8*c**4 + 11*c**3 - m + 6*c**2 + 11*c**3.
(c + 1)**4*(5*c - 2)
Let v = -118/3 + 40. Factor -1/3*x**3 - v*x + 0 + x**2.
-x*(x - 2)*(x - 1)/3
Let r(k) = -5*k + 15. Let c(u) = u**2 + 5*u - 14. Let j(m) = 5*c(m) + 4*r(m). Factor j(x).
5*(x - 1)*(x + 2)
Factor -1/5*j**5 + 2/5*j**3 - 1/5*j**4 + 2/5*j**2 - 1/5*j - 1/5.
-(j - 1)**2*(j + 1)**3/5
Let v(c) be the first derivative of 6*c**5/25 + c**4/2 + 2*c**3/15 - c**2/5 + 3. Factor v(j).
2*j*(j + 1)**2*(3*j - 1)/5
Factor -4/3*k**2 - 4/3*k**4 - 1/3*k**5 - 2*k**3 + 0 - 1/3*k.
-k*(k + 1)**4/3
Suppose -1/2*n**2 + 0 - 1/2*n = 0. What is n?
-1, 0
Let l(t) = -t**2 + t + 3. Let w be l(0). Let h(q) be the first derivative of 0*q**2 - 14/25*q**5 - 1 + 1/2*q**4 + 0*q + 4/15*q**w. Factor h(z).
-2*z**2*(z - 1)*(7*z + 2)/5
Suppose -2 + 17 = 3*j. Let s(o) be the third derivative of -1/24*o**4 + 0 + 1/112*o**8 - 1/15*o**j - 1/60*o**6 + 0*o**3 - o**2 + 2/105*o**7 + 0*o. Factor s(r).
r*(r - 1)*(r + 1)**2*(3*r + 1)
Suppose -57*d - 5 = -58*d. Determine p, given that 3*p**4 - 27/7 + 6/7*p**2 - 6*p**3 + 45/7*p - 3/7*p**d = 0.
-1, 1, 3
Let o(d) be the third derivative of d**9/15120 - d**8/6720 - d**7/1260 - d**4/8 + 3*d**2. Let j(y) be the second derivative of o(y). Factor j(p).
p**2*(p - 2)*(p + 1)
Let p(k) be the second derivative of 1/18*k**4 - 1/45*k**6 + k + 0*k**2 + 0 + 1/9*k**3 - 1/30*k**5. Factor p(f).
-2*f*(f - 1)*(f + 1)**2/3
Let z(t) be the first derivative of -t**6/18 - t**5/3 - t**4/3 + 16*t**3/9 + 16*t**2/3 + 16*t/3 - 7. Factor z(l).
-(l - 2)*(l + 1)*(l + 2)**3/3
Let a(x) be the third derivative of 0*x + 0*x**5 + 5*x**2 + 1/1176*x**8 + 1/420*x**6 + 0*x**4 + 2/735*x**7 + 0*x**3 + 0. Factor a(w).
2*w**3*(w + 1)**2/7
Let p(t) be the first derivative of -1 + 10*t**5 - 4*t**2 - 5/2*t**4 + 0*t - 32/3*t**3. Factor p(v).
2*v*(v - 1)*(5*v + 2)**2
Let w(s) be the second derivative of s**7/105 - 2*s**6/25 + 9*s**5/50 + 2*s. Find v such that w(v) = 0.
0, 3
Let p = 46 - 44. Let m(s) be the first derivative of 1 - 2*s**3 - 3/2*s**p + 0*s - 3/4*s**4. Determine f, given that m(f) = 0.
-1, 0
Let q(o) be the first derivative of 27*o**5/110 - 3*o**4/11 + 4*o**3/33 + o**2 + 3. Let u(t) be the second derivative of q(t). Factor u(a).
2*(9*a - 2)**2/11
Let c(k) be the third derivative of -k**7/1470 - k**6/210 - k**5/84 - k**4/84 + 3*k**2. Suppose c(n) = 0. Calculate n.
-2, -1, 0
Let u = 694 + -9096/13. Let a = -318/65 - u. Suppose -2/5*g**5 - 2/5*g**4 + 4/5*g**2 + a*g**3 - 2/5*g - 2/5 = 0. What is g?
-1, 1
Let m(z) = -z**2 - z. Suppose 2*t = -2*t - 2*o + 6, -3*t = -o + 8. Let v(x) = -4*x**2 - 6*x. Let k(s) = t*v(s) + 5*m(s). Determine g so that k(g) = 0.
0, 1
Let k(c) be the first derivative of -c**6/24 - c**5/20 + c**4/16 + c**3/12 - 10. Solve k(n) = 0 for n.
-1, 0, 1
Let l(d) be the third derivative of d**8/112 - d**7/15 + 19*d**6/120 - d**5/15 - d**4/6 + 6*d**2. Solve l(f) = 0 for f.
-1/3, 0, 1, 2
Let i be ((-28)/210)/((-2)/10). Factor 2/3*w**5 + i - 4/3*w**3 + 2/3*w**4 + 2/3*w - 4/3*w**2.
2*(w - 1)**2*(w + 1)**3/3
Let p(w) = -2*w**2 + 6*w - 2. Let j be p(4). Let o be ((-4)/j)/(2/10). Factor 1 + r - o*r - r - r**2 + 2*r**2.
(r - 1)**2
Let i(j) be the third derivative of j**8/3360 + j**7/840 + j**6/720 - j**4/24 + 3*j**2. Let z(x) be the second derivative of i(x). Factor z(l).
l*(l + 1)*(2*l + 1)
Let d(a) be the second derivative of -a**5/80 + a**4/48 + a**3/24 - a**2/8 - 4*a. Factor d(s).
-(s - 1)**2*(s + 1)/4
Suppose 0 = 5*b + 5*g - 50, 3*b = -5*g + 3*g + 25. Let k(s) be the first derivative of -1/2*s**4 - 4/21*s**3 + 0*s + 2 - 2/7*s**b + 0*s**2. Factor k(x).
-2*x**2*(x + 1)*(5*x + 2)/7
Let n(p) be the third derivative of p**6/10 - 3*p**5/20 - p**4/8 - p**2. Factor n(z).
3*z*(z - 1)*(4*z + 1)
Let v(w) be the third derivative of -w**8/3360 - w**7/420 - w**6/180 - w**4/24 + 3*w**2. Let a(i) be the second derivative of v(i). Factor a(z).
-2*z*(z + 1)*(z + 2)
Let c = -166/3 + 455/6. Let p = -20 + c. Factor -p*u**2 + u + 0 + 1/2*u**5 + 1/2*u**4 - 3/2*u**3.
u*(u - 1)**2*(u + 1)*(u + 2)/2
Suppose -5*a - 5*z + 5 = 0, 8 = 5*a + 2*z - 0. Let g = 1 + a. Find q such that 5*q - 3*q - g*q + q**2 - q**4 + q**3 = 0.
-1, 0, 1
Let w(p) be the first derivative of -p**4/2 + p**3/3 + 2*p**2 + 5*p + 1. Let g(j) = j**2 + j + 1. Let q(i) = 4*g(i) - w(i). Solve q(h) = 0 for h.
-1, 1/2
Factor 3/5*p**4 + 0 + 108/5*p**2 - 36/5*p**3 + 0*p.
3*p**2*(p - 6)**2/5
Let c be 2 - 10/6 - (-6)/36. Factor -1 - c*p + 1/2*p**2.
(p - 2)*(p + 1)/2
Solve 1/5*p + 0 + 1/5*p**2 = 0.
-1, 0
Let n(q) = 86*q**3 + 194*q**2 - 121*q + 15. Let k(l) = -171*l**3 - 389*l**2 + 241*l - 30. Let j(o) = 6*k(o) + 11*n(o). Find p such that j(p) = 0.
-3, 1/4
Let p(k) = -5*k + 12. Let i be p(2). Let v(j) be the second derivative of -2*j + 0 - 1/18*j**4 - 2/9*j**3 - 1/3*j**i. Find q, given that v(q) = 0.
-1
Let a(h) = 49*h - 4. Let p be a(4). Factor 55 - p*s**2 - 59 + 29*s**3 + 48*s + 227*s**3.
4*(4*s - 1)**3
Let v(u) = u**3 + 3*u**2 - 4*u - 7. Let l be v(-3). Factor -6/5*n**4 - 13/5*n**3 - 12/5*n**2 - 4/5*n - 1/5*n**l + 0.
-n*(n + 1)**2*(n + 2)**2/5
Let n = 0 - -7. Suppose 4*h - 4 = 4. Factor -3 + 2*w**2 - w**h + w**2 + n + 6*w.
2*(w + 1)*(w + 2)
Let k(u) be the third derivative of -u**8/60480 + u**7/3780 - u**6/540 + u**5/15 - 10*u**2. Let t(z) be the third derivative of k(z). Factor t(x).
-(x - 2)**2/3
Factor 0*z**3 - z**2 - 2*z**3 + 3*z**3 - z**2.
z**2*(z - 2)
Let u(f) be the second derivative of 2*f + 0*f**3 + 0 + 1/20*f**4 + 0*f**2. Factor u(h).
3*h**2/5
Let z(c) = -12*c**2 - 4*c - 2. Let x(f) = 11*f**2 + 5*f + 2. Let b(r) = -5*x(r) - 4*z(r). Determine m, given that b(m) = 0.
-1, -2/7
Let f(a) = -7*a**3 - 13*a**2 + 3*a + 9. Let b(t) = -15*t**3 - 27*t**2 + 6*t + 18. Let x(q) = -4*b(q) + 9*f(q). Factor x(y).
-3*(y - 1)*(y + 1)*(y + 3)
Let x(v) be the first derivative of -4/9*v**2 - 2/27*v**3 - 8/9*v + 3. Solve x(q) = 0.
-2
Let o = 2 + -2. Let p = -373 + 378. Suppose -5/2*u**4 + 0*u + 2*u**p + 0 + o*u**2 + 1/2*u**3 = 0. Calculate u.
0, 1/4, 1
Let k(f) be the second derivative of 2*f**7/21 - 2*f**6/5 + 3*f**5/5 - f**4/3 + 16*f. Determine q, given that k(q) = 0.
0, 1
Let g be 0 + -1 - (4 - 2). Let f be (-2)/(g - -2) + 1. Factor -2/9*i**4 + 2/9*i - 2/3*i**2 + 0 + 2/3*i**f.
-2*i*(i - 1)**3/9
Let j be 3/14 + (-4)/(-14). Let n be 2/3 + (-1)/6. Factor 1/2 - n*m**3 + 1/2*m - j*m**2.
-(m - 1)*(m + 1)**2/2
Find p such that -12*p**4 + 13*p**3 - 2*p**3 - 16*p**2 + 8*p**4 + 5*p**3 = 0.
0, 2
Factor -3*z**2 + 6*z**3 + z**5 + 5*z**4 + 0*z**2 - 11*z + 4*z + z**2 - 3.
(z - 1)*(z + 1)**3*(z + 3)
Let u(d) be the third derivative of d**5/10 + d**4/6 + d**3/3 + 3*d**2. Let a be u(-2). Solve 2*k**4 - 2*k + 4 + 21*k + a*k**2 - 5*k + 10*k**3 = 0 for k.
-2, -1
Let n = 35 - 30. Let s(x) be the second derivative of -1/10*x**n + 0*x**2 + 0 + 1/3*x**3 + 0*x**4 - 2*x. Solve s(i) = 0.
-1, 0, 1
Let s(a) = -a**3 - 14*a**2 - 12*a + 15. Let j be s(-13). Suppose 0*p**j - 2 + p**2 + 9*p**2 - 6*p - 2*p**2 = 0. What is p?
-1/4, 1
Let b be (1 - 2)/((-2)/4). Let 2*g**2 + g**3 + g**4 - 3*g**3 - g**3 + 0*g**b = 0. What is g?
0, 1, 2
Let l(d) = 13*d**2 + 24*d + 25. Let f(v) = 9*v**2 + 16*v + 17. Let b(a) = -7*f(a) + 5*l(a). Factor b(k).
2*(k + 1)*(k + 3)
Let w(y) = 3*y**3 + 2*y**2 + 3*y + 4. Let l(n) = -7*n**3 - 5*n**2 - 6*n - 9. Let k(m) = 4*l(m) + 9*w(m). Factor k(o).
-o*(o - 1)*(o + 3)
Solve -5/2*m**2 + 15/2*m**3 + 0*m + 10*m**4 + 0 = 0 for m.
-1, 0, 1/4
Let k(o) be the first derivative of 2*o**5/5 + o**4/2 + 2*o**2 + 4*o - 1. Let z(m) = -2*m + 4 + 6*m - 3*m + m**4 - 3. Let s(j) = k(j) - 4*z(j). Factor s(r).
-2*r**3*(r - 1)
Let n be 3 - (-5 + (0 - -4)). Let c(x) be the third derivative of 1/30*x**5 - 1/3*x**n + 0 + 2*x**2 + 0*x + 4/3*x**3. Factor c(o).
2*(o - 2)**2
Suppose 5*k - 4*l = 14, -4*k + 3*l + 10 = -1. Determine q so that 4*q**4 - 2*q**5 - 4*q**k + 3*q - 5*q + 4*q = 0.
-1, 0, 1
Let d(o) be the second derivative of 0*o**2 + 3*o - 1/8*o**4 + 0 + 1/2*o**3. Let d(u) = 0. Calculate u.
0, 2
Let w(l) be the third derivative of -l**7/140 + l**6/12 - 109*l**5/360 + 3*l**4/8 - 2*l**3/9 + 8*l**2 - 1. Suppose w(m) = 0. What is m?
1/3, 2, 4
Let l = 193 - 190. Let z(p) be the first derivative of 1 - 9/4*p**4 - 10*p**l - 8*p - 14*p**2. Let z(b) = 0. Calculate b.
-2, -2/3
Suppose 5*f - 3 = -8. Let i be 2*(0 + f/(-3)). Factor -i + 1/3*c**2 