 - -90. Factor 8/9*n**2 - 2/3*n - v.
2*(n - 1)*(4*n + 1)/9
Let u(h) be the first derivative of -1/2*h**4 + 4/27*h**3 + 15 + h**2 - 4/9*h. Factor u(n).
-2*(n - 1)*(n + 1)*(9*n - 2)/9
Let t(v) be the second derivative of -v**5/360 + v**4/48 - v**3/18 + 13*v**2/2 + 19*v. Let g(y) be the first derivative of t(y). Suppose g(l) = 0. Calculate l.
1, 2
Let b(z) be the second derivative of z**5/110 + z**4/66 - 2*z**3/33 - 15*z + 2. Factor b(g).
2*g*(g - 1)*(g + 2)/11
Suppose 14*d - 6*d = 240. Let o(r) = r**3 - 31*r**2 + 30*r + 2. Let g be o(d). Solve 16/3 + 8/3*f + 1/3*f**g = 0 for f.
-4
Let h(g) = 2*g - 2. Suppose -j = -2*j + 3. Let y(i) be the first derivative of i**4/4 - i**3/3 - 3*i**2/2 + 3*i - 21. Let b(d) = j*h(d) + 2*y(d). Factor b(v).
2*v**2*(v - 1)
Let -36 + 36/5*u**3 - 153/5*u**2 + 276/5*u - 3/5*u**4 = 0. What is u?
2, 3, 5
Let w(h) = h**3 - 14*h**2 + 24*h. Let s be w(12). Let n(u) be the first derivative of -3*u - 3/5*u**5 + 4 + 2*u**3 + 0*u**2 + s*u**4. Factor n(i).
-3*(i - 1)**2*(i + 1)**2
Let b(k) be the third derivative of k**8/53760 + k**7/6720 - k**6/1440 + 19*k**4/24 + 15*k**2. Let z(o) be the second derivative of b(o). Solve z(f) = 0.
-4, 0, 1
Let t(b) = 4*b**3 - 16*b**2 + 25*b - 8. Let w(g) = -2*g**3 + 8*g**2 - 12*g + 4. Let k be (-81)/(-36) - (-3 - -2)/(-4). Let a(f) = k*t(f) + 5*w(f). Factor a(n).
-2*(n - 2)*(n - 1)**2
Let g(z) be the third derivative of z**5/360 - z**4/144 - z**3/6 + 38*z**2. Factor g(p).
(p - 3)*(p + 2)/6
Let f(p) be the first derivative of p**4 + 28*p**3/3 + 8*p**2 - 48*p - 201. Determine q, given that f(q) = 0.
-6, -2, 1
Suppose -3*j = -7*j + 8. Factor -2*q**2 + 0*q**3 + j*q**3 - 2*q - 45 + 47.
2*(q - 1)**2*(q + 1)
Let d(f) = -f + 10. Let k be d(4). Find x such that x**5 + k*x**4 - x**5 + 16*x**2 + 3 + 14*x**3 - 1 + x**5 + 9*x = 0.
-2, -1
Factor -1/6*x**2 - 7/2*x + 11/3.
-(x - 1)*(x + 22)/6
Suppose x - 7 = 5*u, -3*u - 53*x = -56*x + 21. Factor -r**3 - 1/2*r + u - 5/4*r**2 - 1/4*r**4.
-r*(r + 1)**2*(r + 2)/4
Suppose 4*z - 8*z = 24. Let i = -5 - z. Factor 1 - 2 + i + t**2 + 2*t.
t*(t + 2)
Let c(f) be the first derivative of 3*f**5/5 + 9*f**4/4 - 2*f**3 - 18*f**2 - 24*f - 632. Let c(m) = 0. What is m?
-2, -1, 2
Let x = 204 + -203. Let p(a) = 2*a**2 + 8*a - 7. Let q be p(x). Factor 4/5 - 4/5*h**2 - 16/5*h + 16/5*h**q.
4*(h - 1)*(h + 1)*(4*h - 1)/5
Let i be (9/(-1))/(-3) - -1. Let z be -9*i/(-6)*4. Suppose -6*m**4 - 3*m**3 + z*m - 24*m - 3*m**5 = 0. Calculate m.
-1, 0
Let i(n) be the second derivative of 3*n**5/40 - 13*n**4/24 - 11*n**3/12 + 5*n**2/4 + 2*n + 18. Factor i(j).
(j - 5)*(j + 1)*(3*j - 1)/2
Solve -4/5*z**2 + 0*z - 2/5*z**3 + 6/5*z**4 + 0 = 0.
-2/3, 0, 1
Let r = 53 - 47. Factor -z + z**2 + r*z + 4*z**2.
5*z*(z + 1)
Let p(a) be the first derivative of 0*a**2 + 0*a - 1/21*a**3 - 11. Let p(v) = 0. Calculate v.
0
Let d(x) be the second derivative of -5*x**4/12 - 5*x**3/3 + 20*x**2 - 38*x. Factor d(q).
-5*(q - 2)*(q + 4)
Let a = -4758 + 4762. Suppose 1/4*u**3 + 0*u + 1/4*u**a + 0*u**2 + 0 = 0. What is u?
-1, 0
Let l = 34 - 31. Factor l*c**4 + 34 - 9*c**2 - 6*c**3 - 34.
3*c**2*(c - 3)*(c + 1)
Let j(n) = n**4 + n**2 - n + 2. Let m(d) = 52*d**5 + 426*d**4 + 896*d**3 + 130*d**2 - 2*d + 4. Let t(a) = -2*j(a) + m(a). Solve t(u) = 0 for u.
-4, -2/13, 0
Suppose 0 = -3*u - 2*v + 6, 5*u = v + 7 + 3. Suppose -u = -5*z + 10*q - 11*q, 2*z + 2 = q. What is m in z + 2/7*m**3 + 4/7*m - 6/7*m**2 = 0?
0, 1, 2
Let o be (-22)/36 - (-6970)/6273. Suppose 0 - 3/2*p + o*p**2 = 0. What is p?
0, 3
Let y(b) be the second derivative of -2*b**7/21 - 8*b**6 - 270*b**5 - 4500*b**4 - 33750*b**3 - 110*b. Factor y(s).
-4*s*(s + 15)**4
Let a(g) be the third derivative of -3/2*g**4 + 2*g**3 + 2*g**2 - 11/20*g**5 + 0 + 0*g + 3/10*g**6 + 1/10*g**7. Let a(x) = 0. What is x?
-2, -1, 2/7, 1
Let y(w) be the first derivative of 2*w**5/35 - 5*w**4/14 + 2*w**3/7 + 9*w**2/7 + 378. Factor y(x).
2*x*(x - 3)**2*(x + 1)/7
Let r = -90/41 - -581/246. Factor 0*d**4 - 1/6*d**5 + 0*d**2 + 1/3*d**3 + 0 - r*d.
-d*(d - 1)**2*(d + 1)**2/6
Suppose v + z = -4*v + 22, -4*v = 2*z - 14. Suppose 2*y**5 - 5 + 14*y**4 + 2*y**3 + 18*y**2 + v + 28*y**3 = 0. What is y?
-3, -1, 0
Let j(r) be the third derivative of -r**6/30 - 23*r**5/15 - 80*r**4/3 - 200*r**3 - 240*r**2. Determine k so that j(k) = 0.
-10, -3
Let w(b) = 44*b**3 - 108*b**2 + 116*b - 36. Let n(f) = -f**4 - 43*f**3 + 105*f**2 - 117*f + 36. Let i(d) = -4*n(d) - 5*w(d). Factor i(k).
4*(k - 9)*(k - 1)**3
Let m(d) = -5*d**2 - 37*d - 11. Let r be m(-7). Suppose r*q - 4*z = 26, 2*z + 8 = 3*q - 8. Factor 1/2*v**q + 0*v**3 - 1/4*v**5 - 1/2*v**4 + 1/4*v + 0.
-v*(v - 1)*(v + 1)**3/4
Let z(c) = 2*c**2 + 3*c. Let t be z(-2). Factor 4*v**t - 2*v**2 - 3*v**2 + 3*v**2.
2*v**2
Let c(t) be the third derivative of -t**7/420 + 3*t**6/80 - 7*t**5/30 + 3*t**4/4 - 4*t**3/3 - 41*t**2 + t. Solve c(g) = 0.
1, 2, 4
Suppose 0 = 4*b + 5*s - 22, -b + 6*b - 3*s - 9 = 0. Suppose -f - 4*y + 16 = 0, -3*f - y = -4*y - b. Factor -2/7*i**f + 0 + 2/7*i**3 + 0*i + 4/7*i**2.
-2*i**2*(i - 2)*(i + 1)/7
Let z(v) be the second derivative of v**4/42 - 32*v**3/21 + 27*v - 4. Find o such that z(o) = 0.
0, 32
Let -126/17*b**2 - 4/17*b**3 + 64/17 + 66/17*b = 0. What is b?
-32, -1/2, 1
Let w(o) be the second derivative of o**6/72 + o**5/12 + o**3/3 - 7*o. Let i(n) be the second derivative of w(n). Factor i(m).
5*m*(m + 2)
Let u(l) = -5*l - 66. Let s be u(-14). Suppose 0*r - 15 = -5*r. Suppose s + 3*v**r + 3*v**2 - 5 - 3 - 3*v + 1 = 0. What is v?
-1, 1
Suppose -5*q + 28 = d, q + 1 + 0 = 2*d. Let -12*t - 7*t**3 - t**4 - 2*t**3 - 4 - 13*t**2 + d*t**3 = 0. Calculate t.
-2, -1
Let v(d) be the first derivative of 6 + 2*d**5 + 0*d - 10/3*d**3 + 5/6*d**6 + 0*d**4 - 5/2*d**2. What is h in v(h) = 0?
-1, 0, 1
Let o be 32/(1 + -5)*(-36)/72. Let j(z) be the second derivative of 0*z**3 - 1/168*z**7 + 1/48*z**o + z + 0*z**2 - 1/120*z**6 + 0 + 1/80*z**5. Factor j(c).
-c**2*(c - 1)*(c + 1)**2/4
Let c(t) be the second derivative of 5*t**4/12 - 70*t**3/3 - 145*t**2/2 + 220*t. Factor c(n).
5*(n - 29)*(n + 1)
Let k(w) be the first derivative of 9*w**4/8 + 5*w**3/2 - 3*w**2/2 + 105. Solve k(d) = 0.
-2, 0, 1/3
Find l such that 75 + 0*l + 49*l + 48*l - 3*l**2 - 25*l = 0.
-1, 25
Let s be 40/6*54/4. Factor 35*w**4 + 110*w**2 + s*w**3 + 65*w - 72*w**5 + 15 + 35*w**5 + 42*w**5.
5*(w + 1)**4*(w + 3)
Let v(f) = 4*f**2 - 9*f - 5. Let m be v(3). Suppose 3*x - m = l, 5*l + 2*x - 25 = -11. Factor 2/7 + 2/7*t**l + 4/7*t.
2*(t + 1)**2/7
Let h(l) be the third derivative of -16*l**2 - 1/1260*l**7 + 0*l**3 + 0*l + 0*l**5 - 1/720*l**6 + 0 + 0*l**4. Factor h(n).
-n**3*(n + 1)/6
Suppose 0 = 5*p - 64 - 41. Suppose -2*j = -3*j - 3. Let y(h) = -h**2 + h - 1. Let g(t) = -6*t**2 + 3*t - 3. Let v(s) = j*g(s) + p*y(s). Factor v(n).
-3*(n - 2)**2
Let o(h) be the second derivative of 0 + 15*h + 0*h**2 + 2/45*h**3 - 1/30*h**4 + 1/150*h**5. Solve o(q) = 0.
0, 1, 2
Solve -3/2*j**4 - 81/4*j - 4*j**3 + 37/2*j**2 + 1/4*j**5 + 7 = 0 for j.
-4, 1, 7
Solve 26*m**2 + 44*m - 2996*m**3 + 1495*m**3 + 0 + 0 + 1503*m**3 = 0 for m.
-11, -2, 0
Let y(n) be the first derivative of -n**8/6720 + n**7/3360 - n**3 + 2*n - 52. Let r(z) be the third derivative of y(z). Factor r(c).
-c**3*(c - 1)/4
Let s(r) = 3*r**2 + r + 2. Let w(m) = 30*m**2 + 8*m + 8. Let h(j) = -18*s(j) + 2*w(j). Let h(i) = 0. What is i?
-5/3, 2
Solve 6*r**5 - 144/5 - 652/5*r**2 - 552/5*r - 38*r**3 + 68/5*r**4 = 0.
-2, -2/3, -3/5, 3
Suppose -6*l = -4*l + 4, 6 = 4*f - l. Let w be -3 - (f - 6 - -2). Factor 6/7*k**2 + 27/7*k**5 + 0*k + 39/7*k**3 + w + 72/7*k**4.
3*k**2*(k + 2)*(3*k + 1)**2/7
Factor -4/9*p**2 + 2/9*p**3 + 0*p + 0.
2*p**2*(p - 2)/9
Suppose 151*p - 2 = 150*p. Suppose -5*r - 5 = 0, -5*b + 4*r = -0*r - 24. Factor 3*y**3 - y**4 + 0*y**3 - b*y**3 + p*y**2.
-y**2*(y - 1)*(y + 2)
Determine z so that -25 + 0*z**3 - 72*z - 4*z**3 - 72*z**2 - 48 - 60*z + 9 = 0.
-16, -1
Let w(s) = -15*s**3 - 5*s**2 - 30. Let l(z) = -1. Let a be 12/(2/(-7)*(-28)/20). Let y(c) = a*l(c) - w(c). Factor y(k).
5*k**2*(3*k + 1)
Let p = 103 + -101. Factor 2*c**2 + 3 + 0*c**2 - 20*c + p + 13.
2*(c - 9)*(c - 1)
Let l(n) be the second derivative of -n**5/20 - 13*n**2/2 + 25*n. Let o(w) be the first derivative of l(w). Factor o(r).
-3*r**2
Factor 55*d**3 + 3*d - 6*d**2 + 7*d**2 + d**5 - 3*d