
-1/7
Let x be 8 + (1/2 - (-3445)/(-424)). Factor -x*z + 1/8*z**2 - 1/2.
(z - 4)*(z + 1)/8
Let n(k) = -21*k**5 - 69*k**4 - 264*k**3 + 1290*k**2 - 1461*k + 525. Let q(j) = -j**5 + j**3 - j + 1. Let l(w) = -n(w) + 18*q(w). Factor l(h).
3*(h - 1)**3*(h + 13)**2
Let 4*k**4 + 5831 + 80*k**3 - 5831 - 80*k - 4*k**2 = 0. Calculate k.
-20, -1, 0, 1
Let s(b) be the third derivative of 1/36*b**4 - 3*b**2 + 0*b**3 + 0 + 0*b + 1/36*b**5. Factor s(t).
t*(5*t + 2)/3
Let y(h) be the second derivative of -h**5/10 + 4*h**4 - 44*h**3/3 - 36*h - 4. Factor y(i).
-2*i*(i - 22)*(i - 2)
Suppose -3*y + 18 = -3*p, -5*y - 24 = -4*y + 4*p. Factor y + 12/7*h**2 - 8/7*h - 4/7*h**4 + 0*h**3.
-4*h*(h - 1)**2*(h + 2)/7
Let f be 6/(-28)*(-56)/16. Let s be 7/4 + 87/(-87). Factor 0 - 3/2*z**3 + 3/2*z + s*z**2 - f*z**4.
-3*z*(z - 1)*(z + 1)*(z + 2)/4
Let r(j) be the second derivative of j**4/42 + 139*j**3/21 - 20*j**2 + 753*j. Factor r(f).
2*(f - 1)*(f + 140)/7
Let j(n) be the first derivative of -n**5/30 + 2*n**4 - 48*n**3 + 3*n**2 - 35. Let v(d) be the second derivative of j(d). Factor v(w).
-2*(w - 12)**2
Let a(s) = 7*s**3 - 8*s**2 + 7*s. Let m(g) = 120*g**3 - 135*g**2 + 120*g. Suppose 5*h - 8 = h. Let i(y) = h*m(y) - 35*a(y). Factor i(v).
-5*v*(v - 1)**2
Let b(u) be the first derivative of 31 + 0*u + 1/2*u**2 + 1/4*u**4 - 2/3*u**3. Find o, given that b(o) = 0.
0, 1
Let h(u) = u**2 - 10*u. Let f be h(10). Factor f*r - 18*r**2 + 6*r - 2*r**2 + 2*r.
-4*r*(5*r - 2)
Let z(n) be the second derivative of -n**4/4 - 5*n**3 - 24*n**2 + 147*n. Factor z(s).
-3*(s + 2)*(s + 8)
Determine z so that -40/9*z - 4/3 + 7/9*z**2 = 0.
-2/7, 6
Solve 10 - 16 - 2 + 2*a**2 - 6*a = 0 for a.
-1, 4
Let q(v) be the second derivative of -v**7/21 + 2*v**6/15 + v**5/10 - v**4/3 - 71*v. Find j, given that q(j) = 0.
-1, 0, 1, 2
Let r(u) = -23*u**2 + 48*u + 13. Let s(l) be the second derivative of -27*l**4/4 + 28*l**3 + 45*l**2/2 - 7*l. Let v(w) = -18*r(w) + 5*s(w). Factor v(p).
3*(p - 3)*(3*p + 1)
Let z(m) be the first derivative of 0*m**2 + 0*m**4 + 0*m - 1/2*m**6 + 14 + 9/5*m**5 - 4*m**3. Let z(v) = 0. What is v?
-1, 0, 2
Let q(x) be the first derivative of x**3 + 12*x**2 + 36*x + 109. Factor q(y).
3*(y + 2)*(y + 6)
Let h(r) = 2*r**2 + r + 3. Let u(g) = 11*g**2 + 5*g + 17. Let w = 12 - 8. Let z be w*(-9)/30*5. Let v(y) = z*u(y) + 34*h(y). Factor v(t).
2*t*(t + 2)
Let i(d) be the first derivative of -4*d**3/9 + 124*d**2/3 - 3844*d/3 - 10. Determine y, given that i(y) = 0.
31
Suppose 0*v**2 + 0 - 2/3*v**4 + 0*v - 4/3*v**3 = 0. Calculate v.
-2, 0
Find z, given that -7*z**2 + 0 + 1/2*z**3 + 0*z = 0.
0, 14
Let o(n) = n**2 - 7*n + 3. Let b be o(7). Suppose -12 = -9*v + 6*v. Find y, given that 2*y**5 - 2*y**2 + 0*y**3 - 4*y**3 + 2*y**v - 3*y**b + 5*y**3 = 0.
-1, 0, 1
Suppose 4 + 14 = 9*g. Determine c, given that -93*c**2 - 13*c**3 - 9*c**5 + 16*c**4 - 11*c**3 + 21*c**g + 23*c**4 + 48 + 48*c = 0.
-1, -2/3, 2
Let b(r) be the third derivative of 0*r + 1/24*r**6 + 0 - 5/24*r**4 - 11*r**2 + 0*r**5 + 0*r**3. Solve b(z) = 0.
-1, 0, 1
Let o be -31 - -41 - (30/3 + -3). Factor -3/4*c + 0 - 3/4*c**o - 3/2*c**2.
-3*c*(c + 1)**2/4
Suppose -2*h + 3*h + 2*q - 2 = 0, -5*h + 4*q = -10. Let t = h + 2. Find n such that 2*n**t + 21*n**4 + 13*n**2 - 7*n**5 - 2*n - 6*n**3 - 21*n**3 = 0.
0, 2/7, 1
Let y be (0 + 1)*(-16 - 2). Let o(q) = -q**3 - 20*q**2 - 36*q. Let s be o(y). Factor s - 2/5*k - 1/5*k**3 - 3/5*k**2.
-k*(k + 1)*(k + 2)/5
Solve 560/11*r + 6/11*r**2 + 186/11 = 0 for r.
-93, -1/3
Suppose 4 + 7 = 4*s - 5*z, 5*s + 2*z = 22. Let f(i) be the first derivative of s*i**4 - 2*i**3 - 4*i + 4 - 7 - 2*i**4 - 9*i**2 - 2. Factor f(t).
2*(t - 2)*(t + 1)*(4*t + 1)
Let w(r) be the third derivative of -1/245*r**7 + 0 + 0*r - 1/1176*r**8 + 22*r**2 + 1/70*r**5 - 1/420*r**6 + 0*r**3 + 1/42*r**4. Determine u so that w(u) = 0.
-2, -1, 0, 1
Let r = -2326/371 + 90/53. Let q = 16/21 - r. Suppose q*l**5 + 20/3*l**4 + 4*l + 0 + 28/3*l**2 - 76/3*l**3 = 0. Calculate l.
-3, -1/4, 0, 1
Let w(j) be the third derivative of j**8/448 + 47*j**7/1680 + 21*j**6/160 + 17*j**5/60 + 5*j**4/16 + 3*j**3/16 + 88*j**2. Let w(s) = 0. Calculate s.
-3, -1, -1/2, -1/3
Let h = 79 + -73. Factor -32*q**3 - 1 + 28*q**3 - h*q**4 - 7 + 2*q**4 + 12*q**2 + 4*q.
-4*(q - 1)**2*(q + 1)*(q + 2)
Find b, given that -2 + 4*b**3 - 50/3*b**2 + 44/3*b = 0.
1/6, 1, 3
Let g(i) = -2*i**2 - 36*i - 36. Let f be g(-17). Let z be f + (-57)/(-12) + 48/(-64). Factor -2/3*x - 2/9*x**z - 4/9.
-2*(x + 1)*(x + 2)/9
Let t(s) = -s**3 + 38*s**2 + 6*s - 3. Let m(f) = 4*f**3 - f**2 + 1. Let a(w) = -3*m(w) - t(w). Find x such that a(x) = 0.
-3, -2/11, 0
Let i(o) = 38*o**2 - 174*o + 172. Let k(r) = -104*r**2 + 522*r - 517. Let s(n) = -11*i(n) - 4*k(n). Solve s(q) = 0 for q.
-88, 1
Let k = 5543 + -38798/7. Factor 0*z + k*z**2 + 0.
3*z**2/7
Let k = 4 - 0. Suppose -8*b = -k*b - 20. Factor 13*v**2 - 6*v - b*v**3 + 5*v**2 + 5 - 3*v**2 - 9*v.
-5*(v - 1)**3
Let j(o) be the second derivative of o**5/120 - o**4/48 - o**3/6 + 3*o**2 + 11*o. Let f(y) be the first derivative of j(y). Factor f(k).
(k - 2)*(k + 1)/2
Let z be 151/((-321328)/64)*(0 - 42/4). Factor 0 - 2/19*b**3 + 8/19*b + z*b**2.
-2*b*(b - 4)*(b + 1)/19
Let h = 7 - -27. Factor -h*c**3 - 15 - 33 + 21*c**2 - 24*c + 31*c**3.
-3*(c - 4)**2*(c + 1)
Let m(t) = 5*t**4 - 6*t**3 + t**2 + 2*t. Let c(v) = -14*v**2 - 5*v - 9*v**4 - 4*v**3 + 13*v**2 - 2*v**4 + 16*v**3. Let x(l) = 2*c(l) + 5*m(l). Factor x(o).
3*o**2*(o - 1)**2
Let c be -1*(-10)/(-75)*((-45)/6 - -6). Factor 4/5*f + c*f**2 + 3/5.
(f + 1)*(f + 3)/5
Determine z so that 2*z**2 + z**3 + 43*z**4 - 3*z**3 + z**3 - 44*z**4 = 0.
-2, 0, 1
Let y(n) = 6*n**3 + 13*n**2 + 11*n + 4. Let s(d) = -5*d**3 - 11*d**2 - 10*d - 4. Let g(x) = 7*s(x) + 6*y(x). Suppose g(m) = 0. What is m?
-2, -1, 2
What is t in 0*t + 2/11*t**4 + 0*t**2 + 2/11*t**3 + 0 = 0?
-1, 0
Let s(j) be the third derivative of j**5/240 + 4*j**4/3 + 512*j**3/3 - 464*j**2. Factor s(k).
(k + 64)**2/4
Factor 10201/3 + 202/3*q + 1/3*q**2.
(q + 101)**2/3
Let c(f) be the second derivative of 0*f**2 + 1/3*f**6 + 0 - 4/5*f**5 + 30*f - 2/3*f**4 + 0*f**3. Find b, given that c(b) = 0.
-2/5, 0, 2
Let h(v) be the third derivative of -1/8*v**4 + 0 - 1/160*v**6 + 1/20*v**5 + 0*v**3 - 4*v**2 + 0*v. Find c such that h(c) = 0.
0, 2
Let q(z) = -50*z - 798. Let y be q(-16). Factor 400/3*a**3 - 120*a**y - 10/3 + 35*a.
5*(4*a - 1)**2*(5*a - 2)/3
Let y(a) be the second derivative of -1/5*a**2 + 0 + 16*a + 4/3*a**3 - 10/3*a**4. Determine c, given that y(c) = 0.
1/10
Solve -6*l**3 + 3*l**3 - 22*l**2 + 13*l**2 - 3 - 9*l = 0.
-1
Let c(j) = -j**2 + j - 1. Let o(i) = -4*i**2 + 30*i - 31. Let q(s) = 5*c(s) - o(s). Factor q(n).
-(n - 1)*(n + 26)
Let u(y) be the first derivative of -4*y**3/3 + 3258*y**2/7 + 1864*y/7 + 50. Factor u(f).
-4*(f - 233)*(7*f + 2)/7
Factor f**2 - 3025 + 1528 + 4460 + 236*f + 3794 + 7167.
(f + 118)**2
Let z(q) be the second derivative of -q**4/8 - 13*q**3/4 - 27*q**2 - 215*q. Factor z(v).
-3*(v + 4)*(v + 9)/2
Let p(v) = 20*v**4 - 55*v**3 - 145*v**2 - 45*v - 25. Let w(z) = z**4 + z**3 + z - 1. Let q(n) = p(n) - 25*w(n). Suppose q(s) = 0. Calculate s.
-14, -1, 0
Let c(n) be the first derivative of -n**6/48 - 3*n**5/40 + n**3/6 - 246. Let c(z) = 0. What is z?
-2, 0, 1
Let b(x) = 40 - 72*x**2 + 1 + 4 + 35*x - 8*x**2. Let t(c) = c - 9*c**2 - 1 + 6 + 4*c - c. Let k(y) = 4*b(y) - 35*t(y). Solve k(q) = 0 for q.
-1, 1
Suppose -2*s + 56 = 12*s. Factor o**s - 124*o + 124*o - o**2.
o**2*(o - 1)*(o + 1)
Find u such that 12/5*u - 62/5*u**2 + 2*u**3 + 0 = 0.
0, 1/5, 6
Let i be (-105)/462*(-96)/40. Factor -2/11*w**2 - i*w + 0.
-2*w*(w + 3)/11
Let a be -2*3/10 - 4459/(-65). Let t = a + -338/5. Suppose -2/5*d**2 - t*d + 0 + 2/5*d**3 + 2/5*d**4 = 0. Calculate d.
-1, 0, 1
Let d(z) be the third derivative of -2/25*z**7 + 8/15*z**3 - 16*z**2 + 0 - 2/3*z**4 + 0*z + 17/75*z**5 + 2/15*z**6. Let d(v) = 0. What is v?
-1, 2/7, 2/3, 1
What is o in 34/23*o + 32/23 + 2/23*o**2 = 0?
-16, -1
Let p be 1312/(-1344) - (-1 + 0). Let m(f) be the third derivative of -2*f**2 + 1/21*f**3 + 1/210*f**5 + 0 + 0*f - p*f**4. Factor m(b).
2*(b - 1)**2/7
Let s(t) = t**3 + 5*t**2 - t - 2. Let y be s(-5). Suppose y*k = 4*k - 2. What is z in -4 + 9*z**2 - 7*z**k + 2*z + 0*z = 0?
-2, 1
Let r(n) be the first derivati