**2 = 0. Calculate w.
-1, -2/7, 2
Let s(l) be the first derivative of l**4/22 - 8*l**3/33 + 5*l**2/11 - 4*l/11 - 5. Factor s(t).
2*(t - 2)*(t - 1)**2/11
Let c = 1241/7813 + -3/601. Suppose -132/13*z**3 - c*z**5 + 162/13 - 378/13*z + 324/13*z**2 + 2*z**4 = 0. What is z?
1, 3
Let u(w) be the third derivative of -w**5/90 - w**4/18 - w**3/9 + 22*w**2. Factor u(p).
-2*(p + 1)**2/3
Let u = -194 + 197. Let b = 49/129 + -2/43. Factor 0 - b*i**u + 2/3*i - 1/3*i**2.
-i*(i - 1)*(i + 2)/3
Let l = 25 + -11. Let q(d) = 4*d**3 - 10*d**2 - 14*d - 14. Let b(y) = -y**2 + 0*y**2 - y**2 - 3*y - 3 + y**3. Let i(j) = l*b(j) - 3*q(j). Factor i(m).
2*m**2*(m + 1)
Let o = -2 + 4. What is s in 1 - s + s**2 + 1 + 0*s**o - 2*s = 0?
1, 2
Suppose 3*l + 6 = 6*l. Factor -1 + 1 + l*j**2 - j**3 - j**2.
-j**2*(j - 1)
Let f(m) be the third derivative of m**5/80 - 3*m**4/8 + 9*m**3/2 + 22*m**2. Factor f(i).
3*(i - 6)**2/4
Let r(d) = 12*d**3 + 9*d**2 - 3*d - 3. Let m(l) = -l**4 + 13*l**3 + 10*l**2 - 4*l - 4. Let i(z) = 3*m(z) - 4*r(z). Suppose i(b) = 0. Calculate b.
-2, -1, 0
Let i be (-2)/(2 + -2 + -1). Suppose -i = m - 4. Find b such that b**3 + m*b**4 + b**5 + 0*b**4 + 0*b**5 = 0.
-1, 0
Suppose -2*z = -3 - 5. Let h be (z/(-10))/(9/(-45)). What is j in -2/5*j**h - 2/5*j + 2/5*j**3 + 2/5 = 0?
-1, 1
Let u(j) be the first derivative of j**7/105 - j**6/40 + j**4/24 + j**2 + 2. Let z(f) be the second derivative of u(f). Factor z(b).
b*(b - 1)**2*(2*b + 1)
Factor 2/5*o**3 + 0 - 12/5*o**2 - 14/5*o.
2*o*(o - 7)*(o + 1)/5
Let k(s) = -s**3 + 5*s**2 + 6*s - 1. Let r be k(6). Let p be 2/21*(-3)/r. Factor -p*m + 0 + 2/7*m**2.
2*m*(m - 1)/7
Let q(s) be the second derivative of -s**6/6 + s**5/2 - 5*s**3/3 + 8*s**2 + s. Let x(c) = -c**4 + 2*c**3 - 2*c + 3. Let r(g) = -2*q(g) + 11*x(g). Factor r(l).
-(l - 1)**3*(l + 1)
Let x(b) = -4*b**4 - 2*b**3 + 9*b**2 - 3*b. Let t(d) = d**4 + d**3 - 3*d**2 + d. Let w(z) = -21*t(z) - 6*x(z). Let w(o) = 0. Calculate o.
0, 1
Factor 0 + 1/2*n**3 + 2*n**2 + 3/2*n.
n*(n + 1)*(n + 3)/2
Let v(z) be the first derivative of 1/3*z**6 + 0*z**2 - 8/5*z**5 + 5/2*z**4 + 0*z + 2 - 4/3*z**3. Factor v(w).
2*w**2*(w - 2)*(w - 1)**2
Let d(p) = -p**3 + 5*p**2 - 4*p + 2. Let a be d(4). Let m(q) = q**3 - 4*q**2. Let w be m(4). Factor 2/3*i**a - 2/3 + w*i.
2*(i - 1)*(i + 1)/3
Let v(g) = g**3 - g - 1. Suppose 0*i - 12 = -2*i. Let f(y) = -y**2 + i + 2 - 4. Let h(s) = f(s) + 3*v(s). Factor h(r).
(r - 1)*(r + 1)*(3*r - 1)
Let d(k) be the first derivative of -2*k**3/9 - 14*k**2/3 - 98*k/3 - 3. Factor d(n).
-2*(n + 7)**2/3
Suppose 4*a = a. Determine f so that 0*f**4 - 2*f**4 + 4*f**2 + 0*f**4 + a - 2 = 0.
-1, 1
Let m(f) be the third derivative of -f**6/60 + 2*f**5/15 - 5*f**4/12 + 2*f**3/3 - 8*f**2. Determine o so that m(o) = 0.
1, 2
Let z be 1/(-2) + (-77)/(-98). Factor 2/7*h**2 - 2/7*h**3 + 0 - 2/7*h**4 + z*h.
-2*h*(h - 1)*(h + 1)**2/7
Let t(y) = -14*y**3 + 49*y**2 + 44*y - 30. Let n(j) = 3*j**3 - 9*j - j**3 + 6 + j**3 - 10*j**2. Let r(b) = -11*n(b) - 2*t(b). Solve r(a) = 0.
-1, 2/5, 3
Let k be (-1 + 3)/((-16)/(2*-1)). Let 1/4 + k*v**2 + 1/2*v = 0. What is v?
-1
Let r = -91 - 52. Let q = -999/7 - r. Factor -2/7*b**3 - 2/7*b**4 + 0*b + 2/7*b**2 + 0 + q*b**5.
2*b**2*(b - 1)**2*(b + 1)/7
Let v = 1 + 3. Find q such that -10*q**2 - v*q + 4*q + 12*q**2 = 0.
0
Let q(l) = l**2 + l - 1. Let c(n) = -2*n**3 + 3*n**2 + 5*n - 5. Let g(v) = -c(v) + 5*q(v). Factor g(t).
2*t**2*(t + 1)
Factor -2/3*p**2 - 8/3*p - 8/3.
-2*(p + 2)**2/3
Let c(r) be the second derivative of -r**7/7560 - r**6/540 - r**5/90 - 3*r**4/4 - 4*r. Let v(j) be the third derivative of c(j). Suppose v(b) = 0. What is b?
-2
Let x(j) = j**2 + 4*j - 3. Let l be x(-7). Let r = 60 - l. Factor -8 - 4*y**3 - 7*y + 4*y**4 + 10*y**4 + 47*y - r*y**2.
2*(y - 1)**2*(y + 2)*(7*y - 2)
Suppose -7*y - 20*y = -135. Factor 0 + 0*w + 0*w**3 - 2/5*w**y + 6/5*w**4 - 8/5*w**2.
-2*w**2*(w - 2)**2*(w + 1)/5
Let o(j) be the first derivative of -j**6/39 + 8*j**5/65 - 3*j**4/13 + 8*j**3/39 - j**2/13 + 5. Factor o(u).
-2*u*(u - 1)**4/13
Let m(q) = -6*q**2 - 3*q + 12. Let x(b) = 7*b**2 + 4*b - 12. Let u(p) = 4*m(p) + 3*x(p). Factor u(w).
-3*(w - 2)*(w + 2)
Let g = -85 - -91. Let u(n) be the third derivative of 0*n**g - 1/60*n**5 + 0*n + 1/210*n**7 + 0*n**4 + 0 + 0*n**3 - 2*n**2. Suppose u(k) = 0. What is k?
-1, 0, 1
Let g = -35/4 - -9. Let l be 63/36*(-3)/(-7). Find u such that -l*u**2 - 1/2*u + g = 0.
-1, 1/3
Let j = 7 - 5. Let m be ((-1)/(-3))/(j/12). Find r such that -4/9*r**3 + 2/3*r**5 + 0 - 8/9*r**4 + 8/9*r**m - 2/9*r = 0.
-1, 0, 1/3, 1
Let z(a) be the third derivative of -a**8/16800 - 11*a**7/12600 - a**6/300 - a**5/30 + 7*a**2. Let j(l) be the third derivative of z(l). Factor j(q).
-2*(q + 3)*(3*q + 2)/5
Let k(u) be the first derivative of 2*u**2 + 3 - 2/3*u**3 - 2*u. Factor k(v).
-2*(v - 1)**2
Suppose 0 - 3*x**2 - 2/3*x - 7/3*x**3 = 0. Calculate x.
-1, -2/7, 0
Let s(p) be the second derivative of p**2 + 1/6*p**3 - 1/12*p**4 + 5*p + 0. Suppose s(m) = 0. What is m?
-1, 2
Let f(n) = n**3 - n**2 - n - 1. Let d(u) = 2*u**3 - 6*u**2 - 2*u - 6. Let r(s) = -d(s) + 6*f(s). Factor r(i).
4*i*(i - 1)*(i + 1)
Let j be (-6 - -2) + (4 - -6) + -3. Factor -4/13 - 6/13*m - 14/13*m**j + 24/13*m**2.
-2*(m - 1)**2*(7*m + 2)/13
Let l(d) be the second derivative of d**7/42 - d**6/30 - d**5/20 + d**4/12 - 2*d. Determine x, given that l(x) = 0.
-1, 0, 1
Let f(m) be the first derivative of 0*m**3 + 0*m - 28/5*m**5 + 0*m**2 - 6 + 2*m**6 + 2*m**4. Factor f(o).
4*o**3*(o - 2)*(3*o - 1)
Let d = -6/35 + 43/210. Let b(t) be the third derivative of 0 + 0*t - d*t**5 + 1/6*t**4 - 1/3*t**3 - 2*t**2. Factor b(m).
-2*(m - 1)**2
Let u = 26/15 - 538/345. Let v = 7/92 + u. Solve v*k**4 - 3/2*k**3 + 1 - 3*k + 13/4*k**2 = 0.
1, 2
Suppose 3 = 20*v - 19*v. Factor v*c - 9/4*c**2 - 1.
-(3*c - 2)**2/4
Factor 6/5*p**3 - 3/5*p**2 + 0 + 3/5*p**4 - 6/5*p.
3*p*(p - 1)*(p + 1)*(p + 2)/5
Let p(r) = -r**2 + 5*r - 6. Let u be p(3). Let z(t) = 2*t + 5. Let x be z(u). Find b, given that -4/3*b**2 + 2/3*b + 2/3 + 2/3*b**4 - 4/3*b**3 + 2/3*b**x = 0.
-1, 1
Let k(q) be the first derivative of -2 + 1/12*q**3 + 0*q + 0*q**2. Factor k(c).
c**2/4
Let p(u) be the third derivative of u**7/105 - u**6/120 - u**5/10 + 7*u**4/24 - u**3/3 + 3*u**2. Factor p(f).
(f - 1)**2*(f + 2)*(2*f - 1)
Let u(m) be the second derivative of 4*m - 1/3*m**2 + 0 - 1/12*m**4 + 5/18*m**3. Factor u(z).
-(z - 1)*(3*z - 2)/3
Let x(v) = v**2 - 3*v + 12. Let w(t) = 4*t - 12. Suppose 0 = -u - 4*u - 25. Let c(q) = u*w(q) - 4*x(q). Factor c(g).
-4*(g - 1)*(g + 3)
Let v(o) = -o**3 - 3*o**2 - 2*o - 4. Let d(p) = p**2 + p + 1. Let x(t) = 4*d(t) + v(t). Let s(i) = -3*i. Let c(n) = -2*s(n) - 3*x(n). What is m in c(m) = 0?
0, 1
Let h(v) = v**2 - 2. Let s be h(2). Factor -6*u - 8*u**s - 4 - 2*u**3 - 2*u + 4.
-2*u*(u + 2)**2
Suppose 4 - 1 = s. Let y(i) = 4*i**3 - 4*i**2 - 21*i + 21. Let z(c) = 2*c**3 - 2*c**2 - 11*c + 11. Let t(l) = s*y(l) - 5*z(l). Let t(m) = 0. Calculate m.
-2, 1, 2
Let s(d) be the first derivative of -d**8/840 - d**7/105 - d**6/36 - d**5/30 - d**3/3 - 2. Let z(r) be the third derivative of s(r). Factor z(n).
-2*n*(n + 1)**2*(n + 2)
Let x(h) = -h - 1. Let d be x(-3). Let b = 6 - d. Factor 4*z + 0*z + z**4 + 6*z**2 + 0*z**3 + 1 + b*z**3 + 0*z**2.
(z + 1)**4
Let r be 6/15 - 2/5. Let b(z) be the second derivative of 1/15*z**3 + r - 1/60*z**4 - 1/10*z**2 - 2*z. Factor b(k).
-(k - 1)**2/5
Suppose 6*o + a = 3*o + 15, a + 17 = 5*o. Suppose 0 = 3*z - 2*i + o, 6*i = z + 2*i + 18. Factor 3*q**3 - 3*q**2 - z*q**3 - 7*q**4 - 2*q + 11*q**3.
-q*(q - 1)**2*(7*q + 2)
Let w(k) = -7*k**2 + 14*k - 10. Let m(d) = d**2 - d - 1. Let j(u) = 6*m(u) + w(u). Factor j(g).
-(g - 4)**2
Let t = 19 + -131/7. Factor 0*i + 0 + t*i**2 - 2/7*i**3.
-2*i**2*(i - 1)/7
Let x(q) = 486*q**2 - 176*q + 14. Let o(v) = v**2 - 1. Let c(h) = -2*o(h) + x(h). Factor c(m).
4*(11*m - 2)**2
Factor -16/3 + 52/3*l**3 + 20*l**2 - 32*l.
4*(l - 1)*(l + 2)*(13*l + 2)/3
Let n be (-4)/8 - 144/(-46). Let s = n + -3/23. Factor 1 - s*r + 2*r**2 - 1/2*r**3.
-(r - 2)*(r - 1)**2/2
Let z(r) = -3*r + 9. Let c be z(3). Suppose 1/3*t**2 - 1/3*t + c = 0. What is t?
0, 1
Let h(a) = 8*a**2 - 21*a - 5. Let o(g) = 4*g**2 - 10*g - 2. Suppose -3*b = -0*b + 27. Let s(l) = b*o(l) + 4*h(l). Factor s(q).
-2*(q - 1)*(