1
Factor 9/5 - 6*b + 5*b**2.
(5*b - 3)**2/5
Let o(b) be the first derivative of 3/20*b**4 + 24/5*b + 6/5*b**3 + 4 + 18/5*b**2. Solve o(l) = 0.
-2
Let m(v) be the third derivative of v**8/2016 - v**7/252 + v**6/120 + v**5/180 - 7*v**4/144 + v**3/12 - 25*v**2. Find d such that m(d) = 0.
-1, 1, 3
Let p(d) be the second derivative of -d**8/16800 + d**6/600 - d**5/150 + d**4/6 - d. Let v(g) be the third derivative of p(g). Solve v(n) = 0 for n.
-2, 1
Factor 11*o + 6*o**2 - 3*o**4 - 3 - 11*o.
-3*(o - 1)**2*(o + 1)**2
Let p(k) be the third derivative of -k**6/300 - k**5/60 + k**4/30 - k**3/2 - 4*k**2. Let g(w) be the first derivative of p(w). Factor g(o).
-2*(o + 2)*(3*o - 1)/5
Let d be ((-4)/8)/(2/(-1433)). Let s = 360 - d. Factor 3/4*h**2 - 1/2 + 3/4*h**4 + s*h**3 - 3/4*h.
(h + 1)**3*(3*h - 2)/4
Let n(l) be the third derivative of -l**7/10 - 9*l**6/40 + 3*l**5/5 + l**4/2 - 6*l**2. Suppose n(c) = 0. What is c?
-2, -2/7, 0, 1
Suppose 0*w = -0*w + 9*w. Factor 1/2 - d**3 + d + w*d**2 - 1/2*d**4.
-(d - 1)*(d + 1)**3/2
Factor g**2 - 14 + 10 - 5*g + 5*g.
(g - 2)*(g + 2)
Let c = -860 + 864. Factor -16/9*p**2 + 2/3*p + 0*p**c + 0 + 4/3*p**3 - 2/9*p**5.
-2*p*(p - 1)**3*(p + 3)/9
Let c be ((-6)/540*4)/((-1)/5). Find k, given that 2/9*k - c*k**3 - 4/9*k**4 + 4/9*k**2 + 0 = 0.
-1, -1/2, 0, 1
Let t(f) be the first derivative of -f**6/6 - f**5/5 - 8. Solve t(o) = 0.
-1, 0
Let y(r) be the first derivative of r**6/2 + 14*r**5/5 + 4*r**4 + 2*r**3/3 - 3*r**2/2 + 16. Let y(q) = 0. What is q?
-3, -1, 0, 1/3
Let h(q) = -q**3 - 12*q**2 - 11*q + 2. Let j be h(-11). Suppose -j*t**5 - t**4 + 4*t**2 + 0*t + 6*t - 3*t**4 - 4*t = 0. Calculate t.
-1, 0, 1
Find q such that 0*q**3 + 0*q + 4/9*q**2 - 4/9*q**4 + 0 = 0.
-1, 0, 1
Let p(n) be the second derivative of n**7/1680 + n**6/240 + n**5/80 + n**4/48 + n**3/3 - 5*n. Let a(f) be the second derivative of p(f). Factor a(d).
(d + 1)**3/2
Factor 3/5*n**3 + 0 + 3/5*n**4 + 1/5*n**2 + 0*n + 1/5*n**5.
n**2*(n + 1)**3/5
Let k(l) be the third derivative of 0 + 0*l + 1/18*l**4 - 5*l**2 - 1/9*l**3 - 1/90*l**6 + 0*l**5 + 1/315*l**7. Factor k(j).
2*(j - 1)**3*(j + 1)/3
Let n(i) be the third derivative of -i**7/3360 + i**6/1440 - i**3/3 - 4*i**2. Let w(f) be the first derivative of n(f). Solve w(h) = 0 for h.
0, 1
Suppose 40*t - 17*t = 0. Find q such that t - 1/4*q - 1/2*q**2 - 1/4*q**3 = 0.
-1, 0
Suppose 2*t - 8 = -2*t. Let f = -4 + 4. Factor 2 - q**2 + f*q**2 + 3*q - 3*q**2 - q**t.
-(q - 1)*(5*q + 2)
Let v be (-3 + (-20)/(-8))*-4. Let y(x) be the first derivative of -2/3*x**3 + v + 0*x**2 + 2*x. What is j in y(j) = 0?
-1, 1
Let 8/3*z**3 + 10/9*z**4 + 8/9*z**2 + 0*z + 0 = 0. Calculate z.
-2, -2/5, 0
Suppose -2*q = 5*c - 7, -2*q - 2*c + 3 = -c. Suppose f - 4*j = 18, 2*j = -f - q - 5. Factor 2*k**3 + f - 2 - 2*k.
2*k*(k - 1)*(k + 1)
Let d = -280 - -2522/9. Suppose 0*c - 2/9*c**4 + 0*c**2 - d*c**3 + 0 = 0. Calculate c.
-1, 0
Suppose -2*k - 30 = 4*n, -4*n - 10 = 10. Let r be (k/30)/(1/(-3)). Suppose -v**4 - r*v**2 + 0*v - 3/2*v**3 + 0 = 0. What is v?
-1, -1/2, 0
Let l = 36 + -32. Let s(d) be the second derivative of 0 + 3*d - 2*d**3 + 9/4*d**l + 0*d**5 + 3/4*d**2 - 27/20*d**6. Factor s(c).
-3*(c + 1)*(3*c - 1)**3/2
Let u(b) = 2*b**2 - 2. Let c(t) = 4*t**2 - 4. Let s(n) = 6*n**2 - 6. Let z(o) = -8*c(o) + 5*s(o). Let f(p) = 5*u(p) + 6*z(p). Factor f(h).
-2*(h - 1)*(h + 1)
Let u(z) = 2*z - 2. Let g be u(2). Let -16*a - g*a**2 + 29*a - 15*a = 0. Calculate a.
-1, 0
Suppose k = -u + 2, 3*k + 4 = 2*u - 2*k. Let 4*f**4 - 6*f**u + 0*f**4 + 16*f - 8*f**3 + 16 - 2*f**2 - 4*f**2 = 0. What is f?
-1, 2
Suppose 0 + 3/7*u**4 + 3/7*u**3 - 6/7*u**2 + 0*u = 0. What is u?
-2, 0, 1
Factor 2/5*v**4 - 1/5*v**5 - 1/5*v**3 + 0*v + 0 + 0*v**2.
-v**3*(v - 1)**2/5
Let r(l) be the third derivative of l**5/90 - l**4/6 - 7*l**3/9 + 8*l**2. Factor r(a).
2*(a - 7)*(a + 1)/3
Let 0 - 4/5*m**2 + 6/5*m + 2/15*m**3 = 0. What is m?
0, 3
Suppose -4*u + 13 = -3. Factor 2*d - 6 + d**u + 5 + 0 - 2*d**3.
(d - 1)**3*(d + 1)
Let y(b) = b**3 + 2*b**2 - 4*b + 1. Let r be y(-3). Factor p**r - 3*p**3 - 3*p**3 - p**2 - p**5 + 2*p**5 + 5*p**3.
p**2*(p - 1)*(p + 1)**2
Let p(d) be the second derivative of -d**4/6 - 4*d**3 - 36*d**2 - 16*d. Factor p(q).
-2*(q + 6)**2
Let x(r) = 2*r**3 + 2*r**2 + r + 5. Let f(t) = -2*t**3 - 2*t**2 - 2*t - 6. Let i(b) = 5*f(b) + 6*x(b). Factor i(k).
2*k*(k - 1)*(k + 2)
Suppose 0*d = -d. Let j(g) = 1 + g + g**2 - 2*g**4 + g**4 + d. Let i(f) = 2*f**3 - 2*f**2 - f - 1. Let l(v) = i(v) + j(v). Determine c, given that l(c) = 0.
0, 1
Suppose 6*p - 2 = 5*p, 0 = 5*r - 3*p - 64. Factor -2 - r*h - 49/2*h**2.
-(7*h + 2)**2/2
Suppose -5*q + 21 = 3*p, -2*p - 2*p + 5 = -q. Let l(w) be the first derivative of 0*w**2 + 2/35*w**5 + 4/21*w**q - 3/14*w**4 - 1 + 0*w. Factor l(n).
2*n**2*(n - 2)*(n - 1)/7
Let z(a) be the first derivative of 3*a**4/4 + 2*a**3 + 3*a**2/2 - 16. Factor z(m).
3*m*(m + 1)**2
Suppose -2*y - 3*y + 20 = 0. Suppose -d + y*d - 6 = -2*k, 0 = 4*k. Let d + 2*h + 1/2*h**2 = 0. What is h?
-2
Factor 1/3*k**3 + 0*k**2 + 0*k + 0 - 1/3*k**5 + 0*k**4.
-k**3*(k - 1)*(k + 1)/3
Factor -5/7*q + 1/7*q**2 + 6/7.
(q - 3)*(q - 2)/7
Let r(h) be the second derivative of 5/6*h**4 + 3/2*h**3 + 0 + 3/20*h**5 + 3*h + h**2. Determine g, given that r(g) = 0.
-2, -1, -1/3
Suppose 2*s + 7 = -5*k, -2*s + 4*k + 20 = -0. Let y(h) be the first derivative of 1 + 1/6*h**s + 2/3*h**3 + 0*h + 2/3*h**2. Factor y(d).
2*d*(d + 1)*(d + 2)/3
Let q(l) be the second derivative of l**6/240 + l**5/32 + l**4/12 + l**3/12 + 9*l + 1. Factor q(n).
n*(n + 1)*(n + 2)**2/8
Let i = -3 + -6. Let b = i + 11. Factor 1/4*c**b - c + 1.
(c - 2)**2/4
Suppose u - 6 = 3. Let l be (-3)/u + 4/3. Suppose 2*j**4 - 7*j**3 + 4*j**2 + 3*j**2 - 5*j + l + 2*j**2 = 0. Calculate j.
1/2, 1
Let y = 452 - 450. Factor -4/5*p + 2/5 + 2/5*p**y.
2*(p - 1)**2/5
Let g(v) = -2*v**3 - 19*v**2 + 18*v - 9. Let w(j) = j**3 - j**2 + j - 1. Let i(f) = 5*g(f) - 35*w(f). Factor i(k).
-5*(k + 2)*(3*k - 1)**2
Factor 0 + 3/2*x**2 + 0*x**3 - x - 1/2*x**4.
-x*(x - 1)**2*(x + 2)/2
Let b(k) be the first derivative of -k**3 + 24*k**2 - 192*k + 54. Determine w, given that b(w) = 0.
8
Let h = 11 + -17. Let g(k) = 30*k**2 - 72*k + 7. Let a(z) = -5*z**2 + 12*z - 1. Suppose 56 = -2*r - 12. Let y(v) = h*g(v) + r*a(v). Solve y(m) = 0.
2/5, 2
Let d(m) be the second derivative of 0*m**3 - 9/5*m**5 + 0 - 63/25*m**6 + 3*m + 0*m**2 - 7/10*m**7 - 2/5*m**4. Find z such that d(z) = 0.
-2, -2/7, 0
Find a such that 39*a**2 - 100 - 43*a**2 + a + 39*a = 0.
5
Factor 0 - 3/7*s**2 + 6/7*s.
-3*s*(s - 2)/7
Let v be 8/(-32) + (-97)/(-4). Factor 12*f - 24 - 4*f**2 + v.
-4*f*(f - 3)
Let d(w) be the third derivative of -w**8/2352 + w**6/420 - w**4/168 - 12*w**2. Determine u, given that d(u) = 0.
-1, 0, 1
Let f(z) be the third derivative of -z**7/420 + z**6/36 - 2*z**5/15 + z**4/3 + z**3/2 + z**2. Let b(y) be the first derivative of f(y). Factor b(l).
-2*(l - 2)**2*(l - 1)
Let l = 25/21 + 1/7. Find k, given that l*k + 0 + 2/3*k**2 = 0.
-2, 0
Let x(f) be the second derivative of -5*f**4/24 + 7*f**3/12 - f**2/2 - 18*f. Suppose x(n) = 0. Calculate n.
2/5, 1
Let d be 60/105 + (-2)/7. Let m = 72/245 + -2/245. Factor -2/7*v**3 + m*v - d*v**2 + 2/7.
-2*(v - 1)*(v + 1)**2/7
Let l(w) be the first derivative of 2 - 1/9*w**2 - 2/27*w**3 - 3*w + 1/135*w**6 + 1/45*w**5 + 0*w**4. Let z(t) be the first derivative of l(t). Factor z(g).
2*(g - 1)*(g + 1)**3/9
Let x(s) be the second derivative of 0 + 0*s**2 + 2*s + 0*s**3 - 3/70*s**6 - 1/42*s**7 + 0*s**4 - 1/70*s**5. Let x(n) = 0. Calculate n.
-1, -2/7, 0
Let s be 3/12*2*6. Factor 4*u**3 + 15*u + 59*u**2 - 11*u**2 + 0*u**3 - 6 + 23*u**s.
3*(u + 1)**2*(9*u - 2)
Let n = -16 - -20. Find g such that 2/7*g**3 + 0*g + 0 + 6/7*g**n - 4/7*g**2 = 0.
-1, 0, 2/3
Let a(y) = -y**4 - 8*y**3 + 5*y**2 + 3*y + 3. Let c(m) = -6*m**4 - 40*m**3 + 24*m**2 + 16*m + 16. Let p(o) = 16*a(o) - 3*c(o). Factor p(x).
2*x**2*(x - 2)**2
What is p in -4/5*p**3 - 2/5*p**2 - 2/5*p**4 + 0*p + 0 = 0?
-1, 0
Let y(c) = 3*c**2 - 19*c - 8. Let r be y(9). Solve -3 - 100*l**4 - 273*l**2 + 448*l**3 - 39*l**2 - 1 + r*l - 96*l**4 = 0 for l.
1/7, 1
Let t = -160 + 160. Let l(q) be the third derivative of -1/10*q**6 + 0*q + 1/4*q**4 - 2*q**2 + 3/20*q**5 - 1/2*q**3 + t - 2/35*q**7. Factor l(g).
-3*(g + 