f -m**6/10 - 3*m**5/20 + m**4/4 + m**3/2 - 6*m - 4. Let v(x) be the first derivative of w(x). Find o, given that v(o) = 0.
-1, 0, 1
Let x(a) = a**2 + 12*a - 11. Let l be x(-13). Solve u + 4*u**l + 12 - 3*u + 18*u = 0 for u.
-3, -1
Let m(i) = 5*i**3 - 21*i**2 - 3*i - 4. Let t(z) = 2*z**3 - 10*z**2 - 2*z - 2. Let f(c) = -4*m(c) + 9*t(c). Find x such that f(x) = 0.
-1
Determine m so that 1/3*m + 1/3*m**2 + 0 = 0.
-1, 0
Let h be 1*(2 + 5 + -3). Suppose -4*i - 2*y - 14 = -6*i, 2*i - 4*y - 20 = 0. What is n in -2*n + 8*n**2 + i*n + 2*n - 9*n**2 - h = 0?
2
Let b = 113 - 107. Let u(j) be the first derivative of 0*j**3 - 2 + 0*j + 1/27*j**b + 0*j**4 + 2/45*j**5 + 0*j**2. Solve u(d) = 0 for d.
-1, 0
Let w be 5/(-1)*(-8)/20. Let s(i) be the first derivative of -8*i**2 + 32/3*i**3 + 1 + w*i. Factor s(k).
2*(4*k - 1)**2
Let p(w) be the third derivative of -w**6/1080 + w**5/108 - 13*w**2. Suppose p(h) = 0. Calculate h.
0, 5
Let q be (-4)/(-8) + (-3)/18. Factor 1/3*j**2 + 0 + q*j.
j*(j + 1)/3
Let f = -1746/7 + 250. Factor -f*v**3 + 4/7*v**2 + 2/7*v + 2/7*v**5 - 2/7 - 2/7*v**4.
2*(v - 1)**3*(v + 1)**2/7
Let r(u) = -4*u**2 + 5*u + 5. Let t(z) = z**2 - z - 1. Let n(c) = -r(c) - 5*t(c). Let n(w) = 0. What is w?
0
Let d(j) be the second derivative of j**7/252 - j**5/12 + 5*j**4/18 - 5*j**3/12 + j**2/3 - 2*j + 65. Find n, given that d(n) = 0.
-4, 1
Let k(a) be the second derivative of -a**5/120 + a**3/12 - a**2/6 - 11*a. Determine o so that k(o) = 0.
-2, 1
Suppose -8*k = 5*k - 26. Find u, given that 0*u + 0 + 1/6*u**3 - 1/6*u**k = 0.
0, 1
Let w(k) = 3*k**3 - 9*k**2. Let m(y) = y**3 - y - 1. Let c(q) = 2*q**3 + 8*q**2 - 5*q - 5. Let u(d) = -c(d) + 5*m(d). Let v(i) = 3*u(i) - 2*w(i). Factor v(a).
3*a**2*(a - 2)
Let a(j) be the first derivative of -j**3/3 + 3*j**2 + 7*j + 28. Find l, given that a(l) = 0.
-1, 7
Let n(z) be the second derivative of z**8/280 + 2*z**7/105 + 7*z**6/180 + z**5/30 + z**3/6 + z. Let h(y) be the second derivative of n(y). Factor h(t).
2*t*(t + 1)**2*(3*t + 2)
Let f(a) be the third derivative of 0*a**3 + 0*a - 1/1344*a**8 + 0*a**5 + 0*a**4 + 7*a**2 + 0*a**6 - 1/840*a**7 + 0. Factor f(z).
-z**4*(z + 1)/4
Let g(h) = h**5 + h**4 + h**2 + h + 1. Let z(o) = -8*o**5 - 6*o**3 - 4*o**2 - 6*o - 6. Let l(c) = -6*g(c) - z(c). Factor l(s).
2*s**2*(s - 1)**3
Let y(a) = 8*a - a + 0 - 6 - a**2. Let w be y(5). Factor -2*q**2 + w*q**2 - 2*q - 6*q**3 + 2*q**4 + 4*q**2.
2*q*(q - 1)**3
Let s(g) be the third derivative of g**5/20 + 3*g**4/2 + 18*g**3 + 45*g**2. Let s(l) = 0. Calculate l.
-6
Let l = 4 - 4. Let g = -73 + 77. What is i in 18/7*i**3 + 26/7*i**g + 10/7*i**5 - 4/7*i + l - 2/7*i**2 = 0?
-1, 0, 2/5
Let x(b) = -8*b**5 + 6*b**4 - 2*b**3 - 6*b**2 + 2*b + 4. Let g(d) = -d**5 - d**3 + 1. Let a(r) = -4*g(r) + x(r). Determine c, given that a(c) = 0.
-1, 0, 1/2, 1
Let i(f) be the third derivative of f**5/20 - f**4/2 - 5*f**3/2 - 2*f**2. Determine h, given that i(h) = 0.
-1, 5
Factor -1/6*o**3 + 1/6 - 1/2*o + 1/2*o**2.
-(o - 1)**3/6
Solve 13/3*k**3 - 2*k**4 + 1/3*k**5 + 0 + 4/3*k - 4*k**2 = 0.
0, 1, 2
Factor 61*b**5 + 57*b**5 - 116*b**5 + 4*b**4.
2*b**4*(b + 2)
Let s be (-3)/54*(-1 + 0). Let w(c) be the first derivative of -s*c**4 + 2/9*c - 1 + 1/9*c**2 - 2/27*c**3. Factor w(z).
-2*(z - 1)*(z + 1)**2/9
Let u(c) = -3 + 0*c**2 + 0*c**2 + 2*c + c**4 + 1. Let a(v) = 3*v**4 - v**3 + 7*v - 7. Let j(z) = 2*a(z) - 7*u(z). Factor j(n).
-n**3*(n + 2)
Let w(f) = f - 4. Let d be w(6). Suppose o + 3*x - 12 = -d*o, 4*x = 5*o - 2. Determine k, given that -4*k**3 + 2*k**4 + o*k**2 + 7 - 7 = 0.
0, 1
Suppose -5*f = -0*f + 20. Let p = -2 - f. Factor i**4 - 2*i**3 - 2*i**4 - p*i**5 - 3*i**4.
-2*i**3*(i + 1)**2
Let v(n) be the first derivative of 3*n**5/10 - 2*n**4 + 29*n**3/6 - 5*n**2 + 2*n + 25. Let v(h) = 0. What is h?
1/3, 1, 2
Suppose -3 = z - t, -5*t = 5*z - t - 21. Let r(a) = -2*a**3 + 6*a**2. Let y(j) = 1 + j**2 + j - 1. Let o(c) = z*r(c) - 2*y(c). Factor o(v).
-2*v*(v - 1)**2
Suppose -5*a - 4 = -24. Let x(f) be the second derivative of 3*f - 1/20*f**a + 3/5*f**2 + 0 - 1/10*f**3. Factor x(t).
-3*(t - 1)*(t + 2)/5
Let m be (-28)/126*3/(-20). Let z(q) be the second derivative of 1/12*q**4 - q - 1/6*q**3 - m*q**6 + 0*q**2 + 1/20*q**5 + 0. Factor z(p).
-p*(p - 1)**2*(p + 1)
Let u = 4 + 0. Suppose k**2 + 3 - u*k + 3*k**2 - 3 = 0. What is k?
0, 1
Let g(n) be the third derivative of 1/1155*n**7 - 6*n**2 + 0*n**4 + 0*n + 0*n**5 + 0*n**3 + 0 + 1/660*n**6. Solve g(w) = 0.
-1, 0
Let b(c) be the third derivative of c**7/3780 + c**6/1080 - c**5/90 + c**4/24 + 2*c**2. Let w(l) be the second derivative of b(l). Factor w(s).
2*(s - 1)*(s + 2)/3
Let d(w) be the first derivative of -1/8*w**2 - 1/6*w**3 + 0*w + 2 - 1/16*w**4. Factor d(c).
-c*(c + 1)**2/4
Suppose 130 - 10 = -3*m. Let w be (2 - m/(-21))*6. Factor -w*h + 0 - 2/7*h**2.
-2*h*(h + 2)/7
Let s be 1/5 - 78/(-210). Suppose 3*n - 1 = -5*f, -4*f + 14 = -6*n + 4*n. Factor -s + f*m**2 + 10/7*m.
2*(m + 1)*(7*m - 2)/7
Let g(s) = 12*s + 4. Let t be g(7). Factor 3*q**5 + 9*q**4 + t - 12*q**2 - 88.
3*q**2*(q - 1)*(q + 2)**2
Let t(b) be the third derivative of 5*b**2 + 0*b**3 + 0*b + 1/300*b**5 + 0*b**4 + 0. What is n in t(n) = 0?
0
Suppose 3*i + 3 = 12. Suppose r = -i*r, 3*r = 5*w - 25. Factor 9*u**3 + 2*u**w - 2*u**4 - 9*u**3.
2*u**4*(u - 1)
Let i(n) = -2*n**2 + 63*n + 173. Let o be i(34). Factor 0 - 2/9*k**2 + 0*k - 2/9*k**o.
-2*k**2*(k + 1)/9
Let n be (((-4)/5)/2)/((-12)/10). Let p**2 + 1/3*p**4 + 0 - n*p - p**3 = 0. What is p?
0, 1
Let r = 300 - 298. Determine f, given that 2/5*f**5 - 2/5*f**r + 0 + 6/5*f**3 - 6/5*f**4 + 0*f = 0.
0, 1
Let x be (-1 + 2)/((-3)/(-15)). Suppose -x*l + 2 = -4*l. Find d such that -5*d**4 + d**2 + 3*d**2 - l + 3*d**4 = 0.
-1, 1
Let l = 190 - 188. Factor 6/5*h + 4/5*h**l - 2/5*h**3 + 0.
-2*h*(h - 3)*(h + 1)/5
Suppose 0 = 2*f + 5*o - 31, -12 = f - 0*o - 3*o. Suppose -h + 10 = -2*n, 2*h + 3*h - f*n = 22. Determine a, given that -2/5*a**h + 2/5 + 0*a = 0.
-1, 1
Solve -9/5*n + 4/5 - 1/5*n**3 + 6/5*n**2 = 0 for n.
1, 4
Suppose -2/3*x**2 - 8/3*x**3 - 14/9*x**4 + 0 + 4/9*x = 0. What is x?
-1, 0, 2/7
Let x(c) be the third derivative of -1/16*c**4 - 5*c**2 + 0 + 0*c + 1/40*c**5 + 0*c**3. Factor x(i).
3*i*(i - 1)/2
Let q = -116 + 121. Let r(j) be the first derivative of j - 2/3*j**3 + 7/4*j**2 + 1/5*j**q + 7/12*j**6 - 7/4*j**4 - 1. Find l such that r(l) = 0.
-1, -2/7, 1
Suppose -2/3*x**4 + 0*x**3 + 0*x + 0 + 2/3*x**2 = 0. Calculate x.
-1, 0, 1
Let a(q) be the second derivative of -q + 1/4*q**2 + 0 + 0*q**3 - 1/24*q**4. Factor a(z).
-(z - 1)*(z + 1)/2
Let q(r) be the first derivative of 0*r - 2/9*r**3 - 1/6*r**4 - 10 - 1/9*r**2 - 2/45*r**5. Factor q(d).
-2*d*(d + 1)**3/9
Let x = 3/559 - -553/1118. Factor 0 - x*k - 1/2*k**2.
-k*(k + 1)/2
Let i be 3/4 + (-9)/12. Let t(r) be the third derivative of 1/8*r**4 - 1/6*r**3 - 1/20*r**5 + 1/120*r**6 + 0 + i*r - r**2. Suppose t(h) = 0. Calculate h.
1
Let s be (-1)/6 - (-266)/588. Let -s*c**2 + 2/7 + 0*c = 0. Calculate c.
-1, 1
Let y(r) be the second derivative of r**4/84 - r**3/42 - r**2/7 - 9*r. Factor y(p).
(p - 2)*(p + 1)/7
Let t(v) be the second derivative of v**6/1800 - v**5/200 + v**4/60 - v**3/3 + 2*v. Let m(n) be the second derivative of t(n). Factor m(h).
(h - 2)*(h - 1)/5
Let y(c) = 10*c**2 - 20*c - 4. Let g(b) = 2*b**2 - 4*b - 1. Let f be 4/((-29)/7 - -4). Let q(u) = f*g(u) + 6*y(u). Let q(n) = 0. What is n?
1
Suppose 0 = -j + 3*b + 8, 5*j + 19*b - 24*b - 20 = 0. Find m such that 1/5 + 6/5*m**j + 1/5*m**4 + 4/5*m + 4/5*m**3 = 0.
-1
Suppose 5*t = 4 + 1. Find y, given that 8 + 0*y**2 - 3 - t - 6*y + 2*y**2 = 0.
1, 2
Let q(b) be the first derivative of b**6/30 + b**5/30 - b**4/6 - b**3/3 + 7*b**2/2 - 6. Let v(d) be the second derivative of q(d). Find y, given that v(y) = 0.
-1, -1/2, 1
Let c(u) be the first derivative of u**7/840 - u**5/120 + u**3 - 4. Let v(k) be the third derivative of c(k). Factor v(w).
w*(w - 1)*(w + 1)
Let k(u) be the first derivative of -2/5*u**5 + 0*u**2 + 0*u**4 + 2/3*u**3 - 3 + 0*u. Find p, given that k(p) = 0.
-1, 0, 1
Let b(k) = -k**3 - 3*k**2 + 2*k - 4. Let i be b(-4). Let f(a) be the third derivative of -1/120*a**5 + 0 + 2*a**2 + 0*a + 1/24*a**i - 1/12*a**3. Factor f(g).
-(g - 1)**2/2
Let p = 14 - 17. Let t be p - (-2)/16*26. Solve t*b**4 - 1/4*b*