*r**5/4 + 47*r**4/8 + 8*r**3 - 18*r**2. Find w such that n(w) = 0.
-1, 16
Suppose 0 = 7*p - 11 - 17. Factor -p*b**2 - 19*b + 8*b + 4 + 6*b - b**3 - 6.
-(b + 1)**2*(b + 2)
Let m be -12 + 18 + -9 - (-18)/4. Let m*n - 1/2*n**2 + 0 = 0. Calculate n.
0, 3
Factor -12*q**3 + 11/2*q**4 + 0 - q + 15/2*q**2.
q*(q - 1)**2*(11*q - 2)/2
Determine i, given that -1/4*i**4 + 2*i - 11/4*i**2 - 2*i**3 + 3 = 0.
-6, -2, -1, 1
Suppose 2*p = 4*p - 68. Suppose 3 = 3*i, 0*i = 5*d - i - p. Find z such that -10*z + 2 + z + 2*z**4 + 15*z**2 - 4*z**3 + z**4 - d*z**3 = 0.
2/3, 1
Let u be 55/11*(-76)/(-95). Factor 2/3*m**5 + 0*m + 0 - 2/3*m**2 - 2/3*m**3 + 2/3*m**u.
2*m**2*(m - 1)*(m + 1)**2/3
Suppose 0 = 10*d + 3*d - 26. Let k(g) be the second derivative of 0 + 1/4*g**3 + 9/8*g**d + 1/48*g**4 + 4*g. Find w, given that k(w) = 0.
-3
Let y = 30 + -27. Let k(i) be the second derivative of 0 - 1/2*i**y - 9/20*i**5 + 0*i**2 - 2*i + 3/4*i**4 + 1/10*i**6. Determine f so that k(f) = 0.
0, 1
Let j(u) = u**3 - 20*u**2 + 65*u - 13. Let w be j(16). Factor 784/11*x**w - 686/11*x**4 + 32/11 + 1008/11*x**2 + 320/11*x.
-2*(x - 2)*(7*x + 2)**3/11
Let v(t) be the second derivative of 0*t**2 + 0*t**3 + 13*t - 1/5*t**5 + 0*t**4 + 0. Factor v(w).
-4*w**3
Suppose 4*p = 10 + 10, p - 20 = -5*i. Let f(n) be the first derivative of -1/2*n**4 + 2/5*n**5 + 0*n + 2/9*n**i + 2 + 0*n**2 - 1/9*n**6. Factor f(l).
-2*l**2*(l - 1)**3/3
Let f(q) be the second derivative of q**7/21 - 9*q**5/10 + 2*q**4/3 + 4*q**3 + 213*q. Factor f(v).
2*v*(v - 2)**2*(v + 1)*(v + 3)
Let u(r) be the first derivative of r**4/18 - 2*r**3 - 28*r**2/9 + 379. Find s, given that u(s) = 0.
-1, 0, 28
Let z(d) be the second derivative of -d**5/45 + 15*d**2/2 + 20*d. Let k(n) be the first derivative of z(n). Let k(w) = 0. Calculate w.
0
Suppose -t = -3, 5*j + 3*t - 7*t = -112. Let p = j + 24. Factor 3*x**2 - p*x**2 - 3*x + 5*x + 3*x**2.
2*x*(x + 1)
Let n(m) = 2*m**2 + 4*m + 4. Let z be n(-2). Suppose 3*l = z*l. Suppose l*t**2 + 5*t**2 - t**2 - 8*t + 4 = 0. Calculate t.
1
Let -18/13*b**3 + 0 + 12/13*b**2 - 2/13*b = 0. What is b?
0, 1/3
Determine m so that 16/7*m**2 - 52/7*m**3 + 0 - 18/7*m**5 - 86/7*m**4 + 0*m = 0.
-4, -1, 0, 2/9
Factor 160*h - 158*h + 5239 + 25*h**2 + 532*h + 306*h - 2179 - 5*h**3.
-5*(h - 17)*(h + 6)**2
Solve 38/7*k + 40/7*k**2 + 0 + 2/7*k**3 = 0 for k.
-19, -1, 0
Suppose 3*o + 4*j = -6, -o - 2*o - 2*j = 0. What is s in -6*s - 3*s**2 + 3*s**2 + 5*s**o - 24*s = 0?
0, 6
Let l(t) = -3*t**2 - 12*t + 38. Let r be l(-6). Find f such that 1/3*f + 1/6*f**r + 1/6 = 0.
-1
Let m(g) = -4*g**4 + 32*g**3 + 80*g**2 + 84*g + 28. Let v(l) = -l**5 - 5*l**4 + 30*l**3 + 80*l**2 + 82*l + 27. Let k(r) = 3*m(r) - 4*v(r). Factor k(a).
4*(a - 3)*(a + 1)**3*(a + 2)
Let o(d) be the third derivative of d**7/210 + 7*d**6/40 - 2*d**5/5 - 11*d**4/6 - 563*d**2. Factor o(q).
q*(q - 2)*(q + 1)*(q + 22)
Let t be (-44 - -45) + 8/(-10). Factor 1/5*f**2 + 0 - t*f.
f*(f - 1)/5
Let g(q) = -q**2 - 11*q - 8. Let u be g(-10). Factor 7 + 80*k**2 - 45*k - 70*k**3 + 1 + 30*k**4 - 5*k**5 + u.
-5*(k - 2)*(k - 1)**4
Determine f so that 198*f - 25*f**2 - 20*f**2 - 38*f + 46*f**2 + 6400 = 0.
-80
Let f(d) be the third derivative of d**9/12096 + d**8/3360 - d**6/720 - d**5/480 + d**3/2 - 2*d**2. Let k(m) be the first derivative of f(m). Factor k(n).
n*(n - 1)*(n + 1)**3/4
Let r(s) = -s**3 - 7*s**2 - 5*s + 6. Let x(a) = a**2 + 8*a + 6. Let c be x(-6). Let p be r(c). Factor p*m**2 - m**2 + 3*m**3 - 2*m**2.
3*m**2*(m - 1)
Let x(v) be the second derivative of v**7/5040 + v**6/360 - 4*v**4/3 + 24*v. Let a(r) be the third derivative of x(r). Solve a(l) = 0 for l.
-4, 0
Let r(i) = 10*i**4 + 4*i**3 + 6*i**2 - 70*i - 82. Let o(m) = 22*m**4 + 7*m**3 + 11*m**2 - 141*m - 167. Let c(b) = 6*o(b) - 13*r(b). Let c(u) = 0. Calculate u.
-2, -1, 4
Let g = 6/917 + -2683/550200. Let q(c) be the third derivative of 0*c + c**2 - 1/10*c**4 - g*c**6 - 4/15*c**3 + 0 - 1/50*c**5. Factor q(j).
-(j + 2)**3/5
Suppose 0 = 3*h + 2*b - 188, 3*h = -h - 5*b + 260. Let x be 4/2*25/h. Let 1/3*d + 1/6*d**4 + x*d**2 + 0 + 2/3*d**3 = 0. Calculate d.
-2, -1, 0
Let t(h) be the third derivative of -h**9/756 + h**8/105 - 8*h**6/45 + 8*h**5/15 + 3*h**3/2 - 3*h**2. Let p(o) be the first derivative of t(o). Factor p(k).
-4*k*(k - 2)**3*(k + 2)
Suppose 3*m + 3010 = 3082. Let u = -2 + 6. Factor -24*i + 48 - 14*i**4 - 43*i**2 + m*i**3 + 11*i**u - 2*i**2.
-3*(i - 4)**2*(i - 1)*(i + 1)
Let v(r) = -3*r**4 - 65*r**3 - 137*r**2 - 67*r + 2. Let s(j) = 5*j**4 + 64*j**3 + 137*j**2 + 66*j - 3. Let w(h) = -2*s(h) - 3*v(h). Solve w(c) = 0 for c.
-1, 0, 69
Factor -6 - 14*d - 30*d**2 - 6 + 26*d**2.
-2*(d + 2)*(2*d + 3)
Let a = 98828099/414 - 238715. Let f = a + 1/138. Solve 0 + 0*z + f*z**2 + 0*z**3 - 2/9*z**4 = 0.
-1, 0, 1
Let t be (-1 + 1)*((-88)/16 + -6 + 11). Find j such that 0*j + 1/2*j**3 + t - 2*j**2 = 0.
0, 4
Let n be 9/1 - (7 - 11/11). Determine t, given that 0 + 0*t - 2/17*t**4 + 0*t**n + 2/17*t**2 = 0.
-1, 0, 1
Let w(s) = s**2 - 20*s + 41. Let f be w(18). Let t(j) be the third derivative of 5/8*j**4 + 25/24*j**6 - j**2 + 1/6*j**3 + 5/4*j**f + 0*j + 0. Factor t(n).
(5*n + 1)**3
Let j = 62185/11 + -5651. Suppose -16/11*f**2 + 0 - j*f + 2/11*f**3 + 2/11*f**4 = 0. What is f?
-2, 0, 3
Factor 16/9*r - 10/9*r**4 - 2/9*r**5 + 8/9*r**2 - 4/3*r**3 + 0.
-2*r*(r - 1)*(r + 2)**3/9
Determine l so that -66/5*l + 2/5*l**3 + 54/5 + 2*l**2 = 0.
-9, 1, 3
Suppose -8*z + 113*a = 109*a - 12, -5*z + 5 = -5*a. What is o in -12/7 - 4/7*o**z - 16/7*o = 0?
-3, -1
Let x be 0*(22 + -9)/(-26). Suppose 1/8*h**3 + x*h**2 - 1/2*h + 0 = 0. Calculate h.
-2, 0, 2
Let k(d) = -6*d**3 - d**2 + 1. Let c be k(1). Let y be (-14)/c + (-4)/(-6). Factor 0*x**y - 20*x + 4*x**3 + 19*x**2 - 13*x**2 - 2*x**2 + 12.
4*(x - 1)**2*(x + 3)
Let k(s) be the first derivative of 2*s**5/15 - s**4/24 - 8*s**3/9 + s**2/3 - 29. Factor k(x).
x*(x - 2)*(x + 2)*(4*x - 1)/6
Factor 14/23*p**3 + 2/23*p**5 + 0*p + 16/23*p**4 + 0 + 0*p**2.
2*p**3*(p + 1)*(p + 7)/23
Let c(j) be the first derivative of -j**9/22680 + j**8/4200 - j**7/3150 + 16*j**3/3 + 26. Let g(n) be the third derivative of c(n). Factor g(a).
-2*a**3*(a - 2)*(a - 1)/15
Suppose 4*k - 4 = 3*w + w, 0 = k + 2*w - 4. Let l(n) be the first derivative of -81/5*n - 18/5*n**3 - 1/25*n**5 + 1 + 54/5*n**k + 3/5*n**4. Solve l(j) = 0.
3
Let d(n) be the first derivative of 2*n**3/3 + 109*n**2 + 216*n - 684. Suppose d(j) = 0. Calculate j.
-108, -1
Let y(z) = -2*z**2 - 63*z - 24. Let p(o) = -5*o**2 - 123*o - 48. Let q(r) = 4*p(r) - 7*y(r). Find a, given that q(a) = 0.
-8, -1/2
Let p(i) be the second derivative of i**8/33600 + i**7/4200 - 7*i**4/6 + 8*i. Let q(z) be the third derivative of p(z). Factor q(c).
c**2*(c + 3)/5
Let q(c) = 6*c**5 - 3*c**4 - 5*c**3 + 4*c**2 + 5. Let o(x) = -x**5 + x**3 - 1. Let r(u) = -20*o(u) - 4*q(u). Factor r(y).
-4*y**2*(y - 2)**2*(y + 1)
Let y(q) be the first derivative of 3*q**5/5 + 99*q**4/2 + 1153*q**3 + 3168*q**2 + 3072*q - 6. Determine f, given that y(f) = 0.
-32, -1
Let h(j) = -3*j**3 - j - 2. Suppose 28 = -35*b - 7. Let x be h(b). Let 25/7*y**x + 1/7 - 10/7*y = 0. What is y?
1/5
Let i(t) be the third derivative of -t**5/15 - 28*t**4/3 - 137*t**2. Find a, given that i(a) = 0.
-56, 0
Suppose -90*s = 27*s. Factor -1/3*h + 0*h**2 - 1/3*h**5 + 2/3*h**3 + 0 + s*h**4.
-h*(h - 1)**2*(h + 1)**2/3
Find j such that -1/3*j**2 + 7/3 - 2*j = 0.
-7, 1
What is t in 3*t**3 + 0*t**2 + 0*t + 4*t**4 - 3/4*t**5 + 0 = 0?
-2/3, 0, 6
Let g(b) be the first derivative of 0*b + 2 + 3*b**3 + 1/2700*b**6 + 0*b**4 + 0*b**2 + 1/900*b**5. Let h(m) be the third derivative of g(m). Factor h(u).
2*u*(u + 1)/15
Let x be (0/4)/(-8 + 5). Let a(s) be the second derivative of 2/3*s**3 + x*s**5 + 0 + s + 0*s**2 - 1/15*s**6 + 1/2*s**4. Solve a(h) = 0.
-1, 0, 2
Let s(k) be the third derivative of -5/8*k**4 + 5/3*k**3 - 1/12*k**5 + 0*k + 1/8*k**6 + 0 + 8*k**2 - 1/42*k**7. Solve s(o) = 0.
-1, 1, 2
Let w(f) be the second derivative of f**7/30 + 8*f**6/45 - 17*f**5/30 - f**4 + 41*f**3/6 - 45*f. Let d(o) be the second derivative of w(o). Factor d(s).
4*(s - 1)*(s + 3)*(7*s + 2)
Suppose -3/2*p**2 + 33 + 27/2*p = 0. What is p?
-2, 11
Let w(i) = 7*i**4 - 26*i**3 + 93*i**2 - 125*i + 64. Let v(y) = 8*y**4 - 24*y**3 + 92*y**2 - 124*y + 64. Let j(b) = -3