et d = 2 + x. Suppose -2/9*u**d + 0 + 4/9*u = 0. What is u?
0, 2
Let o be 1/9*21/280. Let c(a) be the second derivative of -5/48*a**4 + a - o*a**6 + 0 + 0*a**2 - 1/20*a**5 - 1/12*a**3. Factor c(x).
-x*(x + 1)**2*(x + 2)/4
Let v(t) = 5*t**3 + t**2 - t. Let l be v(1). Suppose 0 = 5*c - 5*j - 25, -31 = -3*c + l*j - 10. Let c*q**5 + 4*q - 6*q + 4*q - 4*q**3 = 0. What is q?
-1, 0, 1
Let g be (3*56/12)/(10 + -5). Factor 2/5*d**3 + g*d - 2*d**2 - 6/5.
2*(d - 3)*(d - 1)**2/5
Factor 2/3*x - 1 + 1/3*x**2.
(x - 1)*(x + 3)/3
Let 10*j**2 - 7 - 7*j**2 - 4*j + 3 + 4*j**3 + j**4 = 0. Calculate j.
-2, -1, 1
Let r(p) be the third derivative of 0 + 1/36*p**4 + p**2 + 1/180*p**5 + 1/18*p**3 + 0*p. Find i, given that r(i) = 0.
-1
Let r(l) be the third derivative of -19/48*l**4 + 0*l - 3/10*l**6 - 1/6*l**3 + 0 + 8*l**2 + 9/224*l**8 - 31/60*l**5 + 0*l**7. Find m, given that r(m) = 0.
-1, -1/3, 2
Suppose 3*c - c = r - 34, 3*c = r - 35. Let a = 162/5 - r. Find p, given that 0*p**2 + 0 + 0*p + a*p**3 = 0.
0
Suppose 0 = 4*c + 11 - 27. Let l(j) be the third derivative of 1/180*j**5 + 0 - 3*j**2 - 1/72*j**c - 1/630*j**7 + 0*j + 0*j**3 + 1/360*j**6. Factor l(r).
-r*(r - 1)**2*(r + 1)/3
Let z(d) be the third derivative of -d**5/20 - d**4/8 + d**3 - 4*d**2. Find n, given that z(n) = 0.
-2, 1
Let i(t) be the second derivative of -t**7/280 + t**6/480 + t**5/40 - t**4/3 - 3*t. Let y(a) be the third derivative of i(a). Suppose y(p) = 0. Calculate p.
-1/2, 2/3
Let p = 3 + -8. Let k be p/(5/3) - -3. Factor k + 1/2*m - 1/2*m**2.
-m*(m - 1)/2
Let -12/11*z + 0 - 2/11*z**2 = 0. What is z?
-6, 0
Let y(j) be the third derivative of j**9/3024 - j**8/840 + j**7/840 + j**3/3 - 5*j**2. Let s(d) be the first derivative of y(d). Factor s(c).
c**3*(c - 1)**2
Let n be 4*(6/(-33) - 15/(-66)). Factor -n*h**3 + 0*h + 0 + 2/11*h**2.
-2*h**2*(h - 1)/11
Let s(m) be the first derivative of 2*m**3/9 - 2*m/3 - 7. Factor s(c).
2*(c - 1)*(c + 1)/3
Let a be (-6)/(-14)*20/6. Find n, given that -16/7*n**2 + 4/7 + 2/7*n + a*n**3 = 0.
-2/5, 1
Let p be -5*1*(1 - 2). Let n(j) = j + 10. Let f be n(-5). Let -4*z - z**f + p*z - z = 0. What is z?
0
Suppose -14 = -3*b + 5*p, -2*b + 5*p + 3 = -8. Determine a, given that 1 - 44*a**b + 42*a**3 + 6*a + 3 = 0.
-1, 2
Let y(m) = 2*m - 14. Let r be y(8). Suppose -a - r*x + 10 = 0, 3*a - 5*x = -2 - 1. Factor 1/6 + 2/3*b**3 + b**2 + 2/3*b + 1/6*b**a.
(b + 1)**4/6
Let j = 5 - 1. Let b be ((-2)/(-4))/(5 - j). Factor -i + b + 1/2*i**2.
(i - 1)**2/2
Suppose 3*q - 3 = -6. Let s(h) = 10*h**3 - 6*h**2 - 3*h - 1. Let y(g) = -g**3 + 1. Let x(c) = q*s(c) - y(c). Determine n so that x(n) = 0.
-1/3, 0, 1
Let n = 2 + 0. Factor -n*u**3 + 2*u**4 + 0*u**3 + 0*u**3.
2*u**3*(u - 1)
Let f(l) be the first derivative of -2*l**3/21 + l**2/7 + 4*l/7 - 9. Suppose f(r) = 0. Calculate r.
-1, 2
Let k(s) be the first derivative of 5*s**4/12 + 20*s**3/9 + 10*s**2/3 + 40. Factor k(t).
5*t*(t + 2)**2/3
Let i(r) be the first derivative of 2/15*r**3 + 1 + 0*r**2 - 2*r - 1/10*r**4 + 1/50*r**5. Let b(y) be the first derivative of i(y). Factor b(p).
2*p*(p - 2)*(p - 1)/5
Let c(n) be the third derivative of n**7/70 - 3*n**6/40 + 3*n**5/20 - n**4/8 - 8*n**2. Factor c(i).
3*i*(i - 1)**3
Suppose q - 6 = 2*q. Let b(g) = g**2 - 9*g - 4. Let r(i) = -i**2 + 8*i + 3. Let f(z) = q*r(z) - 5*b(z). Solve f(x) = 0 for x.
1, 2
Let m(w) be the third derivative of -5*w**8/112 + 11*w**7/35 - 19*w**6/20 + 8*w**5/5 - 13*w**4/8 + w**3 + 16*w**2. Factor m(s).
-3*(s - 1)**4*(5*s - 2)
Let k be 34/66 + (-4)/22. Solve w**2 + 0 + k*w**3 + 2/3*w = 0 for w.
-2, -1, 0
Let y(l) be the second derivative of 25*l**7/63 + l**6/3 - 17*l**5/15 - 7*l**4/9 + l**3 - l**2/3 - 7*l. Suppose y(j) = 0. What is j?
-1, 1/5, 1
Let x = 4992 + -15164/3. Let g = -62 - x. Factor g*m**2 - 4/3*m + 2/3.
2*(m - 1)**2/3
Let i(g) = 16*g**5 - 41*g**3 + 9*g**2 + 16*g + 9. Let n(a) = 4*a**5 - 10*a**3 + 2*a**2 + 4*a + 2. Let c(w) = 2*i(w) - 9*n(w). Suppose c(z) = 0. What is z?
-1, 0, 1
Let a(q) = -q + 1. Let o(l) be the second derivative of 1/12*l**4 + 4*l**2 + 2*l + 0 - 3/2*l**3. Let r(n) = 14*a(n) - 2*o(n). Determine p so that r(p) = 0.
1
Let -8*i**2 + i**5 - i**4 + 2*i + 9*i**2 - 4*i**3 + i**3 = 0. Calculate i.
-1, 0, 1, 2
Let j(a) be the third derivative of a**9/15120 + a**8/6720 - a**7/2520 - a**6/720 + a**4/8 + 6*a**2. Let m(r) be the second derivative of j(r). Factor m(i).
i*(i - 1)*(i + 1)**2
Suppose -y - 13 = -3*q, 0 = 3*q - 0*y - 5*y + 7. Suppose -4 + 2*j**2 + 6 - q*j + 2*j**2 + 0*j**2 = 0. What is j?
1/2, 1
Let d(w) = 22*w**3 - 58*w**2 - 46*w + 22. Let b(j) = -j**3 + j**2 - j - 1. Let z(i) = 6*b(i) + d(i). Determine c so that z(c) = 0.
-1, 1/4, 4
Let y(a) be the first derivative of -2*a**3/21 - 3*a**2/7 - 4*a/7 - 9. Factor y(w).
-2*(w + 1)*(w + 2)/7
Let v = 5/11 - -7/33. Factor v*h + 2/9*h**2 + 2/9*h**4 - 4/9 - 2/3*h**3.
2*(h - 2)*(h - 1)**2*(h + 1)/9
Suppose 0 = u - 3*u - y + 8, -4*u - 3*y = -20. Factor -5*h + 5*h - h**u - 2*h.
-h*(h + 2)
Let d(p) be the first derivative of 3*p**5/25 - 3*p**4/4 + 9*p**3/5 - 21*p**2/10 + 6*p/5 - 3. Factor d(y).
3*(y - 2)*(y - 1)**3/5
Let i(f) = -4*f**5 - 2*f**4 + 2*f**2 + f + 3. Let n(b) = -3*b**5 - b**4 + b**3 + b**2 + 2. Let o(u) = -2*i(u) + 3*n(u). Factor o(m).
-m*(m - 2)*(m - 1)*(m + 1)**2
Let o = 19/60 - 1/15. Factor -1/4*f**3 - o*f**4 + 0 + 1/2*f**2 + 0*f.
-f**2*(f - 1)*(f + 2)/4
Let x(u) be the third derivative of u**7/525 - u**6/150 + 8*u**2. Solve x(v) = 0.
0, 2
Let u(h) = h**4 + h**3 + h + 1. Let z(c) = 4*c**4 + 16*c**3 + 9*c**2 + 6*c + 9. Let d(n) = 44*u(n) - 4*z(n). What is x in d(x) = 0?
-1, -2/7, 1
Let q(g) be the second derivative of -2/9*g**3 + 1/6*g**4 + 0*g**2 + 0 + 1/6*g**5 - 3*g. Determine p, given that q(p) = 0.
-1, 0, 2/5
Let k(m) be the first derivative of -4 + 0*m + 0*m**2 + 2/3*m**3 - 7/4*m**4. Factor k(l).
-l**2*(7*l - 2)
Let p(c) be the first derivative of 4*c - 2/5*c**5 + 3/2*c**4 - 2/3*c**3 - 3 - 3*c**2. Determine q, given that p(q) = 0.
-1, 1, 2
Let n(z) be the second derivative of z**9/504 + z**8/112 + z**7/70 + z**6/120 - z**3/6 + 2*z. Let s(i) be the second derivative of n(i). Solve s(t) = 0.
-1, -1/2, 0
Suppose -15*b - 13*b = -8*b. Solve b - 2/9*o + 2/9*o**2 = 0.
0, 1
Suppose -z + 2 = 0, 4*d - 5*z - 2 = -0. Let x = d - 1. Solve -4*t**2 + 4*t**2 + t - t**x = 0.
0, 1
Let b(a) be the first derivative of -4*a**5/5 - a**4 + 4*a**3 + 2*a**2 - 8*a + 7. Factor b(t).
-4*(t - 1)**2*(t + 1)*(t + 2)
Let u = -58 + 62. Find h, given that 1/3*h**u + 0 - 2/3*h - 1/3*h**2 + 2/3*h**3 = 0.
-2, -1, 0, 1
Factor 4*z + 3/4 + 21/4*z**2.
(3*z + 1)*(7*z + 3)/4
Let s = 3/4 + -1/4. Suppose 0*l + s*l**2 + 0 - 1/2*l**3 = 0. What is l?
0, 1
Let w(h) = -h**2 + 4*h - 1. Let a = 20 + -17. Let v be w(a). Suppose 2/3 - x + 0*x**v + 1/3*x**3 = 0. What is x?
-2, 1
Let g = -3 - -6. Let y = -17 + 17. Factor 5*s**2 + y*s**3 - 3*s**2 - 4*s**g + 2*s**4.
2*s**2*(s - 1)**2
Let x(p) = p**4 + 3*p**3 - 4*p. Let k = -1 - -4. Let y(s) = 2*s**4 + 2*s**3 - 3*s + k*s**3 - 4*s. Let r(l) = 7*x(l) - 4*y(l). Factor r(f).
-f**3*(f - 1)
Factor 2*u**2 - 4/3 - 2*u + 4/3*u**3.
2*(u - 1)*(u + 2)*(2*u + 1)/3
Suppose -2*h - 40 = -3*y, 37 - 2 = y - 5*h. Suppose -4*n = n - y. Factor 1 - 2 + s - 2*s + s**3 + s**n.
(s - 1)*(s + 1)**2
Let y(r) be the third derivative of 3*r**2 + 0*r + 1/240*r**5 + 0*r**3 + 0*r**4 + 1/480*r**6 - 1/1344*r**8 - 1/840*r**7 + 0. Factor y(l).
-l**2*(l - 1)*(l + 1)**2/4
Let d(a) = 2*a - 4*a**2 - 5 - 5*a**3 + 6*a**3 + 0*a. Let u be d(4). Suppose -o**u - o**3 + 3*o + 0*o**3 - o = 0. What is o?
-1, 0, 1
Let b = -2/2623 + 83946/13115. Solve b*h**2 + 2/5 + 16/5*h = 0.
-1/4
Let c be 0/((-8)/2 + 2). Let x(t) be the second derivative of 1/90*t**6 + 0 + 0*t**5 - 2*t + 1/126*t**7 + c*t**3 + 0*t**4 + 0*t**2. Solve x(m) = 0.
-1, 0
Let w be (-3)/(-131)*(-4)/36. Let d = 521/1179 - w. Factor 2/9*z - 2/9*z**5 - 4/9*z**4 + 0*z**3 + d*z**2 + 0.
-2*z*(z - 1)*(z + 1)**3/9
Let v(r) = 15*r**4 + 12*r**3 + 30*r**2 + 24*r + 18. Let m(z) = -z**4 - z**3 - z**2 - 1. Let u(i) = 18*m(i) + v(i). Suppose u(w) = 0. Calculate w.
-2, 0, 2
Factor -2/3*x**3 + 2*x**2 + 2/3 - 2*x.
-2*(x - 1)**3/3
Let z(m) be the first derivative of 2*m**3 + 3*m**2/4 - m/6 + 11. Factor z(u).
(3*u + 1)*(12*u - 1)/6
Let x(f) be the third derivative of -f**8/112 + f**7/10 - 9*f**6/20 + 11*f*