et g = -110 - -221/2. Let s(k) be the first derivative of -3*k**2 - g*k**4 - 2*k - 2*k**3 + 3. Determine n so that s(n) = 0.
-1
Factor -13*f**3 - 180*f + 0*f**2 + 150*f**2 + 138*f**3 + 40.
5*(f + 2)*(5*f - 2)**2
Let l(p) be the third derivative of -p**9/302400 - p**8/100800 - p**5/30 - 7*p**2. Let m(a) be the third derivative of l(a). Factor m(x).
-x**2*(x + 1)/5
Let w = -6 - -10. What is g in 4*g**3 - 3 + 3 - 3*g**4 + g**w = 0?
0, 2
Let u = 12 + -10. Factor -4*f**4 + 0*f + f + 3*f**4 + 2 - 3*f**2 + u*f**4 - f**3.
(f - 2)*(f - 1)*(f + 1)**2
Let c(n) be the second derivative of 1/54*n**4 + 5*n + 0*n**2 - 1/27*n**3 + 0. What is b in c(b) = 0?
0, 1
Suppose -4*g + 15 = -r, 4*r - r + 2*g = -17. Let l = -4 - r. What is b in -6*b + 2*b**3 - 2 - b**2 - l*b**2 - 4*b**3 - 2*b**2 = 0?
-1
Let p(a) be the second derivative of 0 - 4*a - 13/40*a**5 + 19/24*a**4 + 1/2*a**2 - 11/12*a**3 + 1/20*a**6. What is k in p(k) = 0?
1/3, 1, 2
Factor 8*x - 4 + 0 + 5 - 2*x**2 - 7.
-2*(x - 3)*(x - 1)
Let h(s) be the first derivative of s**6/42 - s**4/28 + 3. Suppose h(z) = 0. What is z?
-1, 0, 1
Let j(b) be the third derivative of b**5/60 - b**3/6 - 2*b**2. Let h(i) = i**2 - 6*i + 5. Let a(d) = -h(d) - 2*j(d). Factor a(x).
-3*(x - 1)**2
Let c(l) be the third derivative of -25*l**8/1176 + 8*l**7/49 - 209*l**6/420 + 83*l**5/105 - 5*l**4/7 + 8*l**3/21 - 48*l**2. Find x, given that c(x) = 0.
2/5, 1, 2
Determine v, given that 12/5 + 1323/5*v**2 - 252/5*v = 0.
2/21
Let p(c) be the first derivative of -5/6*c**3 - c + 5 - 7/4*c**2. Factor p(d).
-(d + 1)*(5*d + 2)/2
Let w(y) = -y**2 + 4*y - 4. Let r(x) = -2*x**2 + 8*x - 8. Let l(s) = 2*r(s) - 5*w(s). Determine m so that l(m) = 0.
2
Factor 342*r - 6 - 5*r**2 - 3*r**3 - 7*r**2 - 357*r.
-3*(r + 1)**2*(r + 2)
Suppose 7*y - 4*y - 6 = 0. Factor q**5 + 0*q - 1/4*q**y - 9/4*q**4 + 3/2*q**3 + 0.
q**2*(q - 1)**2*(4*q - 1)/4
Factor 4/3*q - 4/9*q**3 + 0*q**2 - 8/9.
-4*(q - 1)**2*(q + 2)/9
Let c(m) be the third derivative of -m**6/60 + m**5/15 + m**4/3 - 8*m**3/3 + 22*m**2. Suppose c(n) = 0. Calculate n.
-2, 2
Let s(y) be the third derivative of y**7/70 - 3*y**6/20 + 2*y**5/5 + 3*y**4/4 - 9*y**3/2 + 6*y**2. Factor s(d).
3*(d - 3)**2*(d - 1)*(d + 1)
Let p = 1169/1562 - 3/142. Factor 2/11*f**3 - p - 10/11*f**2 + 16/11*f.
2*(f - 2)**2*(f - 1)/11
Let g be 12/(-8)*-1*16/12. Let 1/2 + 1/2*s**g + s = 0. What is s?
-1
Let a = -12 - -18. Let c(o) = -3*o**2 + 23*o - 9. Let j(r) = -19*r**2 + 137*r - 53. Let w(i) = a*j(i) - 34*c(i). Find p, given that w(p) = 0.
1/3, 3
Suppose -3*h - h + 8 = 0. Find r, given that -4*r**h + 4*r - 14 + 31 - 9 = 0.
-1, 2
Let y be (0/(-7 - -3))/3. Let c(w) be the third derivative of 0*w - 1/12*w**4 + 3*w**2 - 1/60*w**5 + y - 1/6*w**3. Suppose c(h) = 0. Calculate h.
-1
Let f be ((-12)/2)/(0 - 2). Solve c**3 - 2*c**4 + 2*c**2 + 2*c - 3*c**f + 0*c = 0 for c.
-1, 0, 1
Suppose 3*f + 2 = 8. Factor -4*z**4 + 0*z**4 - 8*z**3 - 6*z**2 + 2*z**f.
-4*z**2*(z + 1)**2
Let y(r) be the third derivative of -1/12*r**6 - 7/12*r**4 + 2/3*r**3 + 0*r + 3/10*r**5 - 2*r**2 + 1/105*r**7 + 0. Determine p, given that y(p) = 0.
1, 2
Let r(t) be the first derivative of -7*t**6/12 + 23*t**5/10 - 27*t**4/8 + 13*t**3/6 - t**2/2 - 5. What is v in r(v) = 0?
0, 2/7, 1
Suppose 2*i - 3*q = 13, -4*i + 4*q - 28 = -7*i. Suppose -4 - i = -3*m. Factor -2*z + m*z + 3*z**2 - 2*z**2.
z*(z + 2)
Factor m**5 + 5*m - 10*m**3 - 5*m**4 + 9*m**2 + 4*m**5 + 0 - 5 + m**2.
5*(m - 1)**3*(m + 1)**2
Let w(x) = -x**3 + x**2 - 12*x. Suppose 0*a - 4*a = 20. Let y(b) = b**3 + 13*b + 1. Let d(o) = a*w(o) - 4*y(o). Suppose d(r) = 0. Calculate r.
1, 2
Let m be (2 - (0 + 0))*1. Let j be (2/5)/(m/10). Solve 0 + 1/2*p + 0*p**4 + 1/2*p**5 - p**3 + 0*p**j = 0.
-1, 0, 1
Suppose -5*a + 2 + 8 = 0. Suppose 2*p - 3*p = 5*f - 18, a*f + 5*p = -2. Suppose -b**2 - 3 + 4*b**3 - 3*b - f*b**5 + 4 + 3*b**3 = 0. What is b?
-1, 1/2, 1
Factor 3*u - 8*u**2 - 12*u**2 + 15*u**3 + u + u**3.
4*u*(u - 1)*(4*u - 1)
Let m(r) be the second derivative of -r**5/50 + r**4/30 + 4*r**3/15 - 4*r**2/5 - 9*r. Let m(q) = 0. What is q?
-2, 1, 2
Let u(c) be the second derivative of -c**5/10 + 5*c**4/24 - c**3/12 - 12*c. Find i such that u(i) = 0.
0, 1/4, 1
Let g(l) be the second derivative of l**7/3360 + l**6/320 + l**5/80 + l**4/12 - 5*l. Let p(s) be the third derivative of g(s). Factor p(m).
3*(m + 1)*(m + 2)/4
Let l(g) = 95*g**3 + 151*g**2 + 61*g + 11. Let m(t) = 96*t**3 + 152*t**2 + 62*t + 10. Let s(v) = 2*l(v) - 3*m(v). Factor s(j).
-2*(j + 1)*(7*j + 2)**2
Let x(c) = c**3 + 6*c**2 + c + 4. Let t be x(-6). Let a be 12/8*t/(-3). Factor v**2 + 2*v + a + 2 - 2.
(v + 1)**2
Let j(y) = y**3 + 7*y**2 + 7*y + 9. Let q be j(-6). Let 8*o - 2*o**3 - 6*o**2 + 0*o**q + 6*o**4 - 6*o = 0. What is o?
-1, 0, 1/3, 1
Let y(h) = -h**3 - 5*h**2 + 5*h - 3. Let z be y(-6). Suppose 4*l - z = 3*a, -2*a + 5*l = a + 6. Find i, given that -8/3 - 98*i**2 - 343/3*i**a - 28*i = 0.
-2/7
Let k(z) be the third derivative of z**5/75 + 4*z**4/15 - 2*z**2 - 8*z. Factor k(a).
4*a*(a + 8)/5
Determine p, given that -4*p - 4*p - 3*p**2 + 2*p + 3*p = 0.
-1, 0
Let b(o) = 3*o**3 - 29*o**2 + 149*o - 250. Let c(a) = a**3 + a**2 - a. Let f(s) = -2*b(s) + 2*c(s). Find h such that f(h) = 0.
5
Let t(k) be the second derivative of -27*k**5/16 - 225*k**4/16 - 375*k**3/8 - 625*k**2/8 + 25*k. Factor t(i).
-5*(3*i + 5)**3/4
Let k(b) be the second derivative of b**4/6 + b**3 - 4*b**2 - 27*b. Factor k(z).
2*(z - 1)*(z + 4)
Let u = 47/6255 - -1/278. Let c(a) be the second derivative of 1/27*a**3 + 0 + 1/27*a**4 - 4*a - u*a**5 - 2/9*a**2. Factor c(v).
-2*(v - 2)*(v - 1)*(v + 1)/9
Factor 41*m**5 - 62*m**5 + 7*m**3 + 5*m**3 + 36*m**4.
-3*m**3*(m - 2)*(7*m + 2)
Let s(x) = -11*x**3 + 10*x**2 - 9*x - 5. Let u(n) = -17*n**3 + 15*n**2 - 14*n - 8. Let g(i) = 8*s(i) - 5*u(i). Factor g(w).
-w*(w - 1)*(3*w - 2)
Suppose 0 = -3*i + 3*k - 6 + 3, -7 = 4*i - 5*k. Factor 2/3 + j + 1/3*j**i.
(j + 1)*(j + 2)/3
Let o be (15/(-25))/(1/(-5)). Find m, given that m + 6 - 9*m**2 + 2*m + 2*m**3 + 0*m**3 - 5*m**3 + o*m**4 = 0.
-1, 1, 2
Let z(q) be the third derivative of -q**8/20160 + q**7/7560 + q**6/1080 + q**4/24 + 5*q**2. Let i(f) be the second derivative of z(f). Factor i(c).
-c*(c - 2)*(c + 1)/3
Let u be 112/(-8) + 9 - -5. Factor 9/2*c**2 + u + c + 5/2*c**4 + 6*c**3.
c*(c + 1)**2*(5*c + 2)/2
Let f(n) be the first derivative of 1/4*n - 1/12*n**3 + 0*n**2 - 2. Factor f(b).
-(b - 1)*(b + 1)/4
Let d(c) be the second derivative of -c**7/14 + 3*c**5/5 - c**4/2 - 3*c**3/2 + 3*c**2 + 31*c. Factor d(p).
-3*(p - 1)**3*(p + 1)*(p + 2)
Let t = 12 + -8. Suppose s = 3*j - 6*j + 17, 0 = -t*s + 3*j - 7. Factor 0*y - 2/9*y**s + 2/9.
-2*(y - 1)*(y + 1)/9
Solve 3/2 + 3/4*y**2 - 9/4*y = 0.
1, 2
Factor 0 - 1/2*r + 1/4*r**2.
r*(r - 2)/4
Let o(h) = 4*h**2 + 2*h - 2. Let s be o(-3). Suppose -5*w = 4*q - s, -2*q + 5 - 1 = 0. Factor 1/5*d**w - 1/5*d**5 + 0 + 0*d**2 + 0*d**3 + 0*d.
-d**4*(d - 1)/5
Solve 0 - 1/11*p**2 - 2/11*p = 0 for p.
-2, 0
Let w(d) be the third derivative of -d**6/30 + d**5/15 - 6*d**2. Factor w(t).
-4*t**2*(t - 1)
Suppose 2*p + 2*m - 12 = 0, 5*m - 4*m - 9 = -2*p. Factor 30*i**2 + 2 - 3*i**4 + 2 + 20*i + i**2 - 5*i**5 + 13*i**p - 4*i**4.
-(i - 2)*(i + 1)**3*(5*i + 2)
Let z = 11 - 21. Let i be (8/z)/((-14)/35). Factor 2*q**i + 3 + 0 - 3 - 2.
2*(q - 1)*(q + 1)
Let m(j) = 8*j**3 - 4*j**2 - 8*j + 4. Let y(l) = l**3 - l. Let x(k) = m(k) - 2*y(k). Factor x(z).
2*(z - 1)*(z + 1)*(3*z - 2)
Let d(v) be the third derivative of 0*v**5 + 0*v**7 - 1/1008*v**8 - 1/72*v**4 + 0*v**3 + 1/180*v**6 + 9*v**2 + 0*v + 0. Factor d(w).
-w*(w - 1)**2*(w + 1)**2/3
Determine q, given that 8*q + 26*q**2 - 2*q**3 - 2*q**2 - 12*q**3 = 0.
-2/7, 0, 2
Let l = 37/8 + -227/56. What is n in 2*n**4 - l*n**2 - 10/7*n**3 + 0 + 0*n = 0?
-2/7, 0, 1
Let 0 + 0*g**2 + 3/5*g - 3/5*g**3 = 0. What is g?
-1, 0, 1
Let i(g) = 9*g**4 - 18*g**3 + 5*g**2 + 4*g + 2. Let a(j) = -18*j**4 + 37*j**3 - 10*j**2 - 9*j - 5. Let o(w) = 2*a(w) + 5*i(w). Find z such that o(z) = 0.
-2/9, 0, 1
Let n(i) be the first derivative of -i**4/4 - 2*i**3/3 - i**2/2 + 1. Factor n(o).
-o*(o + 1)**2
Let s(x) = x**3 - 2*x**2 - 9*x + 6. Let q be s(4). Factor -14*z - 4*z**2 + 4 + 9*z - q*z**3 + 7*z.
-2*(z - 1)*(z + 1)*(z + 2)
Suppose -2*l + 8 = -3*m + 4*m, 2*m + l = 7. Let j be (1 - (0 + -