) be the first derivative of -1/10*s**5 + 0*s**4 - 1/24*s**6 + 1/8*s**2 + 1/6*s**3 - 3 + n*s. Factor f(h).
-h*(h - 1)*(h + 1)**3/4
Let j be 52/120 - (-2 - (-65)/30). Find o such that -j*o - 2/15*o**2 - 2/15 = 0.
-1
Let f(k) be the third derivative of 0 + 1/2*k**3 - 1/20*k**5 + 0*k - 3*k**2 + 0*k**4. Factor f(b).
-3*(b - 1)*(b + 1)
Let x(a) be the first derivative of -1/20*a**5 - 3/16*a**4 + 0*a + 1/12*a**3 + 1/8*a**2 + 2 + 1/12*a**6. Find r such that x(r) = 0.
-1, -1/2, 0, 1
Let a(v) be the first derivative of -v**7/252 + v**6/60 - v**5/40 + v**4/72 + 5*v**2/2 + 4. Let r(u) be the second derivative of a(u). Let r(z) = 0. What is z?
0, 2/5, 1
Let x(y) = -y**2 - 13*y - 17. Let g be x(-12). Let v(p) = p**3 + 5*p**2 + p + 5. Let h be v(g). What is b in -1/4*b**2 + 0 - 1/4*b**3 + h*b = 0?
-1, 0
Let o = 3 + -1. Let f(v) be the third derivative of 1/9*v**3 + 0 - 1/18*v**4 - v**o + 0*v + 1/90*v**5. Factor f(c).
2*(c - 1)**2/3
Let t(b) = -63*b**4 + 24*b**3 + 33*b**2 + 12*b. Let p(k) = 189*k**4 - 72*k**3 - 99*k**2 - 35*k. Let r(u) = 6*p(u) + 17*t(u). Solve r(o) = 0.
-1/3, -2/7, 0, 1
Let z(h) be the first derivative of h**4 + h**2 + 1/5*h**5 + 5/3*h**3 + 0*h + 1. Determine j, given that z(j) = 0.
-2, -1, 0
Suppose 2*s = -4*c - 2, 16 = -6*c + 4*c - 4*s. Suppose 0*t + 0 - 1/3*t**c = 0. What is t?
0
Let a(b) be the first derivative of -2*b**5/5 - b**4/2 + 2*b**3/3 + b**2 - 2. Find g, given that a(g) = 0.
-1, 0, 1
Let c(j) = j**2 - 11*j. Let l be c(11). Solve -r - r**5 + 0*r**3 + l*r**3 + 2*r**3 = 0 for r.
-1, 0, 1
Suppose 5*i = i + 12, 4*n = -i + 3. Let s be (-11)/(-30) - 360/(-432). Factor -2/5*o**2 + 2/5*o**5 - s*o**4 + 0 + 6/5*o**3 + n*o.
2*o**2*(o - 1)**3/5
Let s be (-28)/245*(-5)/6. Let k(l) be the first derivative of 3 - 1/7*l**2 - s*l**3 + 0*l. Factor k(p).
-2*p*(p + 1)/7
Let b = 79 + -77. Let x(j) be the first derivative of -j**4 - 2*j**3 + 1/2*j**6 + 2 + b*j + 1/2*j**2 + 4/5*j**5. Factor x(f).
(f - 1)*(f + 1)**3*(3*f - 2)
Factor 0 - 1/4*q + 1/2*q**2 - 1/4*q**3.
-q*(q - 1)**2/4
Let h = -51 - -51. Let l(r) be the second derivative of -r + h + 2/5*r**3 - 1/20*r**4 - 6/5*r**2. Factor l(y).
-3*(y - 2)**2/5
Suppose 5*y - 11 - 2 = a, 19 = 2*a + 5*y. Factor -2/13*k**a + 0 + 0*k.
-2*k**2/13
Let s = -1 - -3. Let l be 22/5 - s/5. Factor 0 + 1/5*m**l - 1/5*m**2 + 1/5*m - 1/5*m**3.
m*(m - 1)**2*(m + 1)/5
Find t, given that -4*t**2 + 2320*t + 0*t**3 + 2*t**5 - 2314*t - 8*t**3 + 4 = 0.
-1, 1, 2
Let s(y) be the second derivative of y**8/16800 + y**7/6300 + y**4/12 - 5*y. Let u(g) be the third derivative of s(g). Suppose u(j) = 0. What is j?
-1, 0
Factor 20/9*d - 50/9 - 2/9*d**2.
-2*(d - 5)**2/9
Let h(u) = -1. Let t(o) = -4. Let l(y) = -2*h(y) - t(y). Let r(f) = -f**2 - 11. Let i(g) = 5*l(g) + 2*r(g). Find a such that i(a) = 0.
-2, 2
Let i = 2 - 0. Let n be (-27)/180 - (-4)/10. Factor -13/4*q**4 + 0 - 7/4*q**i + q**5 + 15/4*q**3 + n*q.
q*(q - 1)**3*(4*q - 1)/4
Let c(z) be the third derivative of 0*z**5 + 1/1344*z**8 + 0*z + 0*z**7 + 2*z**2 + 0*z**3 - 1/480*z**6 + 0 + 0*z**4. Factor c(n).
n**3*(n - 1)*(n + 1)/4
Let p(f) = 10*f + 2. Let g(k) = 5*k + 1. Let n(h) = -7*g(h) + 3*p(h). Let v be n(-1). Solve 0*y + 2/3*y**5 - 2/3*y**3 + 2/3*y**2 - 2/3*y**v + 0 = 0 for y.
-1, 0, 1
Let u(v) = -v**2 - 4*v + 4. Let j be u(-4). Factor 0*t - t**4 - 2*t + 5*t**4 + 14*t**3 + 4*t**2 + j*t**4.
2*t*(t + 1)**2*(4*t - 1)
Let s(q) be the third derivative of 0*q - 1/840*q**7 + 1/240*q**5 + 1/480*q**6 + 0*q**3 - 9*q**2 - 1/1344*q**8 + 0 + 0*q**4. Factor s(w).
-w**2*(w - 1)*(w + 1)**2/4
Let x(i) = -4*i**3 + 9*i**2 + 16*i + 1. Let z(v) = v**2 + v - 1. Let q(c) = x(c) - 2*z(c). Factor q(s).
-(s - 3)*(s + 1)*(4*s + 1)
Let a(l) be the second derivative of 5*l**7/273 - 8*l**6/195 - 2*l**5/65 + 5*l**4/39 - l**3/39 - 2*l**2/13 - l - 2. Suppose a(b) = 0. What is b?
-1, -2/5, 1
Let v(w) be the second derivative of -3/2*w**2 + 1/4*w**3 + 1/8*w**4 + 0 - 5*w. Factor v(q).
3*(q - 1)*(q + 2)/2
Let b = 262/315 + -2/63. Let l = b + -3/5. Factor 1/5*c**3 - 1/5*c - 1/5 + l*c**2.
(c - 1)*(c + 1)**2/5
Let c be 415/(-1050) - (-2)/10*2. Let m(b) be the third derivative of 0*b - 1/21*b**3 - c*b**6 + b**2 + 1/42*b**4 + 0 + 0*b**5 + 1/735*b**7. Factor m(i).
2*(i - 1)**3*(i + 1)/7
Suppose 0 = u + u - 6. Let c(a) be the second derivative of 0 + 0*a**4 - 3*a + 1/3*a**u + 0*a**2 - 1/10*a**5. Factor c(s).
-2*s*(s - 1)*(s + 1)
Let c(s) be the second derivative of s**6/360 + s**5/24 + s**4/6 - s**3/6 - 6*s. Let v(h) be the second derivative of c(h). Factor v(u).
(u + 1)*(u + 4)
Let n = -7 + 15. Find v such that -n*v**3 + 18*v - 18*v - 4*v**2 + 12*v**4 = 0.
-1/3, 0, 1
Let w(b) be the second derivative of b**6/135 + 7*b**5/90 + 17*b**4/54 + 17*b**3/27 + 2*b**2/3 + 43*b + 2. Let w(a) = 0. What is a?
-3, -2, -1
Let g(m) be the third derivative of -m**5/60 + 2*m**3/3 + 3*m**2. Solve g(y) = 0.
-2, 2
Factor -20*a**2 + 24*a**3 - 16 - 38*a**2 + 143*a - 31*a - 42*a**2.
4*(a - 2)**2*(6*a - 1)
Find i such that -6*i - 14*i - 3*i**2 - 12 + 8*i = 0.
-2
Suppose 0*h - 2*h = 0. Suppose h*p = 3*b - 3*p + 3, 5*b = 3*p - 3. What is x in 0*x - 1/3*x**2 + b = 0?
0
Let c = 2 - -3. Let y = -10 + 13. Factor c*i**2 - 7*i**3 - 2*i**2 - i**2 + 8*i**4 - y*i**5.
-i**2*(i - 1)**2*(3*i - 2)
Let p(j) be the first derivative of -1/16*j**4 + 0*j + 2 - 1/6*j**3 - 1/8*j**2. Find c such that p(c) = 0.
-1, 0
Let f = -157 - -157. Let w(z) be the third derivative of 0*z**3 - 1/40*z**6 + 0*z + f*z**4 + 2*z**2 + 0 + 0*z**5. Let w(b) = 0. What is b?
0
Let z(d) = d**4 + 17*d**3 + 25*d**2 + 19*d + 4. Let r(t) = 18*t**3 + 24*t**2 + 18*t + 3. Let f(p) = -2*r(p) + 3*z(p). Factor f(q).
3*(q + 1)**3*(q + 2)
Let x be 15/(-45)*(-2 - (-5)/4). Let u(n) be the first derivative of -1/12*n**3 + 0*n**2 - 3 - 1/6*n**6 + 1/20*n**5 + x*n**4 + 0*n. Let u(s) = 0. Calculate s.
-1, 0, 1/4, 1
Let w(b) be the first derivative of 2*b**3/33 + 6*b**2/11 + 18*b/11 - 21. Factor w(y).
2*(y + 3)**2/11
Let d = -34 - -240/7. Determine t, given that 2/7*t**3 - 2/7*t**2 + d*t**4 + 0 - 2/7*t = 0.
-1, 0, 1
Suppose -2*g + 12 = 2*g. Factor g*y**2 + 2*y**3 - y**2 - y - 2 - y.
2*(y - 1)*(y + 1)**2
Factor 18*n**2 + 15*n**3 + 5*n**4 - 2*n**4 + 0*n**2 - 12*n + 0 - 24.
3*(n - 1)*(n + 2)**3
Let a(r) be the first derivative of -r**4/18 + 10*r**3/27 - 8*r**2/9 + 8*r/9 - 8. Suppose a(i) = 0. Calculate i.
1, 2
Suppose -4*w + 20 = 4. Factor -8/5*f**5 - 8*f**3 + 0*f - w*f**2 + 2/5 - 6*f**4.
-2*(f + 1)**4*(4*f - 1)/5
Let i(d) be the first derivative of d**8/336 - d**6/60 + d**4/24 - d**2/2 - 5. Let u(m) be the second derivative of i(m). Suppose u(l) = 0. Calculate l.
-1, 0, 1
Factor 1/4 + 1/2*q + 1/4*q**2.
(q + 1)**2/4
Let v(l) be the second derivative of l**8/30240 + l**7/5670 + l**6/3240 + l**4/2 - 6*l. Let t(u) be the third derivative of v(u). Suppose t(b) = 0. Calculate b.
-1, 0
Let t(k) = 8*k**3 - 4*k**2 - 20*k. Let i(h) = -h**4 + 25*h**3 - 11*h**2 - 59*h. Let o(n) = 4*i(n) - 11*t(n). Let o(m) = 0. Calculate m.
-1, 0, 2
Let x = 573 - 573. Factor x + 0*y**2 + 2/7*y**3 - 4/7*y**4 + 2/7*y**5 + 0*y.
2*y**3*(y - 1)**2/7
Factor w - 2*w**2 - 12*w**3 + 11*w**3 - 2*w.
-w*(w + 1)**2
Let r(t) be the third derivative of 0*t + 0*t**3 + 0 + 2*t**2 - 1/18*t**4 + 1/20*t**6 - 7/90*t**5. Factor r(p).
2*p*(p - 1)*(9*p + 2)/3
Factor 8/3*k**2 + 0 + 2/3*k**3 + 0*k.
2*k**2*(k + 4)/3
Find k such that -3*k - 21/2*k**4 + 0 + 3*k**3 + 21/2*k**2 = 0.
-1, 0, 2/7, 1
Let a(m) = -4*m**2 + 18*m - 30. Let p(n) = 5*n**2 - 19*n + 29. Let k(q) = 3*a(q) + 2*p(q). Let k(j) = 0. Calculate j.
4
Let m be 1*-2 - (-28)/7. Factor 2*s + 3*s**2 + 0*s**m + s + 3*s**3 + 3*s**2.
3*s*(s + 1)**2
Let n be (3 - 32/12)*3/2. Solve -n + 3*z**2 - 5/2*z**4 - 1/4*z + 1/4*z**3 = 0.
-1, -2/5, 1/2, 1
Factor -10/3*x - 2/3*x**3 - 8/3*x**2 - 4/3.
-2*(x + 1)**2*(x + 2)/3
Suppose 0 = 3*n + 4*k - 2, 0*k + 2 = 2*n + 2*k. Let b(m) = 2*m - 6. Let g be b(4). Factor -3*u**3 + 0 + n*u**g - 1/2*u + 2*u**4 - 1/2*u**5.
-u*(u - 1)**4/2
Let u(k) be the second derivative of 1/135*k**6 - 1/90*k**5 - 1/18*k**4 - 2/9*k**2 + 5/27*k**3 - 5*k + 0. Solve u(n) = 0.
-2, 1
Let q = 4 - 2. What is d in -d**3 - 5*d**4 + 5*d**3 - 2*d**q + 3*d**4 = 0?
0, 1
Solve 0 + 57/7*i**3 - 12/7*i**4 - 18/7*i - 57/7*i**2 = 0.
-1/4, 0, 2, 3
Let i(k) be the first derivative of -4*k**5 - 4 + 17*k**4 - 8*k - 28*k**3 + 