*(a + 1)*(a + 2)*(a + 3)**2/3
Suppose -3*n + 0*n + 9 = 0. Factor -14*b**4 + 2*b**4 + 0*b**4 - 2*b**n - b**3.
-3*b**3*(4*b + 1)
Let i(y) be the third derivative of -y**8/84 + 17*y**7/210 - 2*y**6/15 + y**5/20 - 3*y**2. Determine n, given that i(n) = 0.
0, 1/4, 1, 3
Suppose -8 = -4*a - 4*i - 4, 5*a = -4*i + 8. Factor 14/5*n**a + 12/5*n**5 + 4/5*n**3 + 0*n + 0*n**2 + 0.
2*n**3*(2*n + 1)*(3*n + 2)/5
Let i(j) = 2*j**2 - 4*j - 4. Let m(h) = -4*h**2 + 9*h + 9. Let n(x) = -14*i(x) - 6*m(x). Solve n(a) = 0 for a.
-1/2, 1
Let z = -8098/23 + 352. Let r = z - -31/92. Factor 0 + 1/4*j**2 + 0*j + r*j**3.
j**2*(j + 1)/4
Let l(a) be the second derivative of -a**7/11340 - a**6/3240 + a**4/4 + 3*a. Let q(h) be the third derivative of l(h). Factor q(n).
-2*n*(n + 1)/9
Let o = 3 + 0. Let y(l) = -3*l + 4*l + 6*l**2 - 1 - 6*l**o + 0*l. Let d(n) = -5*n**3 + 5*n**2 + n - 1. Let f(p) = -5*d(p) + 4*y(p). Suppose f(k) = 0. What is k?
-1, 1
Let b(x) be the third derivative of 8*x**2 - 1/360*x**5 + 0*x + 0*x**3 + 1/72*x**4 + 0. Determine q, given that b(q) = 0.
0, 2
Let m(f) be the second derivative of -2/3*f**2 + 1/30*f**6 + 0 + 19/36*f**4 + 7/30*f**5 + 2/9*f**3 - f. What is r in m(r) = 0?
-2, -1, 1/3
Let j(n) be the second derivative of n**8/26880 - n**7/3360 + 5*n**4/12 - 6*n. Let z(g) be the third derivative of j(g). Suppose z(r) = 0. What is r?
0, 3
Let t(a) be the second derivative of a**7/21 - a**6/5 + a**5/5 + a**4/3 - a**3 + a**2 - 8*a. Suppose t(k) = 0. What is k?
-1, 1
Suppose -7*w = -2*w - 15. Suppose 4*g + w*u - 69 = -2*u, -4*u = 3*g - 53. Factor 11 - 2*q**2 - g.
-2*q**2
Let a(r) = 4*r - r**3 + 6 - 4 + 7*r**2 + 3. Let q(y) be the third derivative of y**5/60 + y**4/24 + y**3/6 - 2*y**2. Let c(v) = -3*a(v) + 15*q(v). Factor c(t).
3*t*(t - 1)**2
Find l, given that 0 + 0*l + 12/7*l**2 - 4/7*l**4 - 8/7*l**3 = 0.
-3, 0, 1
Suppose -11*q = 16*q. Factor 0*z**2 + 0 + 1/5*z**5 + q*z + 1/5*z**3 + 2/5*z**4.
z**3*(z + 1)**2/5
Factor 3/2*m + 0 - 1/2*m**2.
-m*(m - 3)/2
Let z(k) be the second derivative of k**5/15 + 2*k**4/9 - 2*k**3/9 - 4*k**2/3 + 34*k. Solve z(v) = 0.
-2, -1, 1
Let s(g) = 2*g**2 - 3*g - 3. Let b be s(3). Suppose h - 9 - b = -4*p, 4*p - 24 = -4*h. Factor -2/3*w + 2/9 + 2/3*w**2 - 2/9*w**p.
-2*(w - 1)**3/9
Let l(x) = -4*x**3 + 10*x**2 + x. Let v(j) = 2*j**3 - 5*j**2. Let y(g) = 2*l(g) + 5*v(g). Solve y(i) = 0 for i.
0, 1/2, 2
Suppose 0 + 9 = 2*f - l, -4*f = 4*l + 12. Factor -4/5*k**4 + 0*k**f + 0*k - 2/5*k**5 - 2/5*k**3 + 0.
-2*k**3*(k + 1)**2/5
Let x = -17 - -10. Let n = 9 + x. Factor w**2 + w**2 + 3*w**4 + 6*w**3 + n*w**2 - w**4.
2*w**2*(w + 1)*(w + 2)
Let o(g) be the second derivative of 0*g**2 + 0 + 0*g**3 + 1/15*g**6 + 5*g - 1/2*g**4 - 1/5*g**5. Factor o(t).
2*t**2*(t - 3)*(t + 1)
Let v(n) be the first derivative of 0*n**2 - 1/30*n**4 - 2 - 1/15*n**3 - 2*n. Let d(a) be the first derivative of v(a). Let d(b) = 0. Calculate b.
-1, 0
Find o, given that 2/5*o**2 + 0 + 2/5*o = 0.
-1, 0
Let r be (-10)/(-3) - 1 - 16/24. Factor -8/3*d**2 - r*d**3 + 2/3 - 1/3*d.
-(d + 1)**2*(5*d - 2)/3
Let 10/7 + 2/7*u**2 - 12/7*u = 0. What is u?
1, 5
Let m(b) be the second derivative of 0*b**2 + 9/20*b**5 + 1/6*b**3 - 5/12*b**4 + 1/21*b**7 + 0 + 2*b - 7/30*b**6. Suppose m(c) = 0. What is c?
0, 1/2, 1
Solve 0*q**2 - 11 + 13 - 2*q**3 + 4 + 2*q**2 + 10*q = 0.
-1, 3
Suppose -v**2 + v**4 + 0*v**3 + 0*v**2 + v**3 + 0*v**3 - v = 0. What is v?
-1, 0, 1
Suppose 0*m - 4*m = -84. Suppose 3*a + m = 5*k, k + 0*k = -4*a - 5. Factor -2/3*d**k - 2/3*d**5 + 0*d + 4/3*d**4 + 0*d**2 + 0.
-2*d**3*(d - 1)**2/3
Let z = 23/4 - 689/120. Let y(v) be the second derivative of 0*v**5 + 0*v**3 + 3*v - 1/24*v**4 + 0 + 1/8*v**2 + z*v**6. Factor y(x).
(x - 1)**2*(x + 1)**2/4
Suppose -2*x + 3*x = 3. Suppose -x*l = -0*l. Let -2/3*b + l + 0*b**2 + 2/3*b**3 = 0. Calculate b.
-1, 0, 1
Let q(w) = w**2 + 7*w - 22. Let h be q(-9). Let j(d) = 6*d**3 - 3*d**2 - d + 2. Let c(y) = 19*y**3 - 9*y**2 - 3*y + 7. Let s(t) = h*c(t) + 14*j(t). Factor s(p).
2*p*(p - 1)*(4*p + 1)
Suppose -11*b + 17*b = 18. Let z(j) be the third derivative of 0*j + 0*j**b + 1/12*j**4 + 0 + 1/30*j**5 - j**2. Solve z(p) = 0.
-1, 0
Let u = 1/13 - 21/104. Let a = 5/24 - u. Factor a*s**5 - 1/3 + 10/3*s**3 - 10/3*s**2 - 5/3*s**4 + 5/3*s.
(s - 1)**5/3
Let k be 4/(-7)*(-7)/1. Factor -2 + 49*u**2 - k + 3*u - 45*u**3 - u**2 + 0.
-3*(u - 1)*(3*u + 1)*(5*u - 2)
Let b(z) be the third derivative of -5*z**8/336 - 2*z**7/21 + 7*z**5/6 + 85*z**4/24 + 5*z**3 - 38*z**2. What is d in b(d) = 0?
-3, -1, 2
Solve 0*k - 1/2*k**4 + 0*k**2 + 0*k**3 + 0 = 0.
0
Let a(z) be the first derivative of 1 - z**2 - 1/2*z**4 + z + 1/10*z**5 + z**3. Let v(i) be the first derivative of a(i). Determine f, given that v(f) = 0.
1
Let z = 1655/27 + -52645/864. Let h = -1/32 + z. Find m such that 2/3*m**2 - h*m + 0 - 1/3*m**3 = 0.
0, 1
Let f(w) be the second derivative of -w**6/60 + w**5/15 - w**4/12 - 5*w**2/2 - 3*w. Let u(m) be the first derivative of f(m). Let u(b) = 0. Calculate b.
0, 1
Suppose 0 = 8*h - 3*h + 20. Let g = 7 + h. Suppose 1/3*z**g + 1/3*z**2 - 1/3*z**5 + 0 - 1/3*z**4 + 0*z = 0. Calculate z.
-1, 0, 1
Let l(r) be the third derivative of r**6/600 - r**5/100 + r**4/40 - r**3/30 + 16*r**2. Determine n so that l(n) = 0.
1
Factor 3*z**2 - 8 + 3*z - 10 + 15 - 3*z**3.
-3*(z - 1)**2*(z + 1)
Let c be ((-16)/60)/((-4)/6). Factor -2/5 + c*o**2 + 0*o.
2*(o - 1)*(o + 1)/5
Let g be 136/45 + 27/(-9). Let r(l) be the second derivative of l - 1/60*l**5 + 1/18*l**3 + g*l**6 + 1/6*l**2 - 1/12*l**4 + 0. Solve r(j) = 0 for j.
-1, -1/2, 1
Factor 4/3*g**3 - 40/3*g - 4/3*g**2 - 32/3.
4*(g - 4)*(g + 1)*(g + 2)/3
Let u(y) = -4*y**3 + 11*y**2 - 41*y + 7. Let d(q) = q**3 - 3*q**2 + 10*q - 2. Let i(j) = -18*d(j) - 4*u(j). Factor i(x).
-2*(x - 2)**2*(x - 1)
Let p = -4 + 10. Factor -g**3 - 4*g + 8 + 5*g**3 - 2*g**4 - p.
-2*(g - 1)**3*(g + 1)
Suppose -5*m = -0 - 10. Factor 0 - 2/5*p**m + 2/5*p.
-2*p*(p - 1)/5
Let y(r) be the second derivative of 2*r**4/3 - r**3 - r**2 + 23*r. Let y(p) = 0. Calculate p.
-1/4, 1
Determine l so that -12/5 - 3/5*l**2 + 3*l = 0.
1, 4
Let t(s) be the first derivative of 1 - 4/3*s**2 - 1/6*s**4 - 8/9*s**3 + 0*s. Factor t(u).
-2*u*(u + 2)**2/3
Factor -3*w**2 - 2 - 5*w**2 + w**2 + 9*w.
-(w - 1)*(7*w - 2)
Let m(h) be the first derivative of 2/5*h**2 + 2/5*h + 2/15*h**3 + 3. Factor m(t).
2*(t + 1)**2/5
Let n(t) = -3*t**2 + 3*t. Let w be n(1). Let m(r) be the second derivative of 0 + r + 1/60*r**6 + 0*r**5 - 1/84*r**7 + 0*r**3 + w*r**2 + 0*r**4. Factor m(f).
-f**4*(f - 1)/2
Determine l so that 0*l**2 + 1/2*l**4 + 0*l**3 + 0*l + 0 - 1/2*l**5 = 0.
0, 1
Let a(t) be the third derivative of -t**10/529200 + t**8/23520 - t**7/8820 + t**5/6 + 8*t**2. Let s(g) be the third derivative of a(g). What is j in s(j) = 0?
-2, 0, 1
Let -2*b**2 + 0*b**2 - 54*b**3 - 36*b**4 - 60 + 0*b**2 + 58 + 14*b = 0. What is b?
-1, 1/6, 1/3
Let z(k) = k**3 - k**2 - 3*k + 3. Let a be z(1). What is o in a*o**2 + 0 - 1/4*o + 1/4*o**3 = 0?
-1, 0, 1
Let n(c) be the third derivative of -1/180*c**6 + 1/504*c**8 - 1/315*c**7 + 0*c**3 + 0 + 1/90*c**5 + 2*c**2 + 0*c**4 + 0*c. Solve n(h) = 0.
-1, 0, 1
Factor 48/7*w + 22/7*w**2 + 8/7.
2*(w + 2)*(11*w + 2)/7
Let b be (4/40)/(27/6). Let m(f) be the second derivative of -1/18*f**4 + 0*f**2 + 0*f**5 + f + b*f**6 + 0 + 0*f**3. Factor m(g).
2*g**2*(g - 1)*(g + 1)/3
Let j(p) be the third derivative of p**6/8 - 7*p**5/12 + 10*p**3/3 + 5*p**2. Determine w, given that j(w) = 0.
-2/3, 1, 2
Let q(p) = p**2 - p. Let g(o) be the second derivative of -o**5/20 - o**4/4 + o**3 + o**2 + 3*o. Let v(m) = -g(m) - 3*q(m). Let v(z) = 0. Calculate z.
-1, 2
Let s(f) = 4*f**2 + 13*f + 3. Let v be s(-3). Factor 4/5 + v*y**2 + 8/5*y**3 - 8/5*y - 4/5*y**4.
-4*(y - 1)**3*(y + 1)/5
Let n(f) be the first derivative of -f**5/30 + f**3/3 - 2*f**2 + 2. Let s(a) be the second derivative of n(a). Factor s(b).
-2*(b - 1)*(b + 1)
Let z be 48/(-64) - 5/(-4). Factor 1/2*t**3 - 1/4*t**5 + 1/2*t**4 + 7/4*t - 2*t**2 - z.
-(t - 1)**4*(t + 2)/4
Solve -6*j**2 - 3*j**5 - 6*j**3 + 2*j**3 + 13*j**3 = 0 for j.
-2, 0, 1
Let m(k) be the first derivative of -2/5*k**5 + 1 - 1/4*k**4 + 2/3*k**3 + 0*k - 1/4*k**2 + 1/4*k**6. Let m(z) = 0. Calculate z.
-1, 0, 1/3, 1
Let r be 32/5 - 10/25. Let 0 - 15*x**2 - r*x - 9/2*x**3 + 27/4*x**