et p(n) be the second derivative of 8*n**2 - 1/3*n**t + 2*n**3 - 2*n + 0. Find w, given that p(w) = 0.
-1, 4
Suppose 5*b = 14*b + 90. Let z be (-7)/b + 1/(-5). Find v, given that -1/4*v**3 + 1/4*v - 1/2*v**2 + z = 0.
-2, -1, 1
Let j = -1511/70 + 305/14. Factor 0 + j*q + 0*q**2 - 1/5*q**3.
-q*(q - 1)*(q + 1)/5
Let l(m) be the first derivative of -8*m**4/5 + 208*m**3/5 - 153*m**2/5 + 38*m/5 - 206. Suppose l(v) = 0. Calculate v.
1/4, 19
Let c = 102/25 - 1226/325. Factor -6/13*t + 2/13*t**5 - 2/13 - 4/13*t**2 + 6/13*t**4 + c*t**3.
2*(t - 1)*(t + 1)**4/13
Solve -7/2*t**4 + 79/2*t + 65/2*t**3 - 123/2*t**2 - 7 = 0.
2/7, 1, 7
Let c = -19/37 + 1367/2590. Let s(r) be the third derivative of c*r**5 + 0*r**3 + 1/42*r**4 + 0*r + 1/420*r**6 - 5*r**2 + 0. Factor s(u).
2*u*(u + 1)*(u + 2)/7
Factor 24*t - 130 - 4*t**2 + 51 + 239.
-4*(t - 10)*(t + 4)
Let l(s) be the first derivative of -24/5*s**5 - 75/2*s - 435/4*s**2 - 55 - 102*s**3 - 75/2*s**4. Find k, given that l(k) = 0.
-5/2, -1, -1/4
Let d(o) be the second derivative of -o**6/90 - o**5/24 + o**4/18 + o**3/12 + 37*o. Solve d(y) = 0 for y.
-3, -1/2, 0, 1
Let p(o) be the third derivative of -o**5/20 + 3*o**4/4 + 7*o**3/2 - o**2 + 247. Find h, given that p(h) = 0.
-1, 7
Let r(k) be the second derivative of 5*k**4/12 - 15*k**3 + 405*k**2/2 + 5*k + 8. Factor r(x).
5*(x - 9)**2
Factor 162/7 + 24*q + 6/7*q**2.
6*(q + 1)*(q + 27)/7
Let -25*y**2 + 5*y**4 + 5*y**5 + 20 + 482*y + 479*y - 941*y - 25*y**3 = 0. Calculate y.
-2, -1, 1, 2
Let l(x) be the first derivative of -x**4/36 - x**3/18 + x**2/3 - x + 16. Let n(y) be the first derivative of l(y). Factor n(u).
-(u - 1)*(u + 2)/3
Suppose 10*t - t = 0. Let j(q) = 4*q + 3. Let b be j(t). Factor 2/3*m + 0 - 2/3*m**b - 1/3*m**4 + 1/3*m**2.
-m*(m - 1)*(m + 1)*(m + 2)/3
Let t(b) = -b**3 - b**2 - 1. Let f(q) be the first derivative of -q**5/5 - 5*q**4/4 - 4*q**3/3 - 2*q - 9. Let a(d) = -3*f(d) + 6*t(d). Factor a(u).
3*u**2*(u + 1)*(u + 2)
Let d(w) be the third derivative of w**5/60 + w**4/4 + 4*w**2 + 10*w. Let d(n) = 0. What is n?
-6, 0
Suppose 5*d = -k + 29, 4*k - 1 = 15. Let x be (-3 - d/(60/(-68))) + -2. Factor -x*u**2 + 0*u**3 + 2/3*u**4 + 0 + 0*u.
2*u**2*(u - 1)*(u + 1)/3
Suppose -5*v = 2*i - 41 - 5, 4*i - 4 = v. Let s(j) be the first derivative of -j**4 + v*j + 8/5*j**5 - 4 - 8*j**3 - 2*j**2. Find w such that s(w) = 0.
-1, 1/2, 2
Let q = -83 + 88. Factor -32*y**2 - 16*y + y**4 + 18*y**3 - 38*y**3 - q*y**4.
-4*y*(y + 1)*(y + 2)**2
Suppose 4*c + 3 + 1 = 0. Let a(z) = -z**4 - z**3 + z**2 - 3*z + 4. Let s(h) = -h**2 + 1. Let n(y) = c*a(y) + 4*s(y). Suppose n(i) = 0. Calculate i.
-3, 0, 1
Suppose -i - 8 = -3*k, -4*k = i - 5 - 8. Let p(u) be the first derivative of 2 + 12*u**2 + 1/2*u**4 + 4*u**k + 16*u. Factor p(j).
2*(j + 2)**3
Suppose -17 + 25 = 5*u - 7*v, 3*u - 4*v = 5. Find y, given that -y - 5/2*y**2 + 1/2*y**4 - 1/4*y**5 + 2 + 5/4*y**u = 0.
-2, -1, 1, 2
Let t = -7 + 11. Suppose 5 = t*p - 3. Suppose 3*k**2 + 21*k**5 - 3*k**3 + 2*k**p + 36*k**3 - 48*k**4 - 11*k**2 = 0. Calculate k.
0, 2/7, 1
Factor 44/21*g**2 + 46/21*g + 0 - 2/21*g**3.
-2*g*(g - 23)*(g + 1)/21
Let x(f) = -f**4 - f**3 - f**2 + 1. Let c(o) = 12*o**5 - 146*o**4 + 50*o**3 + 2*o**2 - 2. Let y(i) = c(i) + 2*x(i). Factor y(u).
4*u**3*(u - 12)*(3*u - 1)
Let i(c) be the first derivative of -c**3/12 + 3*c**2/8 + 27*c/2 + 120. Find z such that i(z) = 0.
-6, 9
Suppose -4*o = 5*n - 14, -2*n - 12 = 3*o - 19. Factor -4/3*i**n + 0 + 4/3*i + 1/3*i**3.
i*(i - 2)**2/3
Suppose -6*q + 7*q - 5 = 0. Suppose 0 = 2*h + 2*l - 3 + q, -3*h + 3*l = -21. Determine d, given that 1/5*d + 0 - 1/5*d**h + 0*d**2 = 0.
-1, 0, 1
Suppose 25/2*k - 99/8*k**3 + 5/2*k**2 + 0 - 1/8*k**5 - 5/2*k**4 = 0. What is k?
-10, -1, 0, 1
Let u be 1 - 0 - 18*-1. Suppose l = 3*f - 18 + 5, 0 = -3*l + 5*f - u. What is o in 4*o + l*o**2 + o**2 + 2*o = 0?
-2, 0
Let k(a) be the second derivative of -a**8/112 + a**6/40 + a**2 - 12*a. Let b(z) be the first derivative of k(z). Let b(m) = 0. What is m?
-1, 0, 1
Let u(y) be the first derivative of 5*y**3/3 - 3*y**2/4 - 26. Suppose u(w) = 0. Calculate w.
0, 3/10
Let l(a) be the second derivative of -a**4/54 - 4*a**3/9 - 11*a**2/9 - 115*a + 2. Determine y, given that l(y) = 0.
-11, -1
Let a(d) = -7*d**3 + 57*d**2 - 11*d. Let y(m) = -3*m**3 + 29*m**2 - 6*m. Let p(j) = 6*a(j) - 13*y(j). Solve p(x) = 0 for x.
-12, 0, 1/3
Let t(c) be the first derivative of -c**6/12 + 7*c**5/10 + c**4/8 - 7*c**3/6 - 310. Determine q so that t(q) = 0.
-1, 0, 1, 7
Let g(d) = 13*d**4 - 42*d**3 - 9*d**2 + 74*d + 20. Let c(q) = -27*q**4 + 84*q**3 + 21*q**2 - 147*q - 39. Let a(p) = 4*c(p) + 9*g(p). Solve a(t) = 0 for t.
-1, -1/3, 2, 4
Let x = 1287616/15597 - -1/5199. Let l = 83 - x. Let l*g**2 - 2/9*g**5 + 2/9*g - 4/9*g**4 + 0*g**3 + 0 = 0. What is g?
-1, 0, 1
Solve 2*m - 2*m - 4*m - 5*m - 15*m**2 + 27 - 3*m**3 = 0.
-3, 1
Let s(q) be the second derivative of q**5/60 + 35*q**4/36 - 2*q**3 + 903*q. Let s(y) = 0. What is y?
-36, 0, 1
Let f be (28 + -2)/(0 + 2). Suppose 5*v - f = 27. Suppose 5*n - 12*n**3 - 5*n + 4*n**2 + v*n**4 = 0. What is n?
0, 1/2, 1
Let q(s) be the second derivative of s**6/120 - s**5/20 + s**4/8 - s**3/6 + s**2/2 + 11*s. Let v(k) be the first derivative of q(k). What is z in v(z) = 0?
1
Let j(l) = 33*l**2 + 134*l + 8. Let x be j(-4). Let v(s) be the second derivative of 11*s + 0 + 2/3*s**2 - 1/36*s**4 + x*s**3. Let v(d) = 0. Calculate d.
-2, 2
Let c(w) be the third derivative of -w**6/120 - w**5/20 + w**4/4 + 4*w**3/3 - 4*w**2 - 16. Factor c(l).
-(l - 2)*(l + 1)*(l + 4)
Let o(y) = -3*y**2 - 3. Let g(s) = s**2 + 1. Let p(k) = -2*g(k) - o(k). Let c(h) = 7*h**2 - h + 4. Let v(b) = c(b) - 6*p(b). Determine d, given that v(d) = 0.
-1, 2
Suppose 0 = 4*z - 3*i - 1 + 2, -2*z + 4*i - 8 = 0. Factor z*t**4 + 28*t**3 + 2*t**4 - 6*t**2 - t**4 - 31*t**3.
3*t**2*(t - 2)*(t + 1)
Solve -11 + 11*o + 38 + 6*o**2 + 19*o - 3*o**2 = 0 for o.
-9, -1
Suppose -3*c = -0*c + 2*k - 14, -4*c + 2*k = -14. Find s such that -55*s**2 + 17*s - 22*s + 105*s**3 + 15*s - 85*s**c + 25*s**5 = 0.
0, 2/5, 1
Let q(b) be the first derivative of b**6/24 - b**5/4 + 3*b**4/16 + 5*b**3/12 - b**2/2 + 101. Suppose q(z) = 0. Calculate z.
-1, 0, 1, 4
Let u = 1293 - 1292. Let s(z) be the first derivative of 8/21*z**3 - 1/21*z**6 - 3/7*z**4 + 0*z - 1/7*z**2 + u + 8/35*z**5. Determine l, given that s(l) = 0.
0, 1
Let j(k) = -k**3 - 3*k**2 + k. Let y(a) = 2*a**3 + 3*a**2 - 2*a. Let m(g) = -4*j(g) - 4*y(g). Factor m(w).
-4*w*(w - 1)*(w + 1)
Let z(y) = -165*y + 6767. Let i be z(41). Determine x so that -50/11*x**3 - 8/11 + 32/11*x - 10/11*x**i = 0.
-1, 2/5
Let j = 2243/70 - 32. Let i(h) be the third derivative of 0 + 0*h**3 + 1/105*h**6 + 1/42*h**4 + 0*h + 7*h**2 + j*h**5. Factor i(y).
2*y*(y + 2)*(4*y + 1)/7
Let y(r) be the third derivative of 0*r**6 - 17*r**2 + 0*r**3 + 0*r**5 + 0*r**4 - 2/105*r**7 + 0*r + 0. Factor y(a).
-4*a**4
Let z(p) be the second derivative of p**7/14 + 15*p**6/2 + 675*p**5/2 + 16875*p**4/2 + 253125*p**3/2 + 2278125*p**2/2 - 2*p - 57. Suppose z(o) = 0. Calculate o.
-15
Let 97*p**2 - 204 - 140*p - 93*p**2 - 92 = 0. Calculate p.
-2, 37
Let d(w) be the second derivative of 1/165*w**6 + 16*w - 4/33*w**3 + 0 + 0*w**2 + 1/110*w**5 - 2/33*w**4. Solve d(h) = 0.
-2, -1, 0, 2
Let o(k) be the third derivative of k**5/25 + 13*k**4/30 + 8*k**3/15 - 10*k**2 + 2*k. Factor o(a).
4*(a + 4)*(3*a + 1)/5
Let w(c) be the first derivative of 3*c**4/8 - 99*c**3/2 - 603*c**2/4 - 303*c/2 + 842. Find d such that w(d) = 0.
-1, 101
Let x(n) = -n**3 + 12*n**2 - 6*n + 7. Let s(h) = -h**2 - 1. Let d(m) = 14*s(m) + 2*x(m). Suppose d(y) = 0. What is y?
0, 2, 3
Find u such that -29/5*u + 6/5 - 41/5*u**2 - 6/5*u**3 = 0.
-6, -1, 1/6
Let w(i) be the second derivative of -i**6/10 + i**4/4 + 64*i + 1. Factor w(h).
-3*h**2*(h - 1)*(h + 1)
Let f = -3/439 - -1771/2195. Let 2/5*w**2 + 2/5*w - f = 0. Calculate w.
-2, 1
Let c(n) = -n**4 + 160*n**3 - 454*n**2 + 436*n - 145. Let z(u) = u**4 - 320*u**3 + 909*u**2 - 871*u + 290. Let a(d) = 9*c(d) + 4*z(d). Factor a(g).
-5*(g - 29)*(g - 1)**3
Suppose 3*m - 2073*b + 2075*b = -10, 0 = 4*m - 3*b - 15. Factor 0*a**2 - 2/3*a**5 + m + 2/3*a**3 + 0*a + 0*a**4.
-2*a**3*(a - 1)*(a + 1)/3
Let s(t) be the third derivative of -t**7/105 - 2*t**6/5 - 83*t**5/30 - 5*t