Let k(d) be the first derivative of -5*d**6/6 - d**5 + 5*d**4/4 + 5*d**3/3 + 24. Factor k(r).
-5*r**2*(r - 1)*(r + 1)**2
Let k(c) = -c**2 - 5*c - 2. Let i be k(-4). Let f be (1 - 0)*(i + 1). Determine x, given that x**2 + 2*x**2 - 3 + 4*x**f - x**3 - 6*x**3 + 3*x = 0.
-1, 1
Let f be (-12)/(-9)*3/(-2). Let w be (6/(-12))/(3/f). Suppose -w*g + 1/3*g**3 - 1/3*g**2 + 0 + 1/3*g**4 = 0. Calculate g.
-1, 0, 1
Let s(x) be the second derivative of 0*x**3 + 1/105*x**6 + 0*x**2 + 0 + 0*x**5 - 1/42*x**4 - x. Determine m so that s(m) = 0.
-1, 0, 1
Let n be -90*(14/3 - 4). Let s be (-10)/(-4)*(-48)/n. Factor 1/5*r**s - 1/5 + 0*r.
(r - 1)*(r + 1)/5
Find l such that -2*l - 2/7*l**3 - 10/7*l**2 - 6/7 = 0.
-3, -1
Let a(d) be the first derivative of 0*d**2 + 2/3*d**3 + 0*d - 1/3*d**6 + 6/5*d**5 - 8 - 3/2*d**4. Find l such that a(l) = 0.
0, 1
Let s(m) = m + 9. Let i be s(-5). Let a(b) = -b**3 + 5*b**2 - 4*b - 1. Let c be a(3). Factor 0*o**i + 2*o**c - o**5 - 2*o**4 - o + 2*o**2.
o*(o - 1)**3*(o + 1)
Let f(t) be the second derivative of 8/63*t**7 - 4/15*t**6 + 1/18*t**3 + 0 + 1/60*t**5 + 5*t + 0*t**2 + 1/6*t**4. What is g in f(g) = 0?
-1/4, 0, 1
Let u(z) = -z**3 + 4. Let w be u(0). Let s(r) be the third derivative of 0*r + 0*r**w + 0 - r**2 - 1/630*r**7 - 1/360*r**6 + 0*r**3 + 0*r**5. Solve s(n) = 0.
-1, 0
Let x = -1 + 4. Factor 2*n**3 + 3*n**2 + n**4 - 6*n**x + 4*n - 5 + 0 + 1.
(n - 2)**2*(n - 1)*(n + 1)
Let a(v) be the second derivative of -v**9/4536 - v**8/1260 - v**7/1260 + v**3/6 + 4*v. Let r(x) be the second derivative of a(x). Suppose r(k) = 0. What is k?
-1, 0
Let j be 3/6*2 - 1. Suppose -3*u - 3 = -2*o + 18, -3*u - 15 = j. Suppose -2*r**2 + r + 2*r**3 + 0*r**2 - r**o = 0. Calculate r.
0, 1
Let u(s) be the second derivative of -s**4/24 - s**3/6 - s**2/4 - 66*s. Factor u(j).
-(j + 1)**2/2
Let w(j) = -8*j**2 + 24*j + 32. Let n(p) = 12*p**2 - 36*p - 48. Let g(t) = 5*n(t) + 8*w(t). Factor g(f).
-4*(f - 4)*(f + 1)
Let u = 46/33 + -116/99. Factor 0*s**2 - u*s**3 + 0*s + 0 - 2/9*s**4.
-2*s**3*(s + 1)/9
Let w(a) = -2*a**2 + 112*a + 2. Let x be w(56). Find i such that 12/7*i**x - 12/7*i + 4/7 - 4/7*i**3 = 0.
1
Let l(o) be the second derivative of -o**5/30 - 2*o**4/9 - 4*o**3/9 - 8*o. Factor l(x).
-2*x*(x + 2)**2/3
Suppose 2*m - 8 = -2*u, 4*m + m - 20 = 2*u. Let y(r) be the first derivative of -2/5*r**5 - 3 + 0*r**2 + 0*r**3 + u*r**4 + 0*r. Find h such that y(h) = 0.
0
Let i = 21 + -17. Find c such that -162/13*c**i + 0 - 8/13*c + 64/13*c**2 - 90/13*c**3 = 0.
-1, 0, 2/9
What is u in -2/3*u**3 - 2*u**2 + 0 - 4/3*u = 0?
-2, -1, 0
Suppose 2/7*p + 12/7*p**4 + 16/7*p**3 + 0 - 18/7*p**5 - 12/7*p**2 = 0. Calculate p.
-1, 0, 1/3, 1
Let x(q) = -3*q**3 + 6*q**2 + 4*q + 7. Let a(g) = -2*g**3 + 4*g**2 + 3*g + 5. Let v(l) = 7*a(l) - 5*x(l). Factor v(o).
o*(o - 1)**2
Let g(f) = -f + 3. Let j be g(0). Let o(c) = 7*c**2 - 7*c + 2. Let x(h) = -h**2 + h. Let v(s) = j*o(s) + 24*x(s). Find q, given that v(q) = 0.
-1, 2
Let m be ((-312)/(-45))/8 + (-4)/20. Solve 0*n**3 + 0*n + 2/3*n**4 - m*n**2 + 0 = 0.
-1, 0, 1
Let a(f) = f**4 - f. Let s(u) = -2*u**3 - 6*u**2 + 4*u + 4. Let p = -3 - -2. Let l(w) = p*s(w) - 2*a(w). Determine m so that l(m) = 0.
-1, 1, 2
Let a(i) be the second derivative of i**5/20 - i**4/6 + i**3/6 - 7*i. Factor a(h).
h*(h - 1)**2
Let r(f) be the first derivative of -f**4/30 + f**2/5 + 4*f/15 + 11. Factor r(p).
-2*(p - 2)*(p + 1)**2/15
Suppose -4*v - 5 = 7. Let r = v + 5. Factor 11*f + 5*f - 2 - 20*f**2 - 12*f**r.
-2*(4*f - 1)**2
Let a = -435 - -13051/30. Let u(k) be the third derivative of 2/3*k**3 + 0*k - a*k**5 + k**2 + 1/12*k**4 + 0. Suppose u(q) = 0. Calculate q.
-1, 2
Let p = -18 - -20. Solve -7*a - p*a**2 - 3*a**2 + 4*a**2 + 3*a - 4 = 0 for a.
-2
Let h(c) be the second derivative of 0*c**3 - 1/20*c**6 + 0*c**2 + 1/24*c**4 - 3*c + 1/42*c**7 + 0 + 0*c**5. Factor h(o).
o**2*(o - 1)**2*(2*o + 1)/2
Let l(d) be the first derivative of -d**3/3 - d**2 + 2. Determine b so that l(b) = 0.
-2, 0
Let r = 89 + -59. Let b be 12/30 + 8/r. Factor 0*p + b*p**4 - 2/9*p**5 - 2/3*p**3 + 2/9*p**2 + 0.
-2*p**2*(p - 1)**3/9
Factor 15*h**3 - 113*h**3 + 69*h + 8 - 21*h + 42*h**2.
-2*(h - 1)*(7*h + 2)**2
Let g(c) be the second derivative of c**8/840 - c**6/300 - 3*c**2/2 + 5*c. Let a(q) be the first derivative of g(q). Suppose a(h) = 0. What is h?
-1, 0, 1
Suppose -3*r - 3*w + 5 = -7*w, 5*r = -3*w + 18. Suppose 8 = r*f + f. Factor -2*u**2 + 7 - f*u - 7.
-2*u*(u + 1)
Let p be 6/10 + (-12)/20. Let d be (0 - 3/(-2)) + (-2)/(-4). Solve -1/2*f**d + f + p = 0.
0, 2
Let o be 1/(3/9) - (-74)/(-26). Suppose 10/13*x + 2/13*x**5 + o + 20/13*x**3 + 10/13*x**4 + 20/13*x**2 = 0. Calculate x.
-1
Let c = -14 + 18. Factor -8 - 28*s - 2*s**2 + 19*s**3 + 9*s**3 + 20*s**c - 10*s**2.
4*(s - 1)*(s + 1)**2*(5*s + 2)
Let c(j) = -4*j**3 - j**2 - 2*j - 1. Let g be c(-1). Find z, given that 4*z**5 - 12*z**4 + 10*z**5 + g*z**3 - 10*z**5 + 4*z**4 = 0.
0, 1
Let o(j) = -3*j**3 - j**2 + j + 1. Let d be o(-1). Let p(h) be the third derivative of 1/3*h**4 + 0 + 2*h**d + 7/30*h**5 + 0*h + 4/21*h**3. Factor p(y).
2*(7*y + 2)**2/7
Let j = 46 + -41. Suppose 22 = j*g - 4*t, 5*g + 3*t + 2 - 3 = 0. Factor -9/4*x**g - 1/4 + 3/2*x.
-(3*x - 1)**2/4
Let r = -17/3 - -6. Let l(s) be the first derivative of r*s**3 + 0*s**2 + 1/12*s**4 - 4/3*s + 1. Find z, given that l(z) = 0.
-2, 1
Let b(j) be the second derivative of 1/18*j**3 - 2*j + 0 - 1/36*j**4 + 1/180*j**5 - 2*j**2. Let n(z) be the first derivative of b(z). Factor n(i).
(i - 1)**2/3
Suppose d - 15 = -2*d. Suppose 3*g - 4 = d. Let -m**g + 2*m**3 + 0*m**4 - 3*m**4 = 0. What is m?
0, 1/3
Let p(f) = f**4 + 2*f**3 - 2. Let o(h) = 6*h**4 + 10*h**3 - 11. Let u = -3 - -1. Let n(s) = u*o(s) + 11*p(s). Factor n(i).
-i**3*(i - 2)
Let q(r) be the second derivative of -r**6/55 - 13*r**5/110 - r**4/33 + 8*r**3/33 - 7*r. Determine d so that q(d) = 0.
-4, -1, 0, 2/3
Let o = 87 + -84. Factor -q**4 + q**2 + 0 + 0*q**o - 1/2*q**5 + 1/2*q.
-q*(q - 1)*(q + 1)**3/2
Solve -1 + 2*b - 5 - 2*b**2 + 6*b = 0 for b.
1, 3
Suppose 6*k + 0*k = 18. Let m(p) be the first derivative of 0*p**5 - 2 + 0*p**k - 1/6*p**4 + 0*p + 1/18*p**6 + 1/6*p**2. Factor m(n).
n*(n - 1)**2*(n + 1)**2/3
Factor 0 + 2/3*o - 2/3*o**4 + 2/3*o**2 - 2/3*o**3.
-2*o*(o - 1)*(o + 1)**2/3
Let n(l) be the second derivative of -l**6/210 + 4*l. Factor n(j).
-j**4/7
Let f = -8/29 + 359/145. Factor f*z - 9/5*z**2 - 2/5.
-(z - 1)*(9*z - 2)/5
Let i(h) be the first derivative of -1 - 2*h + 1/48*h**4 - 1/8*h**2 + 0*h**3. Let d(n) be the first derivative of i(n). Factor d(c).
(c - 1)*(c + 1)/4
Let h(p) be the second derivative of p**4/32 - 5*p**3/8 + 75*p**2/16 + 38*p. Factor h(i).
3*(i - 5)**2/8
Let r(j) be the second derivative of j**7/147 - j**5/35 + j**3/21 - 3*j. Factor r(a).
2*a*(a - 1)**2*(a + 1)**2/7
Let f = 6 - 3. Solve 2*t**5 - 3 - t + 3 - 4*t**f + 3*t = 0 for t.
-1, 0, 1
Solve 18/11*y - 1/11*y**4 + 8/11*y**3 - 21/11*y**2 + 0 = 0 for y.
0, 2, 3
Let b be (-6)/(-9) + (-4)/(-3). Factor 2*a**3 - a**b + 2*a**3 - 3*a**3.
a**2*(a - 1)
Let x(k) = -8*k**4 - 4*k**3 + 12*k**2 + 4*k + 4. Let n(q) = -9*q**4 - 4*q**3 + 13*q**2 + 5*q + 5. Let z(t) = 4*n(t) - 5*x(t). Factor z(l).
4*l**2*(l - 1)*(l + 2)
Determine k so that 3/4*k**5 + 0*k + 0 + 0*k**2 + 3/2*k**4 + 3/4*k**3 = 0.
-1, 0
Let c = 29 - 27. Let x(u) be the second derivative of 0*u**c + 0 + 1/6*u**3 + 3*u + 1/12*u**4. Let x(o) = 0. What is o?
-1, 0
Determine k, given that -8/3*k**2 + 0 + 8/3*k**4 - 4/3*k + k**5 + 1/3*k**3 = 0.
-2, -1, -2/3, 0, 1
Let j(o) be the first derivative of -o**6/420 - o**2 + 3. Let l(t) be the second derivative of j(t). Let l(r) = 0. Calculate r.
0
Let v(q) = 85*q**2 + 425*q - 475. Let l(h) = 5*h**2 + 25*h - 28. Let g(c) = -35*l(c) + 2*v(c). Determine w, given that g(w) = 0.
-6, 1
Let h(c) be the first derivative of -c**6/360 - c**5/180 + c**2 + 1. Let b(v) be the second derivative of h(v). Find q such that b(q) = 0.
-1, 0
Suppose -10*f + 34 + 6 = 0. Suppose 8*p - 3*p - 10 = 0. Determine m, given that 2*m**3 - 2*m**2 - p*m + m**3 + 2*m**f - 2*m**3 + m**3 = 0.
-1, 0, 1
Let u(v) be the third derivative of -v**5/390 - 5*v**4/156 + 2*v**3/13 - 32*v**2. Factor u(f).
-2*(f - 1)*(f + 6)/13
Let u(s) = 4*s**2 + 2*s - 2. Let a be u(2). Factor v**2 - v**5 + 9*v**4 - 3*v + v + 3*v**3 -