n + 1. Let i(f) = 2*f**5 + 24*f**4 + 52*f**3 + 48*f**2 + 14*f + 2. Let l(q) = i(q) - 2*x(q). Factor l(k).
4*k*(k + 1)**2*(k + 2)**2
Let m = 496 + -494. Suppose -2*i**m - 5/3*i + 1/3 = 0. What is i?
-1, 1/6
Let k(o) be the third derivative of o**6/30 - o**5/15 - o**4/3 - 16*o**2. Factor k(s).
4*s*(s - 2)*(s + 1)
Let z(x) be the second derivative of -x**8/30240 - x**7/3780 - x**6/1620 - 3*x**4/4 + 7*x. Let u(y) be the third derivative of z(y). Factor u(s).
-2*s*(s + 1)*(s + 2)/9
Let t = 1221/532 + -6/133. Let 3*r**2 + t*r**3 + 0 + 3/4*r = 0. What is r?
-1, -1/3, 0
Let a(l) = 6*l**2 - l - 2*l**2 - 3*l**2 + 1 + 2*l. Let t(p) = 5*p**2 + 7*p + 4. Let y(z) = -12*a(z) + 3*t(z). Factor y(d).
3*d*(d + 3)
Suppose 25*n**3 + 494*n**5 - n + n - 10*n**2 - 489*n**5 - 20*n**4 = 0. Calculate n.
0, 1, 2
Let o(v) = 9*v**3 + 16*v**2 + 25*v + 13. Let z(r) = -14*r**3 - 24*r**2 - 38*r - 20. Let x(w) = -8*o(w) - 5*z(w). Factor x(k).
-2*(k + 1)**2*(k + 2)
Let p(v) be the second derivative of v**4/48 - v**3/8 + v**2/4 - 2*v. Determine j so that p(j) = 0.
1, 2
Let y = -13/18 + 7/9. Let f = 23/9 - y. Factor -7/2*s + 1 + f*s**2.
(s - 1)*(5*s - 2)/2
Solve -10/11*a**3 + 0*a + 6/11*a**2 + 0 = 0.
0, 3/5
Let i = 27 + -30. Let v be 0/(i - (-5 - -4)). Factor 2/5*k**2 + 4/5*k - 4/5*k**3 + v - 2/5*k**4.
-2*k*(k - 1)*(k + 1)*(k + 2)/5
Suppose 6*v - 8 = 2*v. What is o in 7*o + 2*o + 8 + v*o**2 - o = 0?
-2
Let d(j) = 5*j**2 - 10*j + 11. Let i(l) = -4*l**2 + 10*l - 10. Let w(r) = 2*d(r) + 3*i(r). Factor w(s).
-2*(s - 4)*(s - 1)
Let m be ((-3)/(-6))/(2/20). Suppose 5*s + m - 15 = 0. Determine z, given that 0 + 8/5*z**s - 2/5*z = 0.
0, 1/4
Let -120*q - 325 - 833*q**2 + 828*q**2 - 395 = 0. What is q?
-12
Let a be 5/5 + (-87)/90. Let d(u) be the second derivative of 0 + u + a*u**6 + 3/40*u**5 + 0*u**2 + 1/24*u**3 + 1/12*u**4 + 1/168*u**7. Let d(l) = 0. What is l?
-1, 0
Let n(y) be the third derivative of y**6/630 + y**5/140 + y**4/84 - y**3/6 + 2*y**2. Let h(i) be the first derivative of n(i). Determine p so that h(p) = 0.
-1, -1/2
Let j = 7/52 - -575/364. Factor 0*h - j*h**4 + 0 - 24/7*h**3 - 16/7*h**2 - 2/7*h**5.
-2*h**2*(h + 2)**3/7
Suppose 3*c = -c - c. Factor 2/3*i**3 - 2/3*i**2 + c - 4/3*i.
2*i*(i - 2)*(i + 1)/3
Let i(o) be the third derivative of 1/30*o**5 + 0 + o**3 + 1/3*o**4 - 2*o**2 + 0*o. Solve i(z) = 0 for z.
-3, -1
Suppose 2*h - 5*l + 6 = -0*h, -l + 9 = -3*h. Let n = 2 - h. Suppose 4*r**4 + 2*r**3 - r + 2*r**n + r = 0. Calculate r.
-1, 0
Let i(d) be the first derivative of -3*d**5/40 + d**4/8 + d**3/4 - d**2 - 5. Let a(l) be the second derivative of i(l). Let a(z) = 0. Calculate z.
-1/3, 1
Let s(z) = -8*z**2 + 4*z - 6. Let x(y) = -y**3 + 5*y**2 + 8*y - 14. Let b be x(6). Let c(t) = -t**2 + t - 1. Let o(l) = b*s(l) + 20*c(l). Factor o(k).
-4*(k - 2)*(k - 1)
Let k be (120/(-24))/((-10)/4). Suppose 3*j + 4 = 13. Factor 0 + 1/4*w**j + 0*w - 1/4*w**k.
w**2*(w - 1)/4
Suppose -2*z + 20 = 3*z. Find g, given that 4*g**2 - 13*g**4 + 24*g**3 + 30*g**4 + 32*g**z + 4*g**3 = 0.
-2/7, 0
Let i = 15 - 10. Let c(d) = d**3 + 3*d**2. Let l be c(-3). Determine h so that l - 1/4*h**3 + 0*h**2 + 1/4*h**i + 0*h**4 + 0*h = 0.
-1, 0, 1
Suppose -4*t = -3*t - 2. Suppose 2*h + 0*a = -a + 6, -t*h - 5*a + 6 = 0. Factor 0*f**2 + 4/11*f + 2/11*f**4 - 2/11 - 4/11*f**h.
2*(f - 1)**3*(f + 1)/11
Let s(h) be the third derivative of -1/12*h**3 + 0*h + 1/140*h**7 - 1/60*h**5 - 1/16*h**4 + 0 + 1/672*h**8 + 1/120*h**6 + h**2. Factor s(m).
(m - 1)*(m + 1)**4/2
Let u(z) = -4*z - 2. Let p be u(-2). Suppose 6*j - p = 3*j. Determine m so that -2*m - 2*m**j + 0*m + 2*m**3 + 0*m**2 + 2 = 0.
-1, 1
Factor 0 + 8/19*n**2 + 8/19*n + 2/19*n**3.
2*n*(n + 2)**2/19
Factor -1/2*a**4 + 0*a**3 + a**2 - 1/2 + 0*a.
-(a - 1)**2*(a + 1)**2/2
Let s(n) be the second derivative of n**5/10 - n**4/6 - 2*n**3/3 - 22*n. Find a, given that s(a) = 0.
-1, 0, 2
Suppose 2 = 71*q - 70*q. Let n(d) be the first derivative of 5/6*d**3 + 0*d - 4 - 1/2*d**q - 3/8*d**4. Find o such that n(o) = 0.
0, 2/3, 1
Let p be (-9)/(-6)*2 + 0. Suppose p*y = -3*v - 2*v - 10, 4*y = -5*v - 10. Determine z so that -4*z**2 + 5*z**2 + y*z - 2*z = 0.
0, 2
Suppose 4*d**2 - 4*d**4 + 4*d**5 + 16*d - 20*d**3 - 6 - 6 + 16*d**2 - 4 = 0. What is d?
-2, -1, 1, 2
Let q(m) be the first derivative of -m**7/84 - m**6/60 + m**5/40 + m**4/24 + 3*m - 2. Let h(p) be the first derivative of q(p). Suppose h(i) = 0. Calculate i.
-1, 0, 1
Let d(n) = -n**2 - 8*n + 52. Let a be d(-12). Suppose -2/5 - 4/5*b**3 + 2/5*b + 4/5*b**2 + 2/5*b**5 - 2/5*b**a = 0. Calculate b.
-1, 1
Let i be 1/(-4) + (-364)/(-112). Factor 13/2*u**2 - 3/2*u**i - 8*u + 2.
-(u - 2)**2*(3*u - 1)/2
Suppose 3*w - 16 = 5. Suppose i - 1 = 3*t - 4, -5*t - 2*i = -16. Solve -9*m**3 + w*m**4 + 2*m**t + 16*m - 16*m = 0 for m.
0, 2/7, 1
Let q = -107 - -110. Determine i so that 7/2*i**q + 3/2*i**4 + 5/2*i**2 + 0 + 1/2*i = 0.
-1, -1/3, 0
Let m(j) be the first derivative of -j**3/5 - 3*j**2/10 + 6*j/5 - 5. Let m(n) = 0. What is n?
-2, 1
Factor 433*l**2 + 2*l**3 + 4 - 4*l - 437*l**2 + 2*l**3.
4*(l - 1)**2*(l + 1)
Factor 0 - 4/13*b**4 + 2/13*b**5 + 0*b + 2/13*b**3 + 0*b**2.
2*b**3*(b - 1)**2/13
Let a(x) = -x - 2. Let c be a(-4). Factor -k**c - 1 + 0*k - k - k.
-(k + 1)**2
Let q = -310 + 310. Solve -8/3*x**2 - 4/3*x**3 + 0 + q*x = 0.
-2, 0
Let r(s) be the first derivative of -s**6/480 - s**5/240 + 5*s**2/2 - 4. Let d(k) be the second derivative of r(k). Let d(v) = 0. Calculate v.
-1, 0
Suppose 0 = r - 2. Factor 5 - 8 + 4*s - r*s**2 + 1 + 0*s.
-2*(s - 1)**2
Let 19*o**3 + 6*o**3 + 12*o**2 - 4*o - 3*o**4 + 3*o**4 + 9*o**4 = 0. What is o?
-2, -1, 0, 2/9
Let k(j) = -j**2 - 7*j - 6. Let c(u) = -6*u - 6. Let n(b) = 4*c(b) - 3*k(b). Factor n(f).
3*(f - 2)*(f + 1)
What is k in 203*k**4 - 3*k + 27*k**2 - 18*k**3 - 200*k**4 + 3*k = 0?
0, 3
Factor 2*h**2 - h + 3*h + 0*h**2.
2*h*(h + 1)
Let x(v) = 4 - 3 - 3 + 2*v**2 + 2*v. Let r be x(-2). Factor -r*o**5 + 0*o**4 + 4*o**4 + 0*o**5 - 2*o**3.
-2*o**3*(o - 1)**2
Let o(c) = 4*c**4 + c**3 - 3*c**2. Let i(v) = v**2 - 3*v**2 + 2*v**3 + 4*v**4 + 0*v**3. Let d(g) = 3*i(g) - 2*o(g). Suppose d(t) = 0. Calculate t.
-1, 0
Let u(b) = -3*b**3 + 34*b**2 - 106*b + 2. Let j(m) = -6*m**3 + 67*m**2 - 211*m + 5. Let k(h) = 2*j(h) - 5*u(h). Suppose k(c) = 0. What is c?
0, 6
Let c(x) = -3*x**2 - 6. Let k(j) = -2*j**2 - 5. Let i(f) = -5*c(f) + 6*k(f). Factor i(r).
3*r**2
Let q be ((-3)/(-9) + 1)/(10/3). Factor 2/5*p**2 - 4/5 - q*p.
2*(p - 2)*(p + 1)/5
Let v = 281 + -278. Factor 0*a**2 - v - 9/2*a + 3/2*a**3.
3*(a - 2)*(a + 1)**2/2
Let j be (-1)/(33/(-15) - -2). Let t = j + -1. Determine o so that 2 + 4*o**3 - 8*o**3 - 2*o**t + 4*o + 0*o**4 = 0.
-1, 1
Let i be (5 - 3) + -3 + 1. Suppose i = -3*q - 0*q. Determine j so that 2/5*j**4 + q - 2/5*j - 2/5*j**2 + 2/5*j**3 = 0.
-1, 0, 1
Let r = 4 + -6. Let u be r + -9*6/(-9). Suppose -3*p**3 + u + 4*p**4 - 5*p**2 - 3 + 0*p**2 + 3*p = 0. What is p?
-1, -1/4, 1
Let m = 10 + 6. Let n be 1*-1 + 20/m. Solve 0 + 1/4*g**2 - n*g = 0.
0, 1
Let y(u) be the first derivative of u**4/4 + 2*u**3/3 + u**2/2 - 6. Suppose y(f) = 0. What is f?
-1, 0
Let s(o) be the third derivative of -o**5/100 + 3*o**4/20 - 4*o**3/5 - 17*o**2. Solve s(i) = 0.
2, 4
Suppose -2*d - 5*n + 2 = 2*d, 5*d - 19 = 2*n. What is p in -6*p + 7*p**2 - d*p + 5 - 3 = 0?
2/7, 1
Let q(o) be the first derivative of -o**3/12 + o**2/2 + 5*o/4 - 11. Factor q(t).
-(t - 5)*(t + 1)/4
Let f(b) be the first derivative of -1/4*b**2 + 1/4*b - 3 + 1/12*b**3. Factor f(y).
(y - 1)**2/4
Find d, given that -3*d**2 + 3*d**2 - 5*d - 8*d**2 + 3*d**2 = 0.
-1, 0
Suppose -28 - 4 = -5*z + j, -4*j = 3*z - 33. Suppose 4*h = z*h. Factor h + 4/5*t**5 - 9/5*t**4 - 1/5*t**2 + 0*t + 6/5*t**3.
t**2*(t - 1)**2*(4*t - 1)/5
Let b(p) be the third derivative of -p**6/60 + p**5/30 + 5*p**4/12 + p**3 + 4*p**2. Determine u, given that b(u) = 0.
-1, 3
Let d(h) be the second derivative of -h**6/180 - h**5/120 + h**4/12 + h**3/9 - 2*h**2/3 + 4*h. Solve d(o) = 0.
-2, 1, 2
Let t = -161/110 + -2/55. Let p = -5/4 - t. Suppose 0 - p*k**3 + 1/2*k**2 - 1/4*k = 0. What is k?
0, 1
Let r(o) = 3*o**3 - o + 2*o**2 + 2 + o**2 - 2*o**3. Let g be r(-3). Solve 2*h**3 - 2*h + g*h**2 - 1 + 0 - 4*h**2 = 0 for h.
-1, -1/2, 1
Let n = -9 - -11. Solve -6*b**3 + 4 + 6*b + 3*b**2 + 0*b**2 - b**4 - 5*b**n