-15*s**4/32 - 3*s**3/2 - 27*s**2/16 - 3*s/4 - 39. Let y(b) = 0. Calculate b.
-1, -2/5
Let x(u) = u**4 + u**2. Let t(l) = 6*l**4 + 12*l**3. Let a(p) = -t(p) - 3*x(p). Determine f, given that a(f) = 0.
-1, -1/3, 0
Let v(c) be the second derivative of -8/5*c**3 - 2*c - 3/25*c**5 - 8/5*c**2 - 11/15*c**4 + 0. Factor v(m).
-4*(m + 1)*(m + 2)*(3*m + 2)/5
Determine o so that 0*o + 0 - 4/3*o**3 + 14/3*o**4 - 8/3*o**5 - 2/3*o**2 = 0.
-1/4, 0, 1
Let g(t) be the third derivative of -t**10/151200 + t**8/20160 + t**5/15 - t**2. Let b(f) be the third derivative of g(f). Determine q so that b(q) = 0.
-1, 0, 1
Let z(j) be the first derivative of -4*j**3/3 - 26*j**2 - 55. Factor z(r).
-4*r*(r + 13)
Let 1/5*z**2 + 2/5*z + 1/5 = 0. What is z?
-1
Let b(n) be the first derivative of -3/5*n**5 - 3*n**2 + 3 + 0*n + 3*n**3 + 0*n**4. Solve b(l) = 0.
-2, 0, 1
Let u = 277/5 - 55. Let v = 2603/5 + -519. Find k, given that v*k**2 - u*k - 6/5*k**3 + 0 = 0.
0, 1/3, 1
Let q(d) be the second derivative of d**4/72 - d**2/12 + 6*d. Factor q(a).
(a - 1)*(a + 1)/6
Let w(k) = 36*k**2 + 66*k + 21. Let i(r) = 7*r**2 + 13*r + 4. Let s(p) = -21*i(p) + 4*w(p). Determine z, given that s(z) = 0.
-3, 0
Suppose 2*m + 545 = -2*g - g, -4*m + 177 = -g. Let l = g + 1269/7. Let 2/7*d**2 - l*d**3 - 2/7*d**4 + 2/7*d + 0 = 0. Calculate d.
-1, 0, 1
Let z = -34 + 54. Suppose 4*v = -4*o + 28, 0*o + 2*o - z = -5*v. Solve 6*q**4 - 3*q**3 - 3*q**4 + q**v - q**4 = 0 for q.
0, 1/2, 1
Let z(j) be the third derivative of j**8/90720 + j**7/22680 - j**5/20 + 2*j**2. Let s(q) be the third derivative of z(q). Factor s(i).
2*i*(i + 1)/9
Let v(f) = -339*f**5 - 1768*f**4 - 1411*f**3 + 2146*f**2 - 712*f + 72. Let y(u) = u**5 - u**4 - u**3 - u**2 - u. Let s(m) = -v(m) + 4*y(m). Factor s(l).
(l + 3)**2*(7*l - 2)**3
Let l = 19 - 14. Let h(x) be the first derivative of -2/15*x**3 + 0*x**2 + 2/25*x**l + 1 + 0*x + 1/15*x**6 - 1/10*x**4. Factor h(o).
2*o**2*(o - 1)*(o + 1)**2/5
Let q(r) = -25*r**2 - 780*r - 2340. Let c(d) = 2*d**2 + 60*d + 180. Let y(v) = 40*c(v) + 3*q(v). Factor y(t).
5*(t + 6)**2
Let b(l) be the third derivative of -l**6/40 + 3*l**4/8 + l**3 - 10*l**2. Factor b(p).
-3*(p - 2)*(p + 1)**2
Factor 3*b**3 - b**2 - 2*b**3 + 0*b**2 + 0*b**3.
b**2*(b - 1)
Suppose 2*w + 68 = 3*j + j, 5*j - 71 = -w. Suppose -20*l = -j*l. Factor l + 2/9*c - 2/9*c**3 + 0*c**2.
-2*c*(c - 1)*(c + 1)/9
Let i be -12*-1*2/6. Suppose 3*c**5 - 4*c**2 - 2*c + 4*c**5 - 2*c**5 + 4*c**i - 3*c**5 = 0. What is c?
-1, 0, 1
Let p(v) be the second derivative of -2/5*v**4 + v + 21/25*v**5 + 0*v**2 + 9/70*v**7 - 3/5*v**6 + 0 + 0*v**3. Factor p(k).
3*k**2*(k - 2)*(3*k - 2)**2/5
Determine p, given that -3/2*p - 3 + 3/2*p**2 = 0.
-1, 2
Let d = 884/33 - 258/11. Solve 2/3*o**4 + 8/3*o**3 + 0 + d*o**2 + 4/3*o = 0.
-2, -1, 0
Suppose -12 = -0*i - 4*i. Factor 4*j**4 + j**2 - j**3 - 2*j - 5*j**4 + i*j**3.
-j*(j - 2)*(j - 1)*(j + 1)
Factor -2*k**2 + 8*k**2 - 13*k + 5*k**2 - 10*k**2.
k*(k - 13)
Let k(m) be the first derivative of 4*m**5/5 + m**4 - 8*m**3/3 - 14. Factor k(y).
4*y**2*(y - 1)*(y + 2)
Let h(q) be the first derivative of -1/24*q**4 - 2*q + 1/80*q**5 + 1/24*q**3 + 3 + 0*q**2. Let z(g) be the first derivative of h(g). Factor z(k).
k*(k - 1)**2/4
Let b(j) = 2*j**2 + 2*j - 3. Suppose 0 = 4*u - 2*u - 4. Let d(h) = -2*h**2 - 2*h + 2. Let v(t) = u*b(t) + 3*d(t). Factor v(w).
-2*w*(w + 1)
Let a(s) be the second derivative of s**5/4 - 5*s**4/12 - 5*s**3/6 + 5*s**2/2 - 18*s. Find y such that a(y) = 0.
-1, 1
Let p be (-1)/(-4) - (-3)/12. Factor -p*x**2 + 0*x + 0*x**3 + 1/4 + 1/4*x**4.
(x - 1)**2*(x + 1)**2/4
Let l(x) be the second derivative of 0*x**2 + 3*x - 1/40*x**4 + 0*x**5 + 1/300*x**6 - 1/30*x**3 + 0. Factor l(t).
t*(t - 2)*(t + 1)**2/10
Let s(z) = z**3 - 8*z**2 + 11*z + 6. Let w be s(6). Factor 0*q**3 - 2/7 + 4/7*q**2 - 2/7*q**4 + w*q.
-2*(q - 1)**2*(q + 1)**2/7
Let b = 17/9 + -14/9. Solve 5/3*r + b + 4/3*r**2 = 0 for r.
-1, -1/4
Let r(c) be the first derivative of -5*c**4/8 - 5*c**3/6 + 29. Factor r(z).
-5*z**2*(z + 1)/2
Let o(m) = 7*m**5 - 16*m**4 + 17*m**3 - 11*m**2 + 3*m. Let k(b) = -8*b**5 + 16*b**4 - 16*b**3 + 12*b**2 - 4*b. Let d(i) = 3*k(i) + 4*o(i). Factor d(t).
4*t**2*(t - 2)*(t - 1)**2
Let v(n) be the second derivative of n**7/1260 + n**6/180 + n**5/90 + 5*n**3/3 + 8*n. Let k(l) be the second derivative of v(l). Factor k(g).
2*g*(g + 1)*(g + 2)/3
Let v(k) be the second derivative of 7*k**6/90 - 4*k**5/15 + 11*k**4/36 - k**3/9 + 4*k. Factor v(b).
b*(b - 1)**2*(7*b - 2)/3
Suppose -2*k - 3*k - 5 = 0. Let g = 4 + k. Factor 2*h - 2*h**2 + 3*h**g + 0*h - 3*h + 4*h**2.
h*(h + 1)*(3*h - 1)
Let b = 1/9 - -5/36. Let a(f) be the second derivative of 3/2*f**2 + b*f**4 + f**3 - 2*f + 0. Let a(u) = 0. Calculate u.
-1
Let w(h) be the second derivative of -1/9*h**4 + 1/63*h**7 + 1/15*h**6 - 2*h + 1/15*h**5 - 1/3*h**3 - 1/3*h**2 + 0. Factor w(m).
2*(m - 1)*(m + 1)**4/3
Let j be (144/27)/(104/12 + -4). Let -6/7*q**4 + 18/7*q**2 + 0*q + 4/7*q**3 - j = 0. What is q?
-1, 2/3, 2
Let f(m) be the first derivative of -m**8/4200 + m**7/700 - m**5/75 - 4*m**3/3 - 3. Let l(k) be the third derivative of f(k). Factor l(x).
-2*x*(x - 2)**2*(x + 1)/5
Let j(z) be the third derivative of -z**10/60480 - z**9/15120 + z**4/12 - z**2. Let h(n) be the second derivative of j(n). Factor h(a).
-a**4*(a + 2)/2
Let o be ((-696)/20)/(2/20). Let g be o/(-462) - 2/11. Determine m so that 2/7*m - g*m**2 - 2/7*m**5 + 4/7*m**4 + 0*m**3 + 0 = 0.
-1, 0, 1
Let d(s) = 9*s + 7 + 8*s**3 + 6*s**2 - 3*s**3 + 2*s**4 + 8*s**3. Let v(a) = -a**4 - 7*a**3 - 3*a**2 - 5*a - 4. Let r(f) = 4*d(f) + 7*v(f). Factor r(y).
y*(y + 1)**3
Let g be ((-3)/10)/(12/(-16)). Let l be (-4)/(-5)*6/12. Find f, given that -l + 0*f + g*f**2 = 0.
-1, 1
Let i(o) be the first derivative of 5*o**6/6 - 2*o**5 + 10*o**3/3 - 5*o**2/2 + 10. Factor i(g).
5*g*(g - 1)**3*(g + 1)
Suppose -4*w - 16 = -5*s + 4*s, 4*s - w = 19. Suppose -3*p = s*o - 59, -5*o + 3*p + 43 = -3*o. Factor -1 + d**4 + 15*d**2 + 2 - o*d**2.
(d - 1)**2*(d + 1)**2
Let t(b) = -16*b**5 - 3*b**4 + 12*b**3 - b**2 + 4*b. Let p(w) = -w**5 - w**2 + w. Let o(k) = 4*p(k) - t(k). Determine l so that o(l) = 0.
-1, -1/4, 0, 1
Suppose -d + 20 = 4*d. Factor -4*h**2 - d + 4 - h**3 - 4*h.
-h*(h + 2)**2
Let g be (-1 - -4) + ((-116)/44 - 0). Find k, given that -6/11*k + g*k**2 + 2/11 = 0.
1/2, 1
Let n(t) be the first derivative of -t**3/2 - 9*t**2/2 - 27*t/2 - 3. Factor n(f).
-3*(f + 3)**2/2
Let o = 559 + -557. What is u in -2/5*u - 1/5 + 0*u**o + 2/5*u**3 + 1/5*u**4 = 0?
-1, 1
Let w be 8/5 + 10/25. Factor w*v**2 - 3*v**3 - v + v + 0*v**2.
-v**2*(3*v - 2)
Solve -6/5 - 21/5*f + 21/5*f**3 - 3/5*f**2 + 9/5*f**4 = 0 for f.
-2, -1, -1/3, 1
Let n(v) be the first derivative of -v**4/2 - 2*v**3 - 54. Suppose n(g) = 0. What is g?
-3, 0
Let a = 106 + -100. Let x(m) be the third derivative of 0*m**4 + 0 + 0*m + 0*m**3 + 1/120*m**a - 4*m**2 - 1/60*m**5. Find i, given that x(i) = 0.
0, 1
Let g(p) be the third derivative of -p**6/360 - p**5/36 - p**4/9 - 2*p**3/9 - 7*p**2. Factor g(u).
-(u + 1)*(u + 2)**2/3
Let j(g) be the first derivative of 2*g + 2 + 1/6*g**3 + g**2. Factor j(k).
(k + 2)**2/2
Let q(z) be the third derivative of 0 - 1/75*z**5 - 2*z**2 + 0*z - 1/60*z**4 - 1/6*z**3 - 1/300*z**6. Let u(m) be the first derivative of q(m). Factor u(w).
-2*(w + 1)*(3*w + 1)/5
Let o be (-1)/(1/4) - 3. Let p = -5 - o. Suppose 3/4*v**4 + v**5 - 3/4*v**p + 1/4*v + 0 - 5/4*v**3 = 0. Calculate v.
-1, 0, 1/4, 1
Let s be 4 - -26*9/(-60). Let a(l) be the third derivative of 0 - 7/60*l**4 - 3/100*l**6 - 1/15*l**3 + 0*l - l**2 - s*l**5. Factor a(f).
-2*(f + 1)*(3*f + 1)**2/5
Factor 0 + 3/4*h**2 + 0*h.
3*h**2/4
Let u(c) be the first derivative of 2*c**5/5 - 2*c**4 + 10*c**3/3 - 2*c**2 - 32. Factor u(q).
2*q*(q - 2)*(q - 1)**2
Let b = 4 - 2. Suppose 4 = 2*w - b. Factor 2/3*r**4 + 0*r - 2/3*r**2 - 2/3*r**5 + 2/3*r**w + 0.
-2*r**2*(r - 1)**2*(r + 1)/3
Suppose 0*j - j + 3 = 0. Determine z so that 3*z**2 + j*z - 23 + 23 = 0.
-1, 0
Suppose -4*a + 4 = -5*u + 8, -8 = u - 3*a. Let x be 6/(-12) + 30/u. Factor 4*v + 4*v**2 + 0*v - 14*v**3 + x*v**2 - v**2.
-2*v*(v - 1)*(7*v + 2)
Let r(f) be the first derivative of -f**6/180 + f**5/90 + f**4/36 - f**3/9 - f**2/2 - 4. Let o(z) be the second derivative of r(z). What is b in o