).
-3*i*(i - 1)*(i + 1)**2
Let p(w) = 13*w + 1. Let i be p(1). Suppose q + 8 = i. Suppose -29/2*x**4 + 8*x**3 - 1/2 - 2*x + 3*x**2 + q*x**5 = 0. Calculate x.
-1/3, -1/4, 1
Let b = -481 - -481. Factor 0 - 3/2*c**2 + b*c.
-3*c**2/2
Determine d, given that 113*d**3 - 16*d**2 - 109*d**3 + 676*d - 88*d**2 = 0.
0, 13
Let n(j) be the second derivative of -9*j**5/80 - j**4/3 - 5*j**3/24 + j**2/4 - j. Solve n(p) = 0 for p.
-1, 2/9
Let v(u) be the first derivative of u**3/9 + 7*u**2/6 - 8*u/3 + 12. Let v(g) = 0. What is g?
-8, 1
Let k(l) = -9*l**4 + 11*l**3 + 5*l**2 - 11*l + 4. Let h(z) = z**4 - z**3 + z - 1. Let v(q) = -40*h(q) - 5*k(q). What is n in v(n) = 0?
-1, 1, 4
Let i(y) be the third derivative of -5*y**8/48 + 8*y**7/21 - 11*y**6/24 + y**5/6 + 3*y**2. What is x in i(x) = 0?
0, 2/7, 1
Let n(h) = h**3 - 6*h**2 + 2. Let x be n(6). Let i = -4543/5 + 909. Factor -2/5*l**4 + 2/5*l**3 + 0 - i*l + 2/5*l**x.
-2*l*(l - 1)**2*(l + 1)/5
Let p be (-2)/2 + (89 - -12). Let w be (10/p)/((-2)/(-72)). Factor 12*g**2 + w*g**3 + 16/5 + 56/5*g.
2*(g + 2)*(3*g + 2)**2/5
Let i be (2 + -5)/((-2)/6). Suppose -5*h + i = -2*h. Factor -1/3 + w**h + 5/3*w**2 + 1/3*w.
(w + 1)**2*(3*w - 1)/3
Factor -4/5*x**2 + 0 - 4/5*x.
-4*x*(x + 1)/5
Let p = -9 - -9. Let t(m) be the first derivative of 1/2*m**4 - 1 + p*m**3 - m**2 + 0*m. Determine k, given that t(k) = 0.
-1, 0, 1
Let w(a) = -3*a + 18. Let p be w(5). Let 0 - 3/5*n + 9/5*n**2 + 12/5*n**p = 0. What is n?
-1, 0, 1/4
Let i(l) be the first derivative of -2*l + 2*l**2 - 2/3*l**3 - 1. Factor i(f).
-2*(f - 1)**2
Let g(p) be the second derivative of 16*p**5/5 - 8*p**4 + 6*p**3 - 2*p**2 - 9*p. Find z such that g(z) = 0.
1/4, 1
Let n(g) be the third derivative of -2*g**7/1575 + 7*g**6/900 - g**5/75 - g**4/180 + 2*g**3/45 + 16*g**2. Find c, given that n(c) = 0.
-1/2, 1, 2
Let w(s) = s**2 + 4. Let g be w(0). Let o(p) be the second derivative of p + 1/12*p**g + 1/6*p**2 + 1/6*p**3 + 1/60*p**5 + 0. What is c in o(c) = 0?
-1
Let w(k) be the first derivative of 2*k**6/9 - 2*k**5/15 - k**4/6 + 15. Determine v so that w(v) = 0.
-1/2, 0, 1
Determine s so that 5/6*s**2 + 0 + 1/6*s + 2/3*s**3 = 0.
-1, -1/4, 0
Solve 14 - 4*z**2 + 11*z**2 - 9*z - 5 - 6*z - z**3 = 0.
1, 3
Suppose 3*m + p - 10 = 0, -m - p = m - 5. Suppose -m*o - 19 = -3*y, -2*y - 5*o = 2 + 2. Suppose -y*s**2 + 2*s**2 + 0*s - s = 0. Calculate s.
-1, 0
Let a(b) be the third derivative of 0*b - 1/30*b**5 - 2*b**2 + 0*b**4 + 0 + 4/21*b**3 + 1/140*b**6. Factor a(g).
2*(g - 2)*(g - 1)*(3*g + 2)/7
Suppose 10*c = 11*c. Let g(y) be the second derivative of 0*y**5 + c*y**2 + 2*y + 0*y**3 + 0 - 1/135*y**6 + 1/54*y**4. Factor g(d).
-2*d**2*(d - 1)*(d + 1)/9
Let u(x) be the first derivative of -5*x**3/3 + 5*x**2/2 + 10*x + 33. Factor u(q).
-5*(q - 2)*(q + 1)
Let u(z) be the third derivative of z**5/270 - 5*z**4/108 + 4*z**3/27 - 3*z**2. Let u(h) = 0. What is h?
1, 4
Suppose 7 = -5*k - 18. Let s = k - -7. Factor 0 - 1/4*r**s + 0*r.
-r**2/4
Factor -8*w + 2/5*w**4 + 36/5*w**2 + 16/5 - 14/5*w**3.
2*(w - 2)**3*(w - 1)/5
Let c(j) be the third derivative of 0 - 7/120*j**6 + 1/40*j**5 + 3*j**2 + 1/12*j**4 + 2/105*j**7 - 1/12*j**3 + 0*j. Find l, given that c(l) = 0.
-1/2, 1/4, 1
Let m = -238 + 715/3. Let o be -1 + -2*(-2)/4. Factor 0*g**3 - m*g**4 + o*g - 1/3 + 2/3*g**2.
-(g - 1)**2*(g + 1)**2/3
Let w(j) be the second derivative of j**7/231 - 4*j**6/165 - 3*j**5/55 + 6*j**4/11 - 9*j**3/11 + 11*j - 2. Find h such that w(h) = 0.
-3, 0, 1, 3
Let a be ((-2)/(-12))/(136/36). Let o = 121/340 + a. Find u, given that 4/5*u - 2/5*u**2 - o = 0.
1
Let j(o) be the first derivative of -o**7/84 + o**6/60 + 2*o - 3. Let w(q) be the first derivative of j(q). Factor w(l).
-l**4*(l - 1)/2
Let y(s) be the second derivative of s**6/540 - s**5/60 + s**4/18 + 5*s**3/6 - 2*s. Let a(w) be the second derivative of y(w). Let a(c) = 0. Calculate c.
1, 2
Let b(q) be the second derivative of 0*q**2 - 1/140*q**5 + 0*q**3 + 0 + q - 1/84*q**4. Determine m, given that b(m) = 0.
-1, 0
Let z(i) be the first derivative of -10*i**3/9 - 14*i**2 - 32*i/3 - 3. Determine g, given that z(g) = 0.
-8, -2/5
Let s be 18/12 - 1 - (-1 + 1). Let l(v) be the first derivative of 2 + s*v**6 + 15/4*v**4 + 0*v - 12/5*v**5 + 0*v**2 - 2*v**3. Factor l(y).
3*y**2*(y - 2)*(y - 1)**2
Suppose -5*j + 2 - 12 = 0. Let u(a) = 13*a**4 + a**3 + 9*a**2 - a + 5. Let h(n) = 3*n**4 + 2*n**2 + 1. Let r(m) = j*u(m) + 9*h(m). Solve r(v) = 0.
-1, 1
Let i(f) be the first derivative of f**8/10920 - f**7/5460 - f**6/2340 + f**5/780 - f**3/3 - 8. Let c(u) be the third derivative of i(u). Factor c(s).
2*s*(s - 1)**2*(s + 1)/13
Let y be (426/(-18))/(0 - 39). Let m = y - 5/13. Factor -4/9*r**2 + m + 2/9*r.
-2*(r - 1)*(2*r + 1)/9
Let n(v) be the third derivative of -v**8/6720 - v**7/840 + v**5/30 + v**4/12 - 2*v**2. Let h(c) be the second derivative of n(c). Factor h(r).
-(r - 1)*(r + 2)**2
Let m(o) be the third derivative of 1/32*o**4 + 0 + 0*o - 2*o**2 + 1/80*o**5 + 1/24*o**3 + 1/480*o**6. Factor m(y).
(y + 1)**3/4
Suppose -32/7*q - 2/7*q**4 - 10/7 - 36/7*q**2 - 16/7*q**3 = 0. Calculate q.
-5, -1
Let c(z) be the first derivative of -4*z**3/33 - z**2/11 - 10. What is g in c(g) = 0?
-1/2, 0
Let x be (-18)/3*6/(-6). Suppose 0 = 4*p - r - 8, -r + 6*r = 3*p - x. Factor 2/5*l**4 - l**3 - 1/5 + 3/5*l**p + 1/5*l.
(l - 1)**3*(2*l + 1)/5
Let c = 9 + -3. Factor 2*j + 5*j**2 - c*j**2 - 3*j.
-j*(j + 1)
Let g(p) be the third derivative of -2*p**7/105 - p**6/30 - 24*p**2. Solve g(f) = 0 for f.
-1, 0
Let a(m) = -m**4 + 9*m**3 + 13*m**2 + 11*m + 6. Let j(v) = -6*v**4 + 46*v**3 + 64*v**2 + 54*v + 31. Let s(n) = 11*a(n) - 2*j(n). Factor s(i).
(i + 1)**3*(i + 4)
Let n = -503/5 + 101. Find z such that -2/5*z**2 + n*z + 4/5 = 0.
-1, 2
Let u(w) be the third derivative of -w**5/90 - w**4/27 + 4*w**3/27 - 3*w**2. Let u(n) = 0. What is n?
-2, 2/3
Let s(u) be the first derivative of 2*u**6/3 + 4*u**5/5 - 3*u**4/4 - 2*u**3/3 + u**2/2 - 1. Factor s(b).
b*(b + 1)**2*(2*b - 1)**2
Let l be ((-3)/4)/((-2)/8). Suppose -u = -l*u + 4. Factor 3*i**2 - i**2 - 3*i**u.
-i**2
Suppose 0*h + 4 = h. Solve 4 - h + 2*l**2 + 3 - 5 = 0.
-1, 1
Let s(u) = u**3 - 5*u**2 - 6*u + 8. Let j be s(6). Suppose -5*d - q = q, d - 4*q - 22 = 0. Factor 2*l**d + 0 + 3 - j*l + 5.
2*(l - 2)**2
Let c(z) = 15*z**4 + 5*z**3 - 10*z**2 - 10*z + 5. Let s(v) = 8*v**4 + 2*v**3 - 5*v**2 - 5*v + 3. Let k(a) = -3*c(a) + 5*s(a). Find h, given that k(h) = 0.
-1, 0, 1
Let q(i) be the second derivative of 0*i**2 + 0 + 6*i + 1/120*i**6 + 1/40*i**5 + 0*i**3 + 1/48*i**4. Factor q(w).
w**2*(w + 1)**2/4
Let k be (-44)/(-12) - (-4 - (-28)/6). Determine r so that 2/7 - 6/7*r - 6/7*r**4 + 4/7*r**k + 4/7*r**2 + 2/7*r**5 = 0.
-1, 1
Solve 0 + 8/5*t + 8/5*t**2 + 2/5*t**3 = 0 for t.
-2, 0
Let p = -30 - -33. Let f(a) be the third derivative of 0*a**p - 1/120*a**5 + 1/48*a**4 + 0 + 0*a + 1/420*a**7 + 2*a**2 - 1/240*a**6. Factor f(t).
t*(t - 1)**2*(t + 1)/2
Let z(m) be the first derivative of m**6/480 + m**5/160 - m**4/16 - m**3 + 2. Let v(l) be the third derivative of z(l). Solve v(n) = 0.
-2, 1
Let t(g) = g**2 + 11*g + 4. Let z(x) = -x**2 - 10*x - 5. Let o(p) = -2*t(p) - 3*z(p). Let l(y) = -4*y - 4. Let u(c) = 5*l(c) + 2*o(c). Factor u(q).
2*(q - 3)*(q + 1)
Let j(y) be the second derivative of 0*y**2 - 1/6*y**4 + 2*y + 0 + 0*y**3. Determine h so that j(h) = 0.
0
Let n(l) = l**3 - 7*l**2 + 6*l - 3. Let r be n(6). Let w(z) = z**2 + 2*z - 3. Let p(f) = -f**2 - 3*f + 4. Let q(h) = r*w(h) - 2*p(h). Find d such that q(d) = 0.
-1, 1
Suppose 0 = -15*l + 10*l + 10. Factor h**3 + 1/2*h + 0 - 3/2*h**l.
h*(h - 1)*(2*h - 1)/2
Factor 7*h**2 - 4*h + 8*h - 3*h**2 - 6*h.
2*h*(2*h - 1)
Let r(a) be the third derivative of a**8/26880 + a**7/10080 - a**6/2880 - a**5/480 + a**4/8 + 2*a**2. Let u(t) be the second derivative of r(t). Factor u(q).
(q - 1)*(q + 1)**2/4
Let m = -10 - -12. Let o be (-2 + 2)/2 + m. Suppose -2/5 - 6/5*s**o - 6/5*s - 2/5*s**3 = 0. What is s?
-1
Let d(c) = c**4 + c**2 + c + 1. Let q(l) = -8*l**4 - 8*l**3 - 8*l**2 - 12*l - 12. Let k(i) = -12*d(i) - q(i). Let k(s) = 0. What is s?
0, 1
Factor 0*z**5 - 2*z**4 + 3*z**4 - z**5.
-z**4*(z - 1)
Let z(n) be the first derivative of -2*n**5/65 + 5*n**4/26 - 6*n**3/13 + 7*n**2/13 - 4*n/13 - 6. Factor z(y).
-2*(y - 2)*(y - 1)**3/13
