(q - 1)**2
Let y(g) be the second derivative of 0 + 1/36*g**6 + 1/12*g**2 - 5/36*g**3 + 5/36*g**4 - 2*g - 1/252*g**7 - 1/12*g**5. Factor y(a).
-(a - 1)**5/6
Let m(k) = k**3 - 2*k**2 + 3*k - 4. Let z be m(2). Suppose -2/3*c**z + 1/3*c**4 + c**5 + 1/3 - 2*c**3 + c = 0. What is c?
-1, -1/3, 1
Suppose 0 = 6*h - 2*h. Suppose t + 4*t - 15 = h. Factor t*n**4 - 2*n**2 - 2*n**5 + 0*n**4 - 6*n**3 - 9*n**4.
-2*n**2*(n + 1)**3
Let w = 118/3 - 39. Let g(f) be the first derivative of -w*f - 2 - 1/9*f**3 + 1/3*f**2. Factor g(x).
-(x - 1)**2/3
Let n = 85 - 254/3. Solve -2/3*b - 1/3*b**2 + n*b**3 + 0 = 0 for b.
-1, 0, 2
Let o(c) = 0 + c + 6*c**4 - c**2 + 1 + 0*c**4 - 5*c**4 - c**3. Let t(p) = p**4 - 11*p**3 + 19*p**2 - 9*p - 5. Let u(f) = 5*o(f) + t(f). Factor u(q).
2*q*(q - 1)**2*(3*q - 2)
Suppose -2*z - f - 17 = 4*f, -z - 5*f - 21 = 0. Factor 0 + 0*c - 2/7*c**3 - 2/7*c**2 + 4/7*c**z.
2*c**2*(c - 1)*(2*c + 1)/7
Let c be 3 - (-26)/39*(-10)/4. Let s(p) = -p**3 - 7*p**2 - 7*p - 3. Let i be s(-6). Determine n so that 0 - c*n**2 + 2/3*n**i + 2/3*n = 0.
0, 1
Let x(y) be the first derivative of -2*y**3/9 + 10*y**2/3 - 50*y/3 - 1. Solve x(o) = 0.
5
Let s(q) be the third derivative of -q**6/720 + q**5/80 - q**4/24 - q**3/2 - 5*q**2. Let f(r) be the first derivative of s(r). Factor f(d).
-(d - 2)*(d - 1)/2
Suppose -88*l + 86*l + 8 = 0. Let c(m) be the second derivative of 0 - 3/2*m**l - 13/10*m**5 + 2*m**2 - 1/3*m**6 + 1/3*m**3 - 4*m. Let c(k) = 0. Calculate k.
-1, 2/5
Let o(s) = 2 + 4*s - 5*s**2 + 4*s**2 - 5*s + 0*s**2. Let n be o(0). Find c, given that 1/4*c - 1/2*c**4 - 1/4*c**5 + 0*c**3 + 1/2*c**n + 0 = 0.
-1, 0, 1
Let a = 1223/11 + -111. Factor -a*w**5 + 0 + 4/11*w**4 + 0*w**3 - 4/11*w**2 + 2/11*w.
-2*w*(w - 1)**3*(w + 1)/11
Let w(s) = -4 + 13*s + 4*s**3 + 13*s**2 - 2*s**3 - 10*s. Let u(p) = -p**3 - 14*p**2 - 3*p + 5. Let j(q) = -4*u(q) - 5*w(q). Find r such that j(r) = 0.
-1, -1/2, 0
Let w(d) be the third derivative of d**7/140 - 3*d**5/40 - d**4/8 - 14*d**2. Suppose w(n) = 0. What is n?
-1, 0, 2
Let w = 28/3 - 49/12. Let -w*t**3 + 0 - 9/4*t**4 - 4*t**2 - t = 0. What is t?
-1, -2/3, 0
Let r(t) be the second derivative of -t**4/12 - 2*t**3/3 - 6*t. Let y be r(-4). Factor 1/2*j**2 - 1/2*j**4 + 0*j**3 + 1/4*j**5 + y - 1/4*j.
j*(j - 1)**3*(j + 1)/4
Let d(t) be the third derivative of t**6/80 - t**5/20 + t**4/16 - 18*t**2. Factor d(b).
3*b*(b - 1)**2/2
Let o(v) be the first derivative of v**5/15 + 2*v**4/3 + 2*v**3 + 5*v**2/2 - 4. Let s(d) be the second derivative of o(d). Find t, given that s(t) = 0.
-3, -1
Let l(x) be the first derivative of x**6/57 + 4*x**5/95 - x**4/38 - 4*x**3/57 - 2. What is g in l(g) = 0?
-2, -1, 0, 1
Let u(q) be the second derivative of q**5/30 - q**4/6 + q**3/3 - q**2/3 + 10*q. Factor u(o).
2*(o - 1)**3/3
Let o(a) = -3*a - 86. Let z be o(-30). Solve 34/5*v**2 - 8/5 + 0*v + 36/5*v**3 + 2*v**z = 0 for v.
-2, -1, 2/5
Suppose 5 = 3*i - 1. Factor 9*m + 0*m + 23*m**2 - 12*m**2 - 6 - 14*m**i.
-3*(m - 2)*(m - 1)
Suppose 0*i**3 + 8*i**2 + 5*i**3 - 13*i**2 = 0. Calculate i.
0, 1
Let t(r) be the third derivative of 2*r**2 + 0*r**3 - 1/420*r**6 - 1/1176*r**8 + 0 + 0*r**5 - 2/735*r**7 + 0*r + 0*r**4. Let t(l) = 0. Calculate l.
-1, 0
Let r(s) = 20*s**3 + 76*s**2 - 16*s - 16. Let q(u) = -4*u**3 - 15*u**2 + 3*u + 3. Let c(g) = -16*q(g) - 3*r(g). Suppose c(z) = 0. What is z?
-3, 0
Let c(h) be the second derivative of -6*h + 1/42*h**4 - 1/294*h**7 + 0*h**2 + 0*h**5 - 1/105*h**6 + 0 + 1/42*h**3. Find o, given that c(o) = 0.
-1, 0, 1
Let j(w) = w**2 + 3*w + 4. Let i be j(14). Let c = -2176/9 + i. Factor 6*u + 2*u**2 + c*u**3 + 6.
2*(u + 3)**3/9
Let h = -5/8 - -23/24. Factor q**2 + h*q**3 - 1/3*q + 0 - q**4.
-q*(q - 1)*(q + 1)*(3*q - 1)/3
Suppose -2*f - 3*f + 3*a = -7, -4 = -f - 2*a. Suppose -k**2 - k**f + 5*k**2 - 7*k + 2 = 0. What is k?
1/3, 2
Let r(l) be the second derivative of -l**6/315 - l**5/105 + 12*l. Find h, given that r(h) = 0.
-2, 0
Let i(z) be the second derivative of -7*z**4/36 - 3*z**3 + 8*z**2/3 + 9*z. Determine h so that i(h) = 0.
-8, 2/7
Let k(j) = j**2 - 6*j + 2. Let i be k(6). Factor -3 + 2*y + y**2 + 2*y + 1 - 3*y**i.
-2*(y - 1)**2
Let k(a) be the first derivative of -a**8/1008 - 4*a**2 - 8. Let o(g) be the second derivative of k(g). Factor o(d).
-d**5/3
Let w(t) = -t + 1 + 0 + t**2 - t. Let b = 8 - 10. Let j(i) = i**2 - i. Let r(f) = b*j(f) + w(f). Determine n so that r(n) = 0.
-1, 1
Factor -4/3*c**3 + 8*c**2 - 20/3*c + 0.
-4*c*(c - 5)*(c - 1)/3
Let s(z) = -z**3 - z**2 + 1. Let m(k) be the first derivative of -1 - 1/4*k**4 - k**2 - k**3 + 3*k. Let a(c) = -m(c) + 3*s(c). Suppose a(i) = 0. What is i?
-1, 0, 1
Let h(c) be the third derivative of -c**5/75 + c**4/5 - 6*c**3/5 - 3*c**2. Let h(k) = 0. What is k?
3
Let s(k) be the third derivative of -k**10/226800 + k**9/30240 - k**8/15120 - k**5/20 + 3*k**2. Let n(o) be the third derivative of s(o). Factor n(c).
-2*c**2*(c - 2)*(c - 1)/3
Let 3*n**3 + 5 + 1 + 0 - 2*n - 7*n = 0. What is n?
-2, 1
Let s be (-6 - -8)*1/1. Suppose 0 = -3*t + s + 4. Find y, given that y**2 + 3*y + y + y**t + 0*y = 0.
-2, 0
Let w(k) be the third derivative of -k**5/120 + k**4/16 - k**3/6 + 2*k**2 - 7*k. Factor w(f).
-(f - 2)*(f - 1)/2
Let x(a) = -6*a - 2. Let v(d) = d + 1. Let k(c) = -5*v(c) - x(c). Let l be k(5). Solve 5*g**3 + g**3 - 4*g**4 - 4*g**4 + 2*g**l = 0.
-1/4, 0, 1
Let m(s) = 1. Let n(c) = -c**2 + 7*c + 4. Let t(l) = 4*m(l) + n(l). Factor t(o).
-(o - 8)*(o + 1)
Let 3*n**3 - 7*n**3 - 5*n**2 - 131*n**4 - 2*n + 130*n**4 = 0. Calculate n.
-2, -1, 0
Let s(c) be the third derivative of -c**8/70560 - c**7/17640 - c**5/60 + 4*c**2. Let q(b) be the third derivative of s(b). Find p, given that q(p) = 0.
-1, 0
Let z(t) = 6 - 3 + 0*t + t. Let q be z(-3). Find s, given that 8 + q*s + 8*s + 0*s + 2*s**2 = 0.
-2
Let x(n) = -3*n**2 + 3*n - 24. Let i(s) = 2*s**2 - 2*s + 23. Let g(t) = 6*i(t) + 5*x(t). Find j, given that g(j) = 0.
-2, 3
Let l(a) = 3*a**2 - 4*a - 2. Let j(b) = 4*b**2 - 4*b - 2. Let y(f) = 5*j(f) - 6*l(f). Factor y(p).
2*(p + 1)**2
Let f(b) be the first derivative of -b**6/720 + b**5/120 - b**3 - 3. Let t(r) be the third derivative of f(r). Let t(o) = 0. Calculate o.
0, 2
Let h(s) be the second derivative of -s**7/231 + 2*s**6/165 - s**4/33 + s**3/33 - 2*s - 6. Factor h(p).
-2*p*(p - 1)**3*(p + 1)/11
Let d = 112 + -112. Suppose 5*t + 3*o = -0*o + 7, 4*o = -2*t. Factor d*i + 0 + 4/7*i**4 + 6/7*i**3 + 2/7*i**t.
2*i**2*(i + 1)*(2*i + 1)/7
Factor 0 - 5*m - 1/2*m**3 - 7/2*m**2.
-m*(m + 2)*(m + 5)/2
Let y(n) be the first derivative of 2*n**5/15 + 5*n**4/6 + 16*n**3/9 + 4*n**2/3 - 8. Determine u, given that y(u) = 0.
-2, -1, 0
Factor -1/2*d**4 + 0*d**2 - 3/2*d**3 + 2*d + 0.
-d*(d - 1)*(d + 2)**2/2
Factor -4/5*n**2 + 0 + 4/5*n.
-4*n*(n - 1)/5
Let z(v) be the first derivative of -8*v**3/3 - 7*v**2 + 4*v - 11. Factor z(g).
-2*(g + 2)*(4*g - 1)
Let k(q) be the first derivative of -4*q**3/3 + 3*q**2 + 4*q + 7. Factor k(r).
-2*(r - 2)*(2*r + 1)
Factor 1/5*u**2 - 2/5 + 1/5*u.
(u - 1)*(u + 2)/5
Let y(v) = -16*v**4 + 10*v**3. Let l(j) = -j**2 + 2*j + 5. Let r be l(5). Let z(h) = 5*h**4 - 3*h**3. Let u(a) = r*z(a) - 3*y(a). Factor u(c).
-2*c**4
Let k(a) be the third derivative of a**5/15 + 2*a**4/3 + 2*a**3 - 13*a**2. Suppose k(o) = 0. Calculate o.
-3, -1
Let v(b) be the second derivative of -b**5/140 - b**4/42 + b**3/42 + b**2/7 + 7*b + 2. Factor v(q).
-(q - 1)*(q + 1)*(q + 2)/7
Let l = 32/5 + -6. Let r(s) = s**3 + 3*s**2 - 7*s - 8. Let a be r(-4). Factor -l*b**a + 2/5*b**2 + 0*b**3 + 0*b + 0.
-2*b**2*(b - 1)*(b + 1)/5
Factor -9/4*t + 3/2 + 3/4*t**2.
3*(t - 2)*(t - 1)/4
Let j = -223/5 - -1571/35. Factor -2/7*k**5 - j*k**3 + 0 - 4/7*k**4 + 0*k**2 + 0*k.
-2*k**3*(k + 1)**2/7
Suppose -3*f - 3*m = 6, 2*f + 5*m + 14 = -2. Suppose 3*n - f*n + 1 = -5*v, 5*v = 2*n + 2. Factor -2/3*p**3 - 1/3*p**4 + 2/3*p + v*p**2 + 1/3.
-(p - 1)*(p + 1)**3/3
Let c be (3/4)/((-9)/(-24)). Find x such that x**3 + c*x**3 - 3 + 0*x**3 - 9*x**2 + 9*x = 0.
1
Let y(u) = -38*u - 225. Let q be y(-6). Solve 0*i - 2/5*i**2 + 0 + 4/5*i**q + 2/5*i**4 - 4/5*i**5 = 0 for i.
-1, 0, 1/2, 1
Let w(d) be the second derivative of -d**7/315 + d**6/72 - d**5/60 + d**4/6 + 4*d. Let j(g) be the third derivative of w(g). Find s such that j(s) = 0.
1/4, 1
Suppose 2 = b - 0. Let