
Factor 1/4*y**4 + 0*y + 0 + 1/4*y**5 - 1/4*y**3 - 1/4*y**2.
y**2*(y - 1)*(y + 1)**2/4
Let a(i) be the third derivative of i**7/11340 - i**5/540 - i**4/8 - i**2. Let z(b) be the second derivative of a(b). Factor z(g).
2*(g - 1)*(g + 1)/9
Let n(s) be the first derivative of -s**7/735 + s**5/105 - s**3/21 + 3*s**2/2 + 3. Let h(d) be the second derivative of n(d). Factor h(t).
-2*(t - 1)**2*(t + 1)**2/7
Determine a so that 2/7 + 0*a - 2/7*a**2 = 0.
-1, 1
Suppose 3*u - 4*u + 2 = 0. Find b, given that 2/5 + 0*b - 2/5*b**u = 0.
-1, 1
Let b(w) be the first derivative of -w**4/36 - 2*w - 2. Let j(k) be the first derivative of b(k). What is l in j(l) = 0?
0
Let k = 6/35 - 1/210. Let b(l) be the second derivative of 0 - l + 1/3*l**3 - l**2 - 1/10*l**5 + k*l**4. Factor b(u).
-2*(u - 1)**2*(u + 1)
Let z = -3/421 - -5067/2105. Factor -2/5*o**4 - 24/5*o**2 + z*o**3 + 0 + 16/5*o.
-2*o*(o - 2)**3/5
Let l(d) be the third derivative of d**8/6720 - d**7/1680 + 7*d**5/60 + d**2. Let h(z) be the third derivative of l(z). Factor h(n).
3*n*(n - 1)
Let n(c) be the second derivative of -c**8/8960 + c**7/672 - c**6/320 - 9*c**5/160 - 5*c**4/6 + 6*c. Let d(z) be the third derivative of n(z). Factor d(o).
-3*(o - 3)**2*(o + 1)/4
Suppose 0 = -r + 4*r - 21. Factor -r + 7 - 3*u**2 - 2*u + 3*u**4 + 2*u**3.
u*(u - 1)*(u + 1)*(3*u + 2)
Let c = -7/120 - -1/10. Let p = c - -5/24. Determine t so that -1/4*t + 0 - p*t**2 = 0.
-1, 0
Let o(j) be the second derivative of -j**7/7560 - j**6/2160 + j**5/180 - j**4/4 + 2*j. Let i(u) be the third derivative of o(u). Factor i(k).
-(k - 1)*(k + 2)/3
Let x(k) = 18*k**2 - 12*k - 15. Let r(a) = -9*a**2 + 6*a + 8. Let q(i) = 9*r(i) + 5*x(i). What is y in q(y) = 0?
-1/3, 1
Let m(i) = i**3 - 11*i**2 + 10*i - 5. Let n be m(10). Let c be 9/n - (1 - 4). Factor 0 + c*f**4 + 2/5*f**2 + 0*f + 2/5*f**5 + 6/5*f**3.
2*f**2*(f + 1)**3/5
Let v = -15 - -17. Let x = 6 + -4. Factor x*z - z**v - 2*z.
-z**2
Let j(u) be the third derivative of u**8/1848 - u**7/1155 - u**6/660 + u**5/330 + 2*u**2. Factor j(t).
2*t**2*(t - 1)**2*(t + 1)/11
Let m(z) be the first derivative of 1/8*z**2 + 1/2*z**4 + 0*z - 1 - 11/24*z**3 - 7/40*z**5. Solve m(w) = 0 for w.
0, 2/7, 1
Suppose g + 8 = 4*p - 4, -g = 5*p - 15. Factor -p - f + 2 - 1 + f**2.
(f - 2)*(f + 1)
Let a be (2 - (-8)/(-6)) + (-42)/63. Factor 4/7*m**2 + 2/7*m**3 - 2/7*m**4 + 0 + a*m.
-2*m**2*(m - 2)*(m + 1)/7
Let v = 10/29 + -1/87. Let x = -29 + 33. Solve -2*j**2 - 1/3*j**x - v - 4/3*j**3 - 4/3*j = 0.
-1
Let f(u) be the first derivative of 0*u**2 + u + 1/54*u**4 - 2 - 1/27*u**3. Let q(d) be the first derivative of f(d). Determine h so that q(h) = 0.
0, 1
Let g(i) be the third derivative of 1/60*i**5 - 2*i**2 + 0*i - 1/6*i**3 - 1/24*i**4 + 1/120*i**6 + 0. Factor g(y).
(y - 1)*(y + 1)**2
Let 10 - 5*q**2 - 5*q + 20 + 3 - 3 = 0. Calculate q.
-3, 2
Factor 0*q - q**3 + 0 + 1/3*q**2.
-q**2*(3*q - 1)/3
Suppose 0 = 5*t - 11 + 1. Let g be t*3/(-30)*-4. Factor -2/5 - 2/5*d**4 + 2/5*d - 4/5*d**3 + 2/5*d**5 + g*d**2.
2*(d - 1)**3*(d + 1)**2/5
Factor -4/3*n + 2*n**2 - 2/3*n**3 + 0.
-2*n*(n - 2)*(n - 1)/3
Let a(l) be the second derivative of 3*l**5/5 - l**4/3 - 2*l**3 + 2*l**2 + l. Suppose a(c) = 0. What is c?
-1, 1/3, 1
Let 1/2*b - 1/2*b**3 + 0 + 1/2*b**2 - 1/2*b**4 = 0. What is b?
-1, 0, 1
Let u(b) be the first derivative of -7*b**8/360 + 11*b**7/180 - 8*b**6/135 + b**5/45 + b**3/3 - 2. Let s(f) be the third derivative of u(f). Factor s(i).
-2*i*(i - 1)*(7*i - 2)**2/3
Let p = -28/3 - -10. Let k be 1 + -1 + (-2)/(-3). Determine c, given that -p*c + 0 - k*c**2 = 0.
-1, 0
Let v(s) = s**2 + 11*s - 11. Let u be v(-12). Let -3*l**3 - l**3 - u - l**2 + 5*l + 2 - l = 0. What is l?
-1, -1/4, 1
Let k(u) = -2*u**2 + 2*u + 3. Let p be k(0). Let t(j) be the first derivative of 1/7*j**2 + 4/21*j**p - 1 + 0*j + 1/14*j**4. Suppose t(b) = 0. What is b?
-1, 0
Let n be (4/3)/((-1034)/(-141)). Factor 4/11*x**4 - n - 10/11*x**3 + 6/11*x**2 + 2/11*x.
2*(x - 1)**3*(2*x + 1)/11
Let c = 0 - -3. Let m(z) be the second derivative of -1/75*z**6 - 1/5*z**4 - 1/5*z**2 + 4/15*z**c + 2/25*z**5 - z + 0. Factor m(j).
-2*(j - 1)**4/5
Let 3/8*h**4 - 3/8*h**2 + 3/8*h**3 + 0 - 3/8*h = 0. Calculate h.
-1, 0, 1
Suppose -t + 5 = 3. Suppose -t*w - 3*s + 5 = 2*w, -5 = 5*s. What is x in 0*x**3 - w*x**3 + 0*x**3 + 3*x**4 = 0?
0, 2/3
Let h(z) = -2*z**5 - 2*z**4 + 2*z**3 + 2*z. Let n(t) = -8*t**5 - 8*t**4 + 8*t**3 - t**2 + 9*t. Let y(j) = -9*h(j) + 2*n(j). Factor y(k).
2*k**2*(k - 1)*(k + 1)**2
Suppose 0 = 5*f - 4*f - 3. Let v(p) be the second derivative of 0*p**f - 1/60*p**5 - 2*p + 0 - 1/36*p**4 + 0*p**2. Solve v(b) = 0 for b.
-1, 0
Let c(v) = -v**3 - 6*v**2 - 9*v + 8. Let x(k) = -k + 1. Let j(o) = c(o) - 4*x(o). Let g be j(-5). Solve -g*p + p**2 + 2*p**2 + 0*p - 9*p**2 = 0 for p.
-2/3, 0
Let u(j) = j**2 - 2*j + 2. Let r(y) = y**2 - y + 1. Let w be (3/(-9))/((-3)/9). Suppose w = -3*h - 5. Let a(n) = h*u(n) + 4*r(n). Factor a(s).
2*s**2
Let y = -59 - -59. Let d(v) be the second derivative of -1/15*v**3 - 1/10*v**4 + y*v**5 + 4*v + 0*v**2 + 4/75*v**6 + 0. Factor d(x).
2*x*(x - 1)*(2*x + 1)**2/5
Let k be (-4)/3*9/78. Let f = 21/52 + k. Find v such that -f*v**2 + 0*v + 0 = 0.
0
Let n(m) be the first derivative of -3*m**4/8 - m**3/2 + 5. Suppose n(p) = 0. What is p?
-1, 0
Let g be 8/(-18)*(-7 - (-22)/4). Let s(o) be the second derivative of 0*o**2 - o + 0 - 1/6*o**4 - g*o**3. Find u such that s(u) = 0.
-2, 0
Suppose 2*x = 5*x. Suppose o - 3*o = x. Factor o*a**3 + 0*a + 3/2*a**4 - a**5 - 1/2*a**2 + 0.
-a**2*(a - 1)**2*(2*a + 1)/2
Let l(x) = 3*x + 30. Let u be l(-10). Suppose 0*f**2 + 1/3*f - 1/3*f**3 + u = 0. Calculate f.
-1, 0, 1
Let x(d) be the third derivative of d**9/272160 + d**8/30240 + d**7/11340 - d**5/20 + 2*d**2. Let s(m) be the third derivative of x(m). Factor s(f).
2*f*(f + 1)*(f + 2)/9
Factor -v**5 + 0*v**3 + 0 + 0*v**2 + 0*v - 2/3*v**4.
-v**4*(3*v + 2)/3
Let z = -137 - -687/5. Let u(c) = -4*c**3 + 1. Let k be u(-1). Factor 0*i + 1/5*i**3 - z*i**4 + 0*i**2 + 0 + 1/5*i**k.
i**3*(i - 1)**2/5
Factor 12*k + 2 - 9*k**4 + 6 - 12*k**3 - 4*k**2 + 5*k**4.
-4*(k - 1)*(k + 1)**2*(k + 2)
Suppose -2*k - 5*q - 250 = 0, -2*k + 0*k - q = 258. Let p be k/(-55) - (-4)/(-2). What is y in 2/11*y**2 + 6/11*y + p = 0?
-2, -1
Let u(a) be the third derivative of -a**6/210 - a**5/35 + a**4/42 + 2*a**3/7 + 5*a**2. Factor u(s).
-4*(s - 1)*(s + 1)*(s + 3)/7
Let o be (0 - 0)/(-15 + 16). Let z = 5/4 + -7/12. Determine l so that z - 2/3*l**2 + o*l = 0.
-1, 1
Let b(z) = -z**3 + 2*z**2 + 5*z - 4. Let s be b(3). Factor -u**2 + 0*u**2 - 3*u + 1 + 6*u + u**3 + 4*u**s.
(u + 1)**3
Let p be ((-1 - 3)/8)/(-1). Factor p*n**3 - 1/2*n**2 - 1/2*n + 1/2.
(n - 1)**2*(n + 1)/2
Let p(m) be the second derivative of -m**4/54 - m**3/9 - 2*m**2/9 - 2*m. Factor p(z).
-2*(z + 1)*(z + 2)/9
Factor -12/7*m + 3/7*m**2 - 15/7.
3*(m - 5)*(m + 1)/7
Let a(h) be the third derivative of 0*h + 1/60*h**5 + 3*h**2 + 0 - 1/3*h**3 + 1/24*h**4. Find c, given that a(c) = 0.
-2, 1
Let a = -4/159 + 179/795. Factor 0*u - 1/5*u**4 + 0 + a*u**3 + 0*u**2.
-u**3*(u - 1)/5
Factor 1/4*z**2 + 1/2 - 3/4*z.
(z - 2)*(z - 1)/4
Let m = -748 - -751. Let l be 1 - 1*(-1 + 2). Factor 0 + l*y + 1/2*y**m - 1/2*y**2.
y**2*(y - 1)/2
Let z(r) be the second derivative of r**4/30 + 2*r**3/5 + 9*r**2/5 + 3*r. Determine k so that z(k) = 0.
-3
Solve -1/8*t**2 - 1/8*t + 1/8*t**3 + 1/8 = 0.
-1, 1
Let m be (4/(-122))/((-60)/712). Let p = m + 2/183. Factor -p*o**2 + 0*o + 0 - 2/5*o**3.
-2*o**2*(o + 1)/5
Let h be (-1258)/555*(-6)/4. Factor -6/5 - g**2 - h*g.
-(g + 3)*(5*g + 2)/5
Let r be (20/15)/(12/2). Solve 0 - r*b**2 + 0*b + 2/9*b**3 = 0.
0, 1
Let w(x) = 3*x**4 + x**3 - 2*x**2 + 2. Let n(s) = -7*s**4 - 3*s**3 + 5*s**2 - 5. Let q(t) = -2*n(t) - 5*w(t). Determine l so that q(l) = 0.
0, 1
Let b(z) = -5*z**5 - 5*z**3 - 5*z**2 + 5*z. Let w(a) = -a**4 - a**3 - a**2 + a. Let m(j) = b(j) - 5*w(j). Factor m(g).
-5*g**4*(g - 1)
Solve 5 - 14*a - 2*a + 7 + 4*a**2 = 0.
1, 3
Let d(r) = 127*r**2 + 44*r + 4. Let p(y) = -y**2. Let c(g) = 5*d(g) + 30*p(g). What is i in c(i) = 0?
-2/11
Let b be (-4 + 1)/(-9) - (-5)/(-18). Let a(f) be the second derivative of -2*f + 4/3*f**2 - 4/9*f**3 + b*f**4 + 0. Factor a(c).
2*(c - 2)**2/3
Suppose -15 = -5*x - 0*x + 5*z, -z - 3 = 5*x. Factor 0*n 