 + 2/3*n + 1/3*n**q.
n*(n + 2)/3
Suppose 9*w = -w. Let y(o) be the second derivative of -1/60*o**4 + 8*o + 1/15*o**3 - 1/50*o**5 + 1/150*o**6 + 0*o**2 + w. Factor y(c).
c*(c - 2)*(c - 1)*(c + 1)/5
Let u(l) be the second derivative of 0*l**2 - 40/3*l**3 - 15*l + 10/3*l**4 + 0 + 15/4*l**5 - 4/3*l**6 + 5/42*l**7. What is j in u(j) = 0?
-1, 0, 1, 4
Suppose 2*v = 3 + 1. Factor -p**2 - p + 2*p**2 + 0*p**2 - 2*p**v + 1 + p**3.
(p - 1)**2*(p + 1)
Let q(x) be the second derivative of 0*x**2 - 5/3*x**3 - 16*x - 1/4*x**5 + 5/4*x**4 + 0. What is s in q(s) = 0?
0, 1, 2
Let 3708*c - 1859*c + 27*c**3 + 60 - 1876*c - 60*c**2 = 0. Calculate c.
-1, 1, 20/9
Let h be (3*-1 + -21 + 15)/(-7). What is s in -3/7*s**3 + h - 9/7*s**2 + 3/7*s = 0?
-3, -1, 1
Let i(z) be the second derivative of -2*z**5/55 + 2*z**4/11 - 3*z**3/11 + 2*z**2/11 - 82*z. Determine y so that i(y) = 0.
1/2, 2
Let g(v) = -5*v**4 - 68*v**3 + 237*v**2 - 71*v + 7. Let m(h) = 2*h**4 + 34*h**3 - 120*h**2 + 36*h - 4. Let f(l) = -4*g(l) - 7*m(l). What is n in f(n) = 0?
-8, 0, 1/3, 2
Let -1/10*j**3 - 21/5 + 0*j**2 + 43/10*j = 0. Calculate j.
-7, 1, 6
Let n be 25/(-125) + (-2)/(-8). Let i(j) be the second derivative of 0*j**3 - n*j**4 + 3*j + 0 + 3/10*j**2. Factor i(y).
-3*(y - 1)*(y + 1)/5
Suppose 3*o = 7*o. Suppose o*a = 4*a. Factor 2*c**3 + a*c**2 + 42 - 5*c**3 - 9*c - 15 - 15*c**2.
-3*(c - 1)*(c + 3)**2
Let z(y) be the first derivative of -5*y**2 - y**5 + 5/2*y**4 + 5/3*y**3 + 30 + 0*y. Factor z(r).
-5*r*(r - 2)*(r - 1)*(r + 1)
Let i be (-2 - -2) + 6 - (-18)/(-3). Let g(k) be the second derivative of 6*k**2 + i + 1/4*k**4 + k + 2*k**3. Factor g(o).
3*(o + 2)**2
Let k(h) = -h**2 - h. Let f = 23 + -28. Let m(g) = 8*g**2 + 13*g + 9. Let o(y) = f*m(y) - 35*k(y). Factor o(z).
-5*(z + 3)**2
Let a(m) be the first derivative of 0*m**4 + 3*m**3 - 3/5*m**5 - 3*m**2 + 1 + 0*m. Suppose a(r) = 0. Calculate r.
-2, 0, 1
Let a(m) = -43*m**4 + 4*m**3 + 11*m**2 + 3*m. Let l(h) = -214*h**4 + 20*h**3 + 54*h**2 + 14*h. Let b(v) = -14*a(v) + 3*l(v). Suppose b(u) = 0. What is u?
-2/5, 0, 1/2
Let o be (-3 + -5)*28/(-112). Suppose 6 = -u + 3*u. Let -1/3*g**u - 1/3*g**o + 0 + 0*g = 0. Calculate g.
-1, 0
Let l be 1/(-4) - (-136)/32. Let v be ((-96)/40)/(l/(-10)). Factor 2*m**3 - 4*m**3 + v*m**3 - 2*m**4 - 2*m**2.
-2*m**2*(m - 1)**2
Let d(y) be the second derivative of y**7/840 - y**6/48 + y**5/10 - 3*y**4/4 + 11*y. Let s(i) be the third derivative of d(i). Factor s(c).
3*(c - 4)*(c - 1)
Let y(l) = 4*l**3 - 69*l**2 - 145*l - 62. Let p(h) = 3*h**3 - 70*h**2 - 145*h - 64. Let u(n) = -5*p(n) + 4*y(n). Let u(f) = 0. Calculate f.
-72, -1
Suppose 28 + 63 = 43*c + 5. Solve 2/15*a**3 + 16/5*a + 6/5*a**c + 32/15 = 0 for a.
-4, -1
Let d = -938 + 938. Let x(m) be the third derivative of 1/60*m**4 - 1/150*m**5 + 0*m + 0*m**3 - 7*m**2 + d. Let x(l) = 0. What is l?
0, 1
Let i(n) be the third derivative of n**7/1365 + n**6/130 - 7*n**5/390 - 4*n**4/13 - 12*n**3/13 + 2*n**2 + 236. Find h such that i(h) = 0.
-6, -2, -1, 3
Let u = -129 - -129. Let y(r) be the third derivative of -4/51*r**3 + 0*r**4 - 7*r**2 + 1/510*r**5 + u + 0*r. Factor y(w).
2*(w - 2)*(w + 2)/17
Let m(q) be the third derivative of -1/9*q**3 + 0 - 1/72*q**4 + 1/180*q**5 - 11*q**2 + 0*q. Factor m(s).
(s - 2)*(s + 1)/3
Let s be 23576/126 - (-1)/(-9). Suppose 3*g + 1076 - s = 4*i, 5*g = -4*i + 865. Factor 220 - i - z**2.
-z**2
Suppose -269 - 1063 = -18*t. Let y = t + -73. Let 3/2*l + y + 1/2*l**2 = 0. Calculate l.
-2, -1
Let y(u) = -u**4 - u**2 + u - 1. Let l(w) = 35*w**4 - 20*w**3 - 5*w**2 - 10*w + 20. Let x = 52 - 72. Let i(j) = x*y(j) - l(j). Factor i(s).
-5*s*(s - 2)*(s + 1)*(3*s - 1)
Let d(x) be the third derivative of -x**7/70 - x**6/10 - x**5/5 - 29*x**2 - x. Factor d(w).
-3*w**2*(w + 2)**2
Suppose 0 = 3*a + 9, 5*a + 6 = -5*p + 2*p. Suppose 2*x - p*x = -5*b + 30, 3*x = 4*b - 24. Let -2 + b*m**2 - 2 + 4*m + 4 = 0. What is m?
-2/3, 0
Suppose -4*x - 3*a + 13 = 2, -4*x - a + 9 = 0. Determine w, given that 3/2*w - 1/2 + 2*w**x = 0.
-1, 1/4
Let d be 2/13 + 6/(-39). Suppose 3 = q - d. Factor -2*x + 2*x**2 - 3*x**2 + 2*x**q + 3*x**2 - 2*x**4 + 0*x.
-2*x*(x - 1)**2*(x + 1)
Let h(n) be the second derivative of -25*n**7/98 - 12*n**6/7 - 177*n**5/140 + 26*n**4/7 + 6*n**3 + 24*n**2/7 - 10*n - 3. Determine c, given that h(c) = 0.
-4, -1, -2/5, 1
Suppose 0 = 75*q - 226 - 74. Determine f so that 0 + 3/7*f**2 - 3/7*f + 3/7*f**3 - 3/7*f**q = 0.
-1, 0, 1
Let u(r) be the second derivative of -r**6/200 + 2*r**5/25 - 14*r**2 - 14*r. Let p(g) be the first derivative of u(g). Factor p(l).
-3*l**2*(l - 8)/5
Let t(p) = 3*p**2 - 3*p. Let j(h) be the first derivative of -h**3 + 3*h**2/2 + 15. Let b(k) = 4*j(k) + 3*t(k). Let b(f) = 0. Calculate f.
0, 1
Find j such that 4608 - 9212 + 4603 - 2*j - j**2 = 0.
-1
Let w(j) = 8*j + 20. Let t be w(-2). Factor 18*a**t + 3*a**4 + 3*a**5 - 7*a**5 - 256*a**2 - 192*a**3 + 39*a**4.
-4*a**2*(a - 8)**2*(a + 1)
Let r(p) = -15*p + 499. Let h be r(33). Determine y so that 4*y**3 - 4/11 - 4*y + 11*y**h - 117/11*y**2 = 0.
-1, -2/11, 1
Let -68/9*y**3 + 0 + 32/3*y**2 + 2/9*y**5 + 0*y + 2/3*y**4 = 0. What is y?
-8, 0, 2, 3
Suppose 5*h - 13 - 2 = 0. Let g = 1073/65 - 212/13. Factor g*p - 4/5*p**h - 3/5*p**2 + 0.
-p*(p + 1)*(4*p - 1)/5
Let x = -20263 + 101321/5. Factor -14/5*j**2 + x*j**4 + 2/5*j**5 - 14/5*j**3 + 36/5*j - 16/5.
2*(j - 1)**3*(j + 2)*(j + 4)/5
Let r(u) be the third derivative of u**8/112 + 4*u**7/35 + u**6/2 + 4*u**5/5 + 3*u**2 - 13*u. Factor r(n).
3*n**2*(n + 2)**2*(n + 4)
Let p = -173 + 52. Let f = 121 + p. Factor 0*j**3 + 0*j + f - 2/5*j**4 + 0*j**2 + 2/5*j**5.
2*j**4*(j - 1)/5
Let -1/3*w**2 + 1/6*w**5 + 5/3*w**3 + 7/6*w**4 - 11/6*w - 5/6 = 0. What is w?
-5, -1, 1
Let u(d) = 3*d**3 + 9*d**2 + 5*d - 1. Let m(b) = -3*b + 19. Let a be m(5). Let r(s) = -9*s**3 - 27*s**2 - 16*s + 2. Let x(f) = a*r(f) + 11*u(f). Factor x(l).
-3*(l + 1)**3
Let o(m) be the first derivative of m**6/18 + 8*m**5/15 + 13*m**4/12 + 2*m**3/3 - 1. Factor o(y).
y**2*(y + 1)**2*(y + 6)/3
Let v = 90 - 85. Find z such that -z - 4*z**2 + 2*z - v*z = 0.
-1, 0
Let g(c) be the first derivative of c**6/160 + 3*c**5/80 + 33*c**2/2 - 6. Let w(l) be the second derivative of g(l). Factor w(n).
3*n**2*(n + 3)/4
Factor 673*j + 228*j + 5*j**3 + 720 + 125*j**2 - 61*j.
5*(j + 1)*(j + 12)**2
Let k(u) be the first derivative of 52/3*u**3 + 2*u**4 + 10*u**2 - 24*u + 29. Factor k(p).
4*(p + 1)*(p + 6)*(2*p - 1)
Let d(k) be the first derivative of 0*k - 3 - 1/3*k**3 + 3/2*k**2. Factor d(j).
-j*(j - 3)
Let j = -5/169 - -373/1183. Let v(i) = -i + 5. Let s be v(0). Factor -4/7*y**2 + 0*y**3 + 4/7*y**4 + 0 + 2/7*y - j*y**s.
-2*y*(y - 1)**3*(y + 1)/7
Let k be (-3)/(8 + 245/(-28)). Let g(o) be the second derivative of o - 1/2*o**3 + 0*o**2 + 0 + 0*o**k + 3/20*o**5. Solve g(v) = 0 for v.
-1, 0, 1
Suppose 152*n - 10*n**2 + 6*n**2 - 498 + 990 = 0. What is n?
-3, 41
Let t(w) be the first derivative of -w**6/45 - 22*w**5/75 + w**4/30 + 22*w**3/45 + 186. Find o, given that t(o) = 0.
-11, -1, 0, 1
Let a be -3 + (12 + -3 - (-4 - -5)). Determine g, given that a + g + 2 - 28*g + 8 + 9*g**2 + 3*g**3 = 0.
-5, 1
Let m(w) = 3*w**2 - w + 2. Let h be m(1). Factor h*q**2 + 15*q**3 + 2*q**2 + 2 - 17*q**3 - 6*q.
-2*(q - 1)**3
Factor -194*n**2 - 206*n**2 - 57 + 64*n + 378*n**2 + 1 + 2*n**3.
2*(n - 7)*(n - 2)**2
Suppose i = 2 - 38. Let r be (2 - 1)*3 + i/16. Factor -1/4*k**4 + 1/4*k - r*k**2 + 3/4*k**3 + 0.
-k*(k - 1)**3/4
Let z be ((-3)/5)/((-31)/155). Let s(l) be the first derivative of 1/6*l**z + 0*l**2 + 0*l + 1/8*l**4 - 4. Solve s(q) = 0.
-1, 0
Factor 2/9*h**2 + 556/9*h + 38642/9.
2*(h + 139)**2/9
Let l be 89/56 + 10/35. Let h(q) be the first derivative of 4 + l*q**4 + 1/4*q**2 - 17/6*q**3 + 1/2*q. Let h(z) = 0. What is z?
-1/5, 1/3, 1
Factor 0 + 3/2*u**2 - 5/2*u**3 + u.
-u*(u - 1)*(5*u + 2)/2
Let w(c) be the second derivative of -c**5/20 - c**4/2 + 6*c**3 - 20*c**2 + 2*c + 21. Factor w(n).
-(n - 2)**2*(n + 10)
Let b(q) be the third derivative of -q**8/168 + 2*q**7/21 - 17*q**6/30 + 26*q**5/15 - 37*q**4/12 + 10*q**3/3 + 153*q**2 - 2. Let b(d) = 0. What is d?
1, 2, 5
Suppose 12*h - 9*h - 45 = 0. Let p be (-16 - -15)/(h/(-12) + 1). Determine i so that -3/4*i - 1/4*i**p + 1/2 + 3/4*i**3 - 1/4*i**2 = 0.
-1, 1, 2
Let h(t) be the first d