 - 2*t, 4*r = 2*t. Let n(p) be the first derivative of 4/35*p**5 + 0*p**3 + 2 + r*p + 0*p**2 - 1/7*p**4. Solve n(h) = 0 for h.
0, 1
Let g(u) = 179*u**4 - 917*u**3 + 1426*u**2 - 684*u - 24. Let j(v) = -v**4 - 2*v**3 - 2*v**2. Let s(n) = g(n) - 4*j(n). Find a such that s(a) = 0.
-2/61, 1, 2
Find v, given that -18680 + v**2 + 12*v + 0*v + 18652 = 0.
-14, 2
Let c be (4*18/(-135))/((-5)/3). Let t(l) be the first derivative of -2/15*l**6 + 4 - 8/15*l**3 + c*l**5 + 0*l**4 + 0*l + 2/5*l**2. Find q, given that t(q) = 0.
-1, 0, 1
Suppose 9 = -2*s - 2*x + 13, s = 4*x + 2. Factor 8/3*k**4 + 32/3*k + 0 + 112/3*k**s - 62/3*k**3.
2*k*(k - 4)**2*(4*k + 1)/3
Let g(x) = x + 37. Let h be g(-17). Let b be (-2)/h*(-1)/(2/75). Factor -3/4*t**5 - 1/2*t + 0 - 11/4*t**4 - b*t**3 - 9/4*t**2.
-t*(t + 1)**3*(3*t + 2)/4
Let i be (-81)/(-90) - 33/(-55). Determine c, given that 1/6*c**2 - c + i = 0.
3
Let h = 115 + -115. Solve 1/2*w - 1/8*w**4 + 1/2*w**2 - 1/8*w**3 + h = 0.
-2, -1, 0, 2
Factor 0 - 2/5*a**3 - 8*a + 42/5*a**2.
-2*a*(a - 20)*(a - 1)/5
Let j(n) be the second derivative of 3*n**4/22 + 326*n**3/33 + 72*n**2/11 + 380*n. Factor j(v).
2*(v + 36)*(9*v + 2)/11
Let l be -5*10/75*2/(-60). Let c(v) be the third derivative of 0 + 0*v**4 - 1/45*v**7 - l*v**5 - 3*v**2 + 0*v + 1/20*v**6 + 0*v**3. Factor c(w).
-2*w**2*(w - 1)*(7*w - 2)/3
Let s = 73 + -69. Let y(r) be the first derivative of 0*r + 3/10*r**s + 7 - 1/5*r**6 - 4/15*r**3 + 4/25*r**5 + 0*r**2. Let y(u) = 0. Calculate u.
-1, 0, 2/3, 1
Let p = -19 + 18. Let a(r) = -8*r**4 + 4*r**2 - 2. Let f(t) = -t**4 - t**3 + t**2 + t - 1. Let h(k) = p*a(k) + 6*f(k). Factor h(o).
2*(o - 2)*(o - 1)**2*(o + 1)
Suppose -5 + 37 = 2*u. Let q(b) = -b + 19. Let c be q(u). Find m, given that -2*m - m**4 + 49*m**3 + 2*m**5 - 49*m**3 + 4*m**2 - c*m**4 = 0.
-1, 0, 1
Let r(i) be the first derivative of -4*i**5/5 - 4*i**4 - 4*i**3/3 + 12*i**2 + 483. Factor r(f).
-4*f*(f - 1)*(f + 2)*(f + 3)
Determine z so that 5123*z + 75187 - 175534 - 115965 - 57063 + 13102*z + 3*z**3 - 405*z**2 = 0.
45
Let u(v) be the first derivative of -2*v**3/15 - 2*v**2 - 48*v/5 - 46. Factor u(i).
-2*(i + 4)*(i + 6)/5
Let f(l) = -2*l**2 + 74*l - 572. Let y be f(11). Suppose y*d + 0 + 2/7*d**3 - 2/7*d**2 = 0. What is d?
0, 1
Solve -3*u**5 - u**5 - 66*u**4 + 36*u**3 + 56*u**2 + 54*u**4 - 12*u**4 = 0 for u.
-7, -1, 0, 2
Let y be 105/(-30) + 4 + 0. Factor y*q + 1/3 + 1/6*q**2.
(q + 1)*(q + 2)/6
Let i(y) be the second derivative of y**6/15 - 7*y**5/10 + 3*y**4 - 20*y**3/3 + 8*y**2 + 73*y. Factor i(m).
2*(m - 2)**3*(m - 1)
Let o be ((-189)/2205)/(2/(-10)). Factor -18/7*u - 27/7 - o*u**2.
-3*(u + 3)**2/7
Let o be ((-1)/(-4))/((-9)/(-36)). Let u = o - -2. Find v such that -70*v**4 + 78*v**u - 8*v + 16 - 16 = 0.
-2/7, 0, 2/5, 1
Suppose 5*r = 2*l + 3*l - 5, l = -r + 7. Suppose 5*d + l*j = j + 18, 2*d - 4 = 2*j. Suppose 0*i + 0 + 0*i**2 + 2/19*i**d = 0. Calculate i.
0
Let m(g) be the third derivative of 23*g**6/24 + g**5/6 - 115*g**4/24 - 5*g**3/3 - 112*g**2. Determine d, given that m(d) = 0.
-1, -2/23, 1
Let o be -2 + 32*(-2)/(-4). Let y = -10 + o. Factor 3*v - 3*v**5 - 6*v**y - 3*v + 3*v + 6*v**2.
-3*v*(v - 1)*(v + 1)**3
Let o be (-23)/(-4) + -2*5/(-40). Let b(x) = x**3 + 5*x**2 + 7*x + 3. Let z(p) = -2*p**3 - 6*p**2 - 6*p - 2. Let q(s) = o*b(s) + 5*z(s). Factor q(d).
-4*(d - 2)*(d + 1)**2
Let p(q) be the second derivative of q**6/180 - q**5/12 + q**3/2 + 19*q. Let y(k) be the second derivative of p(k). Factor y(z).
2*z*(z - 5)
Suppose 4*t + 17 = 29. Let o(n) be the third derivative of -n**2 + 0*n - 1/10*n**5 - 2/9*n**t + 0 - 11/36*n**4. Factor o(v).
-2*(v + 1)*(9*v + 2)/3
Let g(c) = c**2 - 6*c + 5. Let l be (12/16)/((-3)/(-16)). Let k(n) = n**2 - n. Let f(x) = l*k(x) + g(x). What is s in f(s) = 0?
1
Suppose 0 = 2*w + 8 - 16. Let v be 0 + 6*2/w. Factor 4/3*y**3 - 13/3*y - 6*y**2 + v*y**5 + 20/3*y**4 - 2/3.
(y - 1)*(y + 1)**3*(9*y + 2)/3
Let r(u) be the second derivative of u**5/30 + u**4/9 - 8*u**3/9 + 154*u. Let r(y) = 0. Calculate y.
-4, 0, 2
Suppose -5*l + 7*k - 2*k - 10 = 0, -2*l - 2*k = -4. Let y(a) be the first derivative of 0*a**2 + l*a - 2/3*a**3 + 9/4*a**4 - 2 - 7/5*a**5. Factor y(n).
-n**2*(n - 1)*(7*n - 2)
Let g(b) = -b**2 + 6*b - 5. Let i be g(4). Let w(u) = -u**3 + u + 2. Let q be w(0). Factor -3*h**5 - 4*h**q + 6*h**2 + i*h - 6*h**4 + 4*h**2.
-3*h*(h - 1)*(h + 1)**3
Find c, given that -2/9*c**3 + 8/3 + 14/9*c**2 - 32/9*c = 0.
2, 3
Let b be (-3 - -10) + 1 - -4. Suppose 0 = -3*v + 15 + b. Factor -o**3 + 11*o**3 + 2*o**2 + o - v*o**3.
o*(o + 1)**2
Let v be ((-141)/(-94))/(3/4). Solve 1 + g**v + 7/3*g - g**3 - 2/3*g**4 = 0.
-1, 3/2
Find y, given that -8 + 30 + 0*y**2 + 26*y - y**2 + 3*y**2 + 2 = 0.
-12, -1
Let -44*g + 4*g**3 + 0*g**4 + 0*g**4 - 36*g + 64 + 24*g**2 - 2*g**4 = 0. Calculate g.
-4, 2
Suppose 447*b - 3*b**2 + 6*b**3 - 3*b**2 - 462*b - 3*b**3 + 18 = 0. Calculate b.
-2, 1, 3
Let m = 27772 + -27768. Factor 0 + 0*l + 1/2*l**5 + 16*l**3 - 16*l**2 - 5*l**m.
l**2*(l - 4)**2*(l - 2)/2
Let z = -106 + 123. Suppose -3*q + z = j, -3*j + 18 = 3*q - 9. Factor -4/5*l**2 + 6/5*l**3 + 0*l + 0 + 2*l**q.
2*l**2*(l + 1)*(5*l - 2)/5
Factor 10/3*c**3 - 245/6 - 95/2*c**2 + 175*c.
5*(c - 7)**2*(4*c - 1)/6
Let d(c) = -c**3 - 3*c**2 + 6*c + 2. Let a be d(-4). Let i be 8/(-3)*-1*(-9)/a. Solve -1/6*v**3 + 0*v**2 + 0*v**i + 0 + 1/6*v**5 + 0*v = 0.
-1, 0, 1
Let o = -11/3057 - -20413/9171. Factor 22/9*n**2 + 0 - 2/9*n**3 - o*n.
-2*n*(n - 10)*(n - 1)/9
Suppose 16/5 + 28/5*r + 2/5*r**3 + 14/5*r**2 = 0. What is r?
-4, -2, -1
Let c be 2/8*(-126)/(-21). Factor 1/2*l**2 + 1 - c*l.
(l - 2)*(l - 1)/2
Let w = -80 - -82. Factor 26*k**w - 10*k**2 + 20*k - 11*k**2.
5*k*(k + 4)
Let t be 3 + (-2 - -3) + 38. Let r be (-2)/(-3) + (-1)/t*4. Let 4/7*u**3 + 4/7*u**2 - 4/7*u + 0 - r*u**4 = 0. Calculate u.
-1, 0, 1
Factor -3/5*x**5 - 3/5*x**3 + 12/5*x + 24/5 - 6*x**2 + 12/5*x**4.
-3*(x - 2)**3*(x + 1)**2/5
Let q(k) be the second derivative of -4/9*k**3 - 1/36*k**4 - 8/3*k**2 + 4*k + 0. Solve q(s) = 0 for s.
-4
Let y(m) be the second derivative of 3*m**5/40 - m**4/2 - 5*m**3/4 + 40*m + 2. Determine g so that y(g) = 0.
-1, 0, 5
Factor 2*z**3 - 1/3*z**4 + 2*z + 0 - 11/3*z**2.
-z*(z - 3)*(z - 2)*(z - 1)/3
Let o(t) = -3*t**3 + 40*t**2 + 48*t - 22. Let l(i) = -2*i**3 + 20*i**2 + 24*i - 12. Let y(z) = -11*l(z) + 6*o(z). Factor y(j).
4*j*(j + 2)*(j + 3)
Let z(v) be the second derivative of 2*v - 1/12*v**4 + 1/6*v**3 + 1/60*v**5 - 1/6*v**2 + 0. Find x such that z(x) = 0.
1
Let p(i) = -9*i**2 + 9*i. Let m(a) = 17*a**2 - 17*a. Let j be 30/(-16)*6 + (-1)/(-4). Let w(s) = j*p(s) - 6*m(s). Suppose w(f) = 0. Calculate f.
0, 1
Let 27*p + 95*p**2 - 78*p - 98*p**2 = 0. Calculate p.
-17, 0
Let i(n) be the first derivative of n**4 - 16*n**3/3 + 6*n**2 + 78. Factor i(j).
4*j*(j - 3)*(j - 1)
Let u(t) = -21*t**3 + 45*t**2 - 29*t + 1. Let o(a) = -a**3 - a**2 - a - 1. Let k be (-8*(-4)/(-24))/((-4)/(-18)). Let i(m) = k*o(m) + 2*u(m). Factor i(p).
-4*(p - 2)*(3*p - 1)**2
Let i(r) be the third derivative of -r**6/120 + 77*r**5/300 + 5*r**4/12 - 16*r**3/15 + 245*r**2 - r. Factor i(x).
-(x - 16)*(x + 1)*(5*x - 2)/5
Let c(h) be the third derivative of -h**7/1260 + h**6/60 - h**5/12 - 7*h**4/24 - 6*h**2. Let i(g) be the second derivative of c(g). Factor i(m).
-2*(m - 5)*(m - 1)
Let a(s) be the first derivative of -s**6/3 + 6*s**5/5 - 8*s**3/3 - 122. Factor a(o).
-2*o**2*(o - 2)**2*(o + 1)
Let c(n) be the second derivative of -11/12*n**3 + 0 - 1/2*n**2 - 12*n - 13/24*n**4 - 1/10*n**5. Suppose c(r) = 0. Calculate r.
-2, -1, -1/4
Let v(b) be the third derivative of -b**7/140 - 19*b**6/80 - 99*b**5/40 - 81*b**4/16 - 494*b**2. Factor v(g).
-3*g*(g + 1)*(g + 9)**2/2
Let p be (-8)/((-144)/(-45)) - -2*(-39)/(-28). Suppose -2*u - 24/7 - p*u**2 = 0. What is u?
-4, -3
Let s be (3 - 2)/((-2)/(-6)). Let g**2 - s - g - 4 + 5 = 0. What is g?
-1, 2
Suppose 7 - 47 = -20*c. Factor 5/3*f**c + 2/3*f**3 + 1/3*f - 2/3.
(f + 1)*(f + 2)*(2*f - 1)/3
Let u = 6340/2373 - 4/791. Factor 4/3*n**2 - 32/3*n**3 + 20/3*n**4 + u*n + 0.
4*n*(n - 1)**2*(5*n + 2)/3
Let d(v) = -v**2 + 35*v - 274. Let i be d(23). Factor 3/5*j**i + 9/5*j + 0.
3*j*(j + 3)/5
Let l(j) be the third derivative of -j**5/480 + 35*j**4/96 - 1225*j**3/48 - 103*j**2 - 1. Factor l(s).
-(s - 35)**2/8
Let