tive of l**5/150 - l**4/60 - l**2 + 2. Let f(c) be the second derivative of o(c). Determine y, given that f(y) = 0.
0, 1
Let u = 303/335 - 7/67. Let 2/5 - u*y + 2/5*y**2 = 0. Calculate y.
1
Solve 12*k**2 + 5*k + 0*k - 11*k - 4*k**3 - 2*k = 0 for k.
0, 1, 2
Let l(i) be the third derivative of -i**6/240 + i**5/60 + i**4/48 - i**3/6 - 11*i**2. Factor l(k).
-(k - 2)*(k - 1)*(k + 1)/2
Let z(b) be the second derivative of -b**5/30 - b**4/9 + b**3/9 + 2*b**2/3 + 15*b. Factor z(p).
-2*(p - 1)*(p + 1)*(p + 2)/3
Suppose 10*k - 18 - 12 = 0. Let v(l) be the first derivative of 9/4*l**4 + 2*l + 0*l**k - 3 - 7/2*l**2. Determine f so that v(f) = 0.
-1, 1/3, 2/3
Let c(r) be the second derivative of r**7/147 - 3*r**5/70 - r**4/21 - 51*r. Factor c(q).
2*q**2*(q - 2)*(q + 1)**2/7
Let a(k) = -k**3 + 67*k**2 - 293*k + 384. Let v(l) = 71 - 34*l**2 + l**3 - 263 - 58*l + 204*l. Let p(u) = -2*a(u) - 5*v(u). Let p(n) = 0. What is n?
4
Factor -1/3*m**3 + 2/3 + 1/3*m - 2/3*m**2.
-(m - 1)*(m + 1)*(m + 2)/3
Let -21/4*x**2 - 27/4 - 45/4*x - 3/4*x**3 = 0. What is x?
-3, -1
Let u(h) = -h**3 - 16*h**2 - 6. Let g(z) = -z**3 - 31*z**2 - 11. Let p(a) = 6*g(a) - 11*u(a). Solve p(w) = 0 for w.
0, 2
Let t(c) be the first derivative of c**6/9 - 14*c**5/15 + 5*c**4/3 + 4*c**3 - 9*c**2 - 18*c + 9. Factor t(q).
2*(q - 3)**3*(q + 1)**2/3
Find u, given that 64/17*u + 6/17*u**2 - 22/17 = 0.
-11, 1/3
Let m(g) be the first derivative of -g**7/126 - g**6/45 + g**4/18 + g**3/18 - 2*g + 2. Let a(t) be the first derivative of m(t). Determine s so that a(s) = 0.
-1, 0, 1
Let t(h) = -h**4 - h**2 + h. Suppose 2 = -w + 1. Let q(r) = -2*r**4 + 3*r**3 - 4*r**2 + 2*r. Let x(l) = w*q(l) + t(l). Factor x(b).
b*(b - 1)**3
Let l(i) = -i**3 - 2*i**2 + 4*i + 5. Let c be l(-3). Let d(y) be the second derivative of -1/3*y**3 - 1/6*y**4 + 0 - c*y + 0*y**2. Factor d(k).
-2*k*(k + 1)
Let g(d) be the third derivative of d**6/100 + d**5/30 + d**4/60 - d**3/15 - 10*d**2. Factor g(u).
2*(u + 1)**2*(3*u - 1)/5
Let v be 2 + -1 + -1 - 36. Let p be (9/v)/(-1*1). Factor 0 + p*o + 1/4*o**2.
o*(o + 1)/4
Let c(l) be the second derivative of l**8/1680 - l**7/1050 - l**6/600 + l**5/300 - l**2/2 - 2*l. Let h(b) be the first derivative of c(b). Factor h(z).
z**2*(z - 1)**2*(z + 1)/5
Suppose -5 - 3 = -2*f. Let q be (72/f)/((-6)/(-9)). Factor -q - 3*t - 4*t**2 + t**2 - 15*t.
-3*(t + 3)**2
Let t(n) be the first derivative of 0*n**3 + n**2 - 1 - 1/150*n**5 + 0*n - 1/60*n**4. Let v(f) be the second derivative of t(f). Factor v(o).
-2*o*(o + 1)/5
Let z(j) be the second derivative of -j**5/130 + 5*j**4/78 - 8*j**3/39 + 4*j**2/13 + 26*j. Determine p so that z(p) = 0.
1, 2
Let i be 3/(-26)*32/(-24). Factor -4/13*j**2 + 2/13 + 2/13*j**4 + i*j**5 - 4/13*j**3 + 2/13*j.
2*(j - 1)**2*(j + 1)**3/13
Suppose -1/8*t - 1/8*t**2 + 1/4 = 0. What is t?
-2, 1
Let j(o) be the first derivative of o**4/2 + 2*o**3 + 2*o**2 + 13. Factor j(v).
2*v*(v + 1)*(v + 2)
Let 4/3*t**3 - 8/3 + 20/3*t - 16/3*t**2 = 0. What is t?
1, 2
Let p(o) be the first derivative of 2*o**3/9 + 2*o**2/3 - 2*o - 16. Factor p(l).
2*(l - 1)*(l + 3)/3
Let h = 11 - 8. Suppose -h*s = -60 - 12. What is i in -20*i**3 + 4*i + s*i**4 - i + 2*i**3 - 9*i**5 = 0?
-1/3, 0, 1
Let 23*c**4 - 12*c - 46*c**2 - 35*c**4 - 135*c**4 - 50*c**2 - 231*c**3 = 0. Calculate c.
-1, -2/7, 0
Let w(l) = -4*l**3 + 12*l**2 + 16*l + 5. Let r(g) = -10*g**3 + 30*g**2 + 40*g + 12. Let q(b) = 5*r(b) - 12*w(b). Solve q(v) = 0.
-1, 0, 4
Let p(y) = y**3 - 8*y**2 - y - 187. Let s be p(10). Find h such that -6/5*h**s + 6/5*h + 2/5*h**2 - 2/5 = 0.
-1, 1/3, 1
Let z(s) be the third derivative of s**9/19656 + s**8/5460 - s**6/1170 - s**5/780 - s**3/2 - 8*s**2. Let o(t) be the first derivative of z(t). Factor o(c).
2*c*(c - 1)*(c + 1)**3/13
Let a(v) be the third derivative of -v**7/1260 - v**6/144 - v**5/45 - v**4/36 + 2*v**2. Factor a(b).
-b*(b + 1)*(b + 2)**2/6
Let h(n) = 2*n**5 - 4*n**4 + 10*n**3 + 16*n**2 - 28*n + 18. Let r(v) = -v**3 + v - 1. Let g(l) = -2*h(l) - 28*r(l). What is z in g(z) = 0?
-2, 1
Let i(n) be the first derivative of -1/150*n**5 + 1/30*n**4 - 3 - 1/15*n**3 - n**2 + 0*n. Let d(r) be the second derivative of i(r). Factor d(b).
-2*(b - 1)**2/5
Suppose -94*s = -100*s. Solve 6/7*w**2 + 0 - 3/7*w**3 + s*w = 0 for w.
0, 2
Let z = 61/170 + 7/170. What is u in z*u**2 + 4/5 - 6/5*u = 0?
1, 2
Let r(p) = 2*p + 8. Let o be r(-4). Determine k, given that 1/2*k**3 + 0 - 1/2*k**2 + 1/2*k**4 + o*k - 1/2*k**5 = 0.
-1, 0, 1
Let w(x) = 3*x**2 - x. Let k be w(-1). Suppose 4*a = 2*c - 2, 2*a = 8*c - 3*c - 29. Suppose p**4 - 3*p**5 + k*p - p + 0*p**4 + 6*p**2 - c*p**4 = 0. Calculate p.
-1, 0, 1
Suppose -4*o = 4*d + 8, 2*o + 3*d + 8 = -0*d. Factor 4*m**2 + m**o - 3*m**2.
2*m**2
Let k be -9*(-4)/(-36)*-3. Let q = -1/25 - -29/100. Determine s so that 2*s + q*s**k + 1 + 5/4*s**2 = 0.
-2, -1
Let f(d) be the third derivative of -2*d**2 + 1/48*d**4 + 0*d**3 - 1/168*d**8 + 0*d + 11/420*d**7 + 1/120*d**5 + 0 - 3/80*d**6. Factor f(n).
-n*(n - 1)**3*(4*n + 1)/2
Suppose -1/2*z**2 + 0*z + z**3 + 0 - 1/2*z**4 = 0. What is z?
0, 1
Solve -14 + 25*q**2 - 9 + 18 - 15*q**3 - 5*q = 0 for q.
-1/3, 1
Let u(x) = -x**3 + 5*x**2 + 5*x + 8. Let h be u(6). Let v be (-3)/(27/6) + h. Factor -4/3*f - v - 1/3*f**2.
-(f + 2)**2/3
Let b(i) be the first derivative of -2*i**5/15 + i**4/10 + 6*i**3/5 + 5*i**2/3 + 4*i/5 + 4. Find v, given that b(v) = 0.
-1, -2/5, 3
Suppose -18 = -6*z + 6. Suppose 8 + 1/2*x**2 + z*x = 0. What is x?
-4
Let m = 3/1069 - -2111/9621. Factor 4/9*z - 2/9*z**2 - m.
-2*(z - 1)**2/9
Let x be 9*((-7)/((-21)/10) - 3). Let i(b) be the second derivative of -2*b + 0 + 0*b**2 - 1/6*b**4 - 1/3*b**x. Factor i(d).
-2*d*(d + 1)
Suppose -2*q - 3*h = -6, h + 2*h = 2*q + 6. Factor -3/5*i**4 + 0*i**2 + 0*i**3 + 0 + q*i.
-3*i**4/5
Let g(p) be the second derivative of p**6/75 - p**5/25 - p**4/10 + 4*p**3/15 + 4*p**2/5 + 4*p. Find s such that g(s) = 0.
-1, 2
Let i be -3*(-3)/(27/4). Factor 0 - 2/3*k - i*k**2 - 2/3*k**3.
-2*k*(k + 1)**2/3
Determine m so that -4/3 + 14/3*m + 6*m**2 = 0.
-1, 2/9
Let b(l) be the second derivative of l**7/42 + l**6/30 - l**5/4 + l**4/4 + 24*l. What is y in b(y) = 0?
-3, 0, 1
Suppose 5*n + 3*n - 6 + 14 - 4*n**3 - 4*n - 8*n**2 = 0. What is n?
-2, -1, 1
Let y = -6 + 10. Suppose 0*w**y + w**2 + 3*w**2 + 5*w**3 + w + 2*w**4 = 0. Calculate w.
-1, -1/2, 0
Let p = -33 + 38. Let o(i) be the second derivative of 0*i**p + 0*i**2 + 4*i + 0*i**3 - 1/105*i**6 - 1/147*i**7 + 0*i**4 + 0. Factor o(n).
-2*n**4*(n + 1)/7
Let 1/2*n**4 - 1/2*n**5 + 1/2*n**3 + 0 - 1/2*n**2 + 0*n = 0. What is n?
-1, 0, 1
Let q(h) = h**4 - h**3 - 5. Let w(b) = -1. Let o(g) = -3*q(g) + 15*w(g). Factor o(n).
-3*n**3*(n - 1)
Let q(y) be the first derivative of 0*y**3 + 2*y + 3/2*y**2 - 3 - 1/4*y**4. Solve q(c) = 0 for c.
-1, 2
Let x(r) be the first derivative of -r**6/16 + 21*r**5/40 - 57*r**4/32 + 25*r**3/8 - 3*r**2 + 3*r/2 - 1. Find u such that x(u) = 0.
1, 2
Let k(u) be the third derivative of 1/240*u**5 - 3*u**2 + 0*u**3 + 0*u - 1/840*u**7 + 0 - 1/96*u**4 + 1/480*u**6. Factor k(d).
-d*(d - 1)**2*(d + 1)/4
Let z be 14/12 + 2/(-4). Suppose z - 1/3*r**2 + 1/3*r = 0. What is r?
-1, 2
Let s be (9 - 8)/(1 + 0). Let q(x) be the first derivative of 0*x + 4/9*x**3 + s + 1/3*x**2 + 1/6*x**4. Find y, given that q(y) = 0.
-1, 0
Let s(b) be the second derivative of b**7/14 - 13*b**6/50 + 27*b**5/100 + b**4/20 - b**3/5 - 9*b. Factor s(l).
3*l*(l - 1)**3*(5*l + 2)/5
Solve -5*t - 45 + 5*t**3 - 46 + 91 = 0.
-1, 0, 1
Let i(o) be the first derivative of 4/5*o + 4 - 2/15*o**3 - 1/5*o**2. Find w, given that i(w) = 0.
-2, 1
Let q(m) be the second derivative of m**7/105 - m**6/30 + m**5/30 + 7*m**2/2 - 3*m. Let v(s) be the first derivative of q(s). Factor v(d).
2*d**2*(d - 1)**2
Let b = -5 + 10. Suppose -3*s = -4*s + 3*g - 4, 3*s - 2 = 2*g. What is p in 1/3*p - 5/3*p**4 + p**3 + 0 - 4/3*p**b + 5/3*p**s = 0?
-1, -1/4, 0, 1
Let u = 58 - 151. Let o = u - -467/5. What is l in -2/5*l**2 - o*l**4 + 0 + 0*l + 4/5*l**3 = 0?
0, 1
Suppose 5*y + 0*y + 2*h - 13 = 0, 0 = y - 4*h - 7. Suppose 4 = u - 4*c, 4*u - 16 = y*c - c. Find p, given that 7/4*p**u - 9/4*p**3 + 9/4*p - 1/2 - 5/4*p**2 = 0.
-1, 2/7, 1
Let h(l) be the first derivative of 18*l**5/5 - l**4 + 3. Factor h(w).
2*w**3*(9*w - 2)
Suppose 0 = 