32. Determine r, given that -14*r**5 + p*r**5 + 2*r**4 + r**4 = 0.
0, 1
Let u be ((-12)/(-8))/(3/4). Let y = 972 - 969. Factor 9/7*j + 3/7*j**y - 3/7 - 9/7*j**u.
3*(j - 1)**3/7
Let x(r) be the first derivative of r**6/39 - r**4/13 + r**2/13 - 58. Factor x(n).
2*n*(n - 1)**2*(n + 1)**2/13
Let i(x) = -41*x - 246. Let b be i(-6). Let t(f) be the second derivative of -5*f + b + 0*f**3 - 1/8*f**4 + 0*f**2 - 3/20*f**5. Factor t(v).
-3*v**2*(2*v + 1)/2
Let b(v) be the second derivative of -v**5/16 - v**4/3 + 2*v**3/3 + 442*v. Let b(c) = 0. What is c?
-4, 0, 4/5
Let x(c) be the third derivative of -c**9/272160 - c**8/12960 - c**7/3780 + 7*c**5/20 + 10*c**2. Let y(d) be the third derivative of x(d). Factor y(p).
-2*p*(p + 1)*(p + 6)/9
Suppose 0 + 16 = 2*u. Let 8*c**4 - 28*c**5 + 28*c**3 + 80*c - 80*c - u*c**2 = 0. What is c?
-1, 0, 2/7, 1
Let h(c) = c**2 + 20*c + 19. Let p(j) = j**2 + 10*j + 9. Suppose 13 = 2*d - 9. Let k(b) = d*p(b) - 6*h(b). Find o, given that k(o) = 0.
-1, 3
Let a(s) = 110*s**3 - 30*s**2 - 5*s - 5. Let r(t) = t**2 + t - 1. Suppose -6*w + 3*w = -2*l - 5, 0 = -4*w + 20. Let n(c) = l*r(c) - a(c). Factor n(b).
-5*b*(2*b - 1)*(11*b + 2)
Let m = 6710 + -6707. Determine y, given that -1/2*y**5 + 0*y - 1/2*y**2 + 0 - 3/2*y**4 - 3/2*y**m = 0.
-1, 0
Solve 7*t**2 - 3*t**4 - 26*t**3 - 9*t**3 - 2*t**2 - 2*t**2 - 7*t**3 + 42*t = 0 for t.
-14, -1, 0, 1
Let i(j) be the second derivative of -j**5/4 + 13*j**4/6 - 7*j**3/2 - 18*j**2 - 267*j. Factor i(z).
-(z - 3)**2*(5*z + 4)
Let n(y) be the second derivative of 0*y**2 + 0 - 8/45*y**3 + 40*y + 1/90*y**4. Factor n(f).
2*f*(f - 8)/15
Let f(m) be the third derivative of -1/8*m**4 + 0*m - 12*m**2 + 2 + 1/60*m**5 + 1/3*m**3. Solve f(c) = 0.
1, 2
Let n(p) be the second derivative of 11*p - 9/2*p**2 - p**3 + 0 + 1/4*p**4. Factor n(c).
3*(c - 3)*(c + 1)
Let p(t) be the third derivative of 0*t + 0 - 4*t**2 - 1/12*t**5 - 7/24*t**4 + t**3. Solve p(r) = 0 for r.
-2, 3/5
Let n be 3/1 - (-6 + 6). Let f(p) = -2*p**2 + 8*p + 4. Let b be f(4). Factor 4*g - 91 - g**b - g**3 + 89 + 3*g**2 - n*g.
-(g - 1)**2*(g + 1)*(g + 2)
What is w in -6*w**2 + 20*w**2 - 5*w**3 + 80*w + 30 + 21*w**2 + 0*w**2 - 5*w**4 - 15*w = 0?
-2, -1, 3
Suppose -30 = -2*q - 4*u, 36*q - 40*q - 6 = -3*u. Find p, given that 8/7 + 2/7*p**2 + 16/7*p - 6/7*p**q = 0.
-1, -2/3, 2
Factor -9/5*b - 1/5*b**3 + 0 + 6/5*b**2.
-b*(b - 3)**2/5
Let c(j) = -j**4 + 11*j**3 - 11*j. Let v(x) be the first derivative of -x**4/2 + x**2 - 35. Let y(f) = 4*c(f) + 22*v(f). Factor y(t).
-4*t**4
Let c(f) be the second derivative of f**6/75 + 3*f**5/25 - 4*f**4/15 - 2*f**3/5 + 7*f**2/5 + 46*f. Factor c(u).
2*(u - 1)**2*(u + 1)*(u + 7)/5
Let w = -18820/13 + 1448. Determine y, given that 0 + 2/13*y**3 - w*y - 2/13*y**2 = 0.
-1, 0, 2
Let y(w) = -39*w + 195. Let s be y(5). Let -4/7*o**2 + s*o + 2/7*o**4 + 2/7 + 0*o**3 = 0. What is o?
-1, 1
Let n(b) be the second derivative of -5*b**8/336 + b**7/42 + b**2/2 + 7*b. Let y(m) be the first derivative of n(m). Find o, given that y(o) = 0.
0, 1
Suppose -3*f = -6, -2*f + f - 51 = -c. Factor -4*q - c*q - 5*q**2 - 80 + 97*q.
-5*(q - 4)**2
Determine h so that 12/5*h**3 + 2*h**2 + 8/5 - 24/5*h = 0.
-2, 1/2, 2/3
Let s(a) be the second derivative of -3*a**5/40 - 3*a**4/2 + 192*a**2 + 53*a + 1. Find b such that s(b) = 0.
-8, 4
Let p(h) = -h**2 - 14*h + 18. Let o be p(-17). Let m be (22/o)/((-382)/375 + 1). Determine c so that 16/7 - m*c**3 + 300/7*c**2 - 120/7*c = 0.
2/5
Let c be (-7)/(-30) + (455/78 - 6). Let t(v) be the second derivative of -1/10*v**5 + 2*v - 1/63*v**7 + 0*v**3 + 0 + 0*v**2 + c*v**6 + 1/18*v**4. Factor t(j).
-2*j**2*(j - 1)**3/3
Suppose -86/7*u**3 + 10/7*u**5 + 74/7*u**2 + 4/7*u - 16/7 + 2*u**4 = 0. Calculate u.
-4, -2/5, 1
Let t(h) be the third derivative of -h**6/160 + h**5/16 - 3*h**4/16 + 230*h**2. Suppose t(w) = 0. What is w?
0, 2, 3
Let c be (-418)/(-66) - (-2)/(-6). Suppose -25*s**5 - 20*s**4 + 4*s + 24*s**3 + c*s**2 - 3*s**3 + 5*s**2 + 9*s**2 = 0. Calculate s.
-1, -2/5, 0, 1
Let v be 54/(-12) + 7 - 50/(-60). Suppose 8/3*b + 0 + v*b**5 + 16/3*b**4 - 16/3*b**2 - 6*b**3 = 0. What is b?
-2, -1, 0, 2/5, 1
Solve -54/5*o + 26/5 + 6*o**2 - 2/5*o**3 = 0 for o.
1, 13
Determine s, given that 12/7*s**2 - 4/7*s**4 - 10/7*s**3 + 2/7*s**5 + 0 + 0*s = 0.
-2, 0, 1, 3
Let l = -52 + 56. Find q, given that 5*q**3 - q**4 + 16*q + l*q - 9*q**2 - 2 - 13*q = 0.
1, 2
Suppose 4*s - 1 = l, 0 = l + s + 14 - 3. Let x = 12 + l. Find h, given that 2/9*h**4 - 2/9*h**2 + 0 - 2/9*h + 2/9*h**x = 0.
-1, 0, 1
Let l(r) be the first derivative of 2*r**5/45 - 5*r**4/9 + 8*r**3/9 + 8*r**2 + 754. Solve l(y) = 0.
-2, 0, 6
Determine o so that 13/4 - 1/4*o**2 + 3*o = 0.
-1, 13
Let f(c) be the first derivative of 0*c**2 + 0*c + 11 + 10/3*c**3 + 0*c**5 - 15/4*c**4 + 5/6*c**6. Let f(m) = 0. Calculate m.
-2, 0, 1
Let l(s) be the first derivative of s**6/15 + 7*s**5/10 + 11*s**4/6 + 5*s**3/3 + 36*s - 23. Let i(p) be the first derivative of l(p). Solve i(d) = 0 for d.
-5, -1, 0
Suppose 0 = -2*w + 7*w - 10. Let a = w + 0. Factor -a*x**2 - 28*x**4 + 0*x**2 - 3*x**2 + x**2 + 20*x**3 + 12*x**5.
4*x**2*(x - 1)**2*(3*x - 1)
Let p = 22 - 20. Let 2*z**p - 6*z + 2*z**2 - 8 + 4*z - 2*z = 0. Calculate z.
-1, 2
Let r(p) = p**3 - 3*p**2 - 7*p - 3. Let g be r(5). Factor -3*s**3 - 4*s + 19*s**2 - 13*s**2 + g + 7*s**3 - 18*s**2.
4*(s - 3)*(s - 1)*(s + 1)
Let z be (-12)/(-9)*15/5. Factor -8*x**2 + x**z - 3*x**4 + 4*x**3 + 6*x**2.
-2*x**2*(x - 1)**2
Let h(m) be the second derivative of 4/3*m**3 - 6*m**2 + 0 - 4*m + 1/3*m**4. Factor h(o).
4*(o - 1)*(o + 3)
Let u(p) be the third derivative of -p**8/2520 - 2*p**7/525 - 7*p**6/450 - 8*p**5/225 - p**4/20 - 2*p**3/45 + 30*p**2. Solve u(t) = 0 for t.
-2, -1
Suppose 3568*q = 1773*q + 1780*q. Factor 0 + 2/19*w**3 - 2/19*w**2 + q*w.
2*w**2*(w - 1)/19
Let t = 34 - 24. What is b in t + 2 + 15*b**2 + 24*b + 3*b**3 + 0*b**3 = 0?
-2, -1
Let y(i) = 7*i**2 - 30*i + 18. Let b(m) = 11*m**2 - 46*m + 27. Let w(x) = -5*b(x) + 8*y(x). Factor w(v).
(v - 9)*(v - 1)
Suppose -2*t = r + 9, 4*r + 5*t = 57 - 75. Determine l, given that 0*l**2 + 0*l + 4/3*l**5 + 0 - 8/3*l**4 + 0*l**r = 0.
0, 2
Suppose 4*r + 5*k = -r - 40, -28 = r + 5*k. Let l(o) = -6*o - 14. Let n be l(r). Solve 2/5*j**5 - 8/5*j**2 - 8/5*j**n + 0 + 2/5*j + 12/5*j**3 = 0 for j.
0, 1
Suppose -6/5*y + 2/5*y**5 + 4/5*y**3 + 8/5*y**2 + 0 - 8/5*y**4 = 0. Calculate y.
-1, 0, 1, 3
Let s(q) be the second derivative of 7/36*q**4 + 0*q**3 + 2*q + 1/60*q**5 + 0*q**2 - 14. Let s(b) = 0. What is b?
-7, 0
Let 48/5 - 3/5*a**4 + 51/5*a**3 - 9*a**2 - 51/5*a = 0. Calculate a.
-1, 1, 16
Let l(g) be the third derivative of g**7/1365 + g**6/390 + g**5/390 + 27*g**2 + 3. Factor l(x).
2*x**2*(x + 1)**2/13
Let d be (8/10)/((-34)/(-170)). Let b(i) be the second derivative of 0*i**2 + 0 + 1/70*i**6 + 1/14*i**3 - 8*i + 3/28*i**d + 9/140*i**5. Factor b(f).
3*f*(f + 1)**3/7
Let x(b) be the first derivative of 7*b**3/24 + 11*b**2/16 + b/2 + 68. Factor x(u).
(u + 1)*(7*u + 4)/8
Let x(q) be the first derivative of -3*q**4 + 244*q**3/3 + 84*q**2 - 153. Find o, given that x(o) = 0.
-2/3, 0, 21
Let q(a) be the first derivative of 0*a**2 + 3/14*a**4 - 4/21*a**3 - 2/35*a**5 + 0*a - 6. What is j in q(j) = 0?
0, 1, 2
Let z(b) = b**3 + 10*b**2 - b - 6. Let s be z(-10). Suppose 0 = 3*w - s*h - 2, 3 = 3*w - 2*h - h. Find f such that 1/5*f**w - 3/5 - 2/5*f = 0.
-1, 3
Suppose 9 + 11 = 4*t. Let d = -18732 - -18732. Factor -10/9*o**4 + 0 + d*o - 16/9*o**3 - 2/9*o**t - 8/9*o**2.
-2*o**2*(o + 1)*(o + 2)**2/9
Let j(b) be the second derivative of b**5/360 + b**4/72 + 7*b**2/2 + 2*b. Let v(h) be the first derivative of j(h). Factor v(z).
z*(z + 2)/6
Solve -4/19*j - 2/19*j**4 + 6/19*j**2 + 0*j**3 + 0 = 0 for j.
-2, 0, 1
Let z(d) be the first derivative of -7*d**3 + 4*d**3 - 7*d**3 - 5*d**2 - d**5 + 15*d**3 + 18. Determine o, given that z(o) = 0.
-2, 0, 1
Suppose 5 = -y + 2*y. Let x(t) = -5*t**4 + 10*t**3 + 4. Let s(b) = -5*b**4 + 10*b**3 + 5. Let n(f) = y*x(f) - 4*s(f). Find q such that n(q) = 0.
0, 2
Let d(a) = 113*a - 678. Let j be d(6). Suppose j*h**3 + 2/3*h + 0 - h**2 + 1/3*h**4 = 0. Calculate h.
-2, 0, 1
Let s(n) be the first derivative of -n**3/3 - 13*n**2/2 - 9*n - 4. Let z be s(-12). Factor 11*q + 4*q**4 + 8*q**z + 3*q**2 - 11*q + q**2.
4*q*