o(r) = 6*q(r) + 13*y(r). Factor o(p).
-3*(p + 1)**2
Let c(b) be the third derivative of b**5/140 - 3*b**4/56 + b**3/7 + 10*b**2. Factor c(q).
3*(q - 2)*(q - 1)/7
Factor 8/11*w + 0 - 2/11*w**4 + 0*w**2 - 6/11*w**3.
-2*w*(w - 1)*(w + 2)**2/11
Suppose 2/3*c**4 + 4*c**3 + 26/3*c**2 + 8*c + 8/3 = 0. Calculate c.
-2, -1
Let v(y) = -6*y**2 - 4*y + 4. Let i(g) = -g**2 + 1. Suppose -8 = 6*z - 4*z. Let b(s) = z*i(s) + v(s). Determine t, given that b(t) = 0.
-2, 0
Let t(h) be the second derivative of -h**4/12 + h**3/6 + h**2 - 49*h. Let t(p) = 0. What is p?
-1, 2
Find j such that 0*j**2 + 15/2*j**3 + 5/2*j**4 + 0*j + 0 = 0.
-3, 0
Let x(u) = u**2 + 17*u + 32. Let j be x(-2). Determine k so that 10/3*k**j + 0 + 8/3*k**3 + 2/3*k**4 + 4/3*k = 0.
-2, -1, 0
Let c(r) be the first derivative of 3/2*r**2 + 0*r + 3/8*r**4 - 4 - 3/2*r**3. Factor c(v).
3*v*(v - 2)*(v - 1)/2
Let y(g) = -3*g**4 + 3*g**3 + 7*g**2 + 13*g - 3. Let d(f) = -4*f**4 + 2*f**3 + 6*f**2 + 14*f - 4. Let r(n) = -5*d(n) + 6*y(n). Factor r(l).
2*(l + 1)**4
Let m(k) be the second derivative of -k**4/12 + 2*k**3/3 + k**2 + 3*k. Let x be m(4). Suppose b**2 + 1 - 3*b**x - 3*b + 4*b = 0. Calculate b.
-1/2, 1
Let z(g) be the second derivative of 4*g - 1/15*g**6 + 1/6*g**4 + 0*g**2 - 1/10*g**5 + 1/3*g**3 + 0. Suppose z(n) = 0. Calculate n.
-1, 0, 1
Let h(y) be the second derivative of -y**8/6720 + y**7/840 - y**5/30 - y**4/12 + 2*y. Let g(z) be the third derivative of h(z). Factor g(w).
-(w - 2)**2*(w + 1)
Let d(b) = -1 + 0 + 0 + b + 0*b. Let x be d(5). Solve 0*r + 1 - 15/4*r**2 + 15/4*r**x + 5/4*r**3 - 9/4*r**5 = 0.
-2/3, 1
Let -16/7*s - 2/7*s**2 - 32/7 = 0. What is s?
-4
Solve 3*x + 5*x + 3*x**2 + 12 + 4*x = 0 for x.
-2
Let c = 21 + -21. Determine u, given that 0*u**2 + 2/7*u**3 + c + 0*u = 0.
0
Let -4 + 36*v + v**2 - 23*v - 13*v = 0. What is v?
-2, 2
Let r(t) = -t**3 + 9*t**2 + 9*t + 14. Let a be r(10). Suppose a*o + y - 4 = -0*o, 0 = 4*o + 4*y + 8. Factor -3/4*g**2 + o*g - 1.
-(g - 2)*(3*g - 2)/4
Let -1/2*a**2 - 1/2*a + 1 = 0. What is a?
-2, 1
Let r(f) be the second derivative of -f**6/160 - f**5/20 - 3*f**4/32 - 3*f**2 - 2*f. Let z(u) be the first derivative of r(u). Factor z(y).
-3*y*(y + 1)*(y + 3)/4
Let q(c) be the first derivative of 0*c**5 - 1/3*c**6 - 3*c**2 + 2*c**4 + 4*c + 4 - 4/3*c**3. Factor q(f).
-2*(f - 1)**3*(f + 1)*(f + 2)
Let q(s) = -s**2 - 8*s + 9. Let o be q(-11). Let v be 4/8 + 4/o. Factor -v*t**5 - 1/3*t**4 + 0*t + 0 + 1/3*t**2 + 1/3*t**3.
-t**2*(t - 1)*(t + 1)**2/3
Factor 1/5*r - 1/5*r**3 - 2/5 + 2/5*r**2.
-(r - 2)*(r - 1)*(r + 1)/5
Factor 10*d**3 + 10*d**2 - 4*d**3 + 5*d - d**3.
5*d*(d + 1)**2
Let c(g) be the first derivative of -g**4/12 - g**3/3 - 2. Factor c(z).
-z**2*(z + 3)/3
Suppose 4*v = 5*v. Let z = 18 + -15. Solve n**2 - 4/3*n**5 - 1/3*n + 5/3*n**z + v - n**4 = 0 for n.
-1, 0, 1/4, 1
Let z = 3 + -6. Let d be 0 - z*(-12)/(-9). Factor -4*c**d - 2*c**2 + c**4 + 5*c**2 + 2*c**3 + 4*c**3 - 6*c.
-3*c*(c - 2)*(c - 1)*(c + 1)
Find t such that -30*t - 75 - 3*t**2 + 0*t**2 + 0*t**2 + 0*t**2 = 0.
-5
Let f(j) = -j**3 + 4*j**2 + 4*j - 5. Let b be f(5). Let n be ((-8)/b)/((-4)/(-10)). Factor 0 + 1/3*a**4 + 2/3*a - a**n + 0*a**3.
a*(a - 1)**2*(a + 2)/3
Factor -21/2*q**2 + 1/6*q**3 - 3087/2 + 441/2*q.
(q - 21)**3/6
Let j(y) be the third derivative of y**5/30 - 2*y**4/3 + 16*y**3/3 + 11*y**2. Factor j(c).
2*(c - 4)**2
Let n be ((-2)/(-2))/((-4)/(-16)). Factor -3*h**5 + 9*h**n - 9*h**3 + 0*h**4 + 6*h**2 - 3*h**2.
-3*h**2*(h - 1)**3
Let i(n) = 3*n - 21. Let k be i(9). Factor -k*s**2 + 2*s**2 + 8*s**4 - 2*s**3 + 2*s**3 + 4*s**3.
4*s**2*(s + 1)*(2*s - 1)
Factor 0*g**2 + 0*g**4 - 1/8*g - 1/8*g**5 + 1/4*g**3 + 0.
-g*(g - 1)**2*(g + 1)**2/8
Let y(i) = -25*i**2 - 25*i. Let r(c) = 2*c**2 + 2*c. Let n(t) = -40*r(t) - 3*y(t). Solve n(s) = 0 for s.
-1, 0
Let z be 0 - (-1)/2*4. Determine t, given that 3*t + z*t**2 - 3*t = 0.
0
Suppose 4*z = 2*w - 10 - 14, 5*z = -w - 16. Solve 0 + 2/11*k**3 - 2/11*k**w + 0*k + 0*k**2 = 0 for k.
0, 1
Factor -50/17 - 20/17*j - 2/17*j**2.
-2*(j + 5)**2/17
Let x(n) be the first derivative of -n**6/1980 - n**3/3 - 1. Let o(j) be the third derivative of x(j). Factor o(b).
-2*b**2/11
Factor 16*p**5 - 7*p**5 - 4*p**5 + 5*p**4.
5*p**4*(p + 1)
Suppose -y + 1 = i, -2*y - 1 = -3*y. Let l = i - -2. Factor -3*c**2 - 2*c**4 + 4*c**4 - 3*c**l + 4*c.
2*c*(c - 1)**2*(c + 2)
Let x(z) = -z**4 + 2*z**2 + 2. Let g(c) = c**4 - c**2 - 1. Let j(y) = -4*g(y) - 2*x(y). Factor j(v).
-2*v**4
Let b be 4/(-1) + 390/90. Let p = 1/4 + 1/12. Factor b*l**2 - p*l**3 + 2/3*l + 0.
-l*(l - 2)*(l + 1)/3
Let r = -24 - -24. Let h(m) be the second derivative of 0*m**5 + 0*m**4 + 0*m**3 + r - 1/84*m**7 + 0*m**2 - 1/60*m**6 + 2*m. Factor h(j).
-j**4*(j + 1)/2
Let x = -4 + 4. Suppose x = 4*m - m - 15. Factor -13*k**3 + m*k**3 - 2*k**2 + 0*k**2 - 8*k**4.
-2*k**2*(2*k + 1)**2
Let t(r) be the third derivative of r**8/420 - 2*r**7/525 + 5*r**2. Factor t(k).
4*k**4*(k - 1)/5
Let k(s) = s. Suppose -2 + 7 = -d. Let q(w) = 3*w**2 - 13*w + 27. Let g(h) = d*k(h) + q(h). Factor g(i).
3*(i - 3)**2
Let g(x) be the first derivative of x**4/60 - x**3/10 + 2*x - 2. Let t(z) be the first derivative of g(z). Factor t(u).
u*(u - 3)/5
Let i(r) = -r**3 - 5*r**2 + r. Let k(p) = -p**3 - 3*p**2 + p. Let c be ((-2)/4)/((-1)/2). Suppose c = -j - 2. Let g(s) = j*i(s) + 5*k(s). Factor g(m).
-2*m*(m - 1)*(m + 1)
Let x(n) be the third derivative of -n**6/24 + 22*n**2. Factor x(h).
-5*h**3
Let p(d) be the second derivative of -d**5/60 + d**4/8 - d**3/3 - 3*d**2/2 - 4*d. Let t(h) be the first derivative of p(h). Find b, given that t(b) = 0.
1, 2
Let k(b) be the third derivative of -2/15*b**3 - 1/300*b**5 + 1/30*b**4 - 2*b**2 + 0*b + 0. Factor k(u).
-(u - 2)**2/5
Let y(u) be the second derivative of u**10/90720 - u**9/45360 - u**8/20160 + u**7/7560 + 2*u**4/3 + 7*u. Let t(q) be the third derivative of y(q). Factor t(b).
b**2*(b - 1)**2*(b + 1)/3
Let m be 1/7 + (-1)/7. Solve -2/5*c**2 + 0*c - 2/5*c**4 + 4/5*c**3 + m = 0 for c.
0, 1
Suppose -13*s = -7*s + 9*s. Solve -1/3*u**2 + s - 4/3*u**4 - 5/3*u**3 + 0*u = 0 for u.
-1, -1/4, 0
Let k(q) = -q + 8. Let j be k(5). Factor -28*p - 4*p**4 - 20*p**j + 0 - 36*p**2 + 1 - 9.
-4*(p + 1)**3*(p + 2)
Suppose 0 = 2*t - 4*t + 4. Factor y**3 + 2*y**4 - 2*y**t - 2*y**5 + 2*y**3 - y**3.
-2*y**2*(y - 1)**2*(y + 1)
Factor 0 + 2/7*m**3 - 6/7*m**2 + 4/7*m.
2*m*(m - 2)*(m - 1)/7
Let j(q) be the first derivative of q**8/1680 - q**7/420 + q**6/360 - q**3 + 1. Let a(u) be the third derivative of j(u). Let a(r) = 0. Calculate r.
0, 1
Let i be (2/3)/(2/3). Let l be (-1)/((1 + -3)/i). Factor -s**3 - l*s**4 + 0 + 0*s - 1/2*s**2.
-s**2*(s + 1)**2/2
Suppose x - 8 = -3*x. Suppose -1 = -n + 2. Suppose x - n*a + 4*a**2 - 4 - 5*a**2 = 0. Calculate a.
-2, -1
Factor -7/6*g**5 - 1/2*g**4 + 0 + 0*g + 0*g**2 + 2/3*g**3.
-g**3*(g + 1)*(7*g - 4)/6
Let k(g) = g - 4. Let t be k(7). Let c(q) be the second derivative of 0*q**2 - 1/42*q**4 + 1/21*q**t - q + 0. Determine i so that c(i) = 0.
0, 1
Suppose 2*d = 9 - 1, 0 = -3*m - d - 101. Let b be 22/(-55) + (-24)/m. Solve 2/7*a + 0 + b*a**2 = 0 for a.
-1, 0
Let g(a) = -4*a**2 + 5*a. Let f(k) = -4*k**2 + 6*k. Let j(u) = -5*f(u) + 6*g(u). Solve j(m) = 0 for m.
0
Let z be 51*(-2)/84*4. Let p = z - -38/7. Factor p + 2*d - 8/7*d**2.
-2*(d - 2)*(4*d + 1)/7
Let f(q) be the first derivative of -q**6/270 - q**5/54 - q**4/27 - q**3/27 - 2*q**2 - 3. Let c(g) be the second derivative of f(g). Find w such that c(w) = 0.
-1, -1/2
Solve -80/3 - 5/3*k**2 + 40/3*k = 0.
4
Let w(m) be the first derivative of -m**8/3360 + m**7/1680 - 7*m**3/3 + 3. Let f(z) be the third derivative of w(z). Factor f(g).
-g**3*(g - 1)/2
Let v = -195121/828 - 103/828. Let g = v - -236. What is p in -2/3*p**4 + 4/9*p + 8/9*p**2 - 4/9*p**3 - g = 0?
-1, 1/3, 1
Factor -21*y**2 + 9*y**2 + 3*y**3 + 2*y**2 - 2*y**2 + 12*y.
3*y*(y - 2)**2
Factor -10*n**3 + 153*n - 153*n - 30*n**2 - 25*n**3 + 15*n**4.
5*n**2*(n - 3)*(3*n + 2)
Let l(o) be the first derivative of 3*o**4/28 + 2*o**3/7 - 6*o**2/7 - 24*o/7 - 17. Determine z, given that l(z) = 0.
-2, 2
Let m(p) be the second derivative of -p**8/336 - p**7/140 + p**5/120 + p**2 + 2*p. Let k(r) be the first derivative of m(r). Suppose k(n) = 0. Calculate n.
-1, 0, 1/2
Suppose -2*o - 1 = -7. Factor -