*(t - 2)**2*(t + 1)/5
Let p(x) be the first derivative of 5*x**4/4 - 5*x**3 - 45*x**2/2 - 25*x - 28. Factor p(y).
5*(y - 5)*(y + 1)**2
Let t(y) be the third derivative of y**8/84 + 2*y**7/105 - y**6/6 + y**5/5 - 7*y**2. Factor t(a).
4*a**2*(a - 1)**2*(a + 3)
Let g(a) = -a**3 - 15*a**2 + a + 17. Let k be g(-15). Let 1/2*m**k + 1/2 + m = 0. What is m?
-1
Suppose -1 = -2*k + 5. Factor k*a**2 - 4*a**2 - a + 3*a.
-a*(a - 2)
Let j = -178 + 7477/42. Let t(l) be the second derivative of 1/7*l**2 - 2/21*l**3 + 0 - l + j*l**4. Let t(c) = 0. Calculate c.
1
Let d(l) = -l**3 + 4*l**2 + l - 1. Let w be d(4). Factor 2*o**5 - 3*o**5 - o**2 + 2*o**4 - o**4 + 5*o**w - 4*o**3.
-o**2*(o - 1)**2*(o + 1)
Suppose 3/2*h**2 - 6*h + 6 = 0. What is h?
2
Let h(v) be the third derivative of -v**6/2160 + v**5/360 - v**4/144 + 7*v**3/6 + 4*v**2. Let i(d) be the first derivative of h(d). Factor i(q).
-(q - 1)**2/6
Let y(o) be the second derivative of o**6/15 + o**5/4 + o**4/4 - o**3/6 - o**2/2 + o. Factor y(g).
(g + 1)**3*(2*g - 1)
Factor 2*b**2 + 0 + 1/2*b**4 + 0*b - 2*b**3.
b**2*(b - 2)**2/2
Let b = 4465/24 + -186. Let t(u) be the second derivative of -b*u**3 - 1/80*u**5 + 2*u + 0 + 0*u**2 - 1/24*u**4. Factor t(l).
-l*(l + 1)**2/4
Let g(s) be the third derivative of s**8/840 - 2*s**7/525 + s**6/300 + 9*s**2. Factor g(q).
2*q**3*(q - 1)**2/5
Let c(p) = -p**5 + p**2 + 1. Let j = -6 - -7. Let y(k) = -3*k**5 - 12*k**4 + 18*k**3 - 6*k**2 + 3*k + 6. Let f(h) = j*y(h) - 6*c(h). Factor f(x).
3*x*(x - 1)**4
Let d = -307/10 + 156/5. Factor 1/2*l**3 + d*l**2 + 0 + 0*l.
l**2*(l + 1)/2
Factor 5*i**3 + 25*i - 15*i + 0*i**3 - 15*i.
5*i*(i - 1)*(i + 1)
Suppose -3*m + 3 = -3. Factor 6*g**m - 2*g**2 - 4 + 0*g**2.
4*(g - 1)*(g + 1)
Let o(x) be the third derivative of x**7/1365 + x**6/390 - x**5/390 - x**4/78 - 34*x**2. Factor o(c).
2*c*(c - 1)*(c + 1)*(c + 2)/13
Let r be 2/1 - (1 - -4). Let k be ((-1 + -2)/3)/r. Find x such that 0*x - x**4 - 1/3*x**2 + 0 - x**3 - k*x**5 = 0.
-1, 0
What is h in 0 + 14/9*h**2 + 4/9*h = 0?
-2/7, 0
Let k(f) be the first derivative of f**4/4 + f**3/2 - 3*f**2 - 3*f + 4. Let j(p) be the first derivative of k(p). Factor j(n).
3*(n - 1)*(n + 2)
Let r(t) be the first derivative of t**6/24 - t**5/20 - t**4/16 + t**3/12 + 6. Factor r(j).
j**2*(j - 1)**2*(j + 1)/4
Let x(n) be the third derivative of -n**6/80 + 7*n**4/16 + 3*n**3/2 - 2*n**2. Factor x(y).
-3*(y - 3)*(y + 1)*(y + 2)/2
Let h(i) = i**3 - 10*i**2 + 15*i + 11. Let d be h(8). Let c(p) be the first derivative of 2 - 1/3*p**d + 0*p - 1/2*p**2. Suppose c(n) = 0. Calculate n.
-1, 0
Let b(r) be the first derivative of 6*r**6 + 28*r**5/5 - 20*r**4 + 16*r**3/3 + 4. Suppose b(z) = 0. Calculate z.
-2, 0, 2/9, 1
Let z = 10 - 10. Let o(d) be the second derivative of 1/21*d**7 + d - 1/20*d**6 + 0*d**4 + 0 - 1/40*d**5 + 0*d**3 + z*d**2. Suppose o(i) = 0. Calculate i.
-1/4, 0, 1
Let b = 868/3 - 289. Suppose -c**3 - 2/3 + 1/3*c**4 + c + b*c**2 = 0. Calculate c.
-1, 1, 2
Let d = 7 + -3. Suppose l - 4*t + 6 = 0, -l - t - d = -4*t. Solve 10*a - 3*a**2 - 3*a**2 + 3 - l*a**2 - 5 = 0.
1/4, 1
Let v(r) = -r**3 + r**2 + 3*r + 3. Let m(w) = 3*w**2 + 3*w - 4. Let k(d) = d**2 + d - 1. Let o(q) = -7*k(q) + 2*m(q). Let h(z) = -3*o(z) - v(z). Factor h(l).
l**2*(l + 2)
Let o be (10/5)/(1/3). Determine y, given that -14*y**2 - 3*y**5 + 6*y**2 + 6 - 3*y + 6*y**4 + o*y**3 - 4*y**2 = 0.
-1, 1, 2
Let i be 5130/28 + 8/(-16). Let t = 183 - i. Find k such that -2/7*k - 4/7*k**2 - 2/7*k**5 + t + 2/7*k**4 + 4/7*k**3 = 0.
-1, 1
Factor -2*j**2 + 8/3*j - 2/3.
-2*(j - 1)*(3*j - 1)/3
Let k(f) be the third derivative of f**6/70 + 11*f**5/105 + 4*f**4/21 - 8*f**3/21 - 7*f**2. What is r in k(r) = 0?
-2, 1/3
Let o(x) be the third derivative of 0*x - 1/315*x**7 + 2/9*x**3 + 0 + 1/30*x**5 - 5/36*x**4 + 2*x**2 + 1/180*x**6. Factor o(m).
-2*(m - 1)**3*(m + 2)/3
Let l be 5/(-15)*3*-1*2. Let u(a) be the third derivative of -1/9*a**3 + 3*a**l + 0*a + 1/24*a**4 - 1/180*a**5 + 0. Factor u(j).
-(j - 2)*(j - 1)/3
Let g(m) = m**5 - m**3 + m**2 + 1. Let r(h) = -3*h**5 + 7*h**4 + 11*h**3 - 5*h**2 - 6. Let y(c) = 6*g(c) + r(c). Suppose y(o) = 0. What is o?
-1, -1/3, 0
Suppose -2*n = x - 10, -5*x + 6*n - n - 10 = 0. Factor -68*o + 65*o - x + 0*o**2 - o**2.
-(o + 1)*(o + 2)
Let v be (-324)/(-9)*4/6. Suppose c - 8 = v. Factor -32*s**2 - 16*s**3 - c*s - 2/5*s**5 - 64/5 - 4*s**4.
-2*(s + 2)**5/5
Let r(q) = 3*q - 15. Let v be r(6). Find h, given that -1/3 + 1/2*h + 0*h**2 - 1/6*h**v = 0.
-2, 1
Find a, given that -40/7*a - 44/7*a**2 - 4/7*a**3 + 0 = 0.
-10, -1, 0
Let a(s) be the first derivative of 1/15*s**3 + 1 + 1/20*s**4 - 1/10*s**2 + s. Let z(j) be the first derivative of a(j). Factor z(m).
(m + 1)*(3*m - 1)/5
Let n(w) be the first derivative of -2 + 0*w + 0*w**5 + 1/18*w**4 + 0*w**3 + 0*w**2 - 1/27*w**6. Factor n(c).
-2*c**3*(c - 1)*(c + 1)/9
Let j = -1 + 5. Suppose 5*v - 9 = -3*g + 1, 3*g = 0. Factor 2*x**3 + j*x**4 - 2*x - x**4 - x**4 - 2*x**v + 0*x**4.
2*x*(x - 1)*(x + 1)**2
Let k(x) = x**3 + 4*x**2 - 3*x + 2. Let g(a) = -a**2 + a - 1. Let u(d) = -3*g(d) - k(d). Let r(b) = -3*b**2 - 2*b + 3. Let w(l) = -r(l) + 2*u(l). Factor w(c).
-(c - 1)*(c + 1)*(2*c - 1)
Let m = -1 + 3. Suppose m*w = 2*n + 2*n - 4, 5*n - 23 = -2*w. What is d in 2*d**n + 4*d**4 - 2*d**5 + 2*d**5 + 2*d**5 = 0?
-1, 0
Find u such that 0*u - 4/7 + 1/7*u**2 = 0.
-2, 2
Suppose -4*m = -13 - 3. Let w = m - 4. Let w*p - 2/5*p**2 + 2/5 = 0. What is p?
-1, 1
Let x(a) be the first derivative of 1/2*a**2 + 3/4*a**4 + a**3 + 1/5*a**5 + 0*a - 2. Factor x(v).
v*(v + 1)**3
Let s(i) = -i**2 + 8*i - 8. Let l be s(6). Let o(p) = -5*p**2 + 10*p + 4. Let a(c) = -25*c**2 + 51*c + 20. Let w(r) = l*a(r) - 22*o(r). Factor w(b).
2*(b - 2)*(5*b + 2)
Suppose 0 = -5*s - 3*d + 34, -2*s - 5*d + 35 = 2*s. Suppose 0 = 2*v + 2*k + k - 6, 0 = s*v - 4*k - 15. Find n such that 1/5*n**v + 3/5*n**2 + 0*n - 4/5 = 0.
-2, 1
Let r(q) be the third derivative of q**8/6720 - q**6/1440 + q**3/3 - 3*q**2. Let l(i) be the first derivative of r(i). Let l(o) = 0. What is o?
-1, 0, 1
Let a(o) be the third derivative of -o**6/60 + o**5/10 + o**4/12 - o**3 + 26*o**2. Solve a(q) = 0.
-1, 1, 3
Let t(a) = 7 + 0 + 4*a**2 + 8*a + 1. Let y be -3*-2*(-1)/3. Let k(q) = 5*q**2 + 8*q + 8. Let i(n) = y*k(n) + 3*t(n). What is c in i(c) = 0?
-2
Let n(q) be the first derivative of q**3/18 + 7*q**2/12 + q + 8. Let n(t) = 0. Calculate t.
-6, -1
Let q be 72/30 + 2/(-5). Let l(m) be the first derivative of 0*m**2 - 1/3*m**3 + q + m. Suppose l(j) = 0. What is j?
-1, 1
Let a(n) be the third derivative of -n**6/120 - n**5/30 - n**4/24 - 7*n**2. Determine i, given that a(i) = 0.
-1, 0
Let d(t) be the first derivative of -7*t**3/5 - 3*t**2 - 9*t/5 - 5. Suppose d(b) = 0. Calculate b.
-1, -3/7
Let c(r) = 2*r**3 + r**2 - 7*r + 9. Let g(k) = 6*k**3 + 4*k**2 - 22*k + 28. Let y(p) = -16*c(p) + 5*g(p). Solve y(u) = 0.
-1, 1, 2
Let z(j) = -j**2 - 3*j + 22. Let p be z(3). Solve y**3 - 2/5*y + 0 + 7/5*y**2 - 4/5*y**p = 0 for y.
-1, 0, 1/4, 2
Let k(u) be the second derivative of 1/20*u**5 - 1/2*u**2 + 2*u + 0 + 1/6*u**4 + 1/6*u**3. Let p(n) be the first derivative of k(n). Factor p(x).
(x + 1)*(3*x + 1)
Let j(r) be the second derivative of r**2 + 0 - 1/20*r**5 + 1/2*r**3 + 0*r**4 - 3*r. Factor j(m).
-(m - 2)*(m + 1)**2
Let h(i) = -3*i**5 + 10*i**4 - 7*i**3 + 7*i**2 + 7. Let b(v) = v**5 - 3*v**4 + 2*v**3 - 2*v**2 - 2. Let y(l) = 7*b(l) + 2*h(l). Suppose y(f) = 0. Calculate f.
0, 1
Factor 3*v**2 - 1 - 5*v + 5*v - v**4 - v**2.
-(v - 1)**2*(v + 1)**2
Suppose -3*o = -6 - 6. Determine d, given that 0*d**o + 2 + 2*d**3 - 3 - 5*d + d**4 + 3*d = 0.
-1, 1
Let k(d) be the second derivative of d**7/14 - d**6/5 - 9*d**5/20 + 2*d**4 - 2*d**3 - 27*d. Determine i so that k(i) = 0.
-2, 0, 1, 2
Let v(n) be the first derivative of -2*n**3/33 + n**2/11 + 4*n/11 - 11. Factor v(o).
-2*(o - 2)*(o + 1)/11
Let l(y) = 17*y**2 - 28*y - 48. Let u(r) = 33*r**2 - 57*r - 97. Let p(j) = -7*l(j) + 3*u(j). Suppose p(b) = 0. What is b?
-1, 9/4
Let g = -126 + 886/7. Factor g*o + 6/7*o**3 + 0 - 10/7*o**2.
2*o*(o - 1)*(3*o - 2)/7
Let j(d) = -d**2 + 16*d + 9. Let x be j(16). Factor 3*o - 48*o**4 - 3*o**2 - 87*o**3 + 15*o**3 + x*o + 6*o - 3.
-3*(o + 1)**2*(4*o - 1)**2
Let z(k) be the first derivative of 0*k + 3 + 3*k**2 + k**3