(x + 1)/7
Let j(k) be the third derivative of -k**7/168 - k**6/72 + k**5/24 + 5*k**4/24 + k**3 - 8*k**2. Let g(d) be the first derivative of j(d). Solve g(x) = 0.
-1, 1
Solve -21/4*f**2 + 0 - 9/4*f**3 + 3/2*f**5 - 9/4*f + 9/4*f**4 = 0 for f.
-1, 0, 3/2
Factor -18*y**3 - 2*y**4 - 48*y + 5*y**4 - 62*y**2 - 24*y**3 + 27*y**3 - 4*y**2.
3*y*(y - 8)*(y + 1)*(y + 2)
Let x(c) be the first derivative of c**6/120 + c**5/20 - 3*c**4/8 + 7*c**3 - c**2/2 + 36. Let w(z) be the third derivative of x(z). Factor w(k).
3*(k - 1)*(k + 3)
Let b(r) be the first derivative of -r**4/14 - 10*r**3/21 - 3*r**2/7 + 18*r/7 - 56. Factor b(y).
-2*(y - 1)*(y + 3)**2/7
Let f(h) = h**3 + 3*h**2 + h - 1. Let a be f(-2). Let j = 3 + a. Factor b**3 + 20*b - b**2 + 2*b**2 - b**j - 21*b.
-b*(b - 1)**2*(b + 1)
Let b(f) = 7*f**3 + 46*f**2 - 116*f - 4. Let q(c) = -8*c**3 - 44*c**2 + 115*c + 5. Let m(y) = 5*b(y) + 4*q(y). Solve m(n) = 0 for n.
-20, 0, 2
Let o(q) be the third derivative of q**5/30 - 3*q**4/4 + 42*q**2 + 2*q. Let o(i) = 0. Calculate i.
0, 9
Find z, given that 25/4 + 1/4*z**2 + 5/2*z = 0.
-5
Suppose 16 = h + 4*b, 3*h - 57 = 2*b - 9. Let 44*j**5 + 36*j**4 - 10*j**2 - 48*j**3 - h*j**5 - 6*j**2 = 0. What is j?
-2, -2/7, 0, 1
Factor -65*h**2 - 114*h + 37*h**2 + 25*h**2 - 111.
-3*(h + 1)*(h + 37)
Let p(g) be the first derivative of -g**6/2520 - g**5/210 - g**4/56 - 5*g**3 - 2. Let f(h) be the third derivative of p(h). Factor f(x).
-(x + 1)*(x + 3)/7
Let j be ((-2)/24)/(720/(-756)). Let i(o) be the third derivative of 0 + 0*o - 1/4*o**3 + j*o**5 - 5/32*o**4 - 3*o**2. Let i(q) = 0. What is q?
-2/7, 1
Let z(g) be the third derivative of -11*g**8/1512 + 16*g**7/315 - 41*g**6/270 + 34*g**5/135 - g**4/4 + 4*g**3/27 + 116*g**2. Solve z(l) = 0.
4/11, 1
Let a(m) be the first derivative of 5*m**3/6 + 65*m**2/2 - 135*m/2 - 106. What is i in a(i) = 0?
-27, 1
Factor 1/8*k**2 - 8 - 63/8*k.
(k - 64)*(k + 1)/8
Let p(x) be the third derivative of -x**8/126 + x**7/21 - 4*x**6/45 + x**5/30 + x**4/18 + 3*x**2 - 24. Suppose p(m) = 0. Calculate m.
-1/4, 0, 1, 2
Let k be (-3 - (-2)/(-8))*(-96)/5. Let q = k - 62. Determine w so that 2/5*w**2 + q*w**3 - 4/5*w + 0 = 0.
-2, 0, 1
Suppose 16*n - 3*a = 18*n - 25, -22*n = -2*a - 30. Factor 0*t - 2/5*t**n + 0 - 2/5*t**3.
-2*t**2*(t + 1)/5
Suppose 0*l + 7*l = -3*l + 20. Factor -5/3 + 10/3*f - 5/3*f**l.
-5*(f - 1)**2/3
Let r be (2 - 5)/((-3)/(-2)). Let j be 20/(-5) + 2 - r. Find u, given that -1/2*u - 1/4*u**4 + 1/2*u**3 + j*u**2 + 1/4 = 0.
-1, 1
Let k(n) be the second derivative of n**4/18 + n**3 + 8*n**2/3 - 4*n + 9. Determine s so that k(s) = 0.
-8, -1
Let y be 1/4 + 10/(-8) - 0. Let o(g) = 2*g**2 - g - 1. Let b be o(y). Factor -3*n**3 + 0 - 1/2*n**5 - 1/2*n - 2*n**2 - b*n**4.
-n*(n + 1)**4/2
Let n(d) be the first derivative of d**6/21 - 2*d**5/5 + d**4 - 4*d**3/21 - 15*d**2/7 + 18*d/7 - 111. Suppose n(k) = 0. What is k?
-1, 1, 3
Suppose -29*n + 28*n - 3*d = 1, 2 = -2*d. Suppose 0 + 2/3*b**4 + 4/15*b + 2/15*b**5 + 6/5*b**3 + 14/15*b**n = 0. Calculate b.
-2, -1, 0
Factor 241*y**2 - y**5 + 128*y**3 - 29*y**4 - 665*y**2 + 292*y**2.
-y**2*(y - 2)**2*(y + 33)
Let t(g) be the second derivative of -g**7/126 - 11*g**6/270 - g**5/15 - g**4/27 - 125*g. Find h, given that t(h) = 0.
-2, -1, -2/3, 0
Let c(m) be the second derivative of -m**6/120 + m**5/15 - m**4/6 + 6*m**2 - 15*m. Let f(k) be the first derivative of c(k). Factor f(p).
-p*(p - 2)**2
Let q be (-13)/(-78)*1*6. Let -9*t**2 + 18*t + 7 + 0*t - 3*t - q = 0. What is t?
-1/3, 2
Let m(y) be the first derivative of y**5/15 - y**4/12 - 4*y**3/9 + 2*y**2/3 - 48. Determine s so that m(s) = 0.
-2, 0, 1, 2
Let s(k) be the first derivative of -k**4/24 + k**3/18 + k**2/12 - k/6 - 22. Factor s(a).
-(a - 1)**2*(a + 1)/6
Let k = -12 - -15. Let t be (4 + (-32)/12)*k. Suppose t*c**2 - 8/5*c - 6/5*c**3 - 16/5 = 0. What is c?
-2/3, 2
Let x(b) be the third derivative of 0*b + 0 + 1/5*b**5 - 1/2*b**4 + 12*b**2 + 0*b**3 - 1/40*b**6. Solve x(s) = 0.
0, 2
Suppose -21311*m = -21329*m + 36. Factor 0*j + 3/5*j**4 + 0 + 0*j**m + 3/5*j**3.
3*j**3*(j + 1)/5
Let u be (-273)/(-4) - (-3)/(-12). Let w = -68 + u. Factor 0*i**2 - 8/7*i**4 + w - 8/7*i**3 + 6/7*i**5 + 0*i.
2*i**3*(i - 2)*(3*i + 2)/7
Suppose -12*r + 22 = -r. Determine q so that -628*q**r - 730*q - 144 + 3*q**3 - 36*q**4 + 202*q - 294*q**3 + 27*q**3 = 0.
-3, -2/3
Let u(d) = d**2 - d - 1. Let q be u(10). Suppose -g - q = -3*j - 27, j - 23 = -2*g. Factor 4*r**2 - 4 + 21*r - j*r.
4*(r - 1)*(r + 1)
Let a(f) = -f**2 + 17*f - 16. Let n be a(1). Let v(t) be the second derivative of 0 + n*t**3 + 12*t - 1/30*t**4 + 1/5*t**2. Find o such that v(o) = 0.
-1, 1
Let z(j) = 75*j**2 - 69*j - 90. Let r(l) = -11*l**2 + 10*l + 13. Let o(x) = 27*r(x) + 4*z(x). Factor o(s).
3*(s - 3)*(s + 1)
Factor -934*v**2 - 1126*v**2 + 137*v + 398*v + 17 - 22.
-5*(4*v - 1)*(103*v - 1)
Let d(l) = l**3 - l**2 + l + 4. Let h be d(0). Let s(o) be the second derivative of 3/100*o**5 + 0 + 1/2*o**3 + 1/5*o**h + 3/5*o**2 + 2*o. Factor s(m).
3*(m + 1)**2*(m + 2)/5
Let y(t) be the first derivative of 0*t**2 - 1/2*t**4 - 44 - 2/5*t**5 + 0*t + 0*t**3. Let y(b) = 0. Calculate b.
-1, 0
Let a(t) be the first derivative of 0*t - 4/27*t**3 - 1/18*t**4 + 31 + 1/3*t**2. Suppose a(z) = 0. Calculate z.
-3, 0, 1
Let y(m) = 125*m**3 - 335*m**2 + 265*m + 55. Let h(x) = -9*x**3 + 24*x**2 - 19*x - 4. Let v = 2 + -57. Let f(b) = v*h(b) - 4*y(b). What is z in f(z) = 0?
0, 1, 3
Suppose 1271*y = 1276*y - 10. Factor -2/9*v**3 - 6*v + y*v**2 + 6.
-2*(v - 3)**3/9
Let 82*i + 3*i**2 + 784 + 30*i - 2*i**2 + 3*i**2 = 0. What is i?
-14
Let w(s) be the first derivative of 12/35*s**5 - 37 - 3/7*s**2 + 20/21*s**3 + 0*s - 6/7*s**4 - 1/21*s**6. Determine k, given that w(k) = 0.
0, 1, 3
Let z = 1902 - 15215/8. Let l(w) be the second derivative of 0*w**2 - z*w**4 + 0*w**3 + 0 + 6*w. Factor l(j).
-3*j**2/2
Let w(a) = 5 + 4*a - 5*a - 2*a. Let p be w(1). Factor 8 - 50/3*q**3 + 110/3*q**p + 112/3*q.
-2*(q - 3)*(5*q + 2)**2/3
Let q(k) = 7*k**2 + 12*k**2 + 5*k**3 - 4*k**2. Let s(n) = n**2. Let u(r) = -q(r) + 5*s(r). Factor u(c).
-5*c**2*(c + 2)
Suppose 918 = 44*a + 830. Let -18/5*y**a + 4*y + 7/5*y**3 - 8/5 - 1/5*y**4 = 0. Calculate y.
1, 2
Let f(v) = -10*v - 1. Let h(j) = j**2 - 1. Let k(t) = -f(t) - h(t). Let g be k(10). Suppose 2/3 - 1/3*u + 1/3*u**3 - 2/3*u**g = 0. What is u?
-1, 1, 2
Let b be (-1 - (-152)/(-56)) + -1 + 5. Factor -32/7 - b*v**2 + 16/7*v.
-2*(v - 4)**2/7
Let c(t) = -11*t**4 - 11*t**3 + 6*t**2 - 7*t - 13. Let d be (-6)/(-21) + (-80)/35. Let x(a) = a**4 + a**3 + a + 1. Let l(v) = d*c(v) - 18*x(v). Factor l(o).
4*(o - 1)**2*(o + 1)*(o + 2)
Determine d, given that 0 - 28/5*d + 174/5*d**3 - 122/5*d**4 - 38/5*d**2 + 14/5*d**5 = 0.
-2/7, 0, 1, 7
Factor 8*q**3 + 9*q**2 + 22*q**3 + q**2 + 25*q - 30 - 35*q**3.
-5*(q - 3)*(q - 1)*(q + 2)
Let y(b) be the third derivative of -b**5/570 + 43*b**4/228 + 44*b**3/57 - 51*b**2. Factor y(d).
-2*(d - 44)*(d + 1)/19
Suppose 2*m - f + 0*f - 6 = 0, 0 = -3*m + 5*f + 16. Let i(k) = -4*k - 2. Let c(j) = j**2 - 20*j - 11. Let o(h) = m*c(h) - 11*i(h). Factor o(b).
2*b*(b + 2)
Let q(r) = -5*r**2 + 432*r - 46650. Let w(d) = 2*d**2 - 3. Let z(f) = -3*q(f) - 6*w(f). Factor z(a).
3*(a - 216)**2
Let i(p) = p**5 - p**3 + p**2 - p + 1. Let b(y) = y**5 + 14*y**4 - 23*y**3 + 15*y**2 - 7*y + 5. Let w(x) = -b(x) + 5*i(x). Factor w(r).
2*r*(r - 1)**3*(2*r - 1)
Let i be (-15)/(-50)*(10 - 90/12). Factor -3 - 3/4*r**3 + 9/4*r**4 - 9*r - 33/4*r**2 + i*r**5.
3*(r - 2)*(r + 1)**3*(r + 2)/4
Let j(l) be the first derivative of -l**4/8 - l**3/2 + 9*l**2/4 - 5*l/2 + 82. Factor j(n).
-(n - 1)**2*(n + 5)/2
Let v(h) = -2*h**2 + 33*h - 68. Let j be v(14). Let p(g) be the third derivative of -1/20*g**5 + 0 - 8*g**j + 0*g**4 + 0*g + 1/2*g**3. Factor p(i).
-3*(i - 1)*(i + 1)
Let h = 28 + -30. Let i be 82/(-42) - h - (-12)/42. Factor 0 + 0*t**4 + 2/3*t**3 + 0*t**2 - 1/3*t - i*t**5.
-t*(t - 1)**2*(t + 1)**2/3
Let l(z) be the second derivative of z**5/2 - 35*z**4/4 + 50*z**3 - 125*z**2/2 - 4*z. Factor l(u).
5*(u - 5)**2*(2*u - 1)
Factor -76 - 56*c**2 - 2*c**3 - 5*c**2 + 110*c + 29*c**2.
-2*(c - 2)*(c - 1)*(c + 19)
Let c(t) be the second derivative of 0 - 3/2*t**2 - 5/8*t**3 - 12*t - 1/16*t**4. What is q in c(q) = 0?
-4, -1
Suppose -4*t + 8 = -2*t. Le