- 3*c = 0.
-1, 2
Suppose -20 + 2/3*i**3 + 62/3*i - 20/3*i**2 = 0. Calculate i.
2, 3, 5
Suppose 6*n - n - 15*n = 0. Let i(v) be the third derivative of 1/240*v**5 - 7*v**2 + 0 + n*v**3 - 1/96*v**4 + 0*v. Factor i(j).
j*(j - 1)/4
Let k(i) be the first derivative of 3*i**5/5 + 3*i**4/2 - 3*i**3 - 6*i**2 + 12*i - 668. Factor k(y).
3*(y - 1)**2*(y + 2)**2
Let h(z) = -3*z**3 - z**2 - 10*z - 9. Let c be h(-1). Factor 4/7*j**c + 4/7*j**5 + 40/7*j**2 - 32/7 - 16/7*j**4 - 16/7*j.
4*(j - 2)**3*(j + 1)**2/7
Let o = 24 - 20. Factor 4*c**3 - 2*c**o + 3 + 0*c**4 - 2*c**2 - 3.
-2*c**2*(c - 1)**2
Let c be 588/(-686) - (-102)/21. Suppose 0*l - 5/4*l**2 + 15/4*l**3 + 5/4*l**5 - 15/4*l**c + 0 = 0. What is l?
0, 1
Suppose -14 = -5*t - b, 0 = -t + 2*t + 3*b. Solve -216*a**3 - 6*a**4 - a**5 + 220*a**t + 3*a**5 = 0 for a.
0, 1, 2
Determine d, given that 3*d**2 - 4/5*d + 2/5*d**5 + 3/5*d**4 + 0 - 16/5*d**3 = 0.
-4, 0, 1/2, 1
Factor -20*b + 40 - 12*b**2 + 18*b**2 - 11*b**2 - 15*b.
-5*(b - 1)*(b + 8)
What is h in -26/3*h**3 + 150*h - 46*h**2 + 10/3*h**4 - 72 = 0?
-4, 3/5, 3
Suppose -m = -2, f + 0*f = -3*m + 9. Let s(q) = q**2 + 48*q - 47. Let h be s(-49). Factor 2/3*y**5 + 0 - h*y**4 + 4/3*y**f + 0*y + 0*y**2.
2*y**3*(y - 2)*(y - 1)/3
Suppose l + 239*b = 238*b + 4, 5*b - 10 = 0. Suppose -l*s**2 + 0*s + 2/3*s**3 + 0 = 0. What is s?
0, 3
Let b(j) be the first derivative of 0*j - 1/15*j**5 + 1/6*j**4 - 5/2*j**2 - 10 + 0*j**3. Let h(k) be the second derivative of b(k). Solve h(y) = 0.
0, 1
Let n(b) be the first derivative of 4*b**5/5 + 2*b**4 - 16*b**3 + 28*b**2 - 20*b + 68. Determine p so that n(p) = 0.
-5, 1
Let t(y) = -14*y**2 - 11*y - 86. Let x(i) = 33*i**2 + 22*i + 174. Let p(u) = -14*t(u) - 6*x(u). Suppose p(d) = 0. Calculate d.
-5, 16
Suppose -14 - 13*c**2 - 2*c**3 + 25*c**2 + 50*c + 50 = 0. What is c?
-2, -1, 9
Let i be 204/(-10) - 5/(75/(-6)). Let z = i + 22. Factor 0*b + 1/3*b**3 + 1/3*b**z + 0.
b**2*(b + 1)/3
Suppose 0 = 2*n - 81 + 107. Let q be (17/n - -1)*(-1)/2. Factor q*x + 4/13 - 4/13*x**2 - 2/13*x**3.
-2*(x - 1)*(x + 1)*(x + 2)/13
Let q be -7 + 129*5/90. Let y(k) be the first derivative of -3 + 2/3*k**2 - 1/15*k**5 + 1/3*k**3 - q*k**4 - 4/3*k. Factor y(w).
-(w - 1)**2*(w + 2)**2/3
Suppose 3 - 1 = 2*m. Let l(k) = 8*k**3 + 6*k**2 - 2. Let v(c) = -c**3 - c**2 - c + 1. Let q(z) = m*l(z) + 6*v(z). Determine y, given that q(y) = 0.
-2, 1
Let w(c) be the first derivative of c**8/5880 - c**6/1260 - 10*c**3/3 - 6. Let d(z) be the third derivative of w(z). Factor d(l).
2*l**2*(l - 1)*(l + 1)/7
Let q(v) be the first derivative of 21/4*v**4 - 13/3*v**3 - 6*v**2 + 8 + 4*v. What is d in q(d) = 0?
-2/3, 2/7, 1
Let i(k) be the second derivative of k**6/15 - 3*k**5/10 - 2*k**4/3 + 315*k. Determine y, given that i(y) = 0.
-1, 0, 4
Let b(w) = w**3 - 9*w**2 + 26*w - 18. Let a(j) be the first derivative of j**4 - 12*j**3 + 105*j**2/2 - 73*j - 6. Let q(r) = 2*a(r) - 9*b(r). Factor q(x).
-(x - 4)**2*(x - 1)
Let z = 8 - 4. Suppose -4*r = 0, -y - z*r - 2 = -2*y. Factor -6*v - 14*v**2 + 31*v**2 - 15*v**y.
2*v*(v - 3)
Let b be 9*28/378*3. Determine l so that -2/3*l + 1/3 + 1/3*l**b = 0.
1
Factor 8/11*h**3 + 0 - 2/11*h**2 - 1/11*h.
h*(2*h - 1)*(4*h + 1)/11
Suppose d - 5 + 1 = 0. Let b = -5 - -8. Solve -9*x + 9*x - b*x**3 - 3*x**d = 0 for x.
-1, 0
Factor -13*f**5 - 8*f**5 + 24*f**5 - 5*f**5 - 8*f**2 - 10*f**4 - 16*f**3.
-2*f**2*(f + 1)*(f + 2)**2
Let u = 1375 - 1373. Factor -2/13 - 12/13*p - 18/13*p**u.
-2*(3*p + 1)**2/13
Let p(u) be the first derivative of 0*u**2 - 1/360*u**6 + 0*u**5 + 0*u + 2*u**3 + 7 + 1/24*u**4. Let b(o) be the third derivative of p(o). Factor b(x).
-(x - 1)*(x + 1)
Suppose 4*y + 2 = 10. Factor -1 - 3*r - 4*r**2 - 5 + 2*r**y - 5*r.
-2*(r + 1)*(r + 3)
Let t(k) = 13*k**2 + 9*k + 2. Let g(x) = -x**2 + 5864 + 0*x**2 - 5864. Let h be 1/(-1 - (-5)/6). Let s(i) = h*g(i) - t(i). Factor s(q).
-(q + 1)*(7*q + 2)
Let f be 1 + 5/(-6) - 33/(-18). Determine k so that 13*k**3 - k**2 - 7*k**2 - 4*k**4 + f*k**3 - 27*k**3 = 0.
-2, -1, 0
Let w(l) be the second derivative of 21/10*l**2 - 1/20*l**4 + 30*l + 0 + 3/5*l**3. Suppose w(v) = 0. What is v?
-1, 7
Let b = 36253/5 + -7250. Suppose b*n**4 - 6/5*n**3 + 0*n**2 + 3/5*n**5 + 0*n + 0 = 0. Calculate n.
-2, 0, 1
Let 256/5*y**2 + 13*y - 144/5*y**3 - 2/5 = 0. What is y?
-1/4, 1/36, 2
Let p(t) be the second derivative of -3*t**5/20 + 15*t**4/2 - 96*t**3 - 768*t**2 - 71*t. Determine m, given that p(m) = 0.
-2, 16
Let h(g) be the third derivative of -1/56*g**4 + 0*g + 0*g**3 + 2/245*g**7 + 3/70*g**5 + 0 - 38*g**2 - 9/280*g**6. Factor h(p).
3*p*(p - 1)**2*(4*p - 1)/7
Let q be -2 - (-8)/((-160)/52). Let h = q + 263/55. Suppose -12/11 - h*a**2 + 10/11*a = 0. What is a?
2, 3
Determine t, given that -32/3*t + 8 - 2/9*t**3 + 26/9*t**2 = 0.
1, 6
Let n(k) be the first derivative of -45*k - 5/3*k**3 - 15*k**2 + 15. Factor n(w).
-5*(w + 3)**2
Find n such that -9*n**4 - 15*n**3 + 2*n**4 + 20*n + 32*n**4 - 3*n**5 - 2*n**5 - 25*n**2 = 0.
-1, 0, 1, 4
Let c(i) be the first derivative of i**8/1680 + i**7/420 - i**6/120 - i**5/30 + i**4/6 - 5*i**3/3 - 12. Let x(m) be the third derivative of c(m). Factor x(n).
(n - 1)**2*(n + 2)**2
Let o(h) = h**3 - 11*h**2 + 2. Let p be o(11). Suppose -5*r**3 + 7*r + 0*r + 5*r**2 - 7 + 2 - p*r = 0. Calculate r.
-1, 1
Let 11*x - 76*x**2 + 13*x - 11*x**3 + 3*x**3 - 20*x**3 = 0. What is x?
-3, 0, 2/7
Factor 1/5*t**5 + 8/5*t**4 - 44/5*t**3 + 0*t + 0 + 48/5*t**2.
t**2*(t - 2)**2*(t + 12)/5
Let w = 4 - -2. Let v = -251 + 262. Let y(i) = 4*i**2 - 10*i. Let m(h) = -8*h**2 + 19*h. Let f(k) = v*y(k) + w*m(k). Factor f(l).
-4*l*(l - 1)
Let o(w) be the first derivative of w**3/3 + 9*w**2/2 - 22*w - 2. Let s be o(-11). Let -1/4*u - 1/2*u**2 - 1/4*u**3 + s = 0. Calculate u.
-1, 0
Let b(z) = z**3 - z**2 - 9*z - 3. Let k be b(4). Suppose 5*q - k = -i, -i + 5 = q - 4*i. Factor 32*c + 18*c**q - 6*c**2 + 9*c + 12 - c.
4*(c + 3)*(3*c + 1)
Let j = 10777/24 - 449. Let f(l) be the first derivative of 0*l + 0*l**2 + j*l**6 + 1/12*l**3 - 1/16*l**4 - 1/20*l**5 + 7. Suppose f(r) = 0. Calculate r.
-1, 0, 1
Let n(s) = -2*s**2 + 15*s - 6. Let c be n(7). Let q be 1 - c/(-4)*2. Factor q - 3/2*w**2 + 0*w.
-3*(w - 1)*(w + 1)/2
Let i(y) be the first derivative of y**4/24 - y**3/3 + y**2 - 44*y - 8. Let v(l) be the first derivative of i(l). Let v(h) = 0. Calculate h.
2
Let n(z) be the second derivative of 2*z**2 - 7/6*z**3 + 1/20*z**5 + 1/6*z**4 + 0 - 5*z. Factor n(l).
(l - 1)**2*(l + 4)
Let o be 6 - (120*3/171 - 4/38). Suppose 0 + 0*z + 4/15*z**2 - 2/15*z**o + 2/15*z**3 = 0. What is z?
-1, 0, 2
Suppose -3*u + 2*m + 5 = 0, -m + 40 = 5*u + 2*m. Solve -8*r**3 + 13*r**2 - r**2 + 6*r**u + 3*r - r - 8*r**4 + 10 - 14 = 0.
-1, -2/3, 1
Let t(f) be the second derivative of f**7/210 - 257*f**6/150 + 16123*f**5/100 + 49921*f**4/60 + 5044*f**3/3 + 1690*f**2 - 445*f. Factor t(n).
(n - 130)**2*(n + 1)**3/5
Let t = 40 + -36. Let n be (-176)/(-160) - 2/t. Factor -3*w**3 + 6/5 + 27/5*w**2 - 21/5*w + n*w**4.
3*(w - 2)*(w - 1)**3/5
Suppose -12/5*i**3 - 6/5*i**2 + 4*i - 2/5*i**4 + 0 = 0. What is i?
-5, -2, 0, 1
Let n(x) be the third derivative of 0*x - 1/140*x**5 - 1/14*x**3 - 15*x**2 + 0 + 1/28*x**4. Factor n(v).
-3*(v - 1)**2/7
Let c(p) be the second derivative of p**4/96 - p**3/4 + 11*p**2/16 + 50*p - 3. Solve c(v) = 0 for v.
1, 11
Let u(l) = l + 12. Let x be u(-9). Suppose -12 = -7*g + x*g. Factor -2*q - 2*q**2 + g*q**2 + 0*q.
q*(q - 2)
Suppose -261*p - 9 = -264*p. Let n(o) be the second derivative of 0 + 1/2*o**p - 3*o**2 + 5/4*o**4 + 3/10*o**5 + o. Let n(v) = 0. Calculate v.
-2, -1, 1/2
Let m be ((-1442)/(-12))/7 + (-200)/12 + 17. Find p such that -10 + 115/2*p**4 - 50*p + 65/2*p**3 + m*p**5 - 95/2*p**2 = 0.
-2, -1, -2/7, 1
Factor -1/3*i**3 - 13*i + 11/3*i**2 + 15.
-(i - 5)*(i - 3)**2/3
Let i(v) = -16*v**3 + 120*v**2 + 314*v + 14. Let y(a) = -6*a**3 + 40*a**2 + 105*a + 5. Let q(u) = -5*i(u) + 14*y(u). Factor q(j).
-4*j*(j + 5)**2
Determine y, given that -2/19*y**4 - 1210/19*y**3 + 16484816/19 - 243612/19*y**2 - 16239992/19*y = 0.
-202, 1
Let r = -795 + 799. Let n(d) be the third derivative of 0*d**3 - 1/120*d**6 + 0*d + 10*d**2 - 1/48*d**r - 1/48*d**5 + 0 - 1/840*d**7. Factor n(k).
-k*(k + 1)**2*(k + 2)/4
Let n(b) be the third derivative of -b**5/12 + 35*b**4/8 + 55*b