q - 12*b**4 = 0. What is b?
-1, 1
Let v(y) be the first derivative of -y**4/40 - y**3/5 - 3*y**2/20 + y - 76. Factor v(a).
-(a - 1)*(a + 2)*(a + 5)/10
Let -25*k**3 + 6*k**3 + 21*k**3 + 6*k**3 - 105*k**2 + 12*k**3 + 25*k = 0. What is k?
0, 1/4, 5
Let q = -444/13 - -2677/78. Let h(w) be the second derivative of 0*w**4 + 1/120*w**6 - 14*w - q*w**3 + 3/80*w**5 + 0 + 0*w**2. Factor h(f).
f*(f - 1)*(f + 2)**2/4
Let o = 57 + -111/2. Suppose 2*p = 5*m + 24, -4*p + 34*m - 36*m = 0. What is q in 1/2 + 1/2*q**3 + o*q**p + 3/2*q = 0?
-1
What is h in -20/21*h**2 + 8/21*h**4 + 16/21 + 2/21*h**5 - 8/21*h + 2/21*h**3 = 0?
-2, 1
Suppose -1786 = -13*i - 1786. Factor i - 2/5*y**3 + 0*y + 4/5*y**2.
-2*y**2*(y - 2)/5
Let w(h) = h**2 + 3*h - 5. Let l be w(-5). Suppose 0*m + 30 = l*m. Factor -n**5 + n**3 + 3*n**3 - n**5 + m*n - 8*n.
-2*n*(n - 1)**2*(n + 1)**2
Solve 2 - 50*r**2 + 3 - 55*r**4 - 160*r**3 - 100*r**2 - 43*r + 3*r = 0.
-1, 1/11
Let u be 4*(-4)/(-24)*69. Let a = -43 + u. Find l, given that -1/2*l**4 + 1/2*l**a - 1/2*l + 1/2*l**2 + 0 = 0.
-1, 0, 1
Let o(l) be the third derivative of l**7/315 + l**6/36 + l**5/45 - 2*l**4/9 + 13*l**2 - 2. Determine k so that o(k) = 0.
-4, -2, 0, 1
What is y in 5*y**5 + 5*y - 10*y**3 + 18570*y**2 - 18570*y**2 = 0?
-1, 0, 1
Let v(i) be the first derivative of -2*i**6/405 + i**5/54 - i**4/54 - i**3/3 - i**2 - 20. Let p(r) be the third derivative of v(r). Factor p(n).
-4*(n - 1)*(4*n - 1)/9
Let -211/3*q**3 + 9870*q**2 - 934407/2 - 457263*q + 1/6*q**4 = 0. Calculate q.
-1, 141
Suppose 0 = -2*l + w + 8 + 5, -l + 4*w = -17. Solve 10 - m**3 - 25*m + m**3 - l*m**4 + 3*m**2 + 12*m**2 + 5*m**3 = 0 for m.
-2, 1
Let q(p) be the second derivative of p**4/66 - 19*p**3/33 - 20*p**2/11 + 157*p. Determine n so that q(n) = 0.
-1, 20
Let m(x) be the first derivative of -17 - 4/9*x + 1/9*x**2 + 2/27*x**3. Factor m(w).
2*(w - 1)*(w + 2)/9
Let k(w) be the first derivative of -3*w**4/8 - 2*w**3/3 - w**2/4 + 355. Factor k(s).
-s*(s + 1)*(3*s + 1)/2
Determine y so that -1/3*y**3 - 8/3*y**2 + 50/3 - 5/3*y = 0.
-5, 2
Let s(v) = 10*v**4 + 20*v**3 + 20*v**2 + 10*v + 5. Let j = 45 + -40. Let p(w) = 11*w**4 + 21*w**3 + 21*w**2 + 11*w + 6. Let r(q) = j*p(q) - 6*s(q). Factor r(n).
-5*n*(n + 1)**3
Let a(v) be the second derivative of -v**4/30 + 4*v**3 - 180*v**2 - 17*v + 11. Find s such that a(s) = 0.
30
Let a be 3/(63/28)*3. Let n(o) be the first derivative of -1/22*o**a + 0*o - 2/33*o**3 - 10 + 2/11*o**2. Solve n(m) = 0.
-2, 0, 1
Let l(q) be the third derivative of 0 + 0*q + 1/840*q**6 + 0*q**4 - 9*q**2 + 1/420*q**5 + 0*q**3. Factor l(s).
s**2*(s + 1)/7
Suppose -4*q**5 + 20*q**4 - 12*q**3 - 20*q**2 + 697*q - q**3 - 681*q + q**3 = 0. What is q?
-1, 0, 1, 4
Let a(h) be the first derivative of -h**5/10 + 7*h**4/4 - 11*h**3/2 - 28*h**2 - 32*h + 245. Solve a(q) = 0 for q.
-1, 8
Let r(z) be the first derivative of z**6/2 + 48*z**5/5 + 207*z**4/4 + 90*z**3 + 492. Determine w so that r(w) = 0.
-10, -3, 0
Let a(s) be the first derivative of 5*s**3/3 - 95*s**2 + 1805*s - 204. Suppose a(m) = 0. What is m?
19
Suppose n + 6 = 4*n. Suppose n*v = 3*l + 14, -2*v - 2 = -0*v + 5*l. Factor 0*h**2 - 4*h**4 - 3*h**2 + 2*h**4 + h**2 - v*h**3.
-2*h**2*(h + 1)**2
Let f(m) be the first derivative of 0*m**2 + 1/12*m**4 - 4 + 0*m - 1/9*m**3. Factor f(q).
q**2*(q - 1)/3
Let c = 110 + -120. Let j be c/15 + 2/3. Solve 1/4*t**3 + 9/4*t - 3/2*t**2 + j = 0.
0, 3
Let c(k) be the second derivative of -2*k**3 + 4*k**2 + 0 + 1/3*k**4 - 7*k. Factor c(p).
4*(p - 2)*(p - 1)
Let t(y) = -y + 10. Suppose x = 5*c - 31, -3*c = -0*x + 2*x - 29. Let i be t(c). Determine b, given that 0 + 6*b**3 - 2*b**3 - 6 - 9*b - b**i = 0.
-1, 2
Solve 5/4*u**4 - 350*u - 45/2*u**3 - 165*u**2 - 240 = 0 for u.
-2, 24
Let s = 1878 - 1876. Factor -4/13*r**s + 4/13 + 2/13*r**3 - 2/13*r.
2*(r - 2)*(r - 1)*(r + 1)/13
Let z(c) = c**5 + c**4 + c**2 - 1. Let a(y) = -y**5 - 3*y**4 - 4*y**3 + 2*y**2 + 2. Let m(t) = 3*a(t) + 6*z(t). Determine f, given that m(f) = 0.
-2, 0, 1, 2
Let y(z) = 9*z**3 - 113*z**2 + 114*z. Let v(f) = 28*f**3 - 336*f**2 + 340*f. Let x(o) = 5*v(o) - 16*y(o). Determine p so that x(p) = 0.
0, 1, 31
Suppose 7*h - 8 = 5*h. Solve -9*f**4 - 5*f**4 - 15*f**2 + 9*f**h + 29*f**3 - 9*f**3 = 0 for f.
0, 1, 3
Let h(w) be the third derivative of w**5/30 - 13*w**4 + 2028*w**3 - w**2 + 46*w. Suppose h(v) = 0. What is v?
78
Let p(i) be the first derivative of -i**6/3 - 16*i**5/5 - 21*i**4/2 - 12*i**3 - 17. Solve p(v) = 0.
-3, -2, 0
Factor 96/7 - 2/7*s**3 - 6/7*s**2 + 92/7*s.
-2*(s - 6)*(s + 1)*(s + 8)/7
Suppose -5*c = p - 49, 5*c - 2*p - 46 = 6. Let a be 2/4*(c - 2). Factor 6 + 4*k - 23 - 4*k**3 + a*k**2 + 13.
-4*(k - 1)**2*(k + 1)
Let b be (5/10 - 0)*6. Let d(c) be the third derivative of 0*c - 1/33*c**b + 1/330*c**5 - 1/660*c**6 + 10*c**2 + 1/132*c**4 + 0. Factor d(l).
-2*(l - 1)**2*(l + 1)/11
Let b(i) be the third derivative of i**8/952 - 2*i**7/105 + 11*i**6/102 - 24*i**5/85 + 79*i**4/204 - 14*i**3/51 + 5*i**2 + 31*i. Let b(k) = 0. What is k?
1/3, 1, 2, 7
Let z(p) be the second derivative of -5*p**7/126 + p**6/18 + 5*p**5/12 + 5*p**4/12 - 40*p - 1. What is y in z(y) = 0?
-1, 0, 3
Let m = -455 - -258. Let n = 1775/9 + m. Factor 0 + 0*y - 2/9*y**3 - 2/9*y**2 + n*y**5 + 2/9*y**4.
2*y**2*(y - 1)*(y + 1)**2/9
Let k(l) be the third derivative of l**6/30 + 34*l**5/15 + 289*l**4/6 + l**2 + 53. Let k(t) = 0. What is t?
-17, 0
Factor 0 - 1/2*h**3 + 1/2*h**4 - h**2 + 0*h.
h**2*(h - 2)*(h + 1)/2
Suppose 0 = -3*w + 10*w - 7. Let r be w - ((4 - 4) + -2). Factor -3/4*q**2 - 1/4*q**r - 1/4 - 3/4*q.
-(q + 1)**3/4
Let s(r) = r**2 - 8*r + 4. Let g be s(7). Let b be (g - (-1 - -1)) + 39. Factor 0 - b*i + 39*i - i**2 + 0.
-i*(i - 3)
Let z = -703 - -999. Let 4 + z*o - 36*o**4 + 12 + 108*o**2 - 8*o**3 - 200*o = 0. What is o?
-1, -2/9, 2
Find f such that 6847 - 2830*f + 238*f**2 - 2062*f + 115 - 2*f**3 - 305*f - 2001*f = 0.
1, 59
Let -22*d**2 - 1086*d**3 + 2*d**5 - 2*d**2 + 6*d**4 + 1082*d**3 - 16*d = 0. What is d?
-2, -1, 0, 2
Let d(f) be the first derivative of 5/4*f**2 - 3 + 5/12*f**3 + 5/4*f. Solve d(j) = 0 for j.
-1
Let f be 11/2*(-2 - (-8)/2). Let s be 5 - (-1 + f) - 15/(-3). Determine y, given that 0 + 2/3*y**4 + 0*y**3 + 0*y**2 + s*y = 0.
0
Let o be 16/6*3/2. Suppose 16 = 5*d - c, -5*d - 2*c + o*c + 17 = 0. What is n in 1/3*n**5 + 0*n - 1/3*n**d - 1/3*n**4 + 1/3*n**2 + 0 = 0?
-1, 0, 1
Let v(d) = -83*d + 501. Let b be v(6). Factor 0 + 0*s**2 + 0*s**b + 2/13*s**4 + 0*s.
2*s**4/13
Let f(c) be the third derivative of c**6/360 - 13*c**5/180 + 2*c**4/3 - 2*c**3 - 6*c**2 - 11. Factor f(i).
(i - 6)**2*(i - 1)/3
Let b be (-40)/16*4/(-10). Determine d, given that -10*d**2 + 6*d**2 + 5*d**2 + b - 3 + d = 0.
-2, 1
Let t(o) = 2*o**2 - 11*o - 4. Let l be t(6). Determine x so that 11*x - 3*x + 2*x**3 + 6*x**2 + 2 - l*x = 0.
-1
Let t(m) be the first derivative of -81*m**5/25 + 117*m**4/20 - 8*m**3/3 + 2*m**2/5 + 14. Factor t(r).
-r*(r - 1)*(9*r - 2)**2/5
Suppose -2*h - q + 22 = 0, -h + 21 = -8*q + 11*q. Let m be 2*h/(-8) - -6. Let -3/4*y**3 + m*y + 3/4*y**4 - 9/4*y**2 - 3/2 = 0. What is y?
-2, 1
Let c(k) be the third derivative of 0*k + 7/120*k**5 - 1/80*k**6 + 0 - 1/4*k**3 - k**2 + 7/48*k**4. Factor c(i).
-(i - 3)*(i + 1)*(3*i - 1)/2
Let z(y) = 2*y**4 + 23*y**2 - 24*y + 14. Let b(r) = 9*r**4 + 114*r**2 - 120*r + 69. Let n(d) = -5*b(d) + 24*z(d). Suppose n(u) = 0. Calculate u.
-3, 1
Suppose 3*i + 22 = 4*i. Suppose 2*y = -3*f + i, f - 24 = -2*y - 2*y. Factor z**2 - 2*z**3 - 3*z**2 - 2*z**3 + z**y + z**3.
z**2*(z - 2)*(z + 1)**2
Suppose 5*u = -6*u + 3*u. Suppose 2/5*v**2 - 4/5*v**3 + u + 6/5*v = 0. What is v?
-1, 0, 3/2
Let z be ((-3740)/714 - -5)/((-10)/12). Let w be ((-13)/(-14) - 1)*-2. What is o in -w - 1/7*o**2 - z*o = 0?
-1
Find k, given that -1/2*k**3 + 1/2*k + 1/2 - 1/2*k**2 = 0.
-1, 1
Suppose -39*r + 41*r = 10. Suppose -r*m - 15 = -10*m. Factor m*i - 19 + 19 + 3*i**2.
3*i*(i + 1)
Let s be ((-4)/(-5))/(7 - 3846/550). Let m = 221/2 - s. Suppose -3/2*v**2 + 2*v**3 + 2 - 2*v - m*v**4 = 0. What is v?
-1, 1, 2
Let m(w) be the third derivative of 19*w**2 + 1/220*w**6 + 0*w - 1/1155*w**7 + 0*w**3 + 0*w**4 + 0 + 2/165*w**5. Factor m(n).
-2*n**2*(n - 4)*(n + 1)/11
Let i(w) be the third derivative of 0*w + 1/120*w**6 - 1/45*w**5 + 2/315*w**7 + 0*w**3 