 o be 1*1*(b - 2). Suppose 2/5*d + o - 2/5*d**2 = 0. What is d?
0, 1
Let x(p) be the first derivative of 0*p**4 - 1/360*p**5 + 1/3*p**3 - 1/1080*p**6 + 2 + 0*p**2 + 0*p. Let a(g) be the third derivative of x(g). Factor a(z).
-z*(z + 1)/3
Factor 0 - 4/7*d - 18/7*d**2 - 2*d**3.
-2*d*(d + 1)*(7*d + 2)/7
Let i be 5 + -2 - 8/(-10). Find f, given that i*f**3 + 2/5 - 7/5*f**4 + 1/5*f - 3*f**2 = 0.
-2/7, 1
Let s(v) be the third derivative of -1/12*v**3 - 6*v**2 + 0 - 1/32*v**4 + 0*v**5 + 1/480*v**6 + 0*v. Factor s(d).
(d - 2)*(d + 1)**2/4
Let v = -4731436/135 + 35048. Let d = v + 2/27. Let 4/5*z**3 - 4/5*z + 0*z**2 + d - 2/5*z**4 = 0. Calculate z.
-1, 1
Let q(z) be the first derivative of -98*z**3/3 + 56*z**2 - 32*z + 3. Determine r, given that q(r) = 0.
4/7
Let f(n) be the second derivative of 0 + 0*n**3 - 1/2*n**2 + 1/12*n**4 - 2*n. Factor f(y).
(y - 1)*(y + 1)
Let t be ((-4)/(-20))/((-3)/(-5)). Solve 0 + 2/3*g**2 + 0*g**3 + t*g**5 - 2/3*g**4 - 1/3*g = 0 for g.
-1, 0, 1
Suppose 2*w**4 - 10*w**2 - 6*w**3 - 5*w**3 + 5*w**3 + 82*w**5 - 4*w - 80*w**5 = 0. What is w?
-1, 0, 2
Let m(w) = -w - 1. Let f(o) = -o**3 - 2*o**2 + 4*o + 5. Let s(t) = -f(t) - 5*m(t). Factor s(u).
u*(u + 1)**2
Let x be (3 + 15/(-6))*4. Solve -3*w**3 + 3*w**5 + 2*w**2 - 2*w**4 + x*w**5 - w**3 - w**3 = 0 for w.
-1, 0, 2/5, 1
Let y = -319 + 321. What is k in -2/7*k**3 + 0*k + 0 + 2/7*k**y = 0?
0, 1
Let s(i) be the second derivative of -2*i + 0 - 1/5*i**2 - 1/30*i**3 + 1/60*i**4. Factor s(j).
(j - 2)*(j + 1)/5
Let q(r) be the first derivative of -r**5/20 - r**4/4 - r**2/2 - 5. Let j(o) be the second derivative of q(o). Factor j(y).
-3*y*(y + 2)
Suppose 26 - 98 = -2*m. Determine a, given that -30*a**3 + m*a**5 + 12*a**4 + 3*a + 5*a**4 + 16*a**4 - 33*a**2 - 9*a = 0.
-1, -2/3, -1/4, 0, 1
Let w(y) be the third derivative of y**7/1680 - y**6/360 + y**5/240 + y**3/3 + 5*y**2. Let d(s) be the first derivative of w(s). Find h, given that d(h) = 0.
0, 1
Let k(p) = -3*p**2 + p. Let s be k(-1). Let w(u) = -5*u**3 - 3*u - 4. Let t(r) = -6*r**3 - 4*r - 5. Let f(i) = s*t(i) + 5*w(i). Solve f(g) = 0.
-1, 0, 1
Let w(r) = r**2 - 2*r + 4. Let b be w(0). Let k(i) be the second derivative of -1/36*i**b + 0*i**2 + 1/90*i**6 + 0 - 1/60*i**5 + 1/18*i**3 - i. Factor k(p).
p*(p - 1)**2*(p + 1)/3
Suppose 20*u = 12*u + 24. Let n(a) be the second derivative of -1/120*a**6 + 0*a**u - 2*a - 1/8*a**2 + 1/24*a**4 + 0 + 0*a**5. Factor n(s).
-(s - 1)**2*(s + 1)**2/4
Let p(n) = 9*n**2 - 1. Let a be p(-1). Suppose 4*o + g - 4 = 0, a = o - 2*g - 2. Factor -d + o*d**2 - 6*d**2 + 3*d**2.
-d*(d + 1)
Factor i + 0 - 1/4*i**4 - 2*i**2 + 5/4*i**3.
-i*(i - 2)**2*(i - 1)/4
Suppose 0 = -2*k + 4*l + 4, 0*k - 10 = -5*k + 3*l. Factor -3*j + 3/2*j**k + 3/2.
3*(j - 1)**2/2
Factor 0 - 2*a**4 - 14/3*a**2 - 4/3*a - 16/3*a**3.
-2*a*(a + 1)**2*(3*a + 2)/3
Let t be 2 + (2 - -2 - 2). Let o = t + -1. Factor 3*p**2 + 0*p**o + 4*p**3 - 1 + p**2 - p.
(p + 1)*(2*p - 1)*(2*p + 1)
Suppose -o + 18 = -3*o. Let s be (-45)/6*12/o. Suppose -9*x - 7*x - 4 + 18*x**3 - 2*x + 14*x**4 - s*x**2 = 0. Calculate x.
-1, -2/7, 1
Suppose 4*b = 12, 0 = -5*o + 4*b + b - 185. Let y = o + 104/3. Factor -1/3 + a + a**4 - y*a**2 - 1/3*a**5 - 2/3*a**3.
-(a - 1)**4*(a + 1)/3
Suppose 5*v - 27 = -f, 0*f = -4*f + 5*v - 17. Factor -2/15*g + 0 + 4/15*g**f - 2/15*g**3.
-2*g*(g - 1)**2/15
Let m(x) = x**2. Suppose -d + 4*j + 19 = 0, -3*d - 2*j - 20 = -7. Let t(l) = -3*l - 2. Let w(b) = d*m(b) + t(b). Factor w(y).
-(y + 1)*(y + 2)
Let d be (7/(-21))/(1/(-6)). Let c(l) be the first derivative of -1/6*l**3 - d + 1/4*l**2 + 0*l. Determine k, given that c(k) = 0.
0, 1
Factor 3*u + 6*u + 2*u**2 - 6*u - u**3.
-u*(u - 3)*(u + 1)
Let h(u) = u + 7. Let j be h(-4). Solve -1/3*p**j + 0 + 0*p - 1/3*p**2 = 0 for p.
-1, 0
Let p(u) be the first derivative of 4*u**3/3 + 8*u**2 + 16*u + 16. Solve p(h) = 0.
-2
Let k(r) be the second derivative of -r**6/20 - 3*r**5/40 + r**4/8 + r**3/4 + 7*r. Suppose k(l) = 0. What is l?
-1, 0, 1
Suppose -x - 3*x + 16 = 0, -2*u - 2*x + 12 = 0. Suppose 2 = -m - p + 1, -5*m - 2*p = -4. Factor -3*n**u - m*n**2 - 2*n + 3*n**2.
-2*n*(n + 1)
Suppose 2*r - 4*r = 0. Let z = -67/3 - -23. Factor 2/3*c**4 + z*c**3 - 2/3*c**5 + 0 + r*c - 2/3*c**2.
-2*c**2*(c - 1)**2*(c + 1)/3
Suppose 6*g - 2 = 5*g. Suppose 5*b = 17 - 2. Let -2 + g*t**b - 3*t - t**4 + t + 3 = 0. Calculate t.
-1, 1
Let q(l) be the third derivative of -1/12*l**4 + 0*l**3 + 0*l + l**2 + 1/30*l**5 + 0. Find b such that q(b) = 0.
0, 1
Let a = 4 - 5. Let l = -1 - a. Factor l + 2/5*g**2 - 4/5*g.
2*g*(g - 2)/5
Let k = 2/235 + -104/1175. Let j = k + 33/100. Find d such that -j*d**3 + 0*d + 1/2*d**2 + 0 = 0.
0, 2
Let k(i) be the second derivative of i**7/126 + 11*i**6/90 + 23*i**5/30 + 5*i**4/2 + 9*i**3/2 + 9*i**2/2 - 45*i. Suppose k(p) = 0. Calculate p.
-3, -1
Let o(v) be the second derivative of -v**7/273 + 2*v**6/195 + v**5/130 - v**4/39 + 6*v. Solve o(f) = 0.
-1, 0, 1, 2
Let v = -65 + 67. Factor t**4 + 0*t - 1/2*t**3 - 1/2*t**5 + 0 + 0*t**v.
-t**3*(t - 1)**2/2
Let u(l) be the first derivative of l + 5/2*l**2 + 17/12*l**3 + 1/4*l**4 + 1. Factor u(t).
(t + 2)**2*(4*t + 1)/4
Factor 31*p + 2*p**2 + p**3 - 31*p.
p**2*(p + 2)
Let p(k) be the second derivative of k**7/60 + k**6/90 - k**3/6 + 3*k. Let t(l) be the second derivative of p(l). Let t(s) = 0. What is s?
-2/7, 0
Let v(n) = -5*n**4 + 24*n**3 + 16*n**2 - 11*n - 11. Let q(y) = y**4 - 6*y**3 - 4*y**2 + 3*y + 3. Let j(c) = 22*q(c) + 6*v(c). Find k, given that j(k) = 0.
-1/2, 0, 2
Let w(v) be the second derivative of -v**4/90 - v**3/15 - 10*v. Find h such that w(h) = 0.
-3, 0
Let g = 1/35 + 33/70. Suppose 0 = -0*y + 4*y. Factor 1/2*q**2 - g + y*q.
(q - 1)*(q + 1)/2
Factor -y**3 - 21*y**3 - 5*y**4 - 8*y**3.
-5*y**3*(y + 6)
Factor -4/5*z**3 + 12/5*z**2 + 4/5 - 12/5*z.
-4*(z - 1)**3/5
Let x(g) = -g**3 - g**2. Let f = 3 - -1. Let y(r) = 3*r**4 + 8*r**3 + 11*r**2 + 6*r. Let s(b) = f*x(b) - y(b). Factor s(n).
-3*n*(n + 1)**2*(n + 2)
Let n(h) be the third derivative of h**8/84 - 2*h**7/21 + 3*h**6/10 - 7*h**5/15 + h**4/3 - 19*h**2 - 1. Determine k, given that n(k) = 0.
0, 1, 2
Let r(h) be the second derivative of -5*h**4/12 + 10*h**3/3 - 15*h**2/2 - 3*h. Factor r(l).
-5*(l - 3)*(l - 1)
Let c be ((-28)/16)/(15/(-72)). Let s be 6/(6/(-8)*-1). Determine r, given that 8*r - 8/5 + 10*r**4 - c*r**2 - s*r**3 = 0.
-1, 2/5, 1
Suppose 4*c = 6*c - 5*c. Let t(l) be the second derivative of 0*l**2 + c + 1/3*l**4 - 2*l - 1/6*l**3. Solve t(n) = 0 for n.
0, 1/4
Let q be 57*(-3)/(-162) + -1. Let i(z) be the second derivative of 0*z**3 - q*z**4 + 0 + 7/90*z**6 + 0*z**2 + z + 1/12*z**5. Factor i(b).
b**2*(b + 1)*(7*b - 2)/3
Let z(r) be the first derivative of -2/5*r + 0*r**3 + 2/25*r**5 + 1/5*r**4 - 2/5*r**2 + 3. Factor z(x).
2*(x - 1)*(x + 1)**3/5
Let f be ((16/6)/4)/(2/10). Suppose 12 = -3*p - p - 5*q, 0 = -5*p + q + 14. Let 2*u**3 + 0 + 0*u - 4/3*u**p + f*u**4 = 0. Calculate u.
-1, 0, 2/5
Let n(w) be the third derivative of w**8/1008 + w**7/210 - w**6/360 - 7*w**5/180 + 2*w**3/9 - w**2. Let n(b) = 0. What is b?
-2, -1, 1
Let b(n) be the second derivative of 3*n**5/100 + 2*n**4/15 + 7*n**3/30 + n**2/5 + 26*n. Determine c, given that b(c) = 0.
-1, -2/3
Suppose 4*t + 13 = 4*p + 5*t, 33 = 4*p + 5*t. Factor -k**2 - 3 + 3*k**p + 3.
2*k**2
Let -5*p + 0*p**4 - 2 + 4*p**3 - p + 2*p**4 + 2*p = 0. Calculate p.
-1, 1
Let d = 332 + -2984/9. Solve 2/9 + 2/9*l**2 + d*l = 0.
-1
Let r(l) be the third derivative of -3*l**7/490 + l**6/140 + l**5/35 - l**4/28 - l**3/14 + 5*l**2. Solve r(x) = 0.
-1, -1/3, 1
Find s such that -2/11*s**4 - 8/11*s - 8/11 + 10/11*s**3 - 2/11*s**5 + 10/11*s**2 = 0.
-2, -1, 1, 2
Let z(i) = i**3 - 7*i**2 - 18*i + 4. Let m be z(9). Let u(o) be the second derivative of 1/42*o**4 + 0*o**3 + 0 + 0*o**2 + m*o. Factor u(w).
2*w**2/7
Suppose -4*n = -1019 + 3123. Let m = n + 2639/5. Let -27/5*b**3 + 24/5*b + 12/5 - m*b**2 = 0. Calculate b.
-2/3, 1
Suppose -14 + 2 = -3*m, 0 = 5*k + 3*m - 32. Let t(r) be the first derivative of 2 + 4*r**2 + 1/4*r**4 + 5/3*r**3 + k*r. Factor t(a).
(a + 1)*(a + 2)**2
Let g(b) be the first derivative of -b**7/420 - b**6/180 - b**3/3 - 2. Let d(z) be the third derivative of g(z). Factor d(f).
-2*f**2*(f + 1)
Let n(f) = 6*f**3 - 18*f**2 - 29*f - 5. Let y(h) = 9*h**3 - 