i - 21 = 3*v. Factor 0 + k**i + 0*k - 1/2*k**4 + 0*k**2.
-k**3*(k - 2)/2
Let m be 6 - 4/(8/6). Let a(i) be the third derivative of 0*i + 0 + 1/6*i**m + 1/60*i**5 - 1/12*i**4 + 3*i**2. Find s such that a(s) = 0.
1
Let p = 179/6 + -59/2. Let m(y) be the first derivative of -3 + 1/2*y**2 - 1/4*y**4 + y - p*y**3. Determine u so that m(u) = 0.
-1, 1
Suppose -3*x - 3*t = 3, 2*t - 3*t = 3. Factor -100*m**x - 67*m - 10*m - 3*m + 59 - 75.
-4*(5*m + 2)**2
Suppose 4*a - 10 = -a. Factor 11 - 27*w**a - 6*w - 21*w**3 - 11.
-3*w*(w + 1)*(7*w + 2)
Suppose -2*k - 2*k - 6 = -2*d, 5*k - 3*d = -9. Let h(c) be the first derivative of 2/3*c**3 + 1 + 2*c**2 + k*c. Factor h(g).
2*g*(g + 2)
Let g = -14 - -20. Let s(p) be the third derivative of 0*p**3 + 0*p**g + p**2 + 0*p + 0*p**4 + 1/105*p**7 - 1/168*p**8 + 0 + 0*p**5. Factor s(a).
-2*a**4*(a - 1)
Let k(g) = -g**2 + 5*g - 3. Let u be k(3). Factor 0 - 1 + 1 - 2*s**2 + 2*s**u.
2*s**2*(s - 1)
Let w be ((-26)/(-10) - 3)*-5. Suppose 13 = 5*a - w. Suppose 1/4*m + 1/4 - 1/4*m**2 - 1/4*m**a = 0. Calculate m.
-1, 1
Let x be 1 + (-2)/12*-3. Let n = -31 - -34. What is s in -x*s**2 + 2 + 0*s + 1/2*s**n = 0?
-1, 2
Let l(d) be the second derivative of d**4/12 + d**3/6 + 6*d. What is b in l(b) = 0?
-1, 0
Let 1/5*c**4 - c**3 - 7/5*c + 2/5 + 9/5*c**2 = 0. What is c?
1, 2
Let j be (1/2 - -1)*-2. Let g = j + 6. Find d, given that 7*d**4 + 0*d**3 + 8*d**3 + 9*d**4 + 4*d**2 + 6*d**5 + 6*d**g = 0.
-1, -2/3, 0
Suppose -5*y + s + 5 = 0, 4*s + 18 = -4*y - 2. Let h be ((-4)/(-8))/(3/2). Find g such that -2/3*g**5 + 1/3*g + g**4 - g**2 + h*g**3 + y = 0.
-1, 0, 1/2, 1
Let v(s) = -5*s**3 + 11 + s + 12*s**3 - 5 - 10*s**2. Let j(z) = -z**3 + z**2 - z. Let g(q) = 4*j(q) + v(q). Factor g(m).
3*(m - 2)*(m - 1)*(m + 1)
Determine q so that -1/12*q - 1/12*q**3 + 0 - 1/6*q**2 = 0.
-1, 0
Let b be 3 + (2 - 3) + (-117)/(-39). Let -3/4*l**3 - 1/2*l**2 + 0*l + 0 + 3/4*l**b + 1/2*l**4 = 0. What is l?
-1, -2/3, 0, 1
Suppose -3*a = -5*w - 37, 0 = -a + w - 2*w - 1. Suppose -5*x**3 + 0*x - 8*x**2 + 5*x + 3*x**2 + 3*x**a + 2 = 0. What is x?
-1, -1/3, 1, 2
Let s(n) be the third derivative of 7*n**10/4320 + n**9/540 + n**8/1680 - n**4/24 - n**2. Let f(r) be the second derivative of s(r). Factor f(v).
v**3*(7*v + 2)**2
Factor -6/7*a**2 - 2/7*a**3 - 4/7 + 2/7*a**4 + 10/7*a.
2*(a - 1)**3*(a + 2)/7
Let z = 105 - 103. Let p(x) be the first derivative of 2/27*x**3 + 0*x - 1 + 0*x**z. Solve p(l) = 0 for l.
0
Let w(s) = 3*s**2 - 3*s - 3. Let g be w(-1). Let i(c) be the second derivative of -1/21*c**g - c + 0*c**2 + 1/42*c**4 + 0. Find z, given that i(z) = 0.
0, 1
Let i(w) = -2*w**5 - 19*w**4 + 33*w**3 - 14*w**2 - 10*w. Let c(r) = r**5 + 19*r**4 - 32*r**3 + 13*r**2 + 9*r. Let k(f) = -6*c(f) - 5*i(f). Factor k(q).
q*(q - 2)**2*(q - 1)*(4*q + 1)
Let a = -55 + 89. Let 15*u**5 - 10*u**2 - 27*u**5 - u + a*u**4 - 16*u**3 + 5*u = 0. Calculate u.
-1/2, 0, 1/3, 1, 2
Let n(v) be the second derivative of -v**6/1260 + v**4/84 - v**3/3 + v. Let w(g) be the second derivative of n(g). What is j in w(j) = 0?
-1, 1
Factor 75/2 + 3/2*l**4 - 60*l + 9*l**2 + 12*l**3.
3*(l - 1)**2*(l + 5)**2/2
Let x be 7/(-21) + 7/3. Let a be 16/(-20)*5/(-2). Factor 8*u + x*u + 3*u**a + 0*u + 3 - 4*u.
3*(u + 1)**2
Let y be (-5)/(-20) - 9/60. Let t(u) be the first derivative of y*u**4 - 1 + 0*u - 4/15*u**3 + 1/5*u**2. What is d in t(d) = 0?
0, 1
Let m be 4/6 - 8/12. Let -2*b + m*b**2 - 2*b**2 + b**5 + b + 2*b**4 = 0. Calculate b.
-1, 0, 1
Let d be 7/(-14) + (-31)/(-2). Let u be 3/6 - d/54. Factor 2/9*c**2 + 0*c + 0 - 4/9*c**3 + u*c**4.
2*c**2*(c - 1)**2/9
Let o(w) = 10*w**3 - 44*w**2 - 44*w - 26. Let n(t) = -t**3 + 5*t**2 + 5*t + 3. Let c(d) = -52*n(d) - 6*o(d). Factor c(g).
-4*g*(g - 1)*(2*g + 1)
Find p such that -12/5*p**2 + 27/5*p + 6/5 + 27/5*p**5 - 54/5*p**3 + 6/5*p**4 = 0.
-1, -2/9, 1
Let r be (-3 - -2)*-3*3. Find x, given that 2*x**2 - 4*x**2 - 4*x**2 - 3*x**4 + r*x**3 = 0.
0, 1, 2
Let z(a) be the third derivative of -a**5/270 + a**4/36 + 4*a**2. Factor z(y).
-2*y*(y - 3)/9
Let s be 2 + -1 + (-6)/12*2. Let r(t) be the first derivative of 3 + 1/8*t**2 + s*t - 1/12*t**3. Find y, given that r(y) = 0.
0, 1
Let f(x) be the second derivative of x**7/6 + 8*x**6/15 - 3*x**5/20 - 4*x**4/3 - 2*x**3/3 + 6*x. Determine w so that f(w) = 0.
-2, -1, -2/7, 0, 1
Let c be -6*2*(177/45 + -4). Factor -c + 2/5*g + 2/5*g**2.
2*(g - 1)*(g + 2)/5
Determine h, given that -8/7*h + 8/7*h**3 + 2/7*h**2 - 2/7 = 0.
-1, -1/4, 1
Factor 5*s**3 - 32*s**2 + 23*s**2 + 19*s**2.
5*s**2*(s + 2)
Let d be 2/(-4)*6/(-150). Let p(r) be the second derivative of 0*r**4 - 2*r + d*r**5 - 1/150*r**6 - 1/15*r**3 + 0 + 1/10*r**2. Factor p(x).
-(x - 1)**3*(x + 1)/5
Let f(l) be the first derivative of -1/30*l**4 + 3 - 2*l + 0*l**2 - 1/15*l**3. Let k(c) be the first derivative of f(c). Determine s so that k(s) = 0.
-1, 0
Let h(y) be the second derivative of 3*y**5/80 - y**4/16 - y**3/4 - y. Solve h(s) = 0 for s.
-1, 0, 2
Factor -y + 1/2*y**2 + 0.
y*(y - 2)/2
Let j(l) be the third derivative of l**5/75 - l**4/15 - 2*l**3/5 + 2*l**2. Factor j(t).
4*(t - 3)*(t + 1)/5
Let x(g) be the third derivative of -g**8/24 + 11*g**7/105 - 8*g**6/105 + 2*g**5/105 + 14*g**2. Let x(o) = 0. What is o?
0, 2/7, 1
Let p = 477/2 + -873/4. Let m = p - 883/44. Find a such that 6/11*a**4 + 16/11*a**3 + 12/11*a**2 + 0*a - m = 0.
-1, 1/3
Let w(n) = -n**2 + n - 1. Let v(u) = -11*u**2 + 16*u - 6. Let f(z) = v(z) - 6*w(z). Factor f(r).
-5*r*(r - 2)
Let j be (-1 + 2)/((-1)/(-2)). Suppose -3*p + 5 = 2*p - 5*b, 4*b = j*p. Factor 3*g**2 - g**p - 2*g + 0*g.
2*g*(g - 1)
Let s(g) be the second derivative of 0*g**3 - 6*g + 0 - 1/3*g**4 - 1/5*g**5 + 0*g**2. What is d in s(d) = 0?
-1, 0
Let d(t) be the first derivative of 2*t**3/45 - 2*t/15 + 2. Factor d(n).
2*(n - 1)*(n + 1)/15
Let i be (12/8 + -2)/(-2). Let x(m) be the third derivative of 1/18*m**5 - m**2 + 0*m - 1/20*m**6 + i*m**4 - 1/45*m**7 + 2/9*m**3 + 0. What is j in x(j) = 0?
-1, -2/7, 1
Let x be (2/(-6))/((-4)/8). Solve -x*r + 1/3*r**2 + 1/3 = 0.
1
Let b(x) be the second derivative of x**4/42 + x**3/21 + 3*x. Factor b(t).
2*t*(t + 1)/7
Find x, given that -746*x**5 - 15*x**3 + 741*x**5 + 3*x**2 + 15*x**4 + 2*x**2 = 0.
0, 1
Let i = 53/2 + -26. Let k(l) be the first derivative of -1 + i*l**2 + 0*l + 1/3*l**3. Factor k(d).
d*(d + 1)
Let r(y) be the first derivative of -y**6/2 + 3*y**4/4 + 36. Factor r(m).
-3*m**3*(m - 1)*(m + 1)
Factor -2/3*z**3 + 0 + 0*z**2 + 0*z.
-2*z**3/3
Let j(a) = -a - 3*a + 2*a + 3*a + 15. Let g be j(-13). Factor 2*o - g*o**2 - 2/3 + 2/3*o**3.
2*(o - 1)**3/3
Let f = 1 + 1. Suppose -g + s + 18 = -f*s, 2*s = -4*g + 2. Factor g*i + 5*i**3 - i**3 - 3*i**3 - 4*i.
i*(i - 1)*(i + 1)
Factor 3*z**5 - 6*z**4 + 6*z**2 + 2*z**4 - 2*z**4 - 3*z.
3*z*(z - 1)**3*(z + 1)
Let m(r) = -r**2 - r + 1. Let z(g) = 8*g**2 + 8*g - 18. Let o(u) = 12*m(u) + 2*z(u). Factor o(b).
4*(b - 2)*(b + 3)
Let a(i) be the third derivative of i**5/60 + 3*i**4/8 + 34*i**2. Factor a(u).
u*(u + 9)
Let d(p) be the first derivative of 3/4*p**4 + 0*p**2 - 1/5*p**5 + 1 + 0*p - 2/3*p**3. Factor d(c).
-c**2*(c - 2)*(c - 1)
Determine a, given that 0 - 2/19*a**2 + 8/19*a = 0.
0, 4
Let b(k) be the first derivative of -1/40*k**5 + 1/4*k**4 - k**3 + 2*k**2 + 3 - k. Let t(o) be the first derivative of b(o). Let t(g) = 0. What is g?
2
Let o be 1 - 0*4/12. Solve 5 - 9*x**2 - 2*x - x + 0 + o = 0.
-1, 2/3
Let q(n) be the third derivative of 0 + 0*n - 1/315*n**7 + 1/60*n**6 + 1/36*n**4 + 4*n**2 + 0*n**3 - 1/30*n**5. Factor q(f).
-2*f*(f - 1)**3/3
Suppose -3*i + 9 - 3 = 0. Let o(x) be the first derivative of 2/5*x - 3/5*x**2 - i + 2/5*x**3 - 1/10*x**4. Factor o(c).
-2*(c - 1)**3/5
Let d(p) be the first derivative of 3*p**6/2 - 79*p**5/5 + 171*p**4/4 - 43*p**3 + 8*p**2 + 12*p - 15. Solve d(w) = 0.
-2/9, 1, 6
Let a(f) = -3*f - 33. Let s be a(-12). Determine o, given that -4/5*o**2 + 4/5 - 2/5*o + 2/5*o**s = 0.
-1, 1, 2
Let k(b) be the second derivative of b**4/28 - 3*b**2/14 - 5*b. Factor k(p).
3*(p - 1)*(p + 1)/7
Let n(i) be the first derivative of 8 + 0*i + 1/2*i**2 + 1/6*i**3. Find y such that n(y) = 0.
-2, 0
Suppose 4*c - 2 = -3*a, -3*c + 1 = -0*c + 2*a. Let r be 1 - (2/2)/c. Let 1/5*k**r + 0 + 0*k = 0. What is k?
0
Let f = 8 - 6. Suppose 3*n - 4*g = -f*g + 2, 5 = -2*n - 5*