n**5/540 + n**4/108 - 9*n**2. Determine c, given that g(c) = 0.
-2, 0
Let l = 77/18 - 34/9. Suppose -l*a**2 + 0*a - 1/6*a**3 + 0 = 0. Calculate a.
-3, 0
Let l(v) be the second derivative of 0*v**4 - 1/165*v**6 - 1/231*v**7 + 0 + 0*v**3 + 0*v**5 + 8*v + 0*v**2. Factor l(f).
-2*f**4*(f + 1)/11
Suppose 10 = d - 21. Factor -1 - 2*u**5 + 1 - d*u**3 + 33*u**3.
-2*u**3*(u - 1)*(u + 1)
Let f = 211/2 + -105. Determine w so that f*w + 0 + 1/2*w**3 - w**2 = 0.
0, 1
Let i(x) be the third derivative of x**6/240 + x**5/60 - x**4/16 - 16*x**2. Factor i(y).
y*(y - 1)*(y + 3)/2
Let j = 7 - 5. Determine v so that 2*v - v**3 - v - 3*v**j + 3*v**2 = 0.
-1, 0, 1
Let f(w) be the second derivative of w**5/5 + 10*w**4/3 + 50*w**3/3 - 10*w. Suppose f(p) = 0. Calculate p.
-5, 0
Let l(z) be the second derivative of 0 + 1/60*z**5 + 3*z + 0*z**6 - 1/126*z**7 + 0*z**2 + 0*z**4 + 0*z**3. Suppose l(y) = 0. What is y?
-1, 0, 1
Let n(h) be the third derivative of h**8/448 - h**7/280 + 8*h**2. Factor n(k).
3*k**4*(k - 1)/4
Let m(l) be the second derivative of l**7/210 + l**6/75 - l**5/100 - l**4/30 - 28*l. Solve m(y) = 0 for y.
-2, -1, 0, 1
Let f(i) be the first derivative of 5*i**4/6 - 2*i**3/9 + 5. Factor f(q).
2*q**2*(5*q - 1)/3
Suppose -5*k + 5*z = -10, -k + 2*z + 4 = 3*z. Suppose 0*q + 12*q**k - 25/3*q**5 + 10*q**4 + 0 + 8/3*q**2 = 0. What is q?
-2/5, 0, 2
Let c(t) be the third derivative of -t**5/30 - 2*t**4/3 - 4*t**3 - 3*t**2 + 5. Factor c(d).
-2*(d + 2)*(d + 6)
Factor 6*n**2 + 15/2*n + 3 + 3/2*n**3.
3*(n + 1)**2*(n + 2)/2
Let p(l) = -9*l**2 + 3*l + 6. Let c be -1 - -3 - 50/5. Let r(h) = -3*h**2 + h + 2. Let f(u) = c*r(u) + 3*p(u). Factor f(i).
-(i - 1)*(3*i + 2)
Determine a so that 4/7*a**3 + 8/7*a**5 + 2/7 + 16/7*a**2 - 18/7*a**4 - 12/7*a = 0.
-1, 1/4, 1
Let h(r) = 36*r**2 - 9*r + 36. Let d(i) = -7*i**2 + 2*i - 7. Suppose 0 = g + 1 - 5. Let o(q) = g*h(q) + 21*d(q). Factor o(f).
-3*(f - 1)**2
Suppose 0 + 0*s**2 + 2/9*s**3 - 4/9*s**4 + 2/9*s**5 + 0*s = 0. What is s?
0, 1
Let z(i) be the third derivative of -i**5/12 - 35*i**4/24 + 20*i**3/3 + 20*i**2. Suppose z(o) = 0. Calculate o.
-8, 1
Factor 4*v**2 - v**2 - 4*v**3 + 2*v**2 - 4*v + 3*v**2.
-4*v*(v - 1)**2
Suppose -2*k + 50 = 3*k. Let r(u) = 3*u**2 - 2*u - 2. Let p(y) = -5*y + 8*y**2 - 3 - 2 - y**2. Let w(t) = k*r(t) - 4*p(t). Suppose w(q) = 0. Calculate q.
0
Let i(r) = -r**3 - 5*r**2 - 5*r + 1. Let f be i(-4). Factor 3*w**2 - f - 4*w**2 + 1 + 5.
-(w - 1)*(w + 1)
Suppose 39/5*n**2 + 12/5 + 68/5*n - 168/5*n**3 + 49/5*n**4 = 0. What is n?
-2/7, 1, 3
Suppose 36 = -2*n + 6*n. Let i(o) = o**2 - 9*o + 2. Let u be i(n). Let -6/7*x**3 + 2/7*x + 4/7 - 8/7*x**u = 0. What is x?
-1, 2/3
Suppose -15*k = 3*u - 18*k - 21, -10 = 2*k. Factor -1/7*p - 2/7 + 1/7*p**u.
(p - 2)*(p + 1)/7
Let 1/8*n**3 + 1/8*n**2 - 1/8*n - 1/8 = 0. What is n?
-1, 1
Suppose -1/2*c - 1/4*c**2 + 0 = 0. Calculate c.
-2, 0
Let a(b) = 10*b**4 + 4*b**3 - b**2 - 9*b. Let o(d) = -9*d**4 - 4*d**3 + d**2 + 8*d. Let t(p) = -6*a(p) - 7*o(p). Solve t(j) = 0 for j.
-1, 0, 2/3
Let u(v) be the first derivative of v**4/36 - v**3/18 - v**2/3 + 2*v + 4. Let c(k) be the first derivative of u(k). Suppose c(q) = 0. Calculate q.
-1, 2
Let 0*l + 0 + 6/5*l**4 + 8/5*l**3 + 2/5*l**2 = 0. What is l?
-1, -1/3, 0
Let u = 2 + 0. Determine m, given that 2*m + u*m - 4*m + m**4 - m**2 = 0.
-1, 0, 1
Let l = -6 - -5. Let c be 15/((-3)/l) - 3. Let 1/3*i - 2/3 + 1/3*i**c = 0. What is i?
-2, 1
Let r(h) be the first derivative of 5*h**3/3 + 30*h**2 + 180*h - 16. Factor r(t).
5*(t + 6)**2
Let a(p) be the first derivative of 0*p - 1/3*p**2 - 2 + 0*p**3 + 1/3*p**4 - 1/9*p**6 + 0*p**5. Factor a(z).
-2*z*(z - 1)**2*(z + 1)**2/3
Let f be 1/1 - (-1 - 21). Suppose -4*j + f = 5*l, 3*j - 3 = 2*j - 4*l. Factor -2 - j*b - 15*b**2 + 18*b + 0.
-(3*b - 1)*(5*b - 2)
Let m be (-4)/14*(-7)/15. Let c(o) be the first derivative of -1 + 2/5*o - m*o**3 - 1/10*o**4 + 1/5*o**2. Solve c(h) = 0 for h.
-1, 1
Let h(t) be the first derivative of -1/90*t**6 + 1/36*t**4 + 1/60*t**5 + 0*t**2 - 1 - 1/18*t**3 - 2*t. Let w(i) be the first derivative of h(i). Factor w(a).
-a*(a - 1)**2*(a + 1)/3
Suppose 4*g + v + 2*v - 15 = 0, 0 = -g - 5*v + 25. Suppose 2*q - 16 = -x - 2*x, 3*q - 22 = -4*x. Let 0*i**q + g + 0*i - 1/4*i**4 + 1/4*i**3 = 0. What is i?
0, 1
Factor 150/7*c - 180/7*c**2 + 6*c**3 + 375/7 - 3/7*c**4.
-3*(c - 5)**3*(c + 1)/7
Factor -6*n - 10*n**2 + 5*n**2 + 8*n**2.
3*n*(n - 2)
Factor -1 - 8 + 3 - 2*r**2 - 2 - 8*r.
-2*(r + 2)**2
Let r(v) be the third derivative of v**8/560 + v**7/840 - v**6/180 - v**3/6 - v**2. Let t(j) be the first derivative of r(j). Determine w, given that t(w) = 0.
-1, 0, 2/3
Let p(c) be the first derivative of c**6/24 - c**5/20 - c**4/8 - 6. Factor p(g).
g**3*(g - 2)*(g + 1)/4
Let i be (-4*10/40)/((-1)/3). Determine j, given that -6/5*j**i - 1/5*j - 4/5*j**2 - 4/5*j**4 - 1/5*j**5 + 0 = 0.
-1, 0
Let k(h) be the first derivative of -h**3/12 + h/4 + 6. Find v such that k(v) = 0.
-1, 1
Let k be ((-249)/30 - -9)*8/7. Suppose -2/5*w - 2/5*w**3 + 6/5*w**4 + k*w**5 - 6/5*w**2 + 0 = 0. What is w?
-1, -1/2, 0, 1
Suppose -5*z - 4*t + 36 = 0, 3*z + 0*t - 20 = -2*t. Suppose z*n - 2 = -2*h, h = -4*h + 5. Factor 2*s**2 - 2 + n*s + 0*s.
2*(s - 1)*(s + 1)
Suppose -1 = p + 1. Let a be 2 - p - (1 - -1). Factor 0*g + g**a + 1/2*g**3 + 0 - 3/2*g**4.
-g**2*(g - 1)*(3*g + 2)/2
Suppose 0 = g + 2*g - 15. Suppose 4*b + 18 = g*b. Let r(h) = h**2 - h. Let l(u) = 10*u**2 - 11*u. Let q(n) = b*r(n) - 2*l(n). Let q(z) = 0. What is z?
0, 2
Let z(g) be the third derivative of g**6/90 + g**5/10 + g**4/3 - 3*g**3/2 + 4*g**2. Let k(t) be the first derivative of z(t). Factor k(j).
4*(j + 1)*(j + 2)
Let m = -6/67 + 298/335. Suppose 24/5*o**2 - m - 6/5*o - 14/5*o**3 = 0. Calculate o.
-2/7, 1
Suppose 8*y = 6*y. Factor -2*l**3 + y*l**3 + 5*l**2 + 2*l**5 + 4*l**3 - 4*l + l**2 - 6*l**4.
2*l*(l - 2)*(l - 1)**2*(l + 1)
Let f(u) = 6*u - 46. Let s be f(8). Factor -1/2*d + 1/4*d**s + 1/4.
(d - 1)**2/4
Factor 72/7*x**2 + 3/7*x**4 + 96/7*x + 48/7 + 24/7*x**3.
3*(x + 2)**4/7
Let t = 815/962 - 1/962. Let r = t - -19/39. Factor 0 + 1/3*b - r*b**2.
-b*(4*b - 1)/3
Let -1 - 3/2*h + 5/2*h**2 = 0. What is h?
-2/5, 1
Let h(g) be the first derivative of 4*g**6/9 - 22*g**5/15 + g**4/6 + 26*g**3/9 - 5*g**2/3 - 4*g/3 - 2. Suppose h(t) = 0. What is t?
-1, -1/4, 1, 2
Find r, given that 0 + 0*r + 1/4*r**3 - 1/2*r**4 + 0*r**2 + 1/4*r**5 = 0.
0, 1
Solve -5*j**3 - j**2 + 7*j**3 + 5*j**2 + 2*j = 0 for j.
-1, 0
Find z such that 0*z - 1/4*z**2 + 0 = 0.
0
Let n(d) = -5*d**3 + 12*d**2 + 8*d - 15. Let k(t) = -10*t**3 + 23*t**2 + 17*t - 30. Let p(f) = -3*k(f) + 7*n(f). Let p(s) = 0. What is s?
-1, 1, 3
Suppose 23 - 7 = 2*c. Suppose -c - s**2 + 8 = 0. Calculate s.
0
Let p = 4681/3118 - 2/1559. Find m such that 2*m + 1/2 + p*m**2 = 0.
-1, -1/3
Let f = 2/11 - -7/22. Factor 1/2*a + 0*a**2 + 0 - f*a**3.
-a*(a - 1)*(a + 1)/2
Let w(h) = -1 + 3 - 4 + 7*h**2 - 5*h**2. Let g be w(1). Suppose 0 + 0*c**2 - 1/3*c**5 + 1/3*c**4 + 0*c**3 + g*c = 0. What is c?
0, 1
Let n(x) be the third derivative of x**7/105 + x**6/24 + x**5/15 + x**4/24 + 2*x**2. Let n(t) = 0. Calculate t.
-1, -1/2, 0
Suppose 0*m - 3*m = 4*m. Factor 0*g**2 - 6*g**4 + m + 0*g - 3/2*g**5 - 6*g**3.
-3*g**3*(g + 2)**2/2
Let u(k) be the first derivative of 243*k**4/20 + 63*k**3/5 - 51*k**2/10 + 3*k/5 + 7. Let u(l) = 0. Calculate l.
-1, 1/9
Let h = 419 - 419. Suppose -1/3*x**3 + h*x - 1/3*x**2 + 0 = 0. What is x?
-1, 0
What is t in -8*t**4 - 20*t + 21*t**3 + 15*t**2 + 3*t**4 - 15 - 5 - 11*t**3 = 0?
-1, 2
Let m(b) = -6*b**4 - 33*b**3 - 18*b**2 + 33*b + 33. Let n(d) = 3*d**4 + 17*d**3 + 9*d**2 - 17*d - 17. Let o(a) = 5*m(a) + 9*n(a). Solve o(q) = 0 for q.
-2, -1, 1
Let j(c) be the third derivative of -c**8/336 - c**7/210 + c**6/120 + c**5/60 - 3*c**2. Factor j(r).
-r**2*(r - 1)*(r + 1)**2
Let v be -2 + (-1)/(3/6). Let a = v - -6. Let -1 + 2 + 8*y**4 + 2*y**3 + 0 - a*y - 9*y**2 = 0. What is y?
-1, -1/2, 1/4, 1
Suppose 0 = s - 4*j - 20, -3*s + 5*j + 25 = -2*s. Let k(d) be the third derivative of s + 2/15*d**3 + 2*d**2 + 0*d + 1/30*d**5 - 7/60*d**4. Factor k(f).
2*(f - 1)*(5*f - 2)/5
Suppose 24 = 13*p - 12*p. Factor 25*d**3 - 12*d**3 + 8*d + p*d**2 + 5*d**3.
2*d*(3*d + 2)**2
Let i = 162 + -160. What is o in 0*o**i - 2/11*o + 2/11*o**3