e 0/1*(-2)/(-6). Let c(m) be the second derivative of 1/5*m**3 - 1/105*m**7 + a + 1/15*m**4 + 2*m - 1/25*m**5 + 1/5*m**2 - 1/25*m**6. Factor c(g).
-2*(g - 1)*(g + 1)**4/5
Let g(n) = -n**2 - n - 1. Let p(d) = -d**5 + 2*d**4 + d**3 - 6*d**2 - 4*d - 4. Let j(q) = 4*g(q) - p(q). Factor j(a).
a**2*(a - 2)*(a - 1)*(a + 1)
Let x(t) be the third derivative of 0*t + 0 - 1/315*t**7 + 0*t**3 + 0*t**4 - 1/90*t**5 + 1/90*t**6 + 4*t**2. What is h in x(h) = 0?
0, 1
Let t(h) be the third derivative of -h**6/180 - h**5/90 + h**4/36 + h**3/9 + 5*h**2. Factor t(f).
-2*(f - 1)*(f + 1)**2/3
Suppose -16*p = -17*p + 2. Factor -5 + 1 - 4 + 3*m**p + 5.
3*(m - 1)*(m + 1)
Let c(q) be the first derivative of -5*q**3/3 - 10*q**2 - 20*q + 33. Let c(l) = 0. Calculate l.
-2
Let n be (0 + 6)/(1/(-1)). Let x be n/2 + (-810)/(-198). Factor x*k**2 - 24/11*k - 2/11*k**3 + 16/11.
-2*(k - 2)**3/11
Let z(k) = -2*k**2 + 2*k - 2. Let i(v) = v**3 - v**2 - v + 1. Let o(w) = 4*i(w) + 2*z(w). Factor o(g).
4*g**2*(g - 2)
Let l(p) = -p**2 - 2*p + 4. Let d(x) = -x**2 - x + 3. Let w(i) = -4*d(i) + 3*l(i). Find r such that w(r) = 0.
0, 2
Let x be 2 + (0 - 0)/1. Determine v so that -3 + 4*v**x + 7 + 10*v + 6*v**2 - 4*v**2 = 0.
-1, -2/3
Let o(z) be the third derivative of -z**5/15 + z**4 - 6*z**3 + 6*z**2. Factor o(k).
-4*(k - 3)**2
Suppose 4*j - 5*j = 2*v - 184, -4*v + 354 = -5*j. Let m = v - 361/4. What is p in 1/4*p**2 - m*p + 1/2 = 0?
1, 2
Let 0*m + 0 + 2/9*m**4 - 4/9*m**3 + 2/9*m**2 = 0. What is m?
0, 1
Suppose 13 = -3*j + 5*s, 4*j = s - 0*s + 11. Factor -3*h**2 + 4*h**2 - j*h**2.
-3*h**2
Let v(z) = -3*z**4 + 5*z**3 + 2*z + 2. Let j(f) = -6*f**4 + 11*f**3 + 5*f + 5. Let q(t) = -2*j(t) + 5*v(t). Factor q(k).
-3*k**3*(k - 1)
Suppose -4*v - 179 = -3*n - 2*n, n - 2*v = 37. Let o be (1 - -2) + n/(-15). Factor -2*l**3 + 0*l - 2*l**4 + 0 - o*l**2 - 2/3*l**5.
-2*l**2*(l + 1)**3/3
Let t(m) be the second derivative of -m**7/21 - m**6/15 + m**5/10 + m**4/6 - 3*m. Solve t(k) = 0.
-1, 0, 1
Suppose -4*h - h + 122 = -4*u, -2*h - u = -54. Let x = h - 23. Suppose 0*a + 1/3*a**x + 0 - 1/3*a**2 = 0. Calculate a.
0, 1
Let s(t) = 5*t**3 - 15*t**2 + 15*t + 6. Let j(o) = o**3 - 3*o**2 + 3*o + 1. Let k(d) = -11*j(d) + 2*s(d). Find u such that k(u) = 0.
1
Factor 10*x**2 - 4*x**3 + 2*x**3 - 14*x**2 - 2*x.
-2*x*(x + 1)**2
Determine d, given that d**2 + 1/5*d + 3/5*d**4 + 7/5*d**3 + 0 = 0.
-1, -1/3, 0
Let p(y) be the second derivative of -y**5/50 - 4*y**4/15 - 16*y**3/15 + 3*y + 6. Solve p(w) = 0 for w.
-4, 0
Let l(t) = t**2. Let c(q) = 3*q**2 + 2. Let i(s) = c(s) - 6*l(s). Let v(o) = -13*o**2 - o + 9. Let b(x) = -18*i(x) + 4*v(x). Factor b(y).
2*y*(y - 2)
Factor -5*t**2 - 4*t**3 - 8*t - t**4 + 0*t**4 + 6*t.
-t*(t + 1)**2*(t + 2)
Suppose -4*i = -5*i - 6. Let r(k) = k + 8. Let f be r(i). Suppose 4/3*x - 2/3*x**f + 0 - 2/3*x**3 = 0. What is x?
-2, 0, 1
Suppose 3*o - 4 = 5. Let 2*h**2 + 3*h + h - h + o*h + 4 = 0. Calculate h.
-2, -1
Let z(g) be the second derivative of g**4/16 - 3*g**3/4 + 27*g**2/8 + 4*g. Determine p, given that z(p) = 0.
3
Let h = -159733/5 + 32078. Let g = h - 131. Factor -1/5 + 0*p**3 + g*p**2 + 0*p - 1/5*p**4.
-(p - 1)**2*(p + 1)**2/5
Let r(m) = 2*m**3 - m - 3*m**2 + 4*m - 3 + 2. Let c(n) = 6*n**3 + 2*n**3 - 7*n**3. Let l(a) = -c(a) + r(a). Suppose l(j) = 0. What is j?
1
Let d = 6 + -1. Let p(f) = -3*f**3 + 6*f**2 + 16*f + 4. Let q(s) = -4*s**3 + 6*s**2 + 17*s + 3. Let m(k) = d*p(k) - 4*q(k). Factor m(x).
(x + 2)**3
Let q = -4 - -12. Let w(m) be the first derivative of -4*m**2 - q*m - 2/3*m**3 + 1. Factor w(t).
-2*(t + 2)**2
Let z(a) be the first derivative of 8*a + 6*a**3 + 1 + 1/5*a**5 - 7/4*a**4 - 10*a**2. Determine j, given that z(j) = 0.
1, 2
Factor 2/7*d**3 + 2/7*d**2 - 32/7*d + 40/7.
2*(d - 2)**2*(d + 5)/7
Suppose 5*h + 0 = 10. Factor -h*l**2 - 4/3 + 10/3*l.
-2*(l - 1)*(3*l - 2)/3
Let j = -22 + 32. Factor -8*q**3 + j*q**3 - 4*q**2 + 6*q**4 + q - q.
2*q**2*(q + 1)*(3*q - 2)
Let v(n) be the third derivative of 2*n**7/105 + n**6/15 - n**4/3 - 2*n**3/3 - 17*n**2. Let v(j) = 0. What is j?
-1, 1
Let u(i) be the third derivative of -i**8/56 + 17*i**7/105 - 11*i**6/20 + 23*i**5/30 - 4*i**3/3 - i**2. What is l in u(l) = 0?
-1/3, 1, 2
Factor -6*g**4 + 5*g**4 + g**2 + 0*g**2 - g**3 + g.
-g*(g - 1)*(g + 1)**2
Let u(q) be the third derivative of -1/1176*q**8 + 1/735*q**7 + 0*q + 6*q**2 - 1/42*q**5 + 0*q**3 + 0 + 1/42*q**4 + 1/140*q**6. Solve u(g) = 0 for g.
-2, 0, 1
Suppose 5*j + 0*j = 0. Factor 1/2*x**4 + j*x + 1/2*x**3 + 0*x**2 + 0.
x**3*(x + 1)/2
Let a = 5/3 - 1. Find q, given that -a*q**2 + 0 + 2/3*q = 0.
0, 1
Suppose 0 = -5*d + 12 + 13. Factor 5*x**4 + 3*x**2 - 7*x**4 + 2*x**d + 6*x - 2 + x**2 - 4*x - 4*x**3.
2*(x - 1)**3*(x + 1)**2
Suppose w - 2*d - 14 = -3*w, -4*d - 16 = -5*w. Let h(q) be the third derivative of -1/270*q**5 - w*q**2 + 1/540*q**6 + 0 + 0*q**3 + 0*q**4 + 0*q. Factor h(n).
2*n**2*(n - 1)/9
Let d(r) be the third derivative of -r**5/75 - r**4/6 - 8*r**3/15 - r**2. Factor d(k).
-4*(k + 1)*(k + 4)/5
Determine u so that 8/19*u**4 - 2/19*u**5 - 8/19*u**3 - 4/19*u**2 - 4/19 + 10/19*u = 0.
-1, 1, 2
Let a be 8/(0 + 49/7). Suppose -6/7*b**2 - 2/7*b**4 + a - 8/7*b + 8/7*b**3 = 0. What is b?
-1, 1, 2
Let x = 628/2149 - 2/307. Factor -x - 6/7*j - 2/7*j**3 - 6/7*j**2.
-2*(j + 1)**3/7
Suppose -3*t + 13 = s, s = -3*t - 3*s + 16. Let -8*r**4 - 9*r**4 - 2*r**2 - 11*r**3 + r**4 + 4*r**t = 0. Calculate r.
-2/3, -1/4, 0
Let q(h) be the second derivative of h**7/840 + h**6/240 - h**5/20 - h**4/3 + 11*h. Let k(z) be the third derivative of q(z). Factor k(g).
3*(g - 1)*(g + 2)
Suppose a + a = -14. Let i = a - -13. Let i*t**2 + 3*t - 2*t**3 + 3*t**3 + 2*t**3 = 0. Calculate t.
-1, 0
Find c such that 16/15 + 44/5*c**2 - 98/15*c**4 - 104/15*c + 154/15*c**3 = 0.
-1, 2/7, 2
Let s be (-3 - 0)/(9/(-15)). Factor -3*c**4 + 3*c**3 + 3*c**s + 0*c**5 + 12*c**4 + 3*c**5.
3*c**3*(c + 1)*(2*c + 1)
Let j(n) be the first derivative of 2/15*n**3 - 1 + 3/10*n**2 - 2/5*n - 3/20*n**4. Factor j(x).
-(x - 1)*(x + 1)*(3*x - 2)/5
Factor -16/3*v - 10/3*v**2 + 8/3.
-2*(v + 2)*(5*v - 2)/3
Let b(y) = y + 5. Suppose 2*c = -1 - 7. Let p be b(c). Let p - 1 + 6*k - 4 - 2*k**2 = 0. Calculate k.
1, 2
Factor 9*k**2 - 5*k**3 - 192*k + 189 + 67 + k**3 + 39*k**2.
-4*(k - 4)**3
Let h(v) be the first derivative of -v**6/27 - 2*v**5/45 + v**4/9 + 4*v**3/27 - v**2/9 - 2*v/9 - 8. Factor h(l).
-2*(l - 1)**2*(l + 1)**3/9
Let i(b) = b + 12. Let k be i(-6). Factor -8 - 13*y**3 - 126*y**2 - 51*y**3 + 62*y + k*y - 17*y**3.
-(y + 2)*(9*y - 2)**2
Let f(n) be the first derivative of n**4/32 + 56. Let f(m) = 0. What is m?
0
Let w be (-15 + 23)/((-9)/4). Let j = w + 56/9. Suppose 8/3*g**4 + 2/3*g**5 + 2*g**3 - j*g + 0 - 8/3*g**2 = 0. Calculate g.
-2, -1, 0, 1
Let z(v) be the second derivative of v**5/210 - 2*v**4/63 + 5*v**3/63 - 2*v**2/21 + 12*v. Solve z(k) = 0.
1, 2
What is s in 4*s**2 + 0*s**2 - 6*s**3 - s**4 + 3*s**4 = 0?
0, 1, 2
Let y(q) be the second derivative of 0*q**3 - 1/4*q**6 + 9/40*q**5 + 0 + 1/4*q**4 + 7*q + 0*q**2. Factor y(l).
-3*l**2*(l - 1)*(5*l + 2)/2
Let a = 3462 + -287360/83. Let l = a - -818/913. Suppose 8/11*g - l + 6/11*g**2 = 0. What is g?
-2, 2/3
Let y(u) be the third derivative of 0 - 1/720*u**6 - 1/144*u**4 - 1/180*u**5 + 0*u + 0*u**3 - u**2. Solve y(r) = 0 for r.
-1, 0
Suppose 10*u = 12*u. Let c(f) be the first derivative of -1/9*f**3 + u*f - 1/6*f**2 + 3. Factor c(r).
-r*(r + 1)/3
Let k(x) be the second derivative of -x**4/72 - x. Factor k(r).
-r**2/6
Suppose 0 = 17*k - 14*k - 12. Factor 0 + 0*x - 3/4*x**5 - 3/4*x**2 - 9/4*x**3 - 9/4*x**k.
-3*x**2*(x + 1)**3/4
Let a(j) = 8*j + 4*j**2 + 6 + 5*j**2 - 3*j**2 - 2*j**2. Let r(y) = -5*y**2 - 9*y - 7. Let c(f) = -3*a(f) - 2*r(f). Factor c(x).
-2*(x + 1)*(x + 2)
Let t(p) be the third derivative of p**7/175 + p**6/75 - 2*p**5/75 + 14*p**2. Factor t(r).
2*r**2*(r + 2)*(3*r - 2)/5
Let y(k) be the first derivative of -k**5/270 - k**4/108 + 2*k**2 + 4. Let x(f) be the second derivative of y(f). Factor x(t).
-2*t*(t + 1)/9
Let o(k) be the third derivative of 1/20*k**5 + 0 - 3/40*k**6 + 7*k**2 + 0*k - 1/2*k**3 + 3/8*k**4. Suppose o(r) = 0. Calculate r.
-1, 1/3, 1
Let t(u) = 4*u**2 - u - 5. Let o(a) be the first derivative of a**3/3 - a - 5. Let l(x) = -5*o(x) + t(x). Factor l(z).
-z*(z + 1)
Le