 -k**5/30 - k**4/12 + 2*k**3/3 + 35*k**2. Factor z(n).
-2*(n - 1)*(n + 2)
Factor -3/7*w**2 - 6/7*w - 3/7.
-3*(w + 1)**2/7
Let u = 431/2105 + -2/421. Solve 0 + 1/5*h**2 + u*h**3 - 1/5*h - 1/5*h**4 = 0 for h.
-1, 0, 1
Suppose 5*o - 3*o = 10. Suppose -2*m = 3*i - 3 - 3, -o*i = -m - 10. Solve 0*x**2 + 5*x**2 - 5*x**i - 2*x**2 + 2*x**4 = 0.
-1, 0, 1
Let k(b) be the third derivative of -b**8/21 + 6*b**7/35 - b**6/5 + b**5/15 - 3*b**2. Factor k(y).
-4*y**2*(y - 1)**2*(4*y - 1)
Let d = -3 + 3. Suppose 5*h + 4*o = o + 30, d = 3*h - 4*o + 11. Let -1/3 - 2*v**2 + 4/3*v**h + 4/3*v - 1/3*v**4 = 0. What is v?
1
Let i(h) = -2*h. Let c be i(-7). Suppose 5*b - c = -5*z + 21, 5*z - b = 11. Factor 0*k**z + 2*k**3 + 4*k**2 - 2*k**4 + 0*k**4.
-2*k**2*(k - 2)*(k + 1)
Factor -4 - 2/3*y**2 - 10/3*y.
-2*(y + 2)*(y + 3)/3
Let d(x) be the first derivative of x - 3/8*x**4 - 2 + 3/4*x**2 - 1/10*x**5 - 1/6*x**3. Factor d(s).
-(s - 1)*(s + 1)**2*(s + 2)/2
Suppose 0*l = l + 3. Let p be (2/l)/(44/(-12)). Factor 0*u + 0 + p*u**4 + 0*u**3 + 0*u**2 - 2/11*u**5.
-2*u**4*(u - 1)/11
Let i = -33 + 101/3. Solve 0*p**2 + 8/9*p**3 + 2/9 - i*p = 0.
-1, 1/2
Suppose -16 = -3*g - g. Factor 16*r**4 - 1 - 3*r**2 - 13*r**g + 1.
3*r**2*(r - 1)*(r + 1)
Let s = -474 - -479. Let a = -1/20 + 3/10. Let 1/2*b**s + a*b**2 + 0 - 1/4*b**4 - 1/2*b**3 + 0*b = 0. What is b?
-1, 0, 1/2, 1
Let c(z) be the second derivative of z**7/294 + z**6/70 + z**5/70 - 10*z. Factor c(b).
b**3*(b + 1)*(b + 2)/7
Let h(b) be the first derivative of -b**4/16 - 5*b**3/12 - 3*b**2/8 + 9*b/4 - 3. Factor h(d).
-(d - 1)*(d + 3)**2/4
Factor 0*m**5 + 3*m**4 + 2*m**3 + 3*m**5 + 8*m + 2*m**5 - 6*m**5 - 12*m**2.
-m*(m - 2)**2*(m - 1)*(m + 2)
Let g(u) be the third derivative of -u**8/840 - 4*u**7/525 - u**6/60 - u**5/75 - 3*u**2. Factor g(t).
-2*t**2*(t + 1)**2*(t + 2)/5
Suppose 176 = 5*f - 2*b, 2*f + b - 2*b - 71 = 0. Let u = f + -34. Determine p so that 5/3*p**5 + 2/3*p**2 - 5/3*p**3 - 2/3*p**4 + 0*p + u = 0.
-1, 0, 2/5, 1
Let p(r) = -r**4 - 13*r**3 + r**2 + 8*r - 5. Let y be (-7)/14 - (-9)/(-2). Let c(i) = 12*i**3 - 8*i + 4. Let h(j) = y*c(j) - 4*p(j). Factor h(g).
4*g*(g - 2)*(g - 1)*(g + 1)
Suppose 0 = c + 4*n - 9, 4*c = -3*n + 4*n + 2. Let z be (-22)/12*c*-2. Factor -q**5 - z*q - 26/3*q**3 - 8*q**2 - 14/3*q**4 - 2/3.
-(q + 1)**4*(3*q + 2)/3
Let c be (-273)/52*6/(-21) + -1. Factor -1/2*f**5 + c*f**3 + 0 + 1/2*f**2 - 1/2*f**4 + 0*f.
-f**2*(f - 1)*(f + 1)**2/2
Factor 12*x**3 + 92*x**2 + 2*x**4 - 101*x**2 - 5*x**4.
-3*x**2*(x - 3)*(x - 1)
Let q(r) = 4*r**5 - 7*r**4 - 3*r**2 + r. Let j(c) = c**4 - 5*c**5 - 2*c**4 - c**2 + 2*c**5 + 4*c**5. Let i(u) = -5*j(u) + q(u). Factor i(w).
-w*(w - 1)*(w + 1)**3
Let c(h) be the second derivative of -1/24*h**3 + 0 - 1/80*h**5 + 0*h**2 - 1/24*h**4 + 3*h. Factor c(r).
-r*(r + 1)**2/4
Let q(x) be the first derivative of -x**6/2 + 6*x**5/5 + 3*x**4/2 - 8*x**3 + 21*x**2/2 - 6*x - 10. Factor q(w).
-3*(w - 1)**4*(w + 2)
Let c(a) = 3*a - 1. Let l be c(1). Factor -6*t + 3 + 0*t**2 - 5 - 4*t**l + 12*t.
-2*(t - 1)*(2*t - 1)
Solve 3/2 + 3*z**4 - 3*z**3 + 9/4*z**5 + 3/4*z - 9/2*z**2 = 0.
-1, 2/3, 1
Let p = 1/18 - -4/9. Solve -p*f**4 + 0*f - 1/2 + f**2 + 0*f**3 = 0.
-1, 1
Let c(v) be the third derivative of 0*v + 4*v**2 + 8/9*v**3 + 4/9*v**4 + 1/45*v**6 + 2/15*v**5 + 1/630*v**7 + 0. Determine n so that c(n) = 0.
-2
Suppose 0 = 7*s + 13*s - 60. Suppose 0*t + 0*t**2 + 0 + 2/5*t**5 + 2/5*t**4 + 0*t**s = 0. What is t?
-1, 0
Let k(g) be the first derivative of g**6/180 + g**5/60 + g**4/72 - 2*g + 2. Let m(r) be the first derivative of k(r). Factor m(i).
i**2*(i + 1)**2/6
Let z(g) be the third derivative of -g**6/1020 - g**5/510 + 64*g**2. Solve z(d) = 0 for d.
-1, 0
Let o be (8*12/(-30))/((-6)/10). Suppose 1/3 + 5/3*b**2 + 2*b - 16/3*b**3 + o*b**5 - 4*b**4 = 0. Calculate b.
-1/2, -1/4, 1
Let l(k) = k**2. Let j = 9 + -13. Let p(w) = 8*w**2 - w. Let a(d) = j*l(d) + p(d). Factor a(s).
s*(4*s - 1)
Suppose 0 = 2*x + 4 - 8. Factor 2 + r**5 + 2*r**3 + r**4 - 6 + 2*r**4 - x*r**2 + 3 - 3*r.
(r - 1)*(r + 1)**4
Let y be (-2)/(-3) - (-106)/(-168). Let s = y - -13/28. Factor 0*c**3 - c**2 + c**4 - 1/2*c + 0 + s*c**5.
c*(c - 1)*(c + 1)**3/2
Let y(x) be the third derivative of x**8/80640 - x**7/6720 + x**6/1440 - x**5/20 - 5*x**2. Let w(v) be the third derivative of y(v). Let w(q) = 0. Calculate q.
1, 2
Let y(p) = 2*p**2 + 3*p + 3. Let t be y(-3). Suppose -3 - t = -5*c. Suppose -6/5*h**5 + 2*h**c - 2*h**2 + 0 + 2*h**4 - 4/5*h = 0. What is h?
-1, -1/3, 0, 1, 2
Let d = -58 + 19. Let n be 6/d - (-4)/26. Factor 0 + n*g**2 - 3/4*g**3 + 3/4*g.
-3*g*(g - 1)*(g + 1)/4
Let i(z) be the second derivative of -1/12*z**4 - 2*z + 0 + 1/42*z**7 + 1/30*z**6 + 0*z**2 + 0*z**3 - 1/20*z**5. Solve i(m) = 0 for m.
-1, 0, 1
Let a be -1 - (0 - 0) - -21. Suppose 4*p + 5*h = a, 5*p + 5*h = 3*p + 20. Suppose -2/7 + p*f + 2/7*f**2 = 0. Calculate f.
-1, 1
Let k = 9 + -5. Suppose 0 = z + k*m, 2*z = 3*z + m - 3. Solve -14*f**5 - 66*f**3 + 58/3*f**2 - 8/3 + 166/3*f**z + 8*f = 0 for f.
-1/3, 2/7, 1, 2
Let p = 401/35 + -76/7. Determine d, given that -p*d**2 + 2/5*d + 1/5*d**4 + 0 + 0*d**3 = 0.
-2, 0, 1
Let m(s) = -3*s + 27. Let v be m(8). Let g(u) be the first derivative of -5/3*u**2 + 0*u**v + 1/3*u**6 + 1 + 5/3*u**4 - 4/3*u + 4/3*u**5. Factor g(n).
2*(n + 1)**4*(3*n - 2)/3
Let u(c) = -c**2 - 4*c + 3. Suppose 5*m - 6*m - 4 = 0. Let g be u(m). What is w in 7*w**5 + 0 + 3/2*w**2 - 3/2*w**4 - 8*w**g + w = 0?
-1, -2/7, 0, 1/2, 1
Let y(w) be the third derivative of 1/18*w**5 + 0*w**3 + 0*w + 3*w**2 - 7/180*w**6 + 1/18*w**4 + 0. Factor y(n).
-2*n*(n - 1)*(7*n + 2)/3
Let k(i) be the first derivative of -1/10*i**5 + 0*i**4 + 0*i**2 + 2 + 1/6*i**3 + 0*i. Solve k(w) = 0.
-1, 0, 1
Factor -3/5*g**3 + 3/5*g**4 + 3/5*g + 0 - 3/5*g**2.
3*g*(g - 1)**2*(g + 1)/5
Suppose 4*w - 2*f - 10 = -w, -5*f = -2*w + 25. Suppose w = 2*j - 3*j. Factor 0 + j*u - 4/9*u**2 + 2/9*u**3.
2*u**2*(u - 2)/9
Suppose -9*c + 129 = 93. Solve 3*b**3 + 0 + 4*b - 1/2*b**c - 6*b**2 = 0.
0, 2
Let x be 8/(-30) + (-5)/(-50)*6. Let y = -208/3 + 70. Factor y - x*g**3 + 1/3*g - 2/3*g**2.
-(g - 1)*(g + 1)*(g + 2)/3
Let h = -752/3 + 254. Find d such that -14/3*d + 4/3 + h*d**2 = 0.
2/5, 1
Determine j so that 12*j**2 - 16*j**3 - 15*j**3 - 12*j + 35*j**3 - 4*j**2 = 0.
-3, 0, 1
Let l be 16/3 - (-2 + 7/3). Let m(b) be the third derivative of 1/60*b**4 + b**2 + 0 + 1/150*b**l + 0*b - 2/15*b**3. Solve m(r) = 0 for r.
-2, 1
Let n(r) be the third derivative of 0 - 3/20*r**4 + r**2 + 7/150*r**5 + 0*r + 2/15*r**3. Let n(d) = 0. Calculate d.
2/7, 1
Factor 2/9*m**4 - 2/9*m + 0 - 2/9*m**2 + 2/9*m**3.
2*m*(m - 1)*(m + 1)**2/9
Factor 4/9*w - 2/9*w**2 + 0.
-2*w*(w - 2)/9
Let a(m) be the first derivative of -m**6/42 + 3*m**5/35 - 3*m**4/28 + m**3/21 - 3. Determine f so that a(f) = 0.
0, 1
Let a(m) be the second derivative of m**5/130 - m**4/26 + 2*m**3/39 + m. Factor a(u).
2*u*(u - 2)*(u - 1)/13
Let p = 1/66 + 7/22. Factor 0 - p*a**2 - 1/3*a.
-a*(a + 1)/3
Let f(n) = n + 11. Let i be f(-9). Suppose -5 = -i*w + 1. Find j such that 3/2*j**2 + j**w - 1/2 + 0*j = 0.
-1, 1/2
Factor 1/3 + 1/6*u - 1/6*u**2.
-(u - 2)*(u + 1)/6
Let c(a) be the first derivative of 2*a**3/21 + 2*a**2 + 14*a + 52. What is h in c(h) = 0?
-7
Let v(b) be the first derivative of 3*b - 4 + 3*b**3 - 9/2*b**2 - 3/4*b**4. Factor v(l).
-3*(l - 1)**3
Let o = 6669/5 - 1333. Let -3/5*l + 0*l**4 + o*l**3 - 1/5*l**5 + 2/5 - 2/5*l**2 = 0. Calculate l.
-2, -1, 1
Let q(v) be the third derivative of -v**6/180 - v**5/15 - v**4/3 - 8*v**3/9 - 8*v**2. Find d, given that q(d) = 0.
-2
Let s(t) = -4*t**4 - 8*t**3 + 8*t + 8. Let v(l) = -8*l**4 - 16*l**3 + 16*l + 15. Let u(h) = 7*s(h) - 4*v(h). Determine n, given that u(n) = 0.
-1, 1
Let h(t) be the second derivative of t**8/168 + t**7/35 + t**6/20 + t**5/30 + t**2 + 2*t. Let n(v) be the first derivative of h(v). What is s in n(s) = 0?
-1, 0
Let s(l) be the first derivative of 4/15*l**5 + 0*l**2 + 0*l + 1/6*l**4 + 4 - 2/9*l**3. Find p such that s(p) = 0.
-1, 0, 1/2
Suppose -2*c - 4*g + 5 = -9*g, 3 = -3*g. Factor -1/2*b**4 + 2*b**3 + c + 0*b - 2*b**2.
-b**2*(b - 2)**2/2
Let m(y) be the first derivative of -y**4/12 + y**3/2 - y**2 + y - 3. Let h(u) be the first derivative of m(u). Factor h(l).
-(l - 2)*(l - 1)
Let s be (-3)/5*4/(-12). L