). Factor i(c).
2*(c - 2)*(c + 1)
Let f(x) be the second derivative of -x**9/7560 - x**8/840 - x**7/315 + x**4/4 + x. Let m(h) be the third derivative of f(h). Factor m(s).
-2*s**2*(s + 2)**2
Let y(x) = -2*x**3 + 14*x**2 + 10*x + 3. Let g(p) = -p**3 + p**2 + 1. Let z(u) = -6*g(u) + 2*y(u). Factor z(d).
2*d*(d + 1)*(d + 10)
Let z(w) be the first derivative of 2/21*w**3 + 8/7*w + 4 - 4/7*w**2. Factor z(i).
2*(i - 2)**2/7
Let j = -4 - -6. Suppose 5*h - 10 = -5*p + 15, 4*p + h = 5. Factor -2/9*f**j - 2/9*f**4 + p*f - 4/9*f**3 + 0.
-2*f**2*(f + 1)**2/9
Let p = -1 + 4. Determine w so that -2*w**2 + 0*w**4 - 2*w - w**3 - 4*w**4 + 6*w**4 + 3*w**p = 0.
-1, 0, 1
Suppose -4*q = -5*q. Let f = q + 3. Solve 0*p + 0 + 2/9*p**f + 0*p**2 + 10/9*p**4 + 8/9*p**5 = 0 for p.
-1, -1/4, 0
Factor 0 + 4/7*w**3 - 8/7*w**2 + 4/7*w.
4*w*(w - 1)**2/7
Suppose 0*p = 2*p. Let y(g) be the second derivative of 0*g**4 + 0*g**5 + 0 - g + 1/21*g**7 + p*g**2 + 0*g**3 + 1/15*g**6. Factor y(d).
2*d**4*(d + 1)
Let l(h) be the third derivative of h**5/90 + 17*h**4/18 + 289*h**3/9 - 2*h**2 - 2*h. Factor l(c).
2*(c + 17)**2/3
Let w be -3 + (-1 - -4)*1. Let v(t) be the second derivative of w - 3/80*t**5 - 1/12*t**3 + 0*t**2 + 5/48*t**4 + 2*t. Factor v(d).
-d*(d - 1)*(3*d - 2)/4
Suppose 0 = -2*j + 4, 2*o - 3*j + 8 = j. Let k(h) be the second derivative of o + 0*h**3 + 1/18*h**4 + h + 1/30*h**5 + 0*h**2. Factor k(y).
2*y**2*(y + 1)/3
Let x(y) be the first derivative of -5 + 0*y**4 + 0*y**2 + 2/55*y**5 + 0*y + 0*y**3. Suppose x(q) = 0. Calculate q.
0
Let z be 357/(-33) - 4/22. Let w(c) = -2*c**2 + 2*c - 6. Let x(b) = 4*b**2 - 4*b + 11. Let s(t) = z*w(t) - 6*x(t). Factor s(o).
-2*o*(o - 1)
Let g(i) be the third derivative of i**6/220 - 2*i**5/165 + i**4/132 + 15*i**2. Find b, given that g(b) = 0.
0, 1/3, 1
Let u(b) = -b**3 - 10*b**2 + 11*b - 16. Let d be u(-12). What is w in -d*w + w**2 + 140*w = 0?
0
Suppose -3*y**3 - 21 - 11 + 8 - 24 - 24*y + 21*y**2 = 0. Calculate y.
-1, 4
Let i(x) = -x**4 + 5*x**3 + 2*x**2 - 1. Let f(t) = -t**3. Let o(j) = 20*f(j) + 4*i(j). Factor o(m).
-4*(m - 1)**2*(m + 1)**2
Let q(t) = -t - 9. Let c be q(0). Let v(u) = u**2 + 9*u + 2. Let z be v(c). Determine w, given that 0 + 2/3*w**3 - 1/3*w**4 - 1/3*w**z + 0*w = 0.
0, 1
Let r(n) be the second derivative of -n**4/24 - n**3/12 + n**2/2 + n. Solve r(i) = 0 for i.
-2, 1
Let x(y) = -y**3 - 25*y**2 - 25*y - 24. Let f be x(-24). Factor 0*u + f + 1/2*u**2 - 1/2*u**3.
-u**2*(u - 1)/2
Factor -3/5*r**4 - 21/5*r**3 - 12*r - 24/5 - 54/5*r**2.
-3*(r + 1)*(r + 2)**3/5
Let l(q) be the first derivative of q**4/10 + 8*q**3/15 - 11*q**2/5 + 12*q/5 + 8. Factor l(k).
2*(k - 1)**2*(k + 6)/5
Suppose 0*z - 11 = 4*z - 3*t, 0 = 3*z - 3*t + 12. Let o = z + 0. Solve 1 - 5*d**3 - o + 7*d**3 - 2*d = 0.
-1, 0, 1
Let r = -62 - -127/2. What is d in -3/4*d**4 + 3/4 - r*d + 3/2*d**3 + 0*d**2 = 0?
-1, 1
Let p be (-3)/(-2) + 2052/(-48). Let f = p + 42. Solve f*u**5 + 1/4*u**2 - 1/4*u**4 + 0 + 0*u - 3/4*u**3 = 0 for u.
-1, 0, 1/3, 1
Let u = 615 - 612. Factor -1/5*a**u + 4/5*a**2 - a + 2/5.
-(a - 2)*(a - 1)**2/5
Let j(v) be the third derivative of v**6/1080 + v**5/360 - 2*v**3/3 + 5*v**2. Let z(m) be the first derivative of j(m). Solve z(s) = 0.
-1, 0
Let z(t) = -t**2 + 9*t - 14. Let u be z(7). Determine h so that -2/5*h**2 + 2/5*h + u = 0.
0, 1
Suppose 0*y + 7*y - 168 = 0. Let t be ((-16)/y)/(1/(-3)). Suppose -1/3 + k**t + 2/3*k = 0. Calculate k.
-1, 1/3
Let w(x) be the third derivative of -x**5/80 + 9*x**4/8 - 81*x**3/2 - 65*x**2. Let w(b) = 0. What is b?
18
Let w(i) be the first derivative of 2 + 1/3*i**3 + 0*i + 1/4*i**4 + 0*i**2. Suppose w(b) = 0. What is b?
-1, 0
Let p be (-22)/132 - (-38)/12. Let u(c) be the first derivative of 1 + 0*c**2 + 1/14*c**4 + 2/21*c**p + 0*c. Factor u(s).
2*s**2*(s + 1)/7
Let x(c) = -8*c**4 + 4*c**2 + 4*c + 4. Let v(z) = -15*z**4 + 8*z**2 + 7*z + 7. Let y(w) = -4*v(w) + 7*x(w). Factor y(p).
4*p**2*(p - 1)*(p + 1)
Let x(l) be the second derivative of -2/3*l**2 + 1/9*l**4 - 1/9*l**3 + 1/30*l**5 - l + 0. Find q such that x(q) = 0.
-2, -1, 1
Let t(p) be the second derivative of -p**8/3360 - p**7/420 - p**6/120 - p**5/60 - p**4/12 + p. Let b(i) be the third derivative of t(i). Factor b(o).
-2*(o + 1)**3
Let i be (-4)/(-7)*(-28)/(-8). Let t be (-3)/(-84) - (-2)/8. Factor t*b**i + 6/7*b**3 - 4/7*b + 0.
2*b*(b + 1)*(3*b - 2)/7
Let q = 277/1515 - 5/101. Let g(n) be the first derivative of -2 - 1/5*n**2 - q*n**3 + 1/10*n**4 + 2/5*n. Solve g(m) = 0 for m.
-1, 1
Suppose -y - 5*q - 1 = 2*y, -q = 4*y - 10. Suppose 2*b + c - 5 = -2*b, 8 = b - 2*c. Let b*f**4 - f**2 - f**5 + 2*f**4 - y*f**3 - 7*f**4 = 0. Calculate f.
-1, 0
Let r = 1862 - 24142/13. Determine i so that -48/13*i**2 - 2/13*i**4 - r*i - 16/13*i**3 - 32/13 = 0.
-2
Factor 0 - 2/7*s**3 + 0*s - 4/7*s**2.
-2*s**2*(s + 2)/7
Let h(c) be the second derivative of 1/15*c**6 - 1/5*c**5 + c**2 - 1/3*c**4 + 0 + 1/21*c**7 + 1/3*c**3 + c. Suppose h(n) = 0. What is n?
-1, 1
Let l(y) = y - 3. Let v be l(7). Factor -6*f**2 - 8*f - v*f**2 - f**3 - 4 + 5*f**2.
-(f + 1)*(f + 2)**2
Let x = -383 + 1153/3. Factor -x*o + 0 - 2/3*o**2.
-2*o*(o + 2)/3
Let w = -2931/16 + 183. Let h = 7/16 + w. Solve 1/4 - 1/2*d + h*d**2 = 0 for d.
1
Find y such that 2*y**2 - 5*y**2 + 3*y + 6*y**2 - 6 = 0.
-2, 1
Let r(j) be the third derivative of 5*j**8/168 + j**7/14 - j**5/12 - j**2. Factor r(a).
5*a**2*(a + 1)**2*(2*a - 1)
Let b(u) be the first derivative of -u - 2 + 1/9*u**3 + 0*u**2 + 1/36*u**4. Let g(z) be the first derivative of b(z). Suppose g(s) = 0. Calculate s.
-2, 0
Let y(o) be the first derivative of -1/4*o**4 - 27*o - 27/2*o**2 - 3*o**3 - 1. Let y(b) = 0. Calculate b.
-3
Let t be (-28)/(-4) - 6 - -1. Suppose -m - 5*x + 15 = -5*m, -x = -3. Factor m*q**t + 0 - 2/13*q**3 + 2/13*q.
-2*q*(q - 1)*(q + 1)/13
Let x(g) be the first derivative of g**3/3 + g**2 - 1. Suppose x(a) = 0. What is a?
-2, 0
Let d = 5 - 4. Let t be (d - (5 - 2)) + 2. Find m such that t*m**2 + m**2 + m - m**3 + 3*m**4 - 4*m**4 = 0.
-1, 0, 1
Let o(n) be the first derivative of -2/9*n**3 + 0*n + 2 + 0*n**2 + 1/18*n**4. Factor o(f).
2*f**2*(f - 3)/9
Solve 10/3*d - 2/3*d**3 - 4/3 + 2/3*d**4 - 2*d**2 = 0.
-2, 1
Factor 0*v + 0 - 2/9*v**2.
-2*v**2/9
Factor -3*u + 3*u + 3*u**2 - 3*u + 3 - 3*u.
3*(u - 1)**2
Let l(i) be the second derivative of -i**5/10 - i**4/2 + 4*i**2 - 3*i. Factor l(g).
-2*(g - 1)*(g + 2)**2
Let o = -157 + 157. Factor 1/2*d**3 + o + 0*d + 1/2*d**2.
d**2*(d + 1)/2
Let m(y) be the second derivative of y**4/18 - 2*y**3/27 - y**2/9 + 3*y - 2. Factor m(t).
2*(t - 1)*(3*t + 1)/9
Let t be (-56)/(-22)*3/6. Find y, given that 0 + 4/11*y + 32/11*y**3 + 2*y**2 + t*y**4 = 0.
-1, -2/7, 0
Let w(i) be the third derivative of -i**8/84 - 2*i**7/105 + 7*i**2. Factor w(t).
-4*t**4*(t + 1)
Let y(v) be the third derivative of v**8/1008 + v**7/126 + 7*v**6/360 - v**5/180 - v**4/9 - 2*v**3/9 + 18*v**2. Solve y(l) = 0.
-2, -1, 1
Let z be (-13)/(-4) + (1 - 1) + -3. Factor -1/2*b + z*b**2 + 0.
b*(b - 2)/4
Let 0 + 1/9*i**2 + 2/9*i = 0. What is i?
-2, 0
Let d = -21 + 29. Find b, given that -2*b + d*b - 2 + b - 5*b**2 + 0 = 0.
2/5, 1
Let d(x) = -5*x**4 - 17*x**3 - 27*x**2 - 20*x - 2. Let k(v) = -60*v**4 - 205*v**3 - 325*v**2 - 240*v - 25. Let g(h) = 35*d(h) - 3*k(h). Factor g(o).
5*(o + 1)**4
Let t be (-4)/(-26) + 2016/2106. Factor -2*n**2 - 4/9 - 14/9*n - t*n**3 - 2/9*n**4.
-2*(n + 1)**3*(n + 2)/9
Let n(d) be the first derivative of d**7/70 + d**6/20 + d**5/20 + 3*d**2 - 6. Let q(l) be the second derivative of n(l). Suppose q(v) = 0. Calculate v.
-1, 0
Let j(s) = -s**3 + 10*s**2 - 7*s - 16. Let y be j(9). Factor 1/3*p - 4/3*p**y + 0.
-p*(4*p - 1)/3
Let p = 101 - 99. Let t(j) be the second derivative of -1/6*j**3 + 3/80*j**5 + 0 + 0*j**p - 3*j + 0*j**4 - 1/120*j**6. Factor t(z).
-z*(z - 2)**2*(z + 1)/4
Suppose -2*c + 24 = c. Suppose -3*b = b - c. Determine z, given that z**3 - 1/2*z**b - 1/2*z**4 + 0*z + 0 = 0.
0, 1
Let q(d) be the second derivative of -3/2*d**2 + 0*d**3 - 2*d + 0 - 1/108*d**4 + 1/270*d**5. Let i(m) be the first derivative of q(m). Factor i(y).
2*y*(y - 1)/9
Let v(g) be the first derivative of 81/2*g**2 - 9*g**3 + 3/4*g**4 - 81*g - 6. Solve v(h) = 0 for h.
3
Let m(h) be the first derivative of h**6/75 - 3*h**5/50 + h**4/10 - h**3/15 - 2*