(p - 1)**3*(p + 1)/2
Let r(f) be the second derivative of 3*f**5/80 - 3*f**4/16 + 3*f**2/2 - 23*f. Suppose r(d) = 0. What is d?
-1, 2
Let v be -15 - (1 - 2 - 2). Let x be (-8)/v*(-1)/(-2). Factor -1/3*p**5 + x*p**3 + 0 - 1/3*p**4 + 0*p + 1/3*p**2.
-p**2*(p - 1)*(p + 1)**2/3
Let x be (1/(-5))/(4/(-555)). Let o = 28 - x. Factor o*u**4 + 0*u**2 - 1/4*u**5 + 0 + 0*u**3 + 0*u.
-u**4*(u - 1)/4
Suppose 2*m = -3*t - 15, -m + 2 = 3*t + 17. Let l(q) be the first derivative of m*q**3 - 4/15*q**5 + 1/9*q**6 + 1/6*q**4 + 0*q + 0*q**2 - 2. Factor l(d).
2*d**3*(d - 1)**2/3
Factor 64 + 74*i**2 - 22*i**3 + 4*i**4 - 43*i**2 + 65*i**2 - 10*i**3 - 128*i.
4*(i - 2)**4
Let z(i) be the second derivative of -i**6/30 + 3*i**5/40 + i**4/8 - 7*i**3/12 + 3*i**2/4 - 3*i. Determine r so that z(r) = 0.
-3/2, 1
Suppose 5*k - 12 = 4*p - 5, -3*p - k = -9. Let w(b) be the second derivative of 0*b**3 + b + 0*b**p - 1/10*b**6 + 0 + 0*b**4 - 3/20*b**5. Factor w(z).
-3*z**3*(z + 1)
Factor 4*f + 3*f**3 - 4*f**2 - f**3 - 5*f**3.
-f*(f + 2)*(3*f - 2)
Let z(l) be the third derivative of -2*l**5/135 - 5*l**4/108 - l**3/27 - 12*l**2. Solve z(p) = 0 for p.
-1, -1/4
Let c(r) be the second derivative of 0*r**2 + 0*r**3 + 9*r + 0 + 1/4*r**4. Factor c(i).
3*i**2
Let q(t) = -15*t**3 + 40*t**2 - 10*t - 50. Let o(h) = -7*h**3 + 20*h**2 - 5*h - 26. Let f(c) = 5*o(c) - 2*q(c). Factor f(v).
-5*(v - 3)*(v - 2)*(v + 1)
Let f(y) be the third derivative of 1/80*y**5 - 1/12*y**3 + 1/96*y**4 + 0 + 0*y + 3*y**2. Factor f(u).
(u + 1)*(3*u - 2)/4
Let f be ((-3)/(-12))/(((-3)/(-24))/1). Let h(i) be the first derivative of -1/3*i**3 + 0*i - f + i**4 + 0*i**2. Find x such that h(x) = 0.
0, 1/4
Suppose 9*b + 2 = 3*h + 41, 0 = 4*b - 20. Solve 2/5*f**4 - 4/5*f + 2/5*f**5 - 6/5*f**3 + 0 - 2*f**h = 0 for f.
-1, 0, 2
Let m(q) be the third derivative of q**7/525 - q**5/150 + 4*q**2. Factor m(w).
2*w**2*(w - 1)*(w + 1)/5
Let o(z) be the third derivative of 0*z + 0 + 1/6*z**3 + 13/240*z**5 + 1/840*z**7 - 3*z**2 - 1/8*z**4 - 1/80*z**6. Factor o(a).
(a - 2)**2*(a - 1)**2/4
Let c(r) be the second derivative of -r**9/25200 + r**7/2100 - r**5/200 - r**4/3 - 2*r. Let p(x) be the third derivative of c(x). Factor p(v).
-3*(v - 1)**2*(v + 1)**2/5
Let t = 8 + -7. Let j be (5/(-15) + t)/1. Let -4/3*i**4 + 0*i + j*i**5 + 2/3*i**3 + 0 + 0*i**2 = 0. Calculate i.
0, 1
Let u = 291 - 13094/45. Let d(h) be the second derivative of 1/9*h**4 + 0*h**3 - u*h**6 + 0 + h + 0*h**5 - 1/3*h**2. Suppose d(q) = 0. Calculate q.
-1, 1
Let p(a) = -10*a**3 - 9*a**2 + 7*a + 6. Let y(j) = 11*j**3 + 10*j**2 - 8*j - 7. Let g(x) = -7*p(x) - 6*y(x). Factor g(k).
k*(k + 1)*(4*k - 1)
Determine h so that 24/13*h**2 - 2/13 - 4/13*h - 24/13*h**5 + 28/13*h**3 - 22/13*h**4 = 0.
-1, -1/4, 1/3, 1
Let n(q) = -7*q - 7. Let f(o) = -27*o - 27. Let m(v) = 4*f(v) - 15*n(v). Let y be m(-2). Factor -1/4 - 3/2*h**2 - h**y - h - 1/4*h**4.
-(h + 1)**4/4
Let o = -13 - -17. Find r such that 1/3*r**5 - 1/3*r**o + 1/3*r**2 - 1/3*r**3 + 0 + 0*r = 0.
-1, 0, 1
Let s be ((-130)/(-15))/(-13) - -1. Let 0 + s*z**3 - 5/6*z**4 + 0*z + 0*z**2 - 7/6*z**5 = 0. Calculate z.
-1, 0, 2/7
Suppose 3*m = l - 16, -2*m - 3 - 5 = 0. Suppose 0 = -4*v + 4 + l. Determine z, given that 13*z**3 + 3*z**5 + 7*z**4 + 6*z**v + z**5 + z + 5*z**4 = 0.
-1, -1/2, 0
Factor s**3 + 12*s**2 - 13*s**2 - 2*s**3.
-s**2*(s + 1)
Determine h so that -h**3 - 1/2 - 1/4*h**5 - 1/2*h**2 + h**4 + 5/4*h = 0.
-1, 1, 2
Let h = -2 + -4. Let b be (-17)/h - (-24)/(-16). Factor 2/3*r - b + 2/3*r**2.
2*(r - 1)*(r + 2)/3
Let m(v) be the second derivative of -v**4/66 + 2*v**3/33 + 12*v. Factor m(r).
-2*r*(r - 2)/11
Find j such that 6/19*j - 2/19 - 8/19*j**4 - 6/19*j**3 + 10/19*j**2 = 0.
-1, 1/4, 1
Let z(k) be the first derivative of 0*k - 3/4*k**4 - 1/2*k**2 - k**3 - 1/5*k**5 - 2. Find q such that z(q) = 0.
-1, 0
Factor 8/9*r + 0 + 2/9*r**5 - 2/3*r**3 - 4/9*r**4 + 8/9*r**2.
2*r*(r - 2)**2*(r + 1)**2/9
Let c be (3/2)/((-6)/(-8)). Determine s so that 2/3*s - 2/3*s**c + 2/3 - 2/3*s**3 = 0.
-1, 1
Let k(b) = -b**2 - 12*b + 4. Suppose w + 3*w + 48 = 0. Let t be k(w). Factor -1/4*q**t - 1/4*q**3 + 0 + 1/4*q + 1/4*q**2.
-q*(q - 1)*(q + 1)**2/4
Let v(h) = 2*h - 60. Let m be v(30). Factor m - 9/4*i**2 - 3/2*i + 3/4*i**4 + 0*i**3.
3*i*(i - 2)*(i + 1)**2/4
Let v(f) be the third derivative of -1/6*f**4 + 1/15*f**5 + 1/30*f**6 + 0 + 0*f + 2*f**2 - 2/3*f**3. Factor v(g).
4*(g - 1)*(g + 1)**2
Factor -18*x**2 + 5*x**3 - 17*x - 24 - 12*x**3 + 4*x**3 - 19*x.
-3*(x + 2)**3
Let f = 19 - 3. Factor -2*k**2 - 18 - 30*k - f*k**2 + 4*k**2 + 0*k**3 - 2*k**3.
-2*(k + 1)*(k + 3)**2
Let h = -126 - -2015/16. Let l = h + 19/48. Factor -l*t**3 + t**2 - t + 1/3.
-(t - 1)**3/3
Let j(i) = -i**2 - i + 2. Let t be j(0). Suppose 32 = 4*v + 5*n - 13, 3*n - 5 = t*v. Solve 4*b**3 - b**4 - 6*b**2 - 3 - b + 2 + v*b = 0.
1
Suppose -5*p + 10*d + 23 = 13*d, 4*d - 4 = 0. Let 0 + 0*u + 0*u**2 - 3/4*u**3 - 3/4*u**5 + 3/2*u**p = 0. What is u?
0, 1
Let y be (-164)/(-56) - 3 - (-8)/14. What is z in -1/4*z**3 - 1/4*z + y*z**2 + 0 = 0?
0, 1
Let i(o) = -o**3 + 8*o**2 - 4*o - 14. Let u be i(7). Determine z so that 6*z**2 + z**4 + 3*z**5 - 3*z + 0*z**2 - u*z**4 = 0.
-1, 0, 1
Let u(w) be the third derivative of 1/3*w**3 - 1/20*w**5 - w**2 - 1/6*w**4 - 1/180*w**6 + 0*w + 0. Let r(z) be the first derivative of u(z). Factor r(f).
-2*(f + 1)*(f + 2)
Let i = 43/10 - 31/10. Factor i*r**3 + 0*r**4 + 0*r + 0 - 2/5*r**5 + 4/5*r**2.
-2*r**2*(r - 2)*(r + 1)**2/5
Let m(w) = 12*w**2 + 9*w. Let u(j) = -9*j**2 - 9*j**2 + 0 - 14*j + 0. Suppose g + g = -5*z - 25, 2*g = 0. Let h(c) = z*u(c) - 8*m(c). Find f such that h(f) = 0.
-1/3, 0
Suppose 3*t - 5*v - 1109 = 0, -2*v = -4*t - 5*v + 1469. Let k = 2580/7 - t. What is p in 0 - k*p**3 + 4/7*p - 10/7*p**2 + 10/7*p**4 = 0?
-1, 0, 2/5, 1
Let h(l) be the third derivative of l**8/8640 + 23*l**7/15120 + l**6/360 - l**5/15 + 7*l**2. Let p(c) be the third derivative of h(c). Factor p(k).
(k + 3)*(7*k + 2)/3
Let w(t) be the first derivative of 0*t**3 + 0*t + 1/7*t**2 - 1/14*t**4 - 4. Factor w(d).
-2*d*(d - 1)*(d + 1)/7
Let n be ((-8)/12)/((-4)/54). Suppose 0 = 3*m - k - n, 3*m + k = -k + 9. Factor 4*d**3 - 2*d**3 + 0*d**m + 2*d**2.
2*d**2*(d + 1)
Let k be (3/(-4))/((-42)/16). Let z be 15/90 + 4/(-24). Suppose -4/7*l + z + k*l**3 - 2/7*l**2 = 0. Calculate l.
-1, 0, 2
Let d(a) = -a**2 - 6*a + 5. Let w be d(-7). Let c = 5 + w. Factor 14*f**3 - 2 - 3*f**4 - c*f**4 + 9*f - 2*f**2 - 14*f**2 + f**5.
(f - 2)*(f - 1)**4
Let n(r) be the second derivative of 6*r - 1/72*r**4 - 4/3*r**2 + 2/9*r**3 + 0. Suppose n(f) = 0. What is f?
4
Suppose 0 = d - 6 - 0. Suppose 0 = z - 2*z + d. Factor -3*l - z*l - 4*l**2 - 4 + 5*l + 3*l**2.
-(l + 2)**2
Let a = -481/7 + 69. Let j = 1/21 + a. Factor j + 1/3*p**3 + p**2 + p.
(p + 1)**3/3
Suppose -10 = 106*c - 108*c. Let b(d) be the third derivative of -1/30*d**c - 1/630*d**7 + 0*d + 1/90*d**6 - 3*d**2 - 1/18*d**3 + 0 + 1/18*d**4. Factor b(j).
-(j - 1)**4/3
Let i(g) = -g**2 - 6*g - 6. Let f be i(-4). Factor -1 - l - 1/4*l**f.
-(l + 2)**2/4
Let q(s) = -s**2 + 1. Let t(n) be the third derivative of n**5/15 - n**4/8 - 7*n**3/6 + 4*n**2. Let r(c) = -5*q(c) - t(c). What is a in r(a) = 0?
-2, -1
Let w(p) = p**2 + 20*p + 24. Let v(d) = 10*d**2 + 220*d + 265. Let a(k) = 4*v(k) - 45*w(k). Solve a(x) = 0 for x.
-2
Let s(v) be the first derivative of -6*v**5/35 + v**4/14 + 4*v**3/21 - 10. Factor s(t).
-2*t**2*(t - 1)*(3*t + 2)/7
Let z(a) be the third derivative of a**8/120 + 23*a**7/525 + a**6/15 + 2*a**5/75 + 9*a**2. Solve z(n) = 0.
-2, -1, -2/7, 0
Let v(u) be the first derivative of -3*u**4/10 - 26*u**3/15 - 13*u**2/5 - 6*u/5 + 5. Determine y so that v(y) = 0.
-3, -1, -1/3
Let k be 8/(-2) - 244/(-60). Let p(r) be the first derivative of -1/10*r**6 - 1/4*r**4 + 0*r + 0*r**2 - 2 - k*r**3 - 7/25*r**5. Solve p(w) = 0 for w.
-1, -1/3, 0
Let q be (0 - 8/(-6))/(20/45). Factor 3/4*c + 3/4*c**2 + 1/4*c**q + 1/4.
(c + 1)**3/4
Suppose -121*m - 2*m**3 - 3*m**2 + 2*m**2 - 5*m**2 + 117*m = 0. Calculate m.
-2, -1, 0
Let p(j) be the second derivative of -j**4/78 + j**3/39 - 4*j. Factor p(x).
-2*x*(x - 1)/13
Let y(s) = s**3 + 1. Let q be y(-1). Let d(t) be the first derivative of -1/12*t**3 + 1/4*t**2 + 3/20*t**5 + q*t - 1 - 1/4*t**4. Factor d(m).
m*(m - 1)**2*(3*m + 2)/4
Let b