 - 4. Let a(h) = -h**2 + 5*h - 1. Let n(c) = -8*a(c) + 3*o(c). Let r be n(3). Solve -1/3*u + 1/3*u**r + 1/3*u**3 - 1/3 = 0 for u.
-1, 1
Let u = 3 - 4. Let m be (u - 0)/((-4)/12). Find v such that 8*v**m - 18*v**2 + 4 + 4*v + 8*v - 6 = 0.
1/4, 1
Let u = 101/4 - 473/20. Suppose 14 - 4 = 5*j. What is i in -2/5*i**j - 8/5 + u*i = 0?
2
Let s(b) be the first derivative of b**5/100 + b**4/20 - 2*b**2/5 - 4*b - 5. Let n(x) be the first derivative of s(x). Let n(v) = 0. What is v?
-2, 1
Let a be (-4)/30*-21 - 6/(-30). Factor -2/7*m**2 + 4/7*m**a - 2/7*m**4 + 0 + 0*m.
-2*m**2*(m - 1)**2/7
Let s = -37/91 + 9/13. Suppose 0*t + 2/7*t**2 - s = 0. Calculate t.
-1, 1
Let q be (-4)/6 - 11/(-3). Let x(y) = q*y**2 + 2*y**2 + 1 - 4*y**2. Let k(a) = 3*a**2 + 4. Let d(i) = -2*k(i) + 7*x(i). Factor d(f).
(f - 1)*(f + 1)
Suppose 58 = 4*v + 2*y, -3*y = 4*v - 46 - 9. What is t in -3*t**2 + 3*t**4 + 6*t**5 + 7*t**3 + 0*t**2 + 3*t - v*t**3 = 0?
-1, 0, 1/2, 1
Let a(n) be the first derivative of -n**4/16 + 5*n**3/24 + n**2/4 - 2*n + 4. Let r(s) be the first derivative of a(s). Factor r(z).
-(z - 2)*(3*z + 1)/4
Let j be (-54)/(-24)*(-8)/(-6). Let b(w) be the third derivative of -w**2 + 4/9*w**j + 0 + 1/9*w**4 + 0*w + 1/90*w**5. Factor b(t).
2*(t + 2)**2/3
Determine l, given that -2/5*l**3 + 1/5*l - 4/5*l**2 + 2/5 + 1/5*l**5 + 2/5*l**4 = 0.
-2, -1, 1
Let r be (-14)/(-35) + 116/10. Let d = -12 + r. Let 0*h - 1/4*h**4 + d + 0*h**2 + 1/4*h**5 + 0*h**3 = 0. What is h?
0, 1
Factor -g - 9*g + 55*g**2 - 105*g**3 + 0*g - 25*g**5 + 85*g**4.
-5*g*(g - 1)**3*(5*g - 2)
Let a(i) be the first derivative of -i**5/30 + i**4/12 - i**3/18 + 4*i + 4. Let k(z) be the first derivative of a(z). Factor k(g).
-g*(g - 1)*(2*g - 1)/3
Let j = 1 - -1. Suppose -3*n + 12 = s + 2, -2*s + 4 = -2*n. Factor -2*z**2 + 2*z**2 + n*z**4 - 2*z**j.
2*z**2*(z - 1)*(z + 1)
Let f(o) be the second derivative of -3*o**4/4 + 7*o**3/2 + 9*o**2 - 3*o. Suppose f(y) = 0. Calculate y.
-2/3, 3
Suppose 2*l = 3*g - 4, g - 1 - 9 = 5*l. Let u = 172/63 + -22/9. Factor -4/7*p**4 + g*p**2 + 0*p + 0 + 6/7*p**5 - u*p**3.
2*p**3*(p - 1)*(3*p + 1)/7
Determine y, given that -8/5*y**5 + 12/5*y**2 + 32/5*y**3 + 0 + 0*y + 12/5*y**4 = 0.
-1, -1/2, 0, 3
Suppose -2*w - 75 = -7*w. Let k = w + -9. Factor 7*o**2 + o + 0 - 2 - k*o.
(o - 1)*(7*o + 2)
Let s(h) be the first derivative of 3/4*h**4 + 0*h - 1 + 3/2*h**2 + 2*h**3. Factor s(i).
3*i*(i + 1)**2
Let k = -3803/3 + 1268. Find j such that 1/6*j**4 + 1/6 - 1/6*j**5 - 1/6*j + k*j**3 - 1/3*j**2 = 0.
-1, 1
Let a(m) = m**2. Let s(p) = p**2 - 8*p - 8. Let q(l) = -5*l**2 + 32*l + 32. Let w(v) = 2*q(v) + 9*s(v). Let t(z) = a(z) - w(z). Factor t(o).
2*(o + 2)**2
Let a(f) = -68*f**5 + 144*f**4 + 4*f**3 - 65*f**2 - 21*f - 6. Let v(i) = -i**5 + 0 - 3 + i**2 + 2*i**5 + 4. Let g(j) = -a(j) - 4*v(j). Solve g(b) = 0 for b.
-1/4, 1, 2
Let r(z) be the second derivative of z**9/60480 + z**8/13440 + 7*z**4/12 - 9*z. Let i(p) be the third derivative of r(p). Let i(s) = 0. Calculate s.
-2, 0
Let i(d) be the third derivative of 7*d**6/660 - d**5/11 + 3*d**4/11 - 8*d**3/33 - 5*d**2 + 3. Factor i(s).
2*(s - 2)**2*(7*s - 2)/11
Suppose -10 = 2*i - 4*j, -i + 4*j = -0*j + 15. Let k be ((-2)/20)/(i/(-20)). Suppose 4/5*c**2 + 3/5*c**3 - k - c = 0. What is c?
-2, -1/3, 1
Let i(j) be the second derivative of j**6/50 + 9*j**5/50 + 9*j**4/20 + 14*j + 1. Factor i(z).
3*z**2*(z + 3)**2/5
Let u(s) = -s**2 + 10*s - 16. Let f be u(8). Let n(z) be the first derivative of 2/5*z**5 + z**4 + 0*z**2 + 1 + 0*z**3 + f*z. Determine b, given that n(b) = 0.
-2, 0
Determine y so that -77*y**5 + 7*y**3 + 5*y**3 - 8*y + 73*y**5 - 4*y**2 + 4*y**4 = 0.
-1, 0, 1, 2
What is w in 6*w**2 - 3*w**3 - 32*w**2 + 3*w + 3*w**4 + 17*w**2 + 6 = 0?
-1, 1, 2
Let l = -101/2 + 54. What is q in 7/2*q**3 - l*q + q**2 - 1 = 0?
-1, -2/7, 1
Let l(d) be the second derivative of -d**6/240 + d**5/120 + d**4/48 - d**3/12 + 5*d**2/2 + 6*d. Let f(t) be the first derivative of l(t). Factor f(a).
-(a - 1)**2*(a + 1)/2
Suppose -2*w = -4*i - 20, 5*i + 38 = 4*w + 10. Suppose 11 = 2*h - o, 19 = -w*h + 6*h - o. Factor 2/3*f**2 - 16/3*f**3 + 4/3*f + 10/3*f**h + 0.
2*f*(f - 1)**2*(5*f + 2)/3
Let r(o) = o**2 - 30*o + 163. Let l be r(23). Let 0 - 32*y**4 + l*y**2 + 21/2*y**5 - 2*y + 43/2*y**3 = 0. What is y?
-2/7, 0, 1/3, 1, 2
Let b(m) be the second derivative of -3*m**5/20 + m**4/4 + m**3 + 11*m. Factor b(t).
-3*t*(t - 2)*(t + 1)
Let q(z) = 20*z**2 + 29*z - 9. Let h(d) = -5*d**2 - 7*d + 2. Let p(y) = 9*h(y) + 2*q(y). Determine g, given that p(g) = 0.
-1, 0
Suppose -2*v - 5*z - 8 = -z, 3*v - z + 33 = 0. Let a be 16/40 - 28/v. Suppose -4/5 - 6/5*k**3 - 14/5*k - a*k**2 = 0. What is k?
-1, -2/3
Let o = -38700/59 + 656. Let d = 161/236 + o. Factor d*a - 1/4*a**2 - 1/2.
-(a - 2)*(a - 1)/4
Let a(i) = -8*i**4 - 4*i**3 - 6*i**2 + 3*i - 1. Let k(w) = w**4 - w. Let h(x) = 3*a(x) + 21*k(x). Factor h(g).
-3*(g + 1)**4
Let q(x) = x**3 - x. Let l(z) = -4*z**3 + 6*z**2 - 8*z + 6. Let c(w) = -l(w) - 3*q(w). Factor c(g).
(g - 3)*(g - 2)*(g - 1)
Let y(r) be the second derivative of r**5/20 - r**4/6 + r**3/6 - 5*r. Factor y(m).
m*(m - 1)**2
Let o = -11 - -25. Let y be 4/o - (-33)/154. Let k**2 - y*k - 1/2 = 0. What is k?
-1/2, 1
Let m(g) be the third derivative of g**6/120 - g**5/30 + 3*g**2. Suppose m(y) = 0. Calculate y.
0, 2
Let x = -52 - -56. Let k(j) be the second derivative of -8/9*j**2 - 5/27*j**6 + 4*j + 0 - 11/18*j**5 + 1/9*j**x + 28/27*j**3. Find n, given that k(n) = 0.
-2, -1, 2/5
Let a be (-1)/4 - 87/(-12). Let x = a - 4. Factor -m**3 - x + 1 + 6*m - 3*m.
-(m - 1)**2*(m + 2)
Let g(z) be the second derivative of -3/20*z**5 - 1/8*z**4 + 0*z**2 - 3*z + 0 - 1/20*z**6 + 0*z**3. Factor g(s).
-3*s**2*(s + 1)**2/2
Let k = 87 - 2609/30. Let c(m) be the third derivative of k*m**4 - 1/150*m**6 - 2*m**2 + 0*m + 1/15*m**3 - 1/525*m**7 + 0*m**5 + 0. Factor c(i).
-2*(i - 1)*(i + 1)**3/5
Let p(c) be the third derivative of c**6/180 + 2*c**5/45 + c**4/9 + 11*c**2. Factor p(b).
2*b*(b + 2)**2/3
Let c be (2/(-21) + (-40)/(-105))*21. Let c + 3*f - 3/2*f**2 - 3/4*f**3 = 0. Calculate f.
-2, 2
Let d(p) = -85*p**5 + p**4 + 12*p**3 - 5*p - 5. Let b(a) = 43*a**5 - a**4 - 6*a**3 + 2*a + 2. Let u(x) = -5*b(x) - 2*d(x). Factor u(v).
-3*v**3*(3*v + 1)*(5*v - 2)
Let h(v) be the third derivative of v**6/300 + v**5/50 + 6*v**2. Solve h(g) = 0 for g.
-3, 0
Suppose 5*g - 2*x - 19 = 0, -2*g - 13 = -7*g - x. Suppose c + 0 = g. Factor -2 + 6*l**2 + 3*l**3 + 3*l**3 - 2*l**c.
2*(l + 1)**2*(2*l - 1)
Let h = -320/7 + 46. Let g be (-45)/(-84) + (-2)/8. Find m such that g*m**4 + h*m**5 + 0 + 0*m - 2/7*m**2 - 2/7*m**3 = 0.
-1, 0, 1
Factor -131 + 261 - 2*q**3 - 130 + 4*q - 2*q**2.
-2*q*(q - 1)*(q + 2)
Let s(y) = 10*y - 2*y**2 + 3 - 5*y**2 - 2*y**2 + 8*y**2. Let d be s(10). Factor -1/4*o**2 + 0*o + 0 + 1/4*o**d.
o**2*(o - 1)/4
Suppose -12 = 6*k - 11*k + m, -8 = -2*k + 2*m. Solve 0 - 2/3*v + 1/3*v**k = 0.
0, 2
Let p = -13 + 15. Let t be ((-18)/15 + p)*1. Factor -2/5 - 2/5*l**2 + t*l.
-2*(l - 1)**2/5
Suppose 0 = -2*c - 3*c + 10. Suppose 4*u - 3*u = c. Let 0 - 1/4*r**3 + 0*r**u + 0*r = 0. Calculate r.
0
Let q(i) = 5*i**4 + 16*i**3 - 11*i. Let a(g) = -g**4 + 5*g**4 - 2*g + 3*g**3 - 3*g**4. Let x(l) = -22*a(l) + 4*q(l). Factor x(r).
-2*r**3*(r + 1)
Let 8 - 11*h**3 + 0*h**3 + 20*h - 5*h**3 - 16*h**4 + 11*h**2 - 3*h**2 - 4*h**5 = 0. What is h?
-2, -1, 1
Let d(r) be the third derivative of -3*r**5/4 - 35*r**4/24 + 5*r**3/3 - r**2. Factor d(w).
-5*(w + 1)*(9*w - 2)
Let k be (-9)/15 + 52/20. Factor -4*x + 15*x**3 - 11*x**3 - k*x**4 + 0*x + 2*x**2.
-2*x*(x - 2)*(x - 1)*(x + 1)
Let y = -1417 - -1422. Find r, given that 12/5*r**4 - 18/5*r**3 + 12/5*r**2 - 3/5*r**y - 3/5*r + 0 = 0.
0, 1
Suppose 0 = 4*v - 0*v. Suppose -4*x = 3*s - x - 3, 5*x = -5. Let 3/2*d**5 + 1/2*d + v + d**2 - d**4 - s*d**3 = 0. What is d?
-1, -1/3, 0, 1
Let m(f) = f**5 - f**4 + f**2 - 1. Let k(r) = 8*r**5 - 20*r**4 + 12*r**2 - 12. Let a(t) = k(t) - 12*m(t). Factor a(c).
-4*c**4*(c + 2)
Suppose -12/5 - 4/5*l**2 + 16/5*l = 0. What is l?
1, 3
Let s(b) be the first derivative of -2*b**5/25 - b**4/10 + 4*b**3/5 - 36. Factor s(k).
-2*k**2*(k - 2)*(k + 3)/5
Factor 0 - 4/13*g + 2/13*g**2.
2*g*(g - 2)/13
Let n(g) be the third derivative of -g**7/42 + 5*g**6/24 - 3*g**5/4 + 35*g**4/24 -