f 0*s - 1/40*s**5 - 1/48*s**4 + 7*s**m + 0 - 1/80*s**6 + 0*s**3 - 1/420*s**7. Factor f(x).
-x*(x + 1)**3/2
Let a(c) be the first derivative of c**2 - 8/3*c**3 + 0*c - 1. Factor a(h).
-2*h*(4*h - 1)
Factor 3*i - i + 3*i**3 + 54 - 56*i**2 + 3*i**3 + 2*i**2 - 8*i**3.
-2*(i - 1)*(i + 1)*(i + 27)
Suppose -6*n + 2980 = -2*n. Solve 2 - t + t**3 + 0 + n*t**2 - 747*t**2 = 0.
-1, 1, 2
Let a be 6 + ((-31375)/210)/25. Let b(d) be the second derivative of a*d**7 - 1/50*d**5 - 7*d + 0 - 1/50*d**6 + 0*d**3 + 0*d**2 + 0*d**4. Factor b(c).
c**3*(c - 1)*(5*c + 2)/5
Let q(a) = 31*a - 120. Let j be q(4). Let v(x) be the third derivative of 0*x - 1/56*x**j + 1/280*x**6 - 1/7*x**3 + x**2 + 0 + 1/70*x**5. Factor v(c).
3*(c - 1)*(c + 1)*(c + 2)/7
Let y(u) be the third derivative of -u**5/60 + 23*u**4/12 - 529*u**3/6 - 512*u**2. Suppose y(r) = 0. Calculate r.
23
Factor -91 - 45*v + 40*v + 20*v**3 + 91 + 15*v**2.
5*v*(v + 1)*(4*v - 1)
Let v be 50/(-88) + 6/8. Let y = 15/22 - v. Factor 3/2*d**3 + 1/2*d + y*d**4 + 0 + 3/2*d**2.
d*(d + 1)**3/2
Suppose -1/5*c**5 - 4/5*c**2 - 3/5*c**3 + 4/5*c**4 + 0 + 4/5*c = 0. What is c?
-1, 0, 1, 2
Determine l, given that 0*l + 16/13*l**2 - 10/13*l**4 - 2/13*l**5 + 0 - 4/13*l**3 = 0.
-4, -2, 0, 1
Let b(p) be the first derivative of p**7/5460 - p**5/780 - p**3/3 - 12. Let f(g) be the third derivative of b(g). Factor f(m).
2*m*(m - 1)*(m + 1)/13
Factor -1/9*l**3 + 1/9*l - 10*l**2 + 10.
-(l - 1)*(l + 1)*(l + 90)/9
Determine p so that -4*p**3 - 129*p + 66*p + 67*p = 0.
-1, 0, 1
Factor 7 - 7 + 5*q**2 - 6 + 6 - 25*q.
5*q*(q - 5)
Let x = 7 + -5. Let l = x + 3. Factor 3*z**2 + l*z + z + 3 + z - z.
3*(z + 1)**2
Factor 39*t + 36*t**2 + 57*t - 35*t**3 + 19 - 9*t**3 - 3.
-4*(t - 2)*(t + 1)*(11*t + 2)
Suppose -32394 + 8*i + 32394 - 10*i**2 + i**3 + i**4 = 0. Calculate i.
-4, 0, 1, 2
Suppose 119*a = 111*a. Let g = 80 - 397/5. Factor 6/5*j + a + g*j**2.
3*j*(j + 2)/5
Let y(h) be the third derivative of 0 + 0*h**6 + 0*h + 1/6*h**8 + 11/30*h**5 + 1/6*h**4 + h**2 - 41/105*h**7 + 0*h**3. Find m, given that y(m) = 0.
-2/7, -1/4, 0, 1
Let u(a) = -a**2 + 20*a + 49. Let m be u(15). Let v = m + -122. Factor -8/7 + 16/7*r - 6/7*r**v.
-2*(r - 2)*(3*r - 2)/7
Let s(v) = -30*v**4 - 263*v**3 - 707*v**2 - 486*v + 309. Let c(q) = -15*q**4 - 132*q**3 - 354*q**2 - 243*q + 153. Let t(r) = 5*c(r) - 3*s(r). Factor t(k).
3*(k + 3)**3*(5*k - 2)
Let v = 62 + -25. Let q = -29 + v. What is t in 24*t - 63*t**2 + q + 16 - 12 = 0?
-2/7, 2/3
Let n(i) be the first derivative of 2/85*i**5 + 0*i + 0*i**2 + 0*i**3 + 12 + 1/34*i**4. Factor n(s).
2*s**3*(s + 1)/17
Let q(l) be the first derivative of l**6/42 + 4*l**5/35 + l**4/28 - 10*l**3/21 - 2*l**2/7 + 8*l/7 + 605. Factor q(p).
(p - 1)**2*(p + 2)**3/7
Let f(u) = -9*u**2 + 133*u + 15. Let c(l) = 5*l**2 - 67*l - 9. Let h(s) = -14*c(s) - 6*f(s). Suppose h(w) = 0. What is w?
-1/4, 9
Let u(i) be the first derivative of 3/16*i**4 + 5 + 1/4*i**3 - 3/4*i - 3/8*i**2. Factor u(t).
3*(t - 1)*(t + 1)**2/4
Let r(q) = 2*q**2 - 120*q - 128. Let i(v) = 10*v**2 - 602*v - 640. Let u(x) = -6*i(x) + 28*r(x). Factor u(d).
-4*(d - 64)*(d + 1)
Let h(k) be the second derivative of -k**5/12 - 5*k**4/8 - 5*k**3/3 + 2*k**2 - 15*k. Let t(n) be the first derivative of h(n). Let t(p) = 0. What is p?
-2, -1
Suppose 5*g - 2*l = 10, -4*g - 2*l = 1 - 9. Suppose 0 = -7*m + g*m. Factor -12 + 13*z + m - 2*z + z - 3*z**2.
-3*(z - 2)**2
Let h(u) = -5*u**3 + 8*u**2 - 3*u + 2. Let p be -2*(-1 - 4)/5. Let a(k) = -10*k**3 + 15*k**2 - 5*k + 5. Let m(y) = p*a(y) - 5*h(y). Factor m(d).
5*d*(d - 1)**2
Let a(g) be the second derivative of 1/80*g**5 + 9*g + 0*g**2 + 1/6*g**3 + 1/12*g**4 + 0. Solve a(s) = 0 for s.
-2, 0
Let o(y) be the first derivative of y**7/315 - y**2 + 15. Let p(v) be the second derivative of o(v). Factor p(h).
2*h**4/3
Let s be 88/104*((-186)/328)/(-3). Let v = s + -1/164. What is w in -4/13*w + 0*w**3 + 0 - 6/13*w**2 + v*w**4 = 0?
-1, 0, 2
Let v = -17615/2 - -3223795/366. Let s = -1/61 + v. Suppose 0*m + 0 - 4/3*m**4 + 2/3*m**3 + s*m**5 + 0*m**2 = 0. What is m?
0, 1
Suppose -5*p = 0, -c - 4*c - 5*p = -35. Factor -5 + 10*n**3 + 35*n**2 + c + 40*n + 0*n**3 + 13.
5*(n + 1)**2*(2*n + 3)
Let q(b) be the third derivative of b**6/1080 + b**5/45 + 11*b**4/216 + 17*b**2 - 5*b. Solve q(z) = 0 for z.
-11, -1, 0
Let c(r) = 13*r - 111. Let z be c(8). Let i be (z/6)/((-7)/3). Suppose l + 1/2*l**2 + i = 0. What is l?
-1
Let g be (-2)/(-3) + 44/(-12). Let n be (-8 - -2)*1/g. Find w, given that -n*w**2 - 2 - w + 3*w - w**3 - w**3 + 4*w**2 = 0.
-1, 1
Let o(d) be the first derivative of -d**3/9 - 5*d**2/3 + 13*d + 610. Factor o(f).
-(f - 3)*(f + 13)/3
Let j(w) be the third derivative of -13*w**2 + 1/300*w**6 - 1/525*w**7 + 0 + 0*w**4 + 0*w**3 + 1/150*w**5 - 1/840*w**8 + 0*w. Find y such that j(y) = 0.
-1, 0, 1
What is o in 1/2*o**3 + 0 - 1/2*o**2 - o = 0?
-1, 0, 2
Let m(j) be the second derivative of -5*j**7/14 - 25*j**6/6 - 5*j**5/4 + 125*j**4/12 + 20*j**3/3 + 10*j + 17. Suppose m(k) = 0. What is k?
-8, -1, -1/3, 0, 1
Let l be 4/(88/150) - 28/(-154). Factor -3*c - 4*c**3 + 5*c + 34*c**3 + 8*c**5 + 7*c**2 + l*c**2 + 26*c**4.
2*c*(c + 1)**3*(4*c + 1)
Let o be -1 + 0 + (1 - -32)/11. Factor 4/9*q + 2/9*q**o + 0 - 2/9*q**3.
-2*q*(q - 2)*(q + 1)/9
Let l be 1/2*((-12)/(-6) + 4). Let z(i) be the first derivative of 49/6*i**3 - 11 - l*i - 7/4*i**2. Suppose z(h) = 0. Calculate h.
-2/7, 3/7
Let o(z) be the first derivative of z**6/12 + z**5/10 - 9*z**4/8 + 11*z**3/6 - z**2 - 79. What is i in o(i) = 0?
-4, 0, 1
Find l such that 0 + 18/13*l**2 - 2/13*l**4 - 54/13*l + 6/13*l**3 = 0.
-3, 0, 3
Let c(o) = -o**2 + 57*o + 2384. Let q be c(85). Let -1/4*g**2 + 1/4*g**q + 1/4*g + 0 - 1/4*g**3 = 0. Calculate g.
-1, 0, 1
Suppose 3*o - 161 = 2*o. Let d = o + -802/5. What is u in 1/5*u**3 + 1/5 + d*u**2 + 3/5*u = 0?
-1
Let l(n) be the third derivative of -13*n**2 - 1/9*n**4 + 1/9*n**3 + 0 + 2/45*n**5 + 0*n. Find z, given that l(z) = 0.
1/2
Let w(c) be the first derivative of -5*c**3/3 + 25*c**2/2 + 70*c + 387. Let w(j) = 0. Calculate j.
-2, 7
Let p(i) be the first derivative of -i**4/4 - 22*i**3/3 - 41*i**2/2 - 20*i - 434. Determine c, given that p(c) = 0.
-20, -1
Suppose 18*a + 98 = 25*a. Suppose -d - 4*v - a = 0, -2*d - 3*v + 3 - 11 = 0. Factor 0 - 2*g + 2/3*g**3 + 4/3*g**d.
2*g*(g - 1)*(g + 3)/3
Let j = -9/2 + 5. Let k(a) = a**3 - 15*a - 4. Let d be k(4). Factor -j*l**3 + 1/2*l + d*l**2 + 0.
-l*(l - 1)*(l + 1)/2
Determine m so that -6/5*m - 8/5 - 1/5*m**2 = 0.
-4, -2
Let y = -3504/5 + 691. Let d = y - -157/15. Factor -2/3*i**4 + 0*i**3 + d*i**2 + 0*i + 0.
-2*i**2*(i - 1)*(i + 1)/3
Let n(l) be the first derivative of 0*l**4 + 1/30*l**5 + 4*l - 2/3*l**2 - 1/3*l**3 + 8. Let x(u) be the first derivative of n(u). Suppose x(k) = 0. Calculate k.
-1, 2
Let k be 1/(12/9*(-5)/(-240)). Find y such that 36*y**2 - k*y**2 + 3*y - 4*y**3 + y = 0.
-1, 0, 1
Let w(o) be the first derivative of 0*o - 4/9*o**3 + 4/15*o**5 + 0*o**2 - 19 - 1/9*o**6 + 1/6*o**4. What is s in w(s) = 0?
-1, 0, 1, 2
Suppose 0 = 145*g - 146*g + 32. Factor -236*o**2 - 233 - 2*o**4 + 71 + 360*o - 15*o**3 + g*o**3 + 23*o**3.
-2*(o - 9)**2*(o - 1)**2
Factor 0 - 3/4*y + 3/2*y**2 - 3/4*y**3.
-3*y*(y - 1)**2/4
Let t(u) be the second derivative of -56*u**6/5 - 66*u**5/5 - 23*u**4/4 - u**3 - 6*u + 3. Determine m, given that t(m) = 0.
-2/7, -1/4, 0
Let p(r) be the second derivative of -r**5/70 - 17*r**4/42 - 31*r**3/21 - 15*r**2/7 + 91*r. Determine o so that p(o) = 0.
-15, -1
Let z(l) = -l**2 - 17*l + 21. Let g be z(-18). Let f be -9*(-1)/6*6/g. Factor 0*x**2 + 4/9 - 2/3*x + 2/9*x**f.
2*(x - 1)**2*(x + 2)/9
Let q = -2/3055 + 27499/6110. Factor 0*o**3 - 3/2*o**2 + q*o**4 - 3*o**5 + 0*o + 0.
-3*o**2*(o - 1)**2*(2*o + 1)/2
Suppose j - 2*j + 2 = 0. Factor 0*y**j + 1 - 4*y + 0 + y**2 + 6*y.
(y + 1)**2
Factor -190*s + 1994 + 2339 - 14*s + 2*s**2 + 869.
2*(s - 51)**2
Suppose -13*s - 5 + 16 + 15 = 0. Factor -674/23*o**s - 8/23 + 128/23*o + 338/23*o**5 - 1118/23*o**4 + 58*o**3.
2*(o - 1)**3*(13*o - 2)**2/23
Suppose -2*d + 256 = 6*d. Let h be d/(-12)*15/25 - -4. Solve 27/5*v**3 - 36/5*v**5 + 0 - 3/5*v + 0*v**2 + h*v**4 = 0.
-1/2, 0, 1/3, 1
Let i(g) = 2*g**2 + 35*g + 7. Let r be i(-17). Let t(x) = x**3 + 10*x**2 - 2*x - 16. Let l be t(r). Factor 0*p + 10/3*p**l 