**5/15 + 101*p**4/12 + 50*p**3/3 - 500*p**2. Factor u(y).
2*(y + 50)*(2*y + 1)
Let k be (1/(-3))/(-1) - ((-68)/15)/68. Determine w so that 0 + 1/10*w**3 - k*w + 1/10*w**4 - 2/5*w**2 = 0.
-2, -1, 0, 2
Factor 1 + 1/4*a**2 + 5/4*a.
(a + 1)*(a + 4)/4
Let j(t) be the third derivative of t**10/196560 - t**8/43680 - 11*t**4/24 - 4*t**2. Let n(a) be the second derivative of j(a). Suppose n(w) = 0. What is w?
-1, 0, 1
Let z(k) be the second derivative of k**7/210 - k**6/120 - k**5/20 + 5*k**4/24 - k**3/3 - 10*k**2 + 16*k. Let f(a) be the first derivative of z(a). Factor f(i).
(i - 1)**3*(i + 2)
Let x(o) be the third derivative of o**5/15 - 34*o**4/3 + 130*o**3 + 936*o**2. Factor x(a).
4*(a - 65)*(a - 3)
Let a be (2/(-4) - 63/126)*(-24)/33. Let -a + 32/11*h + 6/11*h**3 - 26/11*h**2 = 0. Calculate h.
1/3, 2
Suppose 18*v - 39 = 5*v. Let 5/4*u**4 - 5/4*u**2 - 5/2*u**v + 0 + 5/2*u = 0. Calculate u.
-1, 0, 1, 2
Let f(p) be the first derivative of -p**5/20 - 15*p**4/16 - 77*p**3/12 - 165*p**2/8 - 63*p/2 + 549. Determine i so that f(i) = 0.
-7, -3, -2
Suppose 9*a - 6*a = 6. Suppose a*c - 3*c = -4*c. Let c*h + 1/2*h**2 + 0 + 1/2*h**3 = 0. What is h?
-1, 0
Let f(o) be the first derivative of -o**5/140 - o**4/84 - 5*o - 1. Let u(g) be the first derivative of f(g). Let u(d) = 0. What is d?
-1, 0
Let r(y) be the third derivative of -y**6/80 - 29*y**5/20 + 59*y**4/16 - 51*y**2 + 3*y. Factor r(b).
-3*b*(b - 1)*(b + 59)/2
Let n = 874 - 872. Let b(r) be the first derivative of 0*r**n - 2/9*r**3 - 2 + 2/3*r. Factor b(d).
-2*(d - 1)*(d + 1)/3
Let y(z) = -1. Let h(q) = -4*q**2 - 28*q + 26. Let v(a) = h(a) - 6*y(a). Suppose v(s) = 0. What is s?
-8, 1
Let f(m) = -13*m**5 + 13*m**4 + 16*m**3 - 6*m**2 + 2*m - 2. Let g(b) = b**5 + 2*b**3 + b**2 - b + 1. Let c(h) = 3*f(h) + 6*g(h). Solve c(o) = 0 for o.
-1, 0, 2/11, 2
Suppose -13456*j - 626*j**3 + 2478*j**3 - 21*j**4 - 20539*j**2 + 5*j**4 - 12860*j**2 - 19961*j**2 = 0. What is j?
-1/4, 0, 58
Let o(i) = i**2 - i - 6. Let x be o(3). Suppose 3*n - 5*r = 0, n - 20 = -5*r - x. Solve -33*d**2 - 5*d - 3*d**3 + n*d + 39*d**2 = 0 for d.
0, 2
Let d(a) = a**3 + a**2 + 10*a + 17. Let w(t) = -t**2 - t + 1. Let g(n) = -4*d(n) + 28*w(n). Let g(o) = 0. What is o?
-5, -2, -1
Let z(h) be the second derivative of -h**5/4 + 185*h**4/12 - 335*h**3/6 - 525*h**2/2 + 114*h + 3. Suppose z(g) = 0. Calculate g.
-1, 3, 35
Let h(v) be the third derivative of v**5/30 + 2*v**4 + 32*v**2 + 2*v. Solve h(c) = 0.
-24, 0
Let d(r) be the third derivative of 0*r**4 - 1/210*r**7 - 1/60*r**5 + 0 + 0*r + 1/60*r**6 - 10*r**2 + 0*r**3. Determine x, given that d(x) = 0.
0, 1
Suppose 0 = -2*f - 2*n - 2, f - 2*n = -f + 18. Let l(z) be the first derivative of -6*z**3 - 4 + 14/5*z**5 + f*z - 5/2*z**4 + 5*z**2. Let l(p) = 0. Calculate p.
-1, -2/7, 1
Let k(d) be the first derivative of 1/12*d**4 - 3 + 0*d - 1/30*d**5 + 0*d**3 - 1/2*d**2. Let w(a) be the second derivative of k(a). Let w(p) = 0. What is p?
0, 1
Let i(v) be the first derivative of -40 + 1/5*v**6 - 1/10*v**4 + 0*v + 0*v**2 + 8/25*v**5 - 4/15*v**3. Factor i(d).
2*d**2*(d + 1)**2*(3*d - 2)/5
Let p(u) be the third derivative of u**8/48 - 2*u**7/21 + u**6/10 + 7*u**5/30 - 19*u**4/24 + u**3 - 38*u**2. Factor p(m).
(m - 1)**3*(m + 1)*(7*m - 6)
Factor 36*b - 2*b**3 + 39*b**2 + b**2 - 19*b**2 + 5*b**3.
3*b*(b + 3)*(b + 4)
Let j(s) be the first derivative of 2*s**3/3 - 39*s**2 + 76*s + 3. Suppose j(h) = 0. What is h?
1, 38
Let s(r) = 4162*r**3 - 3077*r**2 + 342*r + 84. Let o(p) = -4161*p**3 + 3076*p**2 - 341*p - 82. Let h(y) = -3*o(y) - 4*s(y). Factor h(x).
-5*(7*x - 3)**2*(17*x + 2)
Let n(t) = 32*t + 160. Let m be n(-5). Let v(f) = -f**2 + 3*f + 3. Let d be v(3). Factor m + 4*x**2 - 7/4*x**d - x.
-x*(x - 2)*(7*x - 2)/4
Suppose 0 = 6*n - 4 - 14. Factor -y**2 + 9*y**4 - 5*y**2 - 6*y + 6*y**3 - n*y**2.
3*y*(y - 1)*(y + 1)*(3*y + 2)
Let -4/5 - 6/5*j**2 + 14/5*j = 0. Calculate j.
1/3, 2
Let n be 1/(2/(-6)) + 6. Solve -3*k**n - 6*k - 8*k + 5*k - 6 + 6*k**3 = 0.
-1, 2
Suppose -3*j - 95 + 35 = 0. Let t(v) = -24*v**3 - 24*v**2 - 20. Let d(a) = -a**3 - a**2 - 1. Let z(b) = j*d(b) + t(b). Let z(y) = 0. Calculate y.
-1, 0
Let x(c) = -6*c**2 + 12*c - 2. Let i be x(1). Factor 2/3*v**5 - 4/3*v**2 + 8/3*v**i - 4/3 + 8/3*v**3 - 10/3*v.
2*(v - 1)*(v + 1)**3*(v + 2)/3
Let h be (-33)/115*-35 - (8 - 1). Factor -50/23 + 2/23*z**3 - 22/23*z**2 + h*z.
2*(z - 5)**2*(z - 1)/23
Determine z, given that -2/3*z**3 - 8710/3*z - 8450/3 - 262/3*z**2 = 0.
-65, -1
Suppose 3*g - 70 = -4*n, 0*g - g = 2*n - 26. Let y be 3/g + 17/6. Factor -20*u**4 + 3*u - 3*u**2 - 9*u**y - 3*u - 3*u**5 + 11*u**4.
-3*u**2*(u + 1)**3
Let m(v) = v - 17. Let x be m(8). Let g be (-4)/(-3)*(x - -10). Factor -g*d**4 - 8/3*d**2 - 4*d**3 + 0 + 0*d.
-4*d**2*(d + 1)*(d + 2)/3
Let g(p) = -190*p**2 - 97*p - 8. Let y(s) = -188*s**2 - 96*s - 8. Let f(m) = 4*g(m) - 5*y(m). Suppose f(v) = 0. Calculate v.
-2/5, -1/9
Let y(w) = -w**3 + 11*w**2 - 2*w + 25. Let b be y(11). Find r such that 25 + 80*r - 21*r**2 + 65*r**2 + 5*r**4 + 46*r**2 + 40*r**b = 0.
-5, -1
Suppose 4*f - 80*c = -81*c - 5, -f - 5*c = 25. Let g(j) be the second derivative of -4*j + f*j**2 - 1/9*j**3 + 0 - 2/9*j**4. Factor g(x).
-2*x*(4*x + 1)/3
Let f = -24580/9 - -2732. Factor -4/9 - 10/9*b - 2/9*b**3 - f*b**2.
-2*(b + 1)**2*(b + 2)/9
Determine p so that 0 - 45/2*p - 14*p**3 + 3/4*p**4 + 171/4*p**2 = 0.
0, 2/3, 3, 15
Let g be (-1)/((-4)/16*1). Suppose 0 = -k - k + g. Determine r so that 2 + 2*r**2 + 4*r**k - 3 - 5*r**2 = 0.
-1, 1
Let f(b) be the second derivative of b**4/12 + 49*b**3/3 + 2401*b**2/2 - b - 20. Factor f(g).
(g + 49)**2
Let u = -557 + 559. Let b(o) be the second derivative of -1/70*o**6 - 4*o + 0 - 2/7*o**4 - 3/28*o**5 - 2/7*o**3 + 0*o**u. Let b(k) = 0. Calculate k.
-2, -1, 0
Let b(h) be the second derivative of -h**4/126 - 2*h**3/21 - 8*h**2/21 + h - 13. Factor b(l).
-2*(l + 2)*(l + 4)/21
Let y be (-3 - -9)/((-2 - -9) + -1 + -3). What is x in 20/3*x**y + 16/3 + 32/3*x + 4/3*x**3 = 0?
-2, -1
Let f be 1 + 9/5 - 2/(-10). Find l, given that 8*l**2 - 9*l**3 - 5*l**3 + 16*l**3 + 2*l**f = 0.
-2, 0
Suppose 0 = -5*f - 5*k + 15, 6*f - f = -2*k + 6. Suppose f = -3*n - 6 + 21. Solve 2*v**3 - 4*v**3 + 2*v**4 + 2*v**n - 2*v**2 - 2*v**3 + 2*v**3 = 0.
-1, 0, 1
Let h(t) be the first derivative of 4*t**5/5 - t**4 - 8*t**3/3 - 5. Factor h(l).
4*l**2*(l - 2)*(l + 1)
Find k such that 60*k**2 - 276*k - 4*k**3 + 432 + 24*k - 36*k = 0.
3, 6
Let o(p) = -3*p + 21. Let f(l) = -l + 7. Let b(n) = -7*f(n) + 2*o(n). Let j be b(9). Let 18*w**2 + 3*w**3 - 5*w**4 + j*w**4 - 24 + 0*w**4 - 12*w = 0. What is w?
-2, -1, 2
Let n = 748875/121 - 6189. Let f = n + 648/1573. Find t, given that -2/13*t**3 - 2/13 - 6/13*t**2 - f*t = 0.
-1
Determine k so that 0 + 8/11*k**2 + 0*k + 2/11*k**3 = 0.
-4, 0
Let z(d) be the first derivative of -4/21*d**3 + 7 + 0*d + 1/14*d**4 + 1/7*d**2. Factor z(t).
2*t*(t - 1)**2/7
Suppose 0 = 5*y - 3*v - 40, 5*y - 5*v - 16 = 14. Let s = 35/3 - y. Factor s*z**2 - 4*z + 6.
2*(z - 3)**2/3
Let i(k) = 10*k**2 - 10*k + 2. Let j be i(0). Suppose -60*v**j + 8*v**3 - 250 - 2/5*v**4 + 200*v = 0. What is v?
5
Factor 0 + 20/3*b**3 - 2/3*b - 2*b**2.
2*b*(2*b - 1)*(5*b + 1)/3
Let o be 5 - -1 - (-60)/(-10). Let j(q) be the first derivative of -3/4*q**4 + 3/2*q**2 + o*q + 3/5*q**5 - q**3 - 5. Factor j(h).
3*h*(h - 1)**2*(h + 1)
Let b(p) = 7*p**2 + 7*p**3 - 6*p**3 + 9*p - 32 + 53. Let j be b(-6). Suppose 2*t**4 + 0 + 2/3*t**5 + 2/3*t**2 + 2*t**j + 0*t = 0. Calculate t.
-1, 0
Find k such that -51/2*k**2 - 141/2*k**4 - 72*k**3 - 3/4*k + 0 - 93/4*k**5 = 0.
-1, -1/31, 0
Let k(p) be the first derivative of -p**4 + 32*p**3/3 + 8*p**2 - 128*p - 321. Solve k(c) = 0 for c.
-2, 2, 8
Let t(r) = 126*r + 5. Let l be t(5). Factor -8*d**2 + 633*d**4 - d**3 - l*d**4 - 7*d**3.
-2*d**2*(d + 2)**2
Let l(u) = u + 5. Let n be l(4). Suppose n*w - 4 = 7*w. Factor -2/9*q**3 + 0 - 4/9*q**w - 2/9*q.
-2*q*(q + 1)**2/9
Let o be 0 - (-35)/14 - 1. Let w(h) be the first derivative of -h**3 - 4 - o*h**2 + 0*h. Suppose w(x) = 0. What is x?
-1, 0
Let f(u) = 9*u**3 + u - 5. Let n = -50 + 40. Let c(o) = 4*o**3 - 2. Let l(d) = n*c(d) + 4*f(d). Factor l(a).
-4*a*(a - 1)*(a + 1)
Suppose -58940*y**2 + 11 + 4 + 58939*y**2 + 11*y + 11 = 0. Calculate y.
-2, 13
Let t(z) = -3*z + 12. Le