5/60 + v**4/168 + 2*v**2. Factor z(b).
b*(b + 1)*(4*b - 1)**2/7
Let s(p) be the second derivative of -p**7/280 - p**6/40 - p**5/20 + p**3/2 - 6*p. Let a(c) be the second derivative of s(c). Let a(k) = 0. What is k?
-2, -1, 0
Let g(d) = -d**2 + 3*d. Let m be g(3). Let z(s) be the second derivative of 0*s**4 + 0*s**2 + 0 - 1/150*s**6 - 1/100*s**5 + m*s**3 + s. Factor z(a).
-a**3*(a + 1)/5
Let v(l) = l**2 + 2*l + 5. Let p be v(3). Solve 17*g**2 - p*g**2 + g + 2*g = 0.
0, 1
Suppose -v + 15 = 4*v. Let h(s) be the first derivative of -1 - 1/2*s - 1/6*s**v + 1/2*s**2. Factor h(a).
-(a - 1)**2/2
Let o = 6 + -6. Suppose -f + 2*y + 6 = 3, 5*y = o. Solve 13/4*g**2 + 1/4*g**4 + 1 + 3/2*g**f + 3*g = 0 for g.
-2, -1
Let l(d) be the third derivative of 2/3*d**3 + 0*d + 0 - 2*d**2 - 1/60*d**5 + 0*d**4. Suppose l(i) = 0. Calculate i.
-2, 2
Let r(k) be the first derivative of 1/24*k**3 + 0*k**2 - 2 - 1/48*k**4 - 2*k. Let z(n) be the first derivative of r(n). Let z(q) = 0. Calculate q.
0, 1
Let k be (2 - -1)*2/6. Suppose 2*n - 5*z = -3*n + 55, n - 5*z + k = 0. Let -213*y**5 - y**2 - n*y**4 + 66*y**5 - 7*y**2 + 44*y**3 = 0. What is y?
-2/3, 0, 2/7
Let z = 29 - 47. Let g = 92/5 + z. Factor g + 4/5*s + 2/5*s**2.
2*(s + 1)**2/5
Let c(h) be the third derivative of -h**6/900 + 2*h**5/225 - h**4/36 + 2*h**3/45 - 15*h**2. Factor c(x).
-2*(x - 2)*(x - 1)**2/15
Let h be (8/(-12))/(2/(-1)). Determine t, given that h + 1/3*t**2 + 2/3*t = 0.
-1
Solve -6/17*j - 4/17 - 14/17*j**3 + 24/17*j**2 = 0.
-2/7, 1
Let z be (-4 - -27) + -2*1. Let f = 23 - z. Factor 8/9 + 2/9*s**f + 8/9*s.
2*(s + 2)**2/9
Let r(i) = 10*i**2 - 16*i + 6. Suppose -4*b = 2 + 26. Let l(k) = 3*k**2 - 5*k + 2. Let m(x) = b*l(x) + 2*r(x). Solve m(n) = 0 for n.
1, 2
Factor 2/3*k**5 + 10/3*k**3 - 22/9*k**4 + 4/9*k - 2*k**2 + 0.
2*k*(k - 1)**3*(3*k - 2)/9
Let k = 8 + -4. Suppose u = 2*x + 8, -3*u + k*x = -5 - 13. Factor -3*p**2 + 3*p - 2*p + 2*p**u - 3*p.
-p*(p + 2)
Let o be ((-5)/(-1) - 3)*1. Let n(h) = h**3 + 4*h**2 - 5*h + 3. Let w be n(-5). Factor 9*x + w + 2 + 5*x**o + x**3 - 1 - x.
(x + 1)*(x + 2)**2
Let m(w) be the third derivative of -7*w**6/40 - w**5/10 + 7*w**4/8 + w**3 + 21*w**2. What is x in m(x) = 0?
-1, -2/7, 1
Let h(a) be the third derivative of a**5/15 - 9*a**2. Solve h(z) = 0 for z.
0
Suppose -484 = 15*v - 11*v. Let f = 367/3 + v. Factor -f*a + 0 - 2*a**3 + 10/3*a**2.
-2*a*(a - 1)*(3*a - 2)/3
Let s(f) be the third derivative of f**8/20160 + f**7/3360 - f**6/720 + f**5/60 - f**2. Let m(d) be the third derivative of s(d). Factor m(u).
(u + 2)*(2*u - 1)/2
Let d = -9 + 19. Find r such that d*r**4 + 12*r**4 + 0*r**4 - 27*r**5 - 3*r**3 - 4*r**4 = 0.
0, 1/3
Let d(y) = y**3 + y**2 + y. Let a(z) = 10*z**3 + 6*z**2 + 8*z. Let v(b) = -a(b) + 12*d(b). Factor v(k).
2*k*(k + 1)*(k + 2)
Let b = -893 - -3573/4. Solve -t**4 - b*t + 0 - 3/2*t**3 - t**2 - 1/4*t**5 = 0.
-1, 0
Let m = 1/14 - -3/7. Suppose -m*q**5 + 2 + 1/2*q**3 + 0*q - 7/2*q**2 + 3/2*q**4 = 0. What is q?
-1, 1, 2
Let o(g) be the third derivative of g**8/560 + g**7/56 + g**6/15 + g**5/10 + 7*g**3/6 + 6*g**2. Let r(j) be the first derivative of o(j). Factor r(m).
3*m*(m + 1)*(m + 2)**2
Let o(n) = -4*n + 3. Let a be o(-4). Suppose -3 + 0 = -2*v + 3*y, -5*v - 4*y = -a. Factor -1/3*i**v - 1/3 + 1/3*i**2 + 1/3*i.
-(i - 1)**2*(i + 1)/3
Let l(v) be the third derivative of 0*v**3 + 1/6*v**4 + 0*v - 3*v**2 + 0 - 1/30*v**5. Factor l(i).
-2*i*(i - 2)
Let k(t) = 2*t**3 + t - 1. Let x be k(1). Let m = x + -2. Factor 0*c**2 + 2/3*c**5 + 4/3*c**4 + m + 2/3*c**3 + 0*c.
2*c**3*(c + 1)**2/3
Let -v**2 - 32*v + 18*v + 12*v = 0. Calculate v.
-2, 0
Factor x**2 + 1/4*x**3 + 0 + x.
x*(x + 2)**2/4
Let n(j) be the second derivative of 1/135*j**6 + 1/27*j**3 + 0*j**2 - 1/90*j**5 + 0 - 1/54*j**4 - 4*j. Determine w so that n(w) = 0.
-1, 0, 1
Let f(i) be the second derivative of i**4/18 - i**3/9 - 2*i**2/3 - i. Factor f(p).
2*(p - 2)*(p + 1)/3
Let v(f) = f**2 + 3*f. Let a be v(-3). Let x(r) be the first derivative of -2/27*r**3 - 2/9*r**4 + a*r + 0*r**2 - 2/15*r**5 - 3. Find p, given that x(p) = 0.
-1, -1/3, 0
Suppose q = 2*m - 3*m - 6, -3*q + 4*m + 3 = 0. Let j be 18/8 + q/12. Suppose 2/7*s - 2/7*s**j + 2/7 - 2/7*s**3 = 0. What is s?
-1, 1
Factor -10*o + 0*o**3 - 386 + 570 + 16*o**2 - 2*o**3 - 284.
-2*(o - 5)**2*(o + 2)
Let r(c) be the first derivative of -c**5/20 + 5*c**4/16 - 2*c**3/3 + c**2/2 + 6. Determine g, given that r(g) = 0.
0, 1, 2
Let i(r) be the second derivative of -r**5/4 + 5*r**4/4 - 5*r**3/2 + 5*r**2/2 - 5*r. Factor i(t).
-5*(t - 1)**3
Factor 0*w - 2/7*w**2 + 2/7.
-2*(w - 1)*(w + 1)/7
Let l(g) be the first derivative of -3*g**5/10 + 3*g**4/4 + g**3/2 - 3*g**2/2 - 49. Factor l(x).
-3*x*(x - 2)*(x - 1)*(x + 1)/2
Suppose -5*s = 6*d - 4*d + 6, -4 = d + 3*s. Let a(v) be the first derivative of 4 + 0*v**d + 0*v - 2/9*v**3. Determine h, given that a(h) = 0.
0
Let p(o) be the third derivative of o**8/1680 - o**7/525 + o**6/600 - 11*o**2. Factor p(q).
q**3*(q - 1)**2/5
Let x(j) be the third derivative of -j**6/360 - j**5/60 + 2*j**3/9 - 7*j**2. Factor x(n).
-(n - 1)*(n + 2)**2/3
Let m = -4 + 7. Let z = -28 - -31. Let -3*n**m + 0*n**2 + z*n**2 + 6*n**3 = 0. Calculate n.
-1, 0
Factor -3*o**3 + 2*o**3 - 8*o + 8*o.
-o**3
Let x(m) be the first derivative of -m**4/24 + 2*m**3/9 - m**2/3 + 3. Factor x(h).
-h*(h - 2)**2/6
Suppose 4*p + 0*w + 2*w + 102 = 0, 0 = 3*w + 9. Let t be (p/10 - -2)*-1. Find m, given that -t*m**2 - 4/5*m - 2/5 = 0.
-1
Let l(q) = -q**3 + q**2 - q. Let t(j) = -15*j**4 - 18*j**3 - 2*j**2 - 2*j. Let z(h) = -2*l(h) + t(h). Factor z(i).
-i**2*(3*i + 2)*(5*i + 2)
Let h(r) be the first derivative of r**4/28 + r**3/21 - 5. Factor h(g).
g**2*(g + 1)/7
Determine n, given that 0 - 2/17*n**4 - 6/17*n**2 + 8/17*n**3 + 0*n = 0.
0, 1, 3
Let i(k) = -9*k**2 + 20*k + 5. Let h(l) = 6*l**2 - 13*l - 3. Let a(j) = 8*h(j) + 5*i(j). Determine y, given that a(y) = 0.
1/3, 1
Factor 67*v**2 + 2*v**3 - 2*v - 136*v**2 + 70*v**2 - v**4.
-v*(v - 2)*(v - 1)*(v + 1)
Factor 0*h**5 - h**2 + 5*h**2 - h**4 - 2*h**4 - h**5.
-h**2*(h - 1)*(h + 2)**2
Suppose 0 = 3*q - 3*r - 14 - 22, q = 5*r - 8. Let f = q + -14. Solve -8/7*u**f + 8/7*u - 2/7*u**2 + 2/7 = 0.
-1, -1/4, 1
Find o such that 3*o**3 + o**3 + 12*o**2 - 8*o + 5*o**5 - o**5 - 12*o**4 = 0.
-1, 0, 1, 2
Let s be (-4)/(-16) - 7/60. Let i(q) be the first derivative of -1 + 0*q**2 + 1/5*q**4 + 0*q - 2/25*q**5 - s*q**3. Let i(k) = 0. Calculate k.
0, 1
Let f = -38 + 38. Let m(q) be the first derivative of 0*q**4 + f*q**2 + 1/21*q**6 + 0*q**3 + 0*q + 2 + 2/35*q**5. Find c such that m(c) = 0.
-1, 0
Factor 0*i + 2/11 - 2/11*i**2.
-2*(i - 1)*(i + 1)/11
Let f(y) be the first derivative of 3*y**4/4 + 3*y**3 - 12*y + 3. Factor f(v).
3*(v - 1)*(v + 2)**2
Factor l**4 - l**4 - 8*l**4 - 8*l**2 - 20*l**3.
-4*l**2*(l + 2)*(2*l + 1)
Let s(a) be the first derivative of a**4/6 - 2*a**3/3 + a**2 + a + 3. Let b(o) be the first derivative of s(o). Factor b(l).
2*(l - 1)**2
Let f(o) be the second derivative of 0*o**3 + 0*o**2 - 1/10*o**5 + 1/6*o**4 - 6*o + 0. Factor f(i).
-2*i**2*(i - 1)
Let r be (6/(-4))/(6/(-16)). Determine g so that 5*g**r - 2*g**4 + 5*g**3 - 4*g**2 + g**3 + 7*g**4 = 0.
-1, 0, 2/5
Let d(s) be the second derivative of 0 + 9*s - 1/4*s**4 - 1/2*s**2 + 1/2*s**3 + 1/20*s**5. Solve d(f) = 0 for f.
1
Let h = 51 - 46. Let o(i) be the second derivative of 2*i - 1/7*i**3 + 24/35*i**h + 0 - 4/15*i**6 - 19/42*i**4 + 2/7*i**2. Find j such that o(j) = 0.
-2/7, 1/2, 1
Let j(a) be the second derivative of 3/5*a**5 + 3/5*a**6 + 0 - 3*a + 5/18*a**4 + 0*a**2 + 3/14*a**7 + 1/18*a**3. Solve j(v) = 0 for v.
-1, -1/3, 0
Factor -4 + 4 + 5*m**3 - 5*m**2 - 15*m**2 + 15*m.
5*m*(m - 3)*(m - 1)
Let z be (5 + -4)/1 - -4. Let r(c) be the first derivative of -16/15*c**z - 1/3*c + 2 - c**2 - 1/9*c**3 + 2*c**4. Determine u so that r(u) = 0.
-1/4, 1
Let w be (9 + 0)*84/189. Solve -4/5*x**3 - 2/5*x**w + 0 + 0*x - 2/5*x**2 = 0 for x.
-1, 0
Let n be 2/(-4) - (-15)/2. Suppose z = 5*l + 17, 2*z - 2*l - n = 3. Find r such that 3*r**3 - 5*r**2 + 5*r - r + 3*r**3 + 15*r**z = 0.
-1, -2/3, 0
Let d(i) = -8*i**3 + 5*i**2 + 8*i - 5. Let t(z) = -z**3 - 1. Let a(k) = 4*d(k) - 36*t(k). Factor a(l).
4*(l + 1)*(l + 2)**2
Let u(y) = -3*y**3 + 3*y + 4. Let i(g) = 4*g**3 - 4*g - 5. Let s = -3 - 1. Let