 + 1)**3/3
Find r, given that 12 - 60*r + 3*r**2 + 6*r**3 + 35*r**2 + 19*r**2 - 21*r**4 + 6*r**2 = 0.
-2, 2/7, 1
Let q(t) = -t**2 + 7*t + 5. Let j be q(8). Let b be 7/(-21)*(j + 0). Find i such that 2*i**2 - b - i**2 + 0 = 0.
-1, 1
Let u(x) = -x**3 - 9*x**2 + 2. Let r be u(-9). Factor -1 - 2*h**3 - 7*h**2 + 3*h + 4*h**r + 3*h**3.
(h - 1)**3
Solve 36 + 2/3*l**4 - 22/3*l**3 - 54*l + 30*l**2 = 0.
2, 3
Let r be 3 + ((-680)/12 - 0). Let z = -1121/21 - r. Factor -2/7 + 2/7*w - 4/7*w**3 - z*w**4 + 2/7*w**5 + 4/7*w**2.
2*(w - 1)**3*(w + 1)**2/7
Let t(i) = 7*i**5 - 15*i**4 + 21*i**3 - 13*i**2 - 4*i + 4. Let p(j) = 13*j**5 - 30*j**4 + 42*j**3 - 25*j**2 - 7*j + 7. Let x(o) = 4*p(o) - 7*t(o). Factor x(r).
3*r**2*(r - 3)*(r - 1)**2
Let i be 45/54 - (-53)/(-78). Factor i*h**2 + 0 + 2/13*h.
2*h*(h + 1)/13
Suppose -o + 4 = f + 2, 5*f - 4*o - 10 = 0. Factor 4/5*u + 0 - 14/5*u**f.
-2*u*(7*u - 2)/5
Let t = 27 - 6. Solve -k**3 + t*k**2 - k**3 + 11*k**3 - 12 = 0 for k.
-2, -1, 2/3
Solve -5/6*b - 5 + 5/6*b**2 = 0 for b.
-2, 3
Let y = -2797/5 - -560. Factor -y*r - 2/5 - 1/5*r**2.
-(r + 1)*(r + 2)/5
Let v(k) be the first derivative of 5*k**4/22 + 2*k**3/33 - 4*k**2/11 + 48. Determine s, given that v(s) = 0.
-1, 0, 4/5
Let g(m) be the third derivative of 5*m**8/48 - 2*m**7/7 - 11*m**6/24 + m**5 + 5*m**4/6 - 13*m**2. Find r such that g(r) = 0.
-1, -2/7, 0, 1, 2
Let p be 4/(12/5)*3. Let x(i) = -9*i**3 - 15*i**2 - 37*i - 16. Let g(o) = -4*o**3 - 8*o**2 - 18*o - 8. Let s(a) = p*g(a) - 2*x(a). Let s(v) = 0. Calculate v.
-2, -1
Let k(l) be the second derivative of -l**5/25 - l**4/5 - 2*l**3/5 - 2*l**2/5 + 21*l. Find h such that k(h) = 0.
-1
Let t(b) be the second derivative of -b**6/105 + b**5/7 - 37*b**4/42 + 20*b**3/7 - 36*b**2/7 - 4*b. Factor t(l).
-2*(l - 3)**2*(l - 2)**2/7
Find b, given that -4/3*b + 1/3*b**3 - 4/3 + 1/3*b**2 = 0.
-2, -1, 2
Let s(q) be the second derivative of -q**4/36 + q**3/18 + q**2/3 + 4*q. Determine b, given that s(b) = 0.
-1, 2
Let a(l) be the third derivative of -l**7/2100 - l**6/300 + l**4/15 - l**3/2 - 3*l**2. Let i(z) be the first derivative of a(z). Let i(q) = 0. What is q?
-2, 1
Let x(j) be the second derivative of -1/15*j**6 + 0*j**5 + 0*j**2 + 0 + 1/6*j**4 - 1/6*j**3 + 1/42*j**7 - j. Factor x(d).
d*(d - 1)**3*(d + 1)
Let w be (0 - (-3 + 0)) + -1. Let z be (-1)/5*(-342)/57. Factor -3*u**w + 12/5*u**3 - 3/5*u**4 + z*u + 0.
-3*u*(u - 2)*(u - 1)**2/5
Let y(l) = 39*l**2 - 183*l + 90. Let m(w) = -3*w**2 + 14*w - 7. Let h(x) = -27*m(x) - 2*y(x). Factor h(f).
3*(f - 3)*(f - 1)
Factor 6*s**3 - 4 - s**3 - 12*s**2 + 2*s**3 - 3*s**3 + 12*s.
4*(s - 1)**3
Let n(t) be the third derivative of -2*t**7/315 - 2*t**6/45 - 4*t**5/45 - 3*t**2. Solve n(a) = 0 for a.
-2, 0
Let z(y) be the first derivative of -11 - 1/4*y**4 - y + 1/3*y**3 + 1/2*y**2. Factor z(x).
-(x - 1)**2*(x + 1)
Factor -6/7*t + 0 + 3/7*t**2.
3*t*(t - 2)/7
Let r(j) be the second derivative of -j**5/20 + j**4/2 - 2*j**3 + 3*j**2/2 - 2*j. Let i(y) be the first derivative of r(y). Find a, given that i(a) = 0.
2
Let q(y) be the second derivative of 7*y**6/90 + 4*y**5/15 + 11*y**4/36 + y**3/9 + 4*y. Factor q(f).
f*(f + 1)**2*(7*f + 2)/3
Suppose -4*v = v - 5, 2*l + 4*v - 8 = 0. Factor 0 + 1/2*w**4 - 1/4*w + 0*w**3 + 1/4*w**5 - 1/2*w**l.
w*(w - 1)*(w + 1)**3/4
Let i(n) = -n**3 - 1. Suppose 2*k + 12 = 4*k. Let d(y) = -12*y**3 + 2*y**2 - 6. Let b(h) = k*i(h) - d(h). Suppose b(o) = 0. Calculate o.
0, 1/3
Factor -4 + 7 + 9*h + 3 + 0 + 3*h**2.
3*(h + 1)*(h + 2)
Suppose 0*d - 19 = -2*j + d, d = -3*j + 31. Suppose 0 = 2*g + j, -2*p - 21 + 6 = 3*g. Factor p + 0*r + r**3 - 2/3*r**2.
r**2*(3*r - 2)/3
Determine v so that 0*v**2 + 2/5*v - 2/5*v**3 + 1/5 - 1/5*v**4 = 0.
-1, 1
Let x = 2/7 + -3/35. Let o(p) be the first derivative of -2/15*p**3 + 0*p + 2 + x*p**4 + 0*p**2 - 2/25*p**5. Solve o(y) = 0 for y.
0, 1
Let i(z) be the first derivative of -z**3/15 + 3*z**2/10 + 8. Find w such that i(w) = 0.
0, 3
Find l such that 1/6*l - 1/3*l**2 + 1/3 - 1/6*l**3 = 0.
-2, -1, 1
Let u be (-2)/4 - (-1)/2. Let k(r) be the first derivative of 0*r + u*r**3 + 0*r**5 + 1/3*r**6 + 3 + r**2 - r**4. Factor k(g).
2*g*(g - 1)**2*(g + 1)**2
Let v be (76/(-28) - -3)*(-28)/(-44). Determine a, given that 0 - 2/11*a + v*a**2 = 0.
0, 1
Let t = -14 - -20. Let n be ((-2)/(-3))/(t/16). What is y in 8/3*y + 2/9*y**3 - 4/3*y**2 - n = 0?
2
Suppose -1 - 3 = -4*a. Let y = 1 + a. Factor 2*x**3 - 2*x**4 + 2 + 3*x**4 - y*x - 3.
(x - 1)*(x + 1)**3
Let q(p) = -p**2 + 5*p - 4. Let f be q(4). Suppose g = -2*t + 4, 0 = -2*t + 4*g + 5 - 21. Factor t + f*b + 2/9*b**3 + 2/9*b**2.
2*b**2*(b + 1)/9
Let z(b) be the third derivative of b**7/420 - b**6/180 - 2*b**3/3 + 4*b**2. Let j(c) be the first derivative of z(c). Factor j(v).
2*v**2*(v - 1)
Let b(s) be the first derivative of s**6/24 + s**5/10 + s**4/16 - 3. Solve b(n) = 0 for n.
-1, 0
Let o(k) be the second derivative of -2/9*k**3 - 8*k + 0 - 2/9*k**4 + 2/3*k**2. Factor o(p).
-4*(p + 1)*(2*p - 1)/3
Suppose -5*b - 3*b = -4*b. Suppose 4*v = -m - 3 - 5, -3*m + 5*v + 10 = 0. Find s such that 4/7*s**3 + b*s + m + 6/7*s**4 + 0*s**2 = 0.
-2/3, 0
Suppose 5*n = -4*w - 310, 2*w = 4*w + 2*n + 156. Let x be 4/2 + w/45. Factor -2/9*z**2 - 4/9*z + x*z**4 + 4/9*z**3 + 0.
2*z*(z - 1)*(z + 1)*(z + 2)/9
Let f(z) be the second derivative of 1/5*z**3 + 0*z**2 + 0 + 10*z - 1/30*z**4. Factor f(u).
-2*u*(u - 3)/5
Let p(s) be the first derivative of -2*s**3/9 - s**2 - 30. Find v such that p(v) = 0.
-3, 0
Let k(g) be the third derivative of 0*g - g**2 + 1/240*g**5 + 1/48*g**4 + 0*g**3 + 1/1344*g**8 - 1/160*g**6 - 1/840*g**7 + 0. What is d in k(d) = 0?
-1, 0, 1, 2
Let s = 931 - 929. What is w in 0*w**s - 6*w + 0 + 3/2*w**3 = 0?
-2, 0, 2
Let o(k) be the second derivative of -k**4/4 - 4*k**3 - 18*k**2 + 23*k. Factor o(m).
-3*(m + 2)*(m + 6)
Let p = -137 + 421/3. Factor -4/9 - 2/9*t - 38/9*t**3 + 14/9*t**4 + p*t**2.
2*(t - 1)**3*(7*t + 2)/9
Let j(p) = -p. Let h(x) = -6*x - 1. Let v(t) = -2*h(t) + 11*j(t). Let z be v(-2). Determine y so that -4 - 4*y**2 - 6*y + z + 2*y**2 = 0.
-2, -1
Suppose k = -5*z - 4, -z - 13 = 5*k + 7. Let z*j - 1/4*j**3 + 0*j**2 + 0 = 0. Calculate j.
0
Let g be (2/15)/((-22)/(-110)). Factor 0 - 28/9*a**3 - 16/9*a + 40/9*a**2 + g*a**4.
2*a*(a - 2)**2*(3*a - 2)/9
Let s(d) = -3*d**5 - 7*d**4 - 8*d**3 - 2*d**2 - 1. Let c(q) = q**5 + q**3 + 1. Let o(n) = c(n) + s(n). Suppose o(g) = 0. Calculate g.
-2, -1, -1/2, 0
Let f be -4*((-15)/6 - -3). Let u be (-2)/f + (6 - 1). Factor -3 + 4 - l + 1 + u*l**2 - 7*l.
2*(l - 1)*(3*l - 1)
Suppose g - 2 = 5*c, 2*c = c + 1. Let s(m) = 3*m**3 + 19*m**2 - 19*m - 3. Let n(f) = f**3 + 9*f**2 - 9*f - 1. Let u(x) = g*n(x) - 3*s(x). Factor u(h).
-2*(h - 1)**3
Let m(d) be the second derivative of -d**4/20 + d**3/10 + 3*d**2/5 - 9*d. Factor m(l).
-3*(l - 2)*(l + 1)/5
Factor -k**5 + 5*k**4 - 3*k**3 - 12*k + 10*k + 6*k - 5*k**2.
-k*(k - 4)*(k - 1)**2*(k + 1)
Let l(z) = -22*z**4 - 35*z**3 + 40*z**2 + 23*z - 3. Let p(g) = 43*g**4 + 70*g**3 - 80*g**2 - 47*g + 7. Let m(s) = -7*l(s) - 3*p(s). Solve m(u) = 0 for u.
-2, -2/5, 0, 1
Let y(f) be the first derivative of f**7/126 - f**6/45 + f**5/180 + f**4/36 + f**2/2 - 1. Let b(i) be the second derivative of y(i). Factor b(x).
x*(x - 1)**2*(5*x + 2)/3
Factor -846*x**2 + 845*x**2 + 7*x - 3 - 7.
-(x - 5)*(x - 2)
Let f(n) be the third derivative of 0 + n**2 + 0*n**3 + 0*n + 1/60*n**5 - 1/24*n**4. Factor f(m).
m*(m - 1)
Let i(a) = -a - 29. Let h be i(0). Let b = h + 31. Let 4/3*p**b + 2/9*p**3 + 16/9 + 8/3*p = 0. What is p?
-2
Let v(y) be the third derivative of y**8/6720 - y**7/3360 - y**6/360 + y**5/120 + 7*y**3/6 - 3*y**2. Let f(u) be the first derivative of v(u). Factor f(t).
t*(t - 2)*(t - 1)*(t + 2)/4
Let s(p) be the first derivative of -p**5/20 - p**4/16 + 18. Factor s(o).
-o**3*(o + 1)/4
Factor 14*a**4 + 17*a**4 - 35*a**4 + 4*a**3.
-4*a**3*(a - 1)
Determine r, given that 1/4*r**4 - 1/2*r + 0*r**3 + 0 - 3/4*r**2 = 0.
-1, 0, 2
Determine u so that 192 - 10*u**2 - 8*u**3 + 240*u + 12*u**3 - u**3 + 61*u**2 = 0.
-8, -1
Let f be ((-16)/(-10) + -2)*-15. Let f*a**3 - 4*a**3 - 6*a + 0*a**2 + a**3 + 3*a**2 = 0. What is a?
-2, 0, 1
Let v be -3 + 6 - 129/45. Let q = 8/15 + v. Let -i - q - 1/3*i**2 = 0. Calculate i.
-2, -1
Let z(o) be the first derivative of -2*o 