**5/30 - n**4/2 + 8*n**2. Find x, given that v(x) = 0.
-3, 0, 1, 2
Let u(f) be the first derivative of f**6/1620 - f**5/540 + 4*f**3/3 - 3. Let a(s) be the third derivative of u(s). Determine h, given that a(h) = 0.
0, 1
Let w(o) be the third derivative of o**8/168 - 2*o**7/315 - o**6/45 + o**5/45 + o**4/36 - 16*o**2 + o. Suppose w(l) = 0. Calculate l.
-1, -1/3, 0, 1
Suppose -g = -24 + 21. Suppose w = 1, 0*l + w - 7 = -3*l. Factor 0*b**l - 2/5*b**g + 2/5*b**4 + 0 + 0*b.
2*b**3*(b - 1)/5
Let j = 0 - -4. Let o = j - 2. Determine s so that 5*s**o - 6*s**3 - s**2 + 8*s**3 = 0.
-2, 0
Let o = 13/720 + -1/240. Let a(i) be the third derivative of -1/360*i**6 + 0 + i**2 + 0*i + 0*i**5 + o*i**4 + 0*i**3. Factor a(q).
-q*(q - 1)*(q + 1)/3
Let b(q) = q**3 + 56*q**2 + 120*q + 79. Let s(m) = 28*m**2 + 60*m + 40. Let l(k) = 4*b(k) - 7*s(k). Factor l(d).
4*(d + 1)*(d + 3)**2
Suppose 5*b - 35 = -0*b. Factor -l**3 - 2*l - 5*l**3 + l**3 - b*l**2.
-l*(l + 1)*(5*l + 2)
Let s(r) be the second derivative of -r**4/66 - 6*r**3/11 - 81*r**2/11 - 34*r. Factor s(m).
-2*(m + 9)**2/11
Suppose 75 = -9*g + 14*g. Suppose -g*a**3 + 12*a**4 + 6*a**2 + a**2 - 4*a**2 = 0. Calculate a.
0, 1/4, 1
Let d be 14/6 + (-4)/12. Factor b**d + b**2 - 2 + 0*b**2.
2*(b - 1)*(b + 1)
Let h = -1 - -8/9. Let y = 2/9 - h. Find c such that y*c**2 + 1/3 + 2/3*c = 0.
-1
Let z = -9365 + 5899951/630. Let v(d) be the third derivative of z*d**7 + 1/30*d**5 + 0*d + 2*d**2 + 1/90*d**6 + 1/18*d**3 + 0 + 1/18*d**4. Factor v(r).
(r + 1)**4/3
Let o(x) be the third derivative of x**5/480 - x**4/64 + 27*x**2. Find h such that o(h) = 0.
0, 3
Let g(u) be the second derivative of u**5/130 + u**4/78 - 10*u. What is i in g(i) = 0?
-1, 0
Let l(s) be the third derivative of 11*s**5/450 - s**4/20 - 2*s**3/45 - 3*s**2. Factor l(t).
2*(t - 1)*(11*t + 2)/15
Let a = 874 - 872. Suppose 1/4 + 1/2*j + 1/4*j**a = 0. Calculate j.
-1
Let f(m) be the third derivative of -m**7/168 + m**6/60 + 3*m**5/80 - m**4/12 - m**3/6 - 2*m**2. Determine g so that f(g) = 0.
-1, -2/5, 1, 2
Let o be (-3)/(-2)*1085/(-21). Let m = 85 + o. Let -4*s**2 + 9/2 - 8*s**3 + m*s = 0. Calculate s.
-3/4, 1
Let j(l) be the third derivative of l**6/60 - 3*l**5/10 + 9*l**4/4 - 9*l**3 + 4*l**2. What is q in j(q) = 0?
3
What is q in -7 + 4 - 3*q**5 - 10*q - 20*q**3 + 20*q**2 + 5 + q**5 + 10*q**4 = 0?
1
Let f(x) be the first derivative of 2*x**5/65 + 2*x**4/13 + 8*x**3/39 + 63. Find m, given that f(m) = 0.
-2, 0
Factor 4/3*u**2 + 0 + 4/3*u.
4*u*(u + 1)/3
Let k = 6 - 7. Let u(z) = -z + 1. Let q(i) = -3*i**2 - 5*i - 10. Let p(a) = k*q(a) - 4*u(a). Solve p(g) = 0 for g.
-2, -1
Let a(n) be the third derivative of n**6/210 + n**5/105 + 26*n**2. Solve a(o) = 0 for o.
-1, 0
Let f(h) = h - 6. Let x be f(8). Factor 0 + 2 + z**x - 2.
z**2
Suppose 7*m - 9*m + 4 = 0. Determine j so that 3/2*j**5 - 1 + 3*j**2 - m*j**3 + 1/2*j - 2*j**4 = 0.
-1, -2/3, 1
Suppose 2 = 5*m - 8. Factor -14*v**2 - 6*v**m + 6 - 8*v + 22*v**2.
2*(v - 3)*(v - 1)
Let g be -2 + -3 + (-6)/2. Let m = g - -11. Find p such that p**4 - 3 - 3*p**2 + 4 + 2 - 5 - 5*p + p**m = 0.
-1, 2
Factor 1/3*v**5 + v**3 + 0*v + v**4 + 1/3*v**2 + 0.
v**2*(v + 1)**3/3
Factor 2/5*p**2 + 0 + 0*p.
2*p**2/5
Suppose 4*f - 2 - 6 = 0. Let -4*w**2 - 2*w**f - 4*w - 4 + 5*w**2 = 0. Calculate w.
-2
Let s(n) be the third derivative of -3*n**8/196 + 11*n**7/245 - n**6/210 - 29*n**5/210 + 5*n**4/21 - 4*n**3/21 + 6*n**2. Solve s(k) = 0.
-1, 1/2, 2/3, 1
Suppose -2*m - 4*b = -12, 6*m - 5*b + 8 = 5*m. What is a in -1/2 - 1/2*a**m - a = 0?
-1
Let t(z) be the third derivative of z**8/5880 + z**7/2940 - 5*z**3/6 - 4*z**2. Let r(x) be the first derivative of t(x). Let r(h) = 0. Calculate h.
-1, 0
Let p(w) be the third derivative of 0*w**3 + 1/40*w**6 - 3*w**2 + 0*w**7 - 1/112*w**8 + 0 + 0*w + 0*w**5 + 0*w**4. Determine n, given that p(n) = 0.
-1, 0, 1
Let u(m) be the first derivative of 3/5*m**2 + 2/5*m**3 + 1/10*m**4 + 1 + 2/5*m. Factor u(t).
2*(t + 1)**3/5
Let i(u) = 8*u**2 - 10*u + 8. Let x(z) = -17*z**2 + 21*z - 17. Let s be (15/20)/(2/16). Let t(m) = s*x(m) + 13*i(m). Factor t(g).
2*(g - 1)**2
Let b(x) be the second derivative of x**6/45 + x**5/6 + x**4/2 + 7*x**3/9 + 2*x**2/3 + 27*x. Factor b(g).
2*(g + 1)**3*(g + 2)/3
Let p = 133 + -1195/9. Factor -4/3*h**2 - 8/9*h**3 - p - 8/9*h - 2/9*h**4.
-2*(h + 1)**4/9
Let l(k) be the second derivative of -k**4/36 - 2*k**3/9 - k**2/2 + 10*k. Let l(d) = 0. What is d?
-3, -1
Let t = 36 + -58. Let b = 24 + t. Solve 3/2*v**b + 0 + 1/2*v**3 + v = 0.
-2, -1, 0
Let r(g) be the second derivative of -g**4/24 - g**3/2 - 9*g**2/4 + 10*g. Solve r(l) = 0 for l.
-3
Let c be ((-72)/(-21))/8 + (-15)/(-63). Factor 4/3 + 2/3*q - c*q**2.
-2*(q - 2)*(q + 1)/3
Suppose -v + u + 3*u - 13 = 0, 21 = 3*v + 3*u. Factor -10*s - 7/2*s**v + 4 - 13*s**2.
-(s + 2)**2*(7*s - 2)/2
Let w(b) = 0 - b**3 - b**2 + 3 + 2*b**3. Let n be w(0). Factor 7*k**4 + 5*k**2 - 8*k - 8*k**3 + 7*k**2 - n*k**4 - 2*k**4 + 2.
2*(k - 1)**4
Let u = -8 - -12. Let g be (2/u)/((-4)/(-24)). Factor 6*y**3 - 4*y + 2*y + 1 - 4*y**g - y**4.
-(y - 1)**3*(y + 1)
Let v(l) be the first derivative of -l**6/720 + l**4/48 - 2*l**3/3 + 3. Let s(r) be the third derivative of v(r). Suppose s(a) = 0. Calculate a.
-1, 1
Let r(l) be the first derivative of 2 + 0*l + 1/2*l**4 + 2/7*l**2 - 6/7*l**3. Let r(o) = 0. Calculate o.
0, 2/7, 1
Suppose -147/2*r**2 - 105*r - 75/2 = 0. What is r?
-5/7
Let l be (-2)/4 + (-33)/(-6). Factor 3*h**2 + 2*h**3 - h - 3 + 4*h - l*h**3.
-3*(h - 1)**2*(h + 1)
Factor -25 + 4*k**3 - 38*k**2 + 1 + 14*k**2 + 44*k.
4*(k - 3)*(k - 2)*(k - 1)
Let m = -3 + 6. Let t(z) = -12*z**2 + 7*z + 4 - z**m + 2*z**3 - 4. Let q(f) = -4*f**2 + 2*f. Let x(w) = 7*q(w) - 2*t(w). Factor x(c).
-2*c**2*(c + 2)
Suppose 2*q = 42 - 36. Factor -12/5 + 0*h + 9/5*h**2 - 3/5*h**q.
-3*(h - 2)**2*(h + 1)/5
Let z(m) be the first derivative of -3*m**4/20 + 6*m**3/5 - 27*m**2/10 + 12*m/5 + 15. Factor z(n).
-3*(n - 4)*(n - 1)**2/5
Suppose 3*l - l = 6. Suppose 0*v - 9 = -l*v. Let 1/2*w**v + 0*w**2 + 0*w - 1/2*w**5 + 0*w**4 + 0 = 0. Calculate w.
-1, 0, 1
Let m(a) = -a**3 + 6*a**2 + a - 4. Let p = 15 + -9. Let n be m(p). Factor 2*g**3 - 4*g**2 - 2*g + 0*g**n + 4*g.
2*g*(g - 1)**2
Let k(n) be the first derivative of -n**7/2100 + n**6/180 - 2*n**5/75 + n**4/15 + 4*n**3/3 - 2. Let p(v) be the third derivative of k(v). Factor p(j).
-2*(j - 2)**2*(j - 1)/5
Let r(q) be the third derivative of -q**7/1890 + q**6/1080 + q**5/540 - q**4/216 - 5*q**2. Factor r(x).
-x*(x - 1)**2*(x + 1)/9
Suppose -4*x = -8*x + 4*s + 28, -2*s - 8 = 0. Determine h, given that 1/2*h**x + 0 + 0*h - 1/2*h**2 = 0.
0, 1
Let r(o) be the first derivative of -2*o**5/5 - 3*o**4/2 + 2*o**3/3 + 3*o**2 + 38. Solve r(f) = 0 for f.
-3, -1, 0, 1
Let t(s) be the second derivative of 3*s + 1/6*s**2 + 0 + 1/36*s**4 - 1/9*s**3. Let t(p) = 0. Calculate p.
1
Let w = -25357897/114 - -222433. Let d = -1/38 - w. Find o such that 14/3*o**4 - 2/3*o + 0 + 8*o**5 - 22/3*o**3 - d*o**2 = 0.
-1, -1/3, -1/4, 0, 1
Let p(v) be the first derivative of 0*v**2 + 0*v - 27/8*v**4 + 18/5*v**5 + 1 - 5/4*v**6 + v**3. Factor p(s).
-3*s**2*(s - 1)**2*(5*s - 2)/2
Let w(c) be the first derivative of c**5/80 - c**3/24 - 3*c - 3. Let u(i) be the first derivative of w(i). Factor u(o).
o*(o - 1)*(o + 1)/4
Let x be -8 - -8 - 105/18 - -6. Let -x*f**5 + 0*f + 1/6*f**3 + 0 - 1/6*f**2 + 1/6*f**4 = 0. Calculate f.
-1, 0, 1
Factor 4*l - 2 - 4*l**2 - 3 + 3*l + 2.
-(l - 1)*(4*l - 3)
Let j = -133 + 667/5. Let u(x) be the first derivative of -1/6*x**6 + 0*x**2 + 0*x**3 + 0*x - 3 - 1/4*x**4 + j*x**5. Factor u(w).
-w**3*(w - 1)**2
Let h(x) be the second derivative of 0 - 1/8*x**4 - 1/8*x**3 - 4*x + 3/4*x**2 + 3/80*x**5. Suppose h(c) = 0. Calculate c.
-1, 1, 2
Let x(t) = -2*t**5 + 9*t**4 + 6*t**3 - 9*t**2 + 3*t - 7. Let v(w) = w**5 - 5*w**4 - 3*w**3 + 5*w**2 - 2*w + 4. Let z(q) = 7*v(q) + 4*x(q). Factor z(d).
-d*(d - 2)*(d - 1)*(d + 1)**2
Let c(r) = -r**2. Let g(k) = 10*k**2 + 2*k. Let m(q) = -36*c(q) - 4*g(q). Solve m(p) = 0.
-2, 0
Let a(p) be the first derivative of 0*p + 1/5*p**3 + 1/25*p**5 + 1/10*p**2 + 2 + 3/20*p**4. Factor a(r).
r*(r + 1)**3/5
Suppose 0*y - 2*y - 2 = -5*t, 3*t + 5*y = 26. Suppose -t*a = -3*j + 3, -4*a + 2 = -j + 3. Factor 4*b - b - 4*b + 3*b**2 + a*b.
b*(3*b - 1)
L