3*(d - 1)**2*(d + 1)**3/4
Let i(m) be the second derivative of -25*m**4/12 + 10*m**3/3 + 5*m**2/2 + 11*m. Determine y so that i(y) = 0.
-1/5, 1
Let t(g) be the first derivative of -4*g**6/3 - 28*g**5/5 - 7*g**4 - 8*g**3/3 - 3. Find l such that t(l) = 0.
-2, -1, -1/2, 0
Let m(y) be the first derivative of -1/14*y**2 - 2/21*y**3 - 1/28*y**4 + 2 + 0*y. Factor m(l).
-l*(l + 1)**2/7
Let v be 8*((-84)/(-16) - -3). Let k be ((-11)/v)/((-2)/8). Let s**4 + 2/3*s - k*s**3 - s**2 + 0 = 0. Calculate s.
-1, 0, 2/3, 1
Let x(n) be the first derivative of -1/4*n**4 - 4 + 1/2*n**2 + 2/5*n**5 - 2/3*n**3 + 0*n. Find s such that x(s) = 0.
-1, 0, 1/2, 1
Let q(n) = 11*n**3 - n + 1. Let a be q(1). Let t = -7 + a. Factor 3*f**t + f + 3*f**2 - 2*f**4 + 0*f**2 - 4*f**2 - f**3.
f*(f - 1)**2*(f + 1)
Suppose -5*t = -4*o + 4, t + 38 = -5*o + 14. Let y(w) = w**2 - 2*w - 3. Let n(a) = -6*a**2 + 9*a + 15. Let b(h) = o*n(h) - 21*y(h). Factor b(v).
3*(v + 1)**2
Let w be 0 + 5 - 0/(-1). Suppose 0 = -w*b - 5 + 25. Let -1/2*u + 1 - 5/2*u**3 - b*u**2 = 0. Calculate u.
-1, 2/5
Let v(b) be the third derivative of -b**5/390 + b**4/52 - 2*b**3/39 + 7*b**2. Suppose v(p) = 0. What is p?
1, 2
Find h, given that -1 - 1/3*h**3 + h**2 + 1/3*h = 0.
-1, 1, 3
Let u = -4 + 4. Let l = 0 + 3. Find n such that 2*n**l - 2/3*n**2 + 0*n + u = 0.
0, 1/3
Let t be -4*(0 + 2/2). Let i(g) = g**3 + 5*g**2 + 3*g - 4. Let k be i(t). Solve 1/4 + 1/2*l**3 - 1/4*l**4 - 1/2*l + k*l**2 = 0 for l.
-1, 1
Let g(z) = -z**2 - 8*z - 1. Let n be g(-7). Suppose 4*p - 18 + n = 0. Factor 0*y - 1/4*y**p + 0*y**2 + 0 - 1/4*y**4.
-y**3*(y + 1)/4
Suppose -3*t = -5*w + 19, 5*t - 2*w + 4*w = -11. Let j be (1 - 1)/(t - -1). What is q in j*q**3 - q**5 - q**4 + 0*q + q**3 + 0*q + q**2 = 0?
-1, 0, 1
Let t(b) be the first derivative of 4/3*b**3 + 0*b + 3 + 0*b**2 - 1/2*b**4. Factor t(w).
-2*w**2*(w - 2)
Let q(f) be the second derivative of 1/8*f**3 + 0 + f + 0*f**4 - 1/80*f**5 - 1/4*f**2. Factor q(j).
-(j - 1)**2*(j + 2)/4
Let y = -18 + 20. Let z(r) be the first derivative of 0*r**2 - y*r + 2/3*r**3 + 2. Factor z(j).
2*(j - 1)*(j + 1)
Let w(n) be the third derivative of -n**5/12 - 5*n**4/8 + 2*n**2 + 6. Suppose w(a) = 0. What is a?
-3, 0
Let a(u) = 3*u**3 - 3*u**2 - 3*u - 3. Let g(p) = -p**2 - 1. Let f(w) = a(w) - 3*g(w). Factor f(y).
3*y*(y - 1)*(y + 1)
Let u = 181 - 723/4. Factor 0*f + u - 1/4*f**2.
-(f - 1)*(f + 1)/4
Suppose -x - 248 = 4*m, -3*m = 2*m - x + 319. Let q be ((-9)/12)/(m/24). Factor 0 + 2/7*b**2 + q*b.
2*b*(b + 1)/7
Let r(p) be the second derivative of 0 - 1/3*p**2 - 5/27*p**3 + 7*p - 1/54*p**4 + 1/90*p**5. Let r(c) = 0. What is c?
-1, 3
Factor -1/4*m + 1/4*m**2 + 1/4*m**3 - 1/4.
(m - 1)*(m + 1)**2/4
Let s be (-2)/(-11) - ((-224)/462 - 10). Suppose -s*j**2 - 26/3*j - 8/3*j**3 - 2 = 0. Calculate j.
-3, -1/2
Let z(k) be the second derivative of 1/24*k**3 + 0 + 1/48*k**4 - k - 1/120*k**6 + 0*k**2 - 1/80*k**5. Factor z(f).
-f*(f - 1)*(f + 1)**2/4
Let i(n) be the first derivative of 2*n**3/33 + 2*n**2/11 - 6*n/11 - 9. Factor i(j).
2*(j - 1)*(j + 3)/11
Let r(j) be the third derivative of -j**8/3360 + j**6/360 - j**4/6 - j**2. Let h(y) be the second derivative of r(y). Factor h(a).
-2*a*(a - 1)*(a + 1)
Solve 8*d**4 + 7*d**4 - 4*d**2 - 2*d**2 - 12*d**4 + 3 = 0 for d.
-1, 1
Let w(a) be the third derivative of -a**8/504 + a**7/315 + a**6/36 - a**5/90 - 2*a**4/9 - 4*a**3/9 - 14*a**2. Suppose w(c) = 0. Calculate c.
-1, 2
Let d = -173 + 1385/8. Let g(q) be the third derivative of 0*q + 0 + 1/70*q**7 - d*q**4 + 3/20*q**5 + 0*q**3 - 3/40*q**6 - 4*q**2. Factor g(i).
3*i*(i - 1)**3
Let n(x) be the first derivative of -4*x**3/15 - 4*x**2/5 - 4*x/5 + 5. Factor n(w).
-4*(w + 1)**2/5
Let l(t) = -t**3 + t - 1. Let m be 6/9 + (-28)/6. Let x(z) = 10*z**3 - 52*z**2 + 30*z + 8. Let i(q) = m*l(q) + x(q). Solve i(h) = 0 for h.
-2/7, 1, 3
Let l = -7 + 8. Let n be 3 + (-2)/4 + l. Factor 0 + n*k**3 - 5/2*k**2 - k.
k*(k - 1)*(7*k + 2)/2
Let d(i) = i + 1. Let v(k) = k**3 - 3*k**2 + 4*k + 2. Let a(y) = -10*d(y) + 5*v(y). Factor a(h).
5*h*(h - 2)*(h - 1)
Suppose 4*c - 9 + 1 = 0. Let -g**c + 4*g - 2*g**2 + 8 + 0 - g**2 = 0. Calculate g.
-1, 2
Determine l so that 2*l - 13*l**2 - 5*l - 5*l**2 - l = 0.
-2/9, 0
Factor -2 - 2 + 3*n**2 + 3 - 2.
3*(n - 1)*(n + 1)
Let v(y) be the first derivative of 6*y**5/5 - 2*y**4 - 4*y**3/3 + 4*y**2 - 2*y - 1. Factor v(b).
2*(b - 1)**2*(b + 1)*(3*b - 1)
Let h(u) = 9*u**2 - 5*u - 13. Suppose 0 = -2*g + 8 + 4. Let l(t) = 4*t**2 - 2*t - 6. Let a(j) = g*h(j) - 13*l(j). Factor a(f).
2*f*(f - 2)
Factor 2*c**5 - 2*c**5 - 8*c**3 - c**5 - 4*c**2 - 2*c**4 - 3*c**4.
-c**2*(c + 1)*(c + 2)**2
Let q(l) be the first derivative of l**5/30 + l**4/24 - l**3/18 - l**2/12 - 2. Let q(c) = 0. What is c?
-1, 0, 1
Let s be 2 - (1/(-2) + -3) - 4. Factor -48*p - s*p**4 - 24 - 36*p**2 - 12*p**3.
-3*(p + 2)**4/2
Suppose 5 = -2*y + 1. Let r be -3*y/21 - 0. Solve -2/7*v**4 + 0 + r*v**2 - 2/7*v**3 + 0*v + 2/7*v**5 = 0 for v.
-1, 0, 1
Let g(v) be the third derivative of -v**8/84 + 2*v**7/105 + v**6/10 - v**5/15 - v**4/3 + v**2. Find d such that g(d) = 0.
-1, 0, 1, 2
Find q such that -8/15*q**2 - 4/15 + 2/3*q + 2/15*q**3 = 0.
1, 2
Suppose -16*g - 4*h - 2 = -13*g, -2*g + 5*h = -14. Factor 5/3*r**g - 2/3*r - 5/3*r**4 + 0 + 2/3*r**3.
-r*(r - 1)*(r + 1)*(5*r - 2)/3
Let p(h) be the third derivative of h**6/480 - h**5/40 + 3*h**4/32 + 27*h**2. What is z in p(z) = 0?
0, 3
Suppose 1/2*v**2 - v + 0 = 0. Calculate v.
0, 2
Determine a, given that -4/7*a**2 + 2/7*a - 2/7*a**3 + 4/7 = 0.
-2, -1, 1
Let o(q) = -14*q - 3. Let y be o(-2). Let s be y/9 + (-8)/(-36). Suppose -8/7*v**s + 2/7 + 8/7*v - 2/7*v**2 = 0. Calculate v.
-1, -1/4, 1
Let b(d) be the second derivative of d**5/100 - d**3/10 - d**2/5 - 7*d. Let b(p) = 0. What is p?
-1, 2
Let f = 15 + -11. Factor -4*a + a**2 - f*a + 9*a.
a*(a + 1)
Let d = -18 - -24. Suppose l - 2 + 0 = 0. Factor l*j**2 - d*j**2 - 6 + 6*j**2 - 4*j.
2*(j - 3)*(j + 1)
Let m(x) be the third derivative of -x**7/21 - 2*x**6/15 - x**5/10 + 2*x**2. Let m(u) = 0. What is u?
-1, -3/5, 0
Factor -3 + 48*i**3 + 3*i**2 + 65*i**3 + 12*i - 125*i**3.
-3*(i - 1)*(i + 1)*(4*i - 1)
Let g(n) be the second derivative of n**5/10 - 2*n. Factor g(k).
2*k**3
Let u(a) = a**4 + a**3 + 13*a**2 + 3*a + 6. Let d(s) = s**4 + 2*s**3 + 12*s**2 + 4*s + 5. Let i(q) = 4*d(q) - 3*u(q). Factor i(m).
(m + 1)**3*(m + 2)
Let l(g) = 5*g**2 - 12*g + 7. Let i(c) = 4*c**2 - 12*c + 8. Let r(x) = -3*i(x) + 4*l(x). Determine k, given that r(k) = 0.
1/2, 1
Let k(p) be the second derivative of 3*p**5/40 - p**4/24 - 2*p**3/3 - p**2 + 3*p. Let k(w) = 0. Calculate w.
-1, -2/3, 2
Let t(c) be the third derivative of 7*c**6/200 + c**5/50 - 6*c**2. Factor t(q).
3*q**2*(7*q + 2)/5
Let s(d) be the third derivative of d**7/70 + d**6/80 - 16*d**2. Factor s(m).
3*m**3*(2*m + 1)/2
Let a(q) = q + 9. Let p be a(-7). Suppose -2*c + 2*c**3 - 3*c**3 - c**4 + 5*c**p + 4*c**3 - c**5 - 4*c**2 = 0. What is c?
-2, -1, 0, 1
Let r(f) be the third derivative of f**7/3780 - f**5/540 - f**3/3 + 2*f**2. Let d(h) be the first derivative of r(h). Factor d(m).
2*m*(m - 1)*(m + 1)/9
Let z(c) = c**3 - 14*c**2 + 14*c - 9. Let y be z(13). Factor -4*x**3 + 3*x**4 - x**y - 8*x**4.
-2*x**3*(3*x + 2)
Let x = -13 - -13. Let j(y) be the second derivative of 0 - 1/60*y**5 - y + 0*y**4 + x*y**2 + 0*y**3. Suppose j(o) = 0. Calculate o.
0
Let i(m) be the third derivative of -m**6/320 - 13*m**5/160 - 3*m**4/4 - 9*m**3/4 + m**2. Factor i(d).
-3*(d + 1)*(d + 6)**2/8
Suppose 0 = -2*t, t - 16 = 4*x + 3*t. Let c(z) = z**2 + 3*z - 2. Let l be c(x). Factor 0 + 4/3*y + 2/3*y**l.
2*y*(y + 2)/3
Let q be (482/6)/(4/(-3)). Let g = q + 62. Factor 1/2 + 5/4*u**2 + g*u.
(u + 1)*(5*u + 2)/4
Let p(r) be the third derivative of r**5/20 - r**4/2 + 2*r**3 - r**2. Let p(x) = 0. Calculate x.
2
Let w be 15/(18/6) + -2. Let c(j) be the third derivative of 3*j**2 + 0 - 1/90*j**5 - 1/315*j**7 + 0*j**4 + 0*j**w + 1/90*j**6 + 0*j. Factor c(v).
-2*v**2*(v - 1)**2/3
Suppose 1 = 2*h - 5. Factor 1/4*p**h - 1/2 + 0*p**2 - 3/4*p.
(p - 2)*(p + 1)**2/4
Find j such that -2/5*j**5 + 24/5*j**2 - 8/5*j + 12/5*j**4 + 0 - 26/5*j**3 = 0.
0, 1, 2
Let t be 6/36 + 58/12. Let m(b) be the first derivative of -4/7*b**2 - 5/14*b**4 - 2/35*b**t + 0*b + 2 - 16/21*b**3. Factor m(j).
-