) be the third derivative of c**7/35 + c**6/60 - c**5/10 - c**4/12 + 9*c**2. Solve q(z) = 0.
-1, -1/3, 0, 1
Let n = 103 - 307/3. Factor 0*i + 2/3*i**2 - n.
2*(i - 1)*(i + 1)/3
Let l be 2/10 - 0/2. Let r(u) be the first derivative of l*u**5 - u**2 + 0*u**3 + 1/2*u**4 - u + 2. Find i such that r(i) = 0.
-1, 1
Factor 0*p**3 + 8/5*p**2 + 0*p - 4/5 - 4/5*p**4.
-4*(p - 1)**2*(p + 1)**2/5
Suppose -3*b = 2*m - 19 - 3, b - 29 = -5*m. Determine j so that 0*j**b + 3*j - 7*j**3 + 3*j**2 - 2 + 3*j**4 + 0*j**4 = 0.
-2/3, 1
Solve -2/5*b - 2/5*b**2 + 0 = 0 for b.
-1, 0
Let z(v) be the first derivative of v**6/135 + v**5/30 + v**4/18 + v**3/27 + 2*v - 3. Let b(h) be the first derivative of z(h). Suppose b(i) = 0. What is i?
-1, 0
Let s(o) = o**4 - 2*o**2 - 4*o + 3. Let p(d) = -2*d**4 + 7*d**2 + d**3 + d**4 - 8 + 13*d - 3*d**4 - 2. Let j(b) = 4*p(b) + 14*s(b). Solve j(m) = 0.
-1, 1
Suppose 362*k = 355*k. Find c such that 1/2*c**4 + 5/4*c**3 + c**2 + 1/4*c + k = 0.
-1, -1/2, 0
Let b = 6/185 + 328/1295. Factor -18/7 - b*i**2 + 12/7*i.
-2*(i - 3)**2/7
Let w(o) = 2*o**2 - 4. Let u be w(-2). Find r such that -r**3 + 8*r**4 - 2*r**4 - 7*r**u + 2*r**5 = 0.
-1/2, 0, 1
Let u(t) be the third derivative of 3/10*t**5 + 7/60*t**6 + 0*t + 0*t**3 + 0 - t**2 + 1/6*t**4. Factor u(p).
2*p*(p + 1)*(7*p + 2)
Let x(k) = -4*k**3 - 8*k**2 - 2*k + 4. Let m(g) = -g**3 - g**2 - g + 1. Let f = 32 + -17. Let l(s) = f*m(s) - 3*x(s). Determine c so that l(c) = 0.
1
Suppose -m - 16 = -3*m. Suppose 7*b**2 - 2*b - b**3 + 3*b**3 + b**4 - m*b**4 = 0. What is b?
-1, 0, 2/7, 1
Let g = -169/3 - -191/3. Let m = g + -7. Factor 0 - m*l + 1/3*l**2.
l*(l - 1)/3
Let z(c) = c**3 + 8*c**2 - 9*c + 2. Let u be z(-9). Let y be u + (-32)/10 + 2. Factor 0 + y*g**2 + 0*g - 2/5*g**3.
-2*g**2*(g - 2)/5
Let z = 49/60 - 5/12. Let r be 2/17 + (-8)/68. Find p such that 2/5*p + 0 - z*p**3 + r*p**2 = 0.
-1, 0, 1
Suppose -2*t + 14 = -10. Suppose -5*a + 8 = -t. Factor 2*j + 8*j**2 - 10*j + 6*j**3 - a - 2*j.
2*(j - 1)*(j + 2)*(3*j + 1)
Let y(u) be the third derivative of u**7/945 - u**6/90 + u**5/30 - u**2. Find s such that y(s) = 0.
0, 3
Let o(n) be the second derivative of n**5/180 - n**4/24 + 2*n**2 + 4*n. Let f(a) be the first derivative of o(a). Factor f(u).
u*(u - 3)/3
Let z = -7 - -12. Let y = z - 5. Suppose 2*u**3 - 2*u**2 + y*u**2 - u**2 + 5*u**2 = 0. Calculate u.
-1, 0
Suppose -5*n + 3*f - 6 = -3*n, f - 2 = 3*n. Suppose -w - w = n. Factor 4*j**2 - 4*j**2 + 2*j**2 + 2*j + w*j**2.
2*j*(j + 1)
Let g(u) be the first derivative of -4*u**3/3 + 16*u - 48. Suppose g(q) = 0. Calculate q.
-2, 2
Suppose -12 + 2 = -2*q - 4*x, -4*q + 3*x = -20. Factor w + 4*w**3 - 6*w**3 + w**3 + q + w**2 - 6.
-(w - 1)**2*(w + 1)
Let r = -428/21 + 62/3. Determine g, given that 2/7*g - 2/7*g**3 - 2/7 + r*g**2 = 0.
-1, 1
Let b(r) be the first derivative of -r**6/540 - r**5/180 - 7*r**3/3 + 8. Let o(g) be the third derivative of b(g). Factor o(i).
-2*i*(i + 1)/3
Let i be (-5)/(-15) + (-3)/(-9). Factor 0 - i*c**4 + 4/3*c**3 - 2/3*c**2 + 0*c.
-2*c**2*(c - 1)**2/3
Let i be (6/(-5))/(6/(-40)). Let q be ((-3)/(-15))/(4/i). Solve 0*l + 2/5*l**3 + 0 - q*l**2 = 0 for l.
0, 1
Let c(w) be the third derivative of w**6/360 + w**5/60 + w**4/24 + w**3/18 + 7*w**2. Factor c(t).
(t + 1)**3/3
Let l(r) = -2. Let x(j) = j + 4. Let q(h) = 5*l(h) + 2*x(h). Let c be q(2). Factor 1/5 - 1/5*i**c + 0*i.
-(i - 1)*(i + 1)/5
Let -26 - 6*p + 6*p**3 + 3*p**4 - 12*p**2 + 18 + 17 = 0. Calculate p.
-3, -1, 1
Let p(m) be the third derivative of 1/420*m**7 - 1/120*m**5 + m**2 + 0 - 1/240*m**6 + 0*m + 0*m**3 + 1/48*m**4. Find v, given that p(v) = 0.
-1, 0, 1
Let l(k) be the third derivative of 0*k**3 + 2*k**2 + 0 + 0*k - 1/54*k**4 - 1/270*k**5. Factor l(d).
-2*d*(d + 2)/9
Let y be -1*3*1/(-6). Let d(k) be the first derivative of 0*k**3 + y*k**4 + 2 - k**2 + 1/5*k**5 - k. Factor d(a).
(a - 1)*(a + 1)**3
Suppose 11*n - n - 60 = 0. Suppose -n*w + w = -10. Determine x, given that -3/4 + 0*x + 3/4*x**w = 0.
-1, 1
Let c(r) = -6*r**3 + 6*r**2 + 8*r - 8. Let v(k) = 7*k**3 - 7*k**2 - 8*k + 8. Let o(b) = 5*c(b) + 4*v(b). Factor o(y).
-2*(y - 2)*(y - 1)*(y + 2)
Factor 0*g**2 + 2/11*g**3 + 0 - 2/11*g.
2*g*(g - 1)*(g + 1)/11
Let -6*u**3 - 6 + 2 - 9*u**4 + 7 - 2 + 8*u**2 + 6*u = 0. What is u?
-1, -1/3, 1
Let b(p) = p**3 - 4*p**2 - 3*p - 4. Let m be b(5). Let c be 57/132 + m/(-33). Factor c*d**5 - 1/4*d**3 + 0 - 1/4*d**4 + 0*d + 1/4*d**2.
d**2*(d - 1)**2*(d + 1)/4
Let x = 329 + -173. Let o = x + -60. Factor 34*g**4 + 95*g**3 + o*g**2 - 176*g**3 - 12*g - 150*g**3 + 113*g**4.
3*g*(g - 1)*(7*g - 2)**2
Let b(v) = -v + 5. Let l be b(0). Let f(t) be the second derivative of 0*t**2 - 1/6*t**4 + t + 0 - 3/20*t**l + 1/6*t**3. Factor f(u).
-u*(u + 1)*(3*u - 1)
Let c(i) be the second derivative of 0 + 2*i + 1/3*i**3 + 1/6*i**4 - 2*i**2. What is x in c(x) = 0?
-2, 1
Let p be 324/48 + 3/(-4). Let 7*b**2 + 0*b**3 + b**3 + 6*b + 8 - b**2 + p*b = 0. Calculate b.
-2
Let d be 3/(-4) - (42/8)/(-7). Let f(y) be the third derivative of 2*y**2 + 0*y**3 + 0 - 1/16*y**4 + d*y - 1/40*y**5. Factor f(i).
-3*i*(i + 1)/2
Factor 0 - 5/4*v**2 + 25/4*v**3 - 5/4*v - 15/4*v**4.
-5*v*(v - 1)**2*(3*v + 1)/4
Let n(g) be the first derivative of -4 + 6*g + 27/2*g**2 + 3*g**4 + 12*g**3. Factor n(b).
3*(b + 2)*(2*b + 1)**2
Solve -2/9*r**2 + 2/9*r**3 - 2/9*r + 2/9 = 0.
-1, 1
Suppose 7*d - 3*d + 6*d + 5*d**2 = 0. What is d?
-2, 0
Let f(t) be the first derivative of -t**7/21 + t**6/15 + t**5/10 - t**4/6 - 4*t + 3. Let n(k) be the first derivative of f(k). What is o in n(o) = 0?
-1, 0, 1
Let f(n) be the first derivative of 0*n + 1/8*n**2 + 1 + 1/6*n**3 - 1/10*n**5 + 0*n**4 - 1/24*n**6. Solve f(r) = 0 for r.
-1, 0, 1
Let x(q) be the third derivative of q**7/1260 - q**6/60 + 3*q**5/20 + q**4/24 - 2*q**2. Let l(r) be the second derivative of x(r). Find n, given that l(n) = 0.
3
Let c be (-1 - -1)/(-2 + 4). Factor 3*u**2 - u**4 + c*u**2 - 2*u**4.
-3*u**2*(u - 1)*(u + 1)
Let y(x) be the third derivative of -x**6/420 + x**5/42 - x**4/12 + x**3/7 - 3*x**2. Factor y(f).
-2*(f - 3)*(f - 1)**2/7
Let g(c) = c**3 - c**2 - c - 1. Let i be (-11 - (-1 + -1)) + 3. Let x(m) = -2*m**4 - 6*m**3 + 8*m**2 + 6*m + 6. Let s(f) = i*g(f) - x(f). Factor s(b).
2*b**2*(b - 1)*(b + 1)
Factor 6/7*q + 4/7 + 2/7*q**2.
2*(q + 1)*(q + 2)/7
Let s(i) be the second derivative of -i**4/30 + i**3/5 - 2*i**2/5 + 9*i. Let s(c) = 0. Calculate c.
1, 2
Let y = 34 + -34. Factor 4/7*b**3 - 2/7*b**2 + y*b - 2/7*b**4 + 0.
-2*b**2*(b - 1)**2/7
Find s such that -2*s - 8 + 2*s**2 - 2*s + 4*s = 0.
-2, 2
Let p(i) = 6*i**3 + 2*i**2 + 6*i - 7. Let o(x) = -x**3 - x + 1. Let w(d) = 14*o(d) + 2*p(d). Determine j so that w(j) = 0.
0, 1
Suppose 28 = -3*l - 4*h, -5*h - 9 = l - 4*h. Let g = l - -13. Solve -s**3 + s - 5*s + g*s = 0 for s.
-1, 0, 1
Factor -o - 7*o**3 + 4*o**2 + o**4 + 2*o**3 + o**4 + 0*o**3.
o*(o - 1)**2*(2*o - 1)
Let t(b) = -b**2 + b + 2. Let r = -3 + 5. Let p be t(r). Find l, given that 0 - 1/3*l**2 + p*l = 0.
0
Suppose -i + 0*i = -4. Suppose 2*g + 12 = i*p, -g - 4*g = -4*p + 18. Factor -1/5*f**4 + 1/5*f**3 + 0 + 0*f + 0*f**p.
-f**3*(f - 1)/5
Let i(a) be the second derivative of 0 + 1/2*a**3 + 0*a**4 - 1/720*a**6 + 0*a**2 + a - 1/240*a**5. Let g(j) be the second derivative of i(j). Factor g(f).
-f*(f + 1)/2
Let y(s) = -s + 9. Let g be y(7). Suppose 5*o + 2*w - 2 = g, 20 = 4*o - 4*w. Factor -q**3 - q**4 + q**o + q**3 - q**3 + q.
-q*(q - 1)*(q + 1)**2
Let u be (4*7/420)/(3/10). Factor 16/9*s - u - 32/9*s**2.
-2*(4*s - 1)**2/9
Factor 18*q + 6*q**4 + 44*q**2 - 22*q**4 - 12*q - 32*q**3 - 18*q.
-4*q*(q + 3)*(2*q - 1)**2
Let t(z) be the first derivative of -4/5*z**5 - 3*z**4 - 3 + 6*z**2 + 8*z - 4/3*z**3. Factor t(g).
-4*(g - 1)*(g + 1)**2*(g + 2)
Let l(o) be the first derivative of -3*o**5/5 + 15*o**4/4 - 9*o**3 + 21*o**2/2 - 6*o + 34. Factor l(f).
-3*(f - 2)*(f - 1)**3
Suppose -5*a + a + 8 = 0. Suppose -3 = -3*y + j, y = -a*j - 4 + 12. Factor y*k**2 + 0*k**2 - 1 - 16*k**2 + 8*k - 2*k**2.
-(4*k - 1)**2
Suppose v + 2 = -4*t, -t - 2*t = -v - 2. Let s(f) be the second derivative of 2/15*f**5 - 8/45*f**6 + t + 0*f**3 + 0*f**2 + f - 1/36*f**4. Factor s(g).
-g**2*(4*g - 1)**2/3
Factor -1/4*u**4 - 2 - 7/4*u**3 - 9/2*u**2 - 5*u.
-(u + 1)*(u + 2)**3/4
Let c(l) = -4*l**5 - 19*l**4 + 24*l**3 - 1