- -2. Find o, given that 7*o**2 + 8 + o**2 - 2*o**3 + o**3 - 12*o - v*o**2 = 0.
2
Let f(t) be the first derivative of 2*t**3/27 - 10*t**2 - 368*t/9 - 708. Factor f(x).
2*(x - 92)*(x + 2)/9
Let v = 6571 - 32711/5. Determine o, given that -6/5*o**4 + 48/5*o**3 - 132/5*o**2 - 54/5 + v*o = 0.
1, 3
Let r(b) = b**3 - 3*b**2 - 4*b + 3. Let c be r(4). Let a be 5 - (-3)/(-7 + 4). Factor a*z + 12/7 + 20/7*z**2 + 4/7*z**c.
4*(z + 1)**2*(z + 3)/7
Let q(a) be the first derivative of a**8/64 - 2*a**7/35 + a**6/40 - 15*a**2/2 - 1. Let l(r) be the second derivative of q(r). Factor l(b).
3*b**3*(b - 2)*(7*b - 2)/4
Determine l, given that -49*l**5 - 10 + 15*l - 23*l**5 + 10*l**2 + 77*l**5 - 20*l**3 = 0.
-2, -1, 1
Let y(u) be the second derivative of 49*u**6/120 - 7*u**5/6 - 13*u**4/6 - 4*u**3/3 + 9*u**2/2 - 13*u. Let n(t) be the first derivative of y(t). Factor n(z).
(z - 2)*(7*z + 2)**2
Let h(i) = 2*i**3 + i. Let c be h(1). Let f(v) = 4*v**3 + 68*v**2 + 80*v. Let p(k) = k**3 + 23*k**2 + 27*k. Let s(l) = c*f(l) - 8*p(l). Factor s(n).
4*n*(n + 2)*(n + 3)
Suppose -32*z + 4340 - 468 = 0. Let k = -353/3 + z. Factor -6*f**3 - 2/3*f**5 + k*f**4 - 4/3*f + 14/3*f**2 + 0.
-2*f*(f - 2)*(f - 1)**3/3
Let r be -1 + 3 - (3 + -5). Suppose -5*a = 3*n - 71, -r*a + n = -0*a - 67. Solve -2*u**2 - u**2 - 14*u + a*u + 2*u**3 - u**2 = 0 for u.
0, 1
Determine x so that -2/5*x**2 + 4*x + 0 = 0.
0, 10
Let 0 - 1/3*w**4 - 8/3*w - 2*w**3 - 4*w**2 = 0. What is w?
-2, 0
Let r(a) = -a**3 - a**2 - 2*a - 2. Let j(c) = -4*c**3 - 340*c**2 - 16*c - 16. Let q(o) = j(o) - 8*r(o). Find f, given that q(f) = 0.
0, 83
Determine s so that -86/7*s**3 - 330/7*s**2 + 125/7 + 13/7*s**4 + 275/7*s + 3/7*s**5 = 0.
-5, -1/3, 1, 5
Let j(r) be the first derivative of 9*r**4/2 + r**3 - 9*r**2 - 3*r - 46. What is d in j(d) = 0?
-1, -1/6, 1
Let k(a) be the third derivative of 19*a**5/100 + 17*a**4/40 - a**3/5 - 379*a**2. Factor k(t).
3*(t + 1)*(19*t - 2)/5
Let z(n) be the second derivative of 7/4*n**5 + 10/9*n**3 + 0*n**2 + 0 + 1/2*n**6 + 20/9*n**4 - 19*n. What is c in z(c) = 0?
-1, -2/3, 0
Let q(v) = -v**2. Let o(y) = 7*y**2 - 2*y + 1. Suppose 2*a + 14 = -3*h, 3 + 1 = -h - a. Let f(g) = h*q(g) - o(g). Find w, given that f(w) = 0.
1
Solve 15/7*v**3 + v**4 - 16/7*v + 5/7*v**2 + 1/7*v**5 - 12/7 = 0.
-3, -2, -1, 1
Factor 19*s**2 + 15 + 35*s + 5*s**3 + 3*s**2 - 4*s**2 + 7*s**2.
5*(s + 1)**2*(s + 3)
Let l(k) be the third derivative of 61*k**6/160 - 3*k**5/160 + 554*k**2. Factor l(x).
3*x**2*(122*x - 3)/8
Let y(q) be the second derivative of q**5/80 - 7*q**4/16 - 15*q**3/8 - 23*q**2/8 - 455*q. Let y(t) = 0. Calculate t.
-1, 23
Suppose -4*m + 12 = -4*v - 4, -v = 3*m - 32. Suppose 2*h**2 + 2*h**3 + 6 + 5*h - m*h - 6*h = 0. What is h?
-3, 1
Factor 1/3*z**3 + 13/3*z**2 + 12 + 40/3*z.
(z + 2)**2*(z + 9)/3
Let q(u) be the first derivative of 0*u**3 + 0*u**4 + 5 + 0*u + 5*u**2 + 1/420*u**6 - 1/70*u**5. Let p(i) be the second derivative of q(i). Factor p(j).
2*j**2*(j - 3)/7
Let x = -55 - -57. Let -3*u**x + u**3 - 5*u**2 - 21*u - 9 - 7*u**2 - 4*u**3 = 0. What is u?
-3, -1
Let p(l) be the third derivative of -l**2 + 0 + 1/75*l**5 + 1/12*l**4 - 1/5*l**3 - 46*l. Solve p(k) = 0 for k.
-3, 1/2
Suppose 0 = -23*p + 5*p. Let y(v) be the first derivative of -1/6*v**4 + p*v + 1/9*v**6 + 2/9*v**3 + 2 + 0*v**2 - 2/15*v**5. Factor y(t).
2*t**2*(t - 1)**2*(t + 1)/3
Let t(j) be the third derivative of 0*j**4 - 8/21*j**7 + 0 + 0*j - 5/48*j**8 + 17*j**2 + 0*j**3 + 0*j**5 - 1/6*j**6. Factor t(o).
-5*o**3*(o + 2)*(7*o + 2)
Suppose 3*k = o - 15, 2*o - k - 2 = 3. Let b be 1*(1 - 2)*o - -3. Suppose 4/5 - 2/5*i**2 - 6/5*i - 2/5*i**4 + 6/5*i**b = 0. Calculate i.
-1, 1, 2
Let i be ((-18)/(-4))/3*(-144)/(-108). Suppose 2*s + l = 6, -2*s - 3*s = -i*l - 6. Factor 0 - 2/9*m - 8/9*m**s - 4/3*m**3 - 2/9*m**5 - 8/9*m**4.
-2*m*(m + 1)**4/9
Let m be (-184)/(-4)*(-18)/12. Let r = m - -70. Find p, given that 1/3*p**2 + r - 4/3*p = 0.
1, 3
Let o(v) = 11*v**2 - 14*v**3 + 21*v**2 - 4 + 741*v - 733*v. Let d(k) = 71*k**3 - 159*k**2 - 40*k + 19. Let u(q) = 4*d(q) + 22*o(q). Factor u(s).
-4*(s - 3)*(2*s + 1)*(3*s - 1)
Let u(a) be the first derivative of -2*a**3/9 + a**2/3 - 222. Factor u(g).
-2*g*(g - 1)/3
Let k(q) = -10*q - 8. Suppose u + 3*v + 13 = 0, 5*v - 8 = 7*v. Let f be k(u). Factor -1/3*z**f + 0 + 1/6*z + 1/6*z**3.
z*(z - 1)**2/6
Let x(o) = -51*o**4 - 183*o**3 - 195*o**2 - 21*o - 10. Let a(p) = -52*p**4 - 182*p**3 - 194*p**2 - 22*p - 12. Let c(h) = 5*a(h) - 6*x(h). Solve c(m) = 0.
-2, -2/23, 0
Let i(d) be the second derivative of -d**4/3 + 10*d**3 + 410*d. Suppose i(q) = 0. Calculate q.
0, 15
Let t be (700/7875)/(2/320). Let 2*n**4 - 32/3*n**3 + 176/9*n**2 - t*n + 32/9 = 0. What is n?
2/3, 2
Let f(m) be the first derivative of -2/3*m + 1/6*m**2 + 5 + 1/9*m**3. What is x in f(x) = 0?
-2, 1
Suppose 0 = 27*o - 106 + 25. Determine k so that -18/5*k**2 + 3/5*k**o - 6/5 + 6/5*k**4 - 21/5*k = 0.
-1, -1/2, 2
Suppose -3*a + 97 = -4*q, -2*a + 2*q = 32 - 94. Let l = a + -23. Let -8*y**3 + 0*y + 7*y**4 + l*y**5 + 8 + 4*y - 16*y**2 + y**4 = 0. Calculate y.
-2, -1, 1
Suppose 0 = -2*h + 8, -3*h = 3*o - 6*h. Let k(u) = -u + 9. Let l be k(o). Let -8*r**3 + 2*r**5 + r**5 + l*r**3 = 0. What is r?
-1, 0, 1
Let s(x) = -x + 1. Let u be s(-5). Suppose 5*t - u - 4 = 0. Determine j so that -8*j**3 + 4*j**t + 20 + 8*j - 6*j**4 + 0*j**2 - 18 = 0.
-1, -1/3, 1
Let g(h) be the third derivative of -h**8/392 + h**7/147 + h**6/60 - 3*h**5/70 - h**4/21 + 4*h**3/21 - 141*h**2. Solve g(y) = 0.
-1, 2/3, 1, 2
Let d = -32 + 35. Factor -4*w**d - 12*w + 7 + 9 - 12 + 12*w**2.
-4*(w - 1)**3
Let q(a) be the first derivative of -a**4 - 32*a**3/3 - 34*a**2 - 40*a + 123. Suppose q(o) = 0. What is o?
-5, -2, -1
Let l(w) be the third derivative of -w**6/60 + w**5/10 - w**4/6 + 32*w**2. Factor l(h).
-2*h*(h - 2)*(h - 1)
Let p be 4 - 3 - -2 - 1. Factor -3*z**2 + z**2 + 2*z + 2*z**2 + 2*z**p.
2*z*(z + 1)
Let y(t) = -t**3 + 10*t**2 + 14*t - 31. Let m be y(11). Let b be 62/36 - 9/12*m. Factor -b*c**2 + 0 + 0*c - 2/9*c**4 - 4/9*c**3.
-2*c**2*(c + 1)**2/9
Let i(r) be the first derivative of 1/24*r**4 + 4 - 1/12*r**2 + 1/30*r**5 + 0*r - 1/18*r**3. Determine k, given that i(k) = 0.
-1, 0, 1
Suppose 303*s - 307*s + 12 = 0. Let a(d) be the second derivative of -1/9*d**s + 1/36*d**4 + 1/6*d**2 - 5*d + 0. What is x in a(x) = 0?
1
Suppose -2*z = -z - 14. Let g be (2 - z/(-10)) + 12/(-30). Solve -4/13*d**g + 4/13*d - 2/13*d**4 + 2/13 + 0*d**2 = 0.
-1, 1
Let a(n) be the first derivative of 10/21*n**3 + 8/7*n**2 + 8/7*n - 5 + 1/14*n**4. Factor a(b).
2*(b + 1)*(b + 2)**2/7
Let b(c) be the first derivative of c**6/120 + c**5/80 - c**4/48 - c**3/24 - 12*c - 10. Let u(w) be the first derivative of b(w). Solve u(y) = 0 for y.
-1, 0, 1
Let r(w) be the second derivative of -1/14*w**2 + 0 + 1/140*w**5 + 1/84*w**4 + 19*w - 1/42*w**3. Factor r(m).
(m - 1)*(m + 1)**2/7
Let w = 9/46 + -31/276. Let y(n) be the second derivative of 0 - 1/40*n**5 - 1/12*n**4 + 0*n**2 - w*n**3 - n. What is v in y(v) = 0?
-1, 0
Let i(a) be the third derivative of -a**7/210 - 11*a**6/120 - a**5/30 + 23*a**4/6 + 20*a**3 - 349*a**2. What is g in i(g) = 0?
-10, -2, 3
Let h(b) be the first derivative of b**4/24 - b**3/6 + b**2/4 - 10*b - 14. Let p(c) be the first derivative of h(c). Solve p(n) = 0.
1
Let p(b) = -32*b**2 - 120*b + 253. Let r(n) = -13*n**2 - 60*n + 126. Let v(o) = -2*p(o) + 5*r(o). Factor v(u).
-(u - 2)*(u + 62)
Determine i so that 70/3*i**2 + 10/3*i**5 - 55/3*i**3 - 40/3 + 20*i - 5*i**4 = 0.
-2, -1, 1/2, 2
Let n be 1/((12/16)/3). Suppose -2*p + n = -p. Solve 4*m**4 - 7*m**p - m + 2*m**3 - m**3 + 4*m**2 - m**4 = 0.
-1, 0, 1/4, 1
Let g(i) be the first derivative of 4*i**6 - 52*i**5/5 + 7*i**4 + 4*i**3/3 - 2*i**2 + 55. Determine y, given that g(y) = 0.
-1/3, 0, 1/2, 1
Suppose -3*t - 62 = 6*s - s, 2*s - 5*t + 31 = 0. Let c = s + 13. Factor -4/9*u + c + 2/9*u**2.
2*u*(u - 2)/9
Let d(o) be the second derivative of 1/66*o**4 - 2/11*o**3 + 0 + 8/11*o**2 - 26*o. Factor d(m).
2*(m - 4)*(m - 2)/11
Suppose -b - 2*b = -4*x + 9, 2*b = 2*x - 4. Determine t so that -16*t - 49*t**x - 22 - 4*t**4 + 6 + 12*t**2 + 57*t**3 = 0.
-1, 2
Let z(c) be the third derivative of c**6/24 - 7*c**5/12 + 35*c**4/24 + 25*c**3/2 + 815*c**2. Solve z(w) = 0 for w.
-1, 3, 5
Let o(d) be