n(x) be the second derivative of x**6/135 + x**5/90 - 2*x**4/9 - 5*x - 37. Suppose n(r) = 0. Calculate r.
-4, 0, 3
Let n(t) = -t**2 - 19*t - 30. Let y be n(-17). Let 2*v**2 + 9*v - v + 2 + y = 0. Calculate v.
-3, -1
Let l(h) = 2*h - 9. Let j be l(6). Determine o, given that -21*o**2 + j + 32*o - 19 + o**2 + 4*o**3 = 0.
1, 2
Let y = -1155 - -1157. Let k = 54 + 169. Let 2*j**4 + 0*j**3 - 2*j - k*j**y + 2*j**3 + 221*j**2 = 0. Calculate j.
-1, 0, 1
Suppose 12*g - 9*g - 17 = 5*d, 3*g + 2*d - 10 = 0. Suppose -5*r - 5*h + 30 = 0, 3 = -4*r + g*h + h. Suppose 2*f**2 + 0 - 2/3*f**r + 0*f = 0. What is f?
0, 3
Suppose -5*h + 11 = -14. Factor 9*g**2 + 16*g**2 + 10*g + 4*g**3 + 16*g**3 + h*g**4.
5*g*(g + 1)**2*(g + 2)
Let r(m) be the third derivative of -1/5*m**5 + 0 - 3/10*m**6 + 0*m**3 + 16*m**2 + 0*m**4 - 1/14*m**7 + 0*m. Let r(n) = 0. What is n?
-2, -2/5, 0
What is u in 0 - 3/2*u - 3/2*u**2 = 0?
-1, 0
Suppose -11 = -205*n + 204*n. Factor -4*q**2 + 8 - 2*q + 29*q - 12*q - n*q.
-4*(q - 2)*(q + 1)
Let v(d) = -2*d - 6. Let t be v(-4). Find x such that 154*x**3 + x**5 + t*x - 156*x**3 - x = 0.
-1, 0, 1
Factor 21*l + 15/2*l**2 + 12.
3*(l + 2)*(5*l + 4)/2
Let q = 2/289 - -568/1445. Suppose -4*g - 3*p + 17 = 0, -6*p = -10*p + 12. Let 0 + q*b + 1/5*b**g = 0. What is b?
-2, 0
Let s be (36/14)/((-15)/(-70)). Find k such that -3*k - k**2 - 9*k + 3*k**3 - 7*k**2 + 5*k**2 + s = 0.
-2, 1, 2
Suppose -12 = -2*s + 3*c, -c - 7 = s + 4*c. Let -10*b**5 + 8*b**5 + 2*b**3 + 6*b**s - 18*b**2 + 4*b**4 + 11*b - b**5 - 2 = 0. Calculate b.
-2, 1/3, 1
Let b(t) = -3 - 1 - 21*t - 1 + 12*t**2 - 16*t. Let m(i) = -35*i**2 + 110*i + 16. Let l(y) = 8*b(y) + 3*m(y). Factor l(w).
-(w - 4)*(9*w + 2)
Suppose 0 = 4*c - 17 - 31. Factor -21*t - 4 - 2 - 3*t**3 + 18*t + c*t.
-3*(t - 1)**2*(t + 2)
Determine v, given that -2/7*v**3 - 4*v - 18/7*v**2 + 0 = 0.
-7, -2, 0
Suppose -101*s = -98*s - 15. Let k(m) be the first derivative of -3/2*m**4 - 11 + 0*m + 2/5*m**s + 1/3*m**6 + 2*m**2 - 2/3*m**3. Factor k(i).
2*i*(i - 1)**2*(i + 1)*(i + 2)
Determine p, given that 4*p**3 - 1/2*p**4 - 13/2*p**2 + 0 + 3*p = 0.
0, 1, 6
Let j(a) = 2*a**2 + 7*a - 9. Suppose 0*q - 2*q + t = 0, -3*t = -5*q - 2. Let m(k) = 7*k + k + 2*k**2 - 8 - q*k. Let h(l) = 4*j(l) - 5*m(l). Solve h(o) = 0.
-2, 1
Let h(f) be the first derivative of 2*f**3/3 - 36*f**2 + 648*f + 84. Factor h(q).
2*(q - 18)**2
Let t be (3/(-9)*0)/2. Suppose -4*k - 10 + 18 = t. Let -k + 142*v**3 + 50*v**5 + 26*v**2 + 115*v**4 + 35*v**4 - 6 - 24*v = 0. What is v?
-1, -2/5, 2/5
Let z(o) = 128*o**3 + 96*o**2 + 36*o + 14. Let x(t) be the first derivative of -t**2/2 - t + 11. Let u(g) = 12*x(g) + z(g). Factor u(c).
2*(4*c + 1)**3
Let q(f) be the second derivative of -f**6/80 - f**5/20 - 11*f**2/2 - 23*f. Let l(t) be the first derivative of q(t). Factor l(c).
-3*c**2*(c + 2)/2
Let u(r) be the second derivative of -r**4/24 + 7*r**3/6 - 48*r. Factor u(t).
-t*(t - 14)/2
Let u = 15/8 + -13/8. Let h(c) be the first derivative of 0*c**2 + 9 + 0*c + 1/3*c**3 - u*c**4. Solve h(j) = 0.
0, 1
Suppose 4 = 2*y - 6*y. Let l be 17 + -11 + y*1 + -3. Factor -4/3*x**3 + 0*x**2 + 0 - 2/3*x**5 + 0*x - l*x**4.
-2*x**3*(x + 1)*(x + 2)/3
Let g(m) be the third derivative of m**8/840 - 4*m**7/1575 - 7*m**6/450 - 2*m**5/225 + m**4/60 - 20*m**2 + 2. Find z, given that g(z) = 0.
-1, 0, 1/3, 3
Let z(w) = -w**3 - 14*w**2 - 3*w - 25. Let o be z(-14). Factor -11 + 12*j**3 - 4*j**4 + 11 + o*j**2 - j**2.
-4*j**2*(j - 4)*(j + 1)
Let s(j) be the first derivative of -j**4/2 - 110*j**3/3 - 783*j**2 - 1458*j + 149. Factor s(v).
-2*(v + 1)*(v + 27)**2
Solve -54/5*g - 12/5*g**2 + 0 - 2/15*g**3 = 0.
-9, 0
Let j(i) = i + 5. Let s be j(5). Let y = -7 + s. Factor -5*x**y + 7*x**4 + 5*x - 3*x**2 - 2*x**2 + 2 - 4*x**2 + 0*x**3.
(x - 1)**2*(x + 1)*(7*x + 2)
Let a(n) = -n**3 + 16*n**2 + 16*n + 21. Let d be a(17). Suppose 10 = 2*o, o + o = -4*f + 30. Factor 0 + 0*s - 3/2*s**f + 0*s**3 + 0*s**2 + s**d.
-s**4*(3*s - 2)/2
Suppose 4*b + 3*b - 126 = 0. Suppose 0*i - 2*i = -4*x - b, -x - 18 = -5*i. Factor -4/5*q**5 + 4/5*q**2 + 14/5*q**4 - 16/5*q**i - 2/5 + 4/5*q.
-2*(q - 1)**4*(2*q + 1)/5
Let q(m) be the second derivative of -m**5/40 - m**4/24 + m**3/12 - 7*m**2 + 16*m. Let w(z) be the first derivative of q(z). What is y in w(y) = 0?
-1, 1/3
Let d(k) be the second derivative of -k**7/21 - k**6/18 + 3*k**5/5 + 13*k**4/6 + 29*k**3/9 + 5*k**2/2 - 898*k. Suppose d(z) = 0. Calculate z.
-1, -5/6, 3
Let c(o) be the second derivative of -o**9/4725 - o**8/600 - o**7/504 - o**6/1200 - 19*o**4/4 - 28*o. Let l(d) be the third derivative of c(d). Factor l(u).
-u*(u + 3)*(4*u + 1)**2/5
Suppose 208 - 414 - 5*c**2 - 300*c + 206 = 0. Calculate c.
-60, 0
Let i(y) = y**3 - 5*y**2 + y. Let d(m) = -m**2 + m. Suppose 4*h - 2*g = 26, 4*h - g - 28 = -h. Let s(x) = h*d(x) - i(x). Factor s(o).
-o*(o - 2)*(o + 2)
Let d(c) be the first derivative of c**8/1680 - c**7/280 + c**6/360 + c**5/40 - c**4/12 - 16*c**3/3 - 10. Let k(z) be the third derivative of d(z). Factor k(g).
(g - 2)*(g - 1)**2*(g + 1)
Let u(r) be the second derivative of r**5/50 - r**3/15 - 230*r - 1. Solve u(h) = 0 for h.
-1, 0, 1
Let n(y) = 10*y + 7*y**2 + 0*y**2 - 11 + 1 - y**2. Let j(b) = -2*b**2 - 3*b + 3. Let c = -22 + 32. Let p(r) = c*j(r) + 3*n(r). Factor p(u).
-2*u**2
Let y = -20 + 26. Factor 69*d**4 + 27*d**3 + 0*d**5 - 21*d**2 + 3*d**5 - 84*d**4 + y*d.
3*d*(d - 2)*(d - 1)**3
Let m(s) be the third derivative of -1/3*s**3 + 0 - s**2 + 1/120*s**6 + 1/30*s**5 - 1/24*s**4 + 0*s. Factor m(f).
(f - 1)*(f + 1)*(f + 2)
Let o(w) be the first derivative of 2*w**3/3 - 52*w**2 + 1352*w + 176. Find m such that o(m) = 0.
26
Factor 56/17 + 24/17*b - 2/17*b**2.
-2*(b - 14)*(b + 2)/17
Let r(s) be the first derivative of -s**2/2 + 5. Let n be r(-1). Solve -3*v**3 + 2*v - 3*v - 4*v - 7*v**2 - n = 0 for v.
-1, -1/3
Let r(u) be the second derivative of 3*u**5/140 - 5*u**4/28 + 2*u**3/7 + 25*u. Factor r(j).
3*j*(j - 4)*(j - 1)/7
Let a = -76 + 71. Let d(f) = 2*f**3 - 24*f**2 - 26*f - 6. Let g(h) = h**3 - 24*h**2 - 27*h - 5. Let l(u) = a*d(u) + 6*g(u). Factor l(j).
-4*j*(j + 2)*(j + 4)
Determine a, given that -12 + 14*a - 2/3*a**5 - 40/3*a**3 + 20/3*a**2 + 16/3*a**4 = 0.
-1, 1, 2, 3
Let z(i) be the third derivative of 0*i + 0*i**4 + 29*i**2 + 1/240*i**5 + 0*i**3 + 1/480*i**6 + 0. Suppose z(s) = 0. What is s?
-1, 0
Let d(w) = w**3 - 12*w**2 - w + 11. Let m be d(12). Let k be (-1)/(-9)*(-2)/m. Find l, given that -8/9*l**2 + 0 - k*l = 0.
-1/4, 0
Suppose z - 2*y = -3*z + 52, z - 13 = -2*y. Let n(w) = -2*w**3 + 25*w**2 + 12*w + 13. Let g be n(z). Factor 1/6*x**4 + 1/3*x**2 + g + 0*x - 1/2*x**3.
x**2*(x - 2)*(x - 1)/6
Solve 6*q**4 - 9*q**2 + 219*q**3 - 3*q**4 + 12 - 213*q**3 - 12*q = 0.
-2, 1
Solve 16/5*t**2 - 2/5*t**5 + 0 + 0*t**4 + 12/5*t**3 + 6/5*t = 0.
-1, 0, 3
Let g(t) = t**2 - 4*t + 5. Let z be g(4). Suppose z*v - 2*v = 0. Factor -3*i + 3*i**2 + v*i - 3*i.
3*i*(i - 2)
Let i(l) be the third derivative of -49*l**7/225 + 833*l**6/450 - 14*l**5/5 + 86*l**4/45 - 32*l**3/45 - l**2. Let i(z) = 0. What is z?
2/7, 4
Let -2/7*g**3 + 6/7*g**4 + 4/7*g - 2/7*g**5 + 0 - 6/7*g**2 = 0. Calculate g.
-1, 0, 1, 2
Let a(q) = -q**3 - 3*q**2 + 25*q + 84. Let j be a(-4). Factor 0*v + 2*v**3 + j + 4/3*v**2 - 2/3*v**5 + 0*v**4.
-2*v**2*(v - 2)*(v + 1)**2/3
Let h = 29 + 157. Suppose 18 = -6*d + h. Determine s so that 5*s**2 + d*s + 2 - 13*s - 2 = 0.
-3, 0
Let t = 44 + -24. Let f be (72/(-30))/((-6)/t). Find j such that -17*j + 9*j**4 - 6*j + 21*j**3 - f - j**2 - j**2 + 3*j = 0.
-2, -2/3, 1
Suppose 6 = 2*w + 2*n, 45 = 5*w - 4*n + 12. Suppose -4*h = 5*v - 18, w*h + 4 = 3*v + 4*h. Let 350/3*z**v + 8 + 98/3*z**3 + 176/3*z = 0. What is z?
-3, -2/7
Let g(a) be the first derivative of -4*a**3/3 - 92*a**2 - 2116*a + 275. Factor g(m).
-4*(m + 23)**2
Let j be ((-18)/(-105))/(324/810). Factor 0 + j*d**2 - 12/7*d.
3*d*(d - 4)/7
Find o, given that 3/8*o**4 + 0 - 15/2*o**2 + 0*o - 57/8*o**3 = 0.
-1, 0, 20
Let b(g) be the first derivative of g**3/33 - 20*g**2/11 + 400*g/11 + 50. Factor b(k).
(k - 20)**2/11
Let f(t) = -2*t - 5. Let g be f(-4). Factor 26*i**5 + 243*i**2 - 11*i**3 - 240*i**2 + 22*i**5 - 10*i**g + 24*i**4.
3*i**2*(i + 1)*(4*i - 1)**2
Let p(w) be the second derivative of w**3 + 2*w + 0 - 1/3*w**4 - 1/5*w**5 - 1/21*w**7 - 