f**3 - 4*f**3.
2*(f - 1)**2*(f + 1)*(5*f - 2)
Let d(k) be the third derivative of -k**6/1080 - k**5/360 + 5*k**3/6 - k**2. Let o(b) be the first derivative of d(b). Factor o(v).
-v*(v + 1)/3
Let d be (-6)/8*(-3 - 7/(-3)). Factor 0 + 0*c + c**2 - d*c**3.
-c**2*(c - 2)/2
Let k(t) be the second derivative of 7*t**6/20 + 57*t**5/40 + 15*t**4/8 + t**3/4 - 3*t**2/2 - 14*t. Determine p so that k(p) = 0.
-1, 2/7
Let q = 3 + -3. Let u be (q + 4)*(-1)/(-2). Factor -6 - 12 - 15*p - u*p**2 + 3*p.
-2*(p + 3)**2
Let i(w) be the first derivative of -3*w**4/14 + 4*w**3/7 + 15*w**2/7 - 36*w/7 - 22. Solve i(z) = 0 for z.
-2, 1, 3
Let i(m) be the second derivative of 0 + 1/3*m**3 + 0*m**2 + 1/6*m**4 + m. Factor i(k).
2*k*(k + 1)
Factor -5*x**2 + 5 - 6*x - x + 2*x - x**3 + 6*x**3.
5*(x - 1)**2*(x + 1)
Let w = -321 + 2249/7. Factor -2/7*d**2 + 2/7*d**4 - 2/7*d**3 + w*d + 0.
2*d*(d - 1)**2*(d + 1)/7
Let i = -580 + 580. Suppose 0*f + i - 2/7*f**2 - 2/7*f**4 + 4/7*f**3 = 0. Calculate f.
0, 1
Let t(v) be the third derivative of 1/210*v**7 + 1/120*v**6 + 0*v**4 - 1/30*v**5 + 0 + 8*v**2 + 0*v**3 + 0*v. Factor t(h).
h**2*(h - 1)*(h + 2)
Suppose f - 2*t - 18 = 0, -4*t = -t. Factor -2*s**5 + 0*s**5 - 63*s + f*s**3 - 30*s**2 - s**5 - 5 - 22 + 9*s**4.
-3*(s - 3)**2*(s + 1)**3
Suppose 0 = -d + 1. Let r = d + 1. Factor -y + 3*y**4 - 4*y**4 + y + y**r.
-y**2*(y - 1)*(y + 1)
Suppose -50 = -5*n - 35. Factor -27/4*v**2 + 9/2*v + n*v**3 - 3/4.
3*(v - 1)**2*(4*v - 1)/4
Let c be (2/(-11) - (-777)/462) + 0. Factor -1/2 - 1/2*u**3 - c*u - 3/2*u**2.
-(u + 1)**3/2
Solve 2*y**2 - 3*y - 3 - 1 + 2 - 3*y**2 = 0 for y.
-2, -1
Let r(g) be the second derivative of -g**6/6 + g**5/2 - 5*g**4/12 + 2*g. Factor r(t).
-5*t**2*(t - 1)**2
Solve 0*r + r**2 + 2*r + 2*r**2 + r = 0 for r.
-1, 0
Let j(u) be the first derivative of u**3/18 + u**2/6 - u/2 + 1. Let j(d) = 0. What is d?
-3, 1
Let r(d) be the first derivative of -2/9*d**3 - 8/3*d + 3 - 4/3*d**2. Let r(s) = 0. Calculate s.
-2
Let c(o) be the second derivative of 2*o**6/105 - 4*o**5/35 + 2*o**4/7 - 8*o**3/21 + 2*o**2/7 - 9*o. Let c(d) = 0. Calculate d.
1
Let f(m) be the first derivative of m**5/20 - m**4/12 - 3*m + 1. Let s(y) be the first derivative of f(y). Factor s(c).
c**2*(c - 1)
Let l(u) be the second derivative of u**6/120 + u**5/40 - 19*u**4/48 + 7*u**3/6 - 3*u**2/2 - 23*u + 2. Let l(d) = 0. What is d?
-6, 1, 2
Let r(s) be the third derivative of -s**5/300 - s**4/120 + s**3/5 - 10*s**2 + 3*s. Find h such that r(h) = 0.
-3, 2
Let g(d) be the second derivative of -d**6/6 + 3*d**5/2 - 65*d**4/12 + 10*d**3 - 10*d**2 + 2*d. Factor g(n).
-5*(n - 2)**2*(n - 1)**2
Let q(a) be the first derivative of a**4/20 - 3*a**2/10 + 2*a/5 - 9. Solve q(u) = 0 for u.
-2, 1
Let l(n) be the second derivative of -n**7/21 - 3*n**6/20 - n**5/20 + 5*n. Factor l(y).
-y**3*(y + 2)*(4*y + 1)/2
Let r(p) be the third derivative of -p**8/2184 + p**7/455 - p**6/390 - p**5/195 + p**4/52 - p**3/39 - 2*p**2. Factor r(n).
-2*(n - 1)**4*(n + 1)/13
Factor 8*b**3 + 28*b**2 + 13*b + 24*b + 8 - 9*b.
4*(b + 1)*(b + 2)*(2*b + 1)
Factor 2/19*b + 2/19*b**2 + 0.
2*b*(b + 1)/19
Let b(t) be the third derivative of -t**9/151200 - t**8/50400 + t**5/60 + t**2. Let k(d) be the third derivative of b(d). Factor k(l).
-2*l**2*(l + 1)/5
Let q(z) be the third derivative of z**8/1176 + 3*z**7/245 + z**6/14 + 23*z**5/105 + 11*z**4/28 + 3*z**3/7 - 3*z**2. Factor q(i).
2*(i + 1)**3*(i + 3)**2/7
Let c be (-50)/(-20)*(-1)/(10/(-8)). Suppose -3*x + 3/2*x**c + 3/2 = 0. What is x?
1
Let c = 13 - 11. Let y(z) = -z - 2. Let s be y(-2). Factor -2*i**c + 4/3*i + s + 2/3*i**3.
2*i*(i - 2)*(i - 1)/3
Suppose -2 = -i - i. Let n(s) = -s**3 + s**2. Let h(o) = -2*o**4 - 2*o**3 + 2*o**2 + 2*o. Let v(u) = i*h(u) - 8*n(u). Factor v(l).
-2*l*(l - 1)**3
Let p(h) be the first derivative of -3*h**5/20 + 3*h**4/4 + h**3/2 - 9*h**2/2 - 5*h - 3. Let v(k) be the first derivative of p(k). Factor v(o).
-3*(o - 3)*(o - 1)*(o + 1)
Factor 3*s**2 - 139*s + 55*s + 3 + 45*s + 45*s.
3*(s + 1)**2
Let -2047 - 3*f**4 + 12*f + 21*f**2 + 2047 + 6*f**3 = 0. Calculate f.
-1, 0, 4
Let g(d) be the third derivative of -d**5/210 - d**4/42 - d**3/21 + 22*d**2. Solve g(q) = 0 for q.
-1
Let t(r) be the third derivative of -1/560*r**8 + 0*r**3 - 1/350*r**7 + 0 + 0*r + 0*r**4 + 1/200*r**6 + 2*r**2 + 1/100*r**5. Suppose t(l) = 0. What is l?
-1, 0, 1
Suppose 3*t + 16 = 7. Let f(w) = 4*w**2 - w - 5. Let h(b) = -3*b**2 + b + 4. Suppose 3*r + r = -8. Let u(y) = r*f(y) + t*h(y). Find i, given that u(i) = 0.
-1, 2
Factor -5/2*a**3 + 0 - 5/2*a**2 + 5*a.
-5*a*(a - 1)*(a + 2)/2
Find w, given that -4/5*w**3 - 4*w + 8/5 + 16/5*w**2 = 0.
1, 2
Let x(v) be the third derivative of -v**6/80 - v**5/10 + v**4/16 + v**3 - 7*v**2. Factor x(m).
-3*(m - 1)*(m + 1)*(m + 4)/2
Suppose w + 5*u = 2*w + 3, 33 = w + 4*u. Let i be w/4 - 5/20. Let 0*j**2 - j - i - 5*j - 2*j**2 + 0 = 0. Calculate j.
-2, -1
Find c such that 4*c**4 - 44*c**3 + 81*c**3 - 33*c**3 = 0.
-1, 0
Let q = -3/4 + 13/12. Let u = 4 + -4. Factor u + q*f**2 + 0*f.
f**2/3
Let r(c) = 2*c + 3*c - 9*c + 3*c. Let z be r(-2). Factor -t**3 + 24*t**2 + 4 + 9*t**3 + 12*t + 6*t + z*t**3.
2*(t + 1)**2*(5*t + 2)
Suppose -p + 8 = 3*p. Factor 1 + 2*h**p - 2 + 4*h - 3 + 6.
2*(h + 1)**2
Let m(d) be the first derivative of 1/12*d**4 + 0*d - 1 - 1/6*d**2 + 0*d**3. Factor m(x).
x*(x - 1)*(x + 1)/3
Let k be 4 - ((-129)/(-12) + -7). Let z = -12/11 - -35/22. Factor z - 3/4*r + k*r**2.
(r - 2)*(r - 1)/4
Let d(g) be the third derivative of -g**8/84 - 2*g**7/21 - g**6/6 + g**5/3 + g**4 - g**2 + 21*g. Let d(a) = 0. What is a?
-3, -2, -1, 0, 1
Let q(t) be the third derivative of 2*t**7/105 - t**6/15 - t**5/5 + 2*t**4/3 + 8*t**3/3 - 6*t**2. Factor q(w).
4*(w - 2)**2*(w + 1)**2
Let k(r) = -r**4 - 20*r**3 - 11*r**2 + 26*r + 6. Let i(z) = 4*z**4 + 59*z**3 + 32*z**2 - 77*z - 18. Let d(y) = -3*i(y) - 8*k(y). Find m, given that d(m) = 0.
-3, -2, -1/4, 1
Let i(s) = s**2 + s + 4. Let k be i(-5). Let l be 122/k - 4/(-16). Find v such that 15*v**4 - 4/3 - 82/3*v**3 + l*v + 25/3*v**2 = 0.
-2/5, 2/9, 1
Suppose -7 = -5*j - 2*o, -3*j - 1 = 3*o + 2. Suppose -j*h = 4 - 10. Factor 0 + 0*v + 1/5*v**5 - 1/5*v**3 + 0*v**4 + 0*v**h.
v**3*(v - 1)*(v + 1)/5
Factor 6/5*y + 2/15*y**3 + 0 - 4/5*y**2.
2*y*(y - 3)**2/15
Let q(t) be the third derivative of t**6/20 - 4*t**5/15 + 7*t**4/12 - 2*t**3/3 - 35*t**2. Solve q(d) = 0.
2/3, 1
Let y = 6/11 + -205/33. Let n = -31/6 - y. Factor n*j**2 + 0 - 1/2*j.
j*(j - 1)/2
Suppose -19*z = -15*z - 12. Let 0*g + 2/5*g**2 + 2/5*g**z + 0 = 0. What is g?
-1, 0
Let i(m) = -m**4 - 5*m**3 - 8*m**2 - 4*m - 7. Let q(d) = -d**4 - 5*d**3 - 8*d**2 - 4*d - 6. Let j be 24/(-14)*42/(-12). Let r(h) = j*i(h) - 7*q(h). Factor r(l).
l*(l + 1)*(l + 2)**2
Factor 40*t + 12*t**4 - 4*t**5 - 40*t - 8*t**3.
-4*t**3*(t - 2)*(t - 1)
Let k(f) be the second derivative of -f**6/240 + 3*f**5/40 - 9*f**4/16 + 9*f**3/4 - 81*f**2/16 + 18*f. Factor k(g).
-(g - 3)**4/8
Let b = -230/3 - -77. Determine z so that 0 - b*z + 1/3*z**2 = 0.
0, 1
Suppose -r - 4*x - 10 + 4 = 0, -3*r = x - 4. Factor -a**2 - 4*a**3 - 2*a**2 + 3*a**2 - r*a**4 - 2*a**2.
-2*a**2*(a + 1)**2
Let a(n) = -6*n**5 + 6*n**3 - 3*n**2 - 3*n. Let x(r) = -11*r**5 + r**4 + 12*r**3 - 7*r**2 - 6*r + 1. Let h(q) = -5*a(q) + 3*x(q). Let h(k) = 0. Calculate k.
-1, 1
Let n(x) be the third derivative of x**8/10080 + x**7/630 + x**6/90 + x**5/15 + x**2. Let p(h) be the third derivative of n(h). Factor p(u).
2*(u + 2)**2
Let u = -11 - -16. Suppose -u*s + 6 = -4. Factor 3 - 4 + 2 - d**s.
-(d - 1)*(d + 1)
Let u(c) be the first derivative of -c**5/100 + c**4/30 - 2*c + 2. Let l(w) be the first derivative of u(w). Factor l(a).
-a**2*(a - 2)/5
Let a(f) be the second derivative of 2/7*f**4 - f + 3/28*f**5 - 3/7*f**2 + 1/14*f**3 + 0. Factor a(h).
3*(h + 1)**2*(5*h - 2)/7
Let o(q) be the first derivative of 0*q**2 - 1/18*q**6 + 0*q - 1 + 1/12*q**4 - 1/15*q**5 + 1/9*q**3. Suppose o(w) = 0. Calculate w.
-1, 0, 1
Let j be 1/(66/(-18) - -4). Factor -9/5*y**2 + j*y + 6/5.
-3*(y - 2)*(3*y + 1)/5
Let x = 3 + -1. Suppose 20 = 5*n - 5*r - 5, -5*r = 3*n + 9. Suppose -x*o**n + 0 - 8/3*o**3 + 2/3*o = 0. Calculate o.
-1, 0, 1/4
Suppose -4*m + 12 = -2*m. Factor 2 - 2 + m*q + 18 + 6*q + 2*q**2.
2*(q + 3)**2
Let u(b) be the second derivative