*h + 36. Find s, given that t(s) = 0.
-4, -2, -1, 2/3, 4
Let q(w) be the first derivative of w**5/60 - 5*w**4/24 - 31*w**2/2 - 13. Let l(a) be the second derivative of q(a). What is n in l(n) = 0?
0, 5
Factor -15/4*r - 9/4 - 1/4*r**3 - 7/4*r**2.
-(r + 1)*(r + 3)**2/4
Let h(v) be the first derivative of -1/5*v**5 + 0*v**2 - 1/6*v**6 + 1/3*v**3 + 1/4*v**4 + 0*v + 3. Factor h(a).
-a**2*(a - 1)*(a + 1)**2
Let j be 5 + (-12)/4 + -1. Suppose -3*y = f - 12, 22 = 3*y + 4*f + j. Factor 2/7*u**y + 0 - 4/7*u - 2/7*u**2.
2*u*(u - 2)*(u + 1)/7
Suppose 3*m + 9 = 5*t, -3*t - 2 = -2*m - 8. Factor -2/3*s + t + 2/3*s**2.
2*s*(s - 1)/3
Let s = -502 + 505. Determine p so that 4/3*p + 0 + 8/3*p**2 + 1/3*p**4 + 5/3*p