= 8*u - 3*u. Factor -t*c + 3*c - 2*c - u*c**2.
-c*(2*c + 1)
Factor 2/5*m**5 + 0 + 0*m + 2/5*m**3 + 0*m**2 + 4/5*m**4.
2*m**3*(m + 1)**2/5
Let j(i) = -9*i + 56. Let f be j(6). Let p(y) be the second derivative of 1/35*y**6 + 0*y**f + 4/21*y**4 - 4/21*y**3 + 0 + 3*y + 11/70*y**5. Factor p(a).
2*a*(a + 2)**2*(3*a - 1)/7
Let m(y) be the first derivative of -14/3*y**3 + 3 - 7*y**2 - y**4 - 4*y. Suppose m(t) = 0. Calculate t.
-2, -1, -1/2
Determine v so that 1/6*v + 0 + 1/6*v**2 = 0.
-1, 0
Let v(y) = 10*y**4 - 15*y**3 + 30*y**2 - 15*y + 10. Let z(n) = 9*n**4 - 16*n**3 + 30*n**2 - 16*n + 9. Let t(g) = 4*v(g) - 5*z(g). What is k in t(k) = 0?
1
Let c = -9 - -9. Suppose c = 5*n - 36 + 11. What is k in 0*k - 1/3*k**4 + 0*k**3 + 4/3*k**n + 0*k**2 + 0 = 0?
0, 1/4
Let n = 67/300 - -2/75. Solve 1/2*i**2 - 1/4*i**4 + 0*i + 0*i**3 - n = 0 for i.
-1, 1
Let s be (3/(-4))/((-4)/32). Factor 10*c**2 - 4*c + 1 - s*c**2 - 1.
4*c*(c - 1)
Let o = -5/2 - -3. Let a = 2/3 - o. Factor 1/6*d**3 + 0 - a*d**4 + 0*d + 1/3*d**2.
-d**2*(d - 2)*(d + 1)/6
Let l(m) be the first derivative of m**4/4 + 2*m**3/3 + m**2/2 - 3. Factor l(i).
i*(i + 1)**2
Let l(g) be the second derivative of -g**4/12 + 5*g**3/6 + g**2 - 2*g. Let w be l(5). Find v such that 2*v**5 - 2*v**3 + 0*v**4 + w*v**4 + 0*v**5 - 2*v**2 = 0.
-1, 0, 1
Let m be 16/6*9/10. Let n be (-1 + (-3)/(-2))*4. Suppose 2/5*t**3 + 16/5 + m*t**n + 24/5*t = 0. What is t?
-2
Let h(a) be the first derivative of a**7/3360 - a**6/288 + a**5/60 - a**4/24 + 7*a**3/3 + 6. Let d(i) be the third derivative of h(i). Factor d(r).
(r - 2)**2*(r - 1)/4
Let x(i) be the first derivative of i**4 - 20*i**3/9 + 4*i**2/3 + 6. Determine r so that x(r) = 0.
0, 2/3, 1
Let c = 223 + -9579/43. Let n = 222/215 - c. Determine d so that 2*d**5 + n - 2/5*d - 8/5*d**3 + 16/5*d**4 - 4*d**2 = 0.
-1, 2/5, 1
Suppose 5*f = 3*f + 4. Let c = 4 - f. Factor 3 + 0 + 2*x**c - 3*x - 2.
(x - 1)*(2*x - 1)
Let i(v) be the second derivative of -v**4/16 + v**3/8 + 3*v**2/4 + 2*v. Solve i(u) = 0.
-1, 2
Suppose c + u = 5, -4*c - 5*u = -10 - 12. Let i be (8/(-12))/(c/(-9)). Find l such that -1/2*l**i + 1/2 + 7/4*l - 7/4*l**3 = 0.
-1, -2/7, 1
Let r = 0 - 2. Let w = r - -4. Factor 3*g**2 - 2*g + 3*g**3 + g**w - 5*g**3.
-2*g*(g - 1)**2
Let o be 0 + 1 + 1/(-3). Let p(q) be the second derivative of -o*q**3 + 0 + 7/15*q**6 - q + 6/5*q**5 + 1/2*q**4 + 0*q**2. Factor p(f).
2*f*(f + 1)**2*(7*f - 2)
Let b = -90 + 92. Suppose 0 - 2/5*y + 2/5*y**b = 0. What is y?
0, 1
Let m(j) = -10*j**3 - 42*j**2 - 16*j + 8. Let h(a) be the first derivative of -a**4/4 + a**3/3 - 5. Let f(l) = 4*h(l) + m(l). Factor f(k).
-2*(k + 1)*(k + 2)*(7*k - 2)
Let t(x) = 19*x**3 - 11*x**2 - 56*x + 59. Let h(g) = -5*g**3 + 3*g**2 + 14*g - 15. Let z(q) = -22*h(q) - 6*t(q). Factor z(m).
-4*(m - 2)*(m - 1)*(m + 3)
Suppose 0 = 3*w + 3*c - 12, -3*w + 5*c = -4*w. Let q = 0 - 0. Factor -1/2*z**4 - 1/4*z + q + 1/4*z**w + 0*z**3 + 1/2*z**2.
z*(z - 1)**3*(z + 1)/4
Let v(i) be the second derivative of i**7/273 - i**5/65 + i**3/39 - 11*i. Factor v(u).
2*u*(u - 1)**2*(u + 1)**2/13
Solve 2/7 + 12/7*p**2 + 2/7*p**4 + 8/7*p + 8/7*p**3 = 0.
-1
Let a be 1 - (-1 - 5/(-3)). Let c = 4 - 4. What is u in -2/3*u + 2/3*u**3 - 1/3 + c*u**2 + a*u**4 = 0?
-1, 1
Let i(n) be the first derivative of -n**3/3 + 6*n**2/7 + 4*n/7 + 36. Solve i(c) = 0 for c.
-2/7, 2
Let z(y) be the third derivative of y**6/40 + 3*y**5/20 + y**4/4 - 4*y**2. Factor z(s).
3*s*(s + 1)*(s + 2)
Let d be 4 - ((-8)/6 + (-8)/(-2)). Let -2/3*w**2 + d - 2/3*w = 0. Calculate w.
-2, 1
Determine z so that 0*z**2 + 2*z**2 + z**2 - 15*z**3 + 7*z**2 = 0.
0, 2/3
Let s = 284 + -9091/32. Let y = 37/288 - s. What is z in y*z**5 + 0 + 2/9*z**3 - 4/9*z + 2/3*z**2 - 2/3*z**4 = 0?
-1, 0, 1, 2
Let q(x) = -2*x + 21. Let f be q(9). Suppose -f*w + 12 = -w - 4*j, -2*w - 5*j = 15. Factor 1/4*n**2 - 1/4 + w*n.
(n - 1)*(n + 1)/4
Let k(l) be the second derivative of l**6/10 + l**5/2 + l**4/3 - 4*l**3/3 + 7*l. Solve k(m) = 0.
-2, 0, 2/3
Let d = 129 - 513/4. Let h = -8/3 + 35/12. Suppose 0*q + h*q**5 + d*q**4 + 0 + 1/4*q**2 + 3/4*q**3 = 0. Calculate q.
-1, 0
Suppose y = -3*g + 10, 2*y + 2*g = -0*g. Let o = y + 8. Factor -2/3*s + 2/3*s**o - 1/3 + 1/3*s**4 + 0*s**2.
(s - 1)*(s + 1)**3/3
Factor 0 + 8/9*n**3 + 2/9*n - 8/9*n**2.
2*n*(2*n - 1)**2/9
Factor -4/9*w**4 + 4/9*w**2 + 2/9*w + 0*w**3 + 0 - 2/9*w**5.
-2*w*(w - 1)*(w + 1)**3/9
Factor -19*m**2 + 23*m**2 + 1 + 3 + 8*m.
4*(m + 1)**2
Let i(x) = 6*x**2 - 3*x - 6. Let n(j) = -7*j**2 + 4*j + 7. Let u = 2 + 2. Let o(z) = u*i(z) + 3*n(z). Let o(b) = 0. Calculate b.
-1, 1
Let m = 13 - 16. Let z be 3 - 90/m - -3. Let -45/2*w + 24*w**3 + 3 + z*w**2 = 0. What is w?
-2, 1/4
Let z(n) be the first derivative of n**7/210 - n**5/30 + n**3/6 - 2*n**2 - 4. Let f(y) be the second derivative of z(y). Factor f(i).
(i - 1)**2*(i + 1)**2
Suppose -1 + 3 = 2*m. Suppose -m - 8 = -3*g. Determine d, given that -2/3*d**5 + 0 + 0*d**g - 4/3*d**4 + 2/3*d + 4/3*d**2 = 0.
-1, 0, 1
Suppose 2*h - 1 = -b - 2*b, 5*h + 10 = 5*b. Suppose -b = -d + 1. Suppose 0*o - 4*o - 14*o**d + 5*o**3 + 6*o**2 = 0. Calculate o.
-2/5, 0, 2
Suppose 3 = 5*j - 12. Factor -3*v**4 + j*v - 12*v**2 + 9*v**3 + 3*v**2 + 2*v - 2*v.
-3*v*(v - 1)**3
Suppose 2*t - 7*t = -15. Suppose t*l + 2 = 2*l. Let x(v) = -8*v**2 - 3*v + 3. Let c(y) = 17*y**2 + 6*y - 6. Let u(n) = l*c(n) - 5*x(n). Factor u(j).
3*(j + 1)*(2*j - 1)
Let g(i) be the first derivative of 10*i**3/13 + 17*i**2/13 + 4*i/13 + 9. Determine f, given that g(f) = 0.
-1, -2/15
Let p(x) = -x**2 - 6*x + 10. Let d be p(-7). Let k(f) = -f**2 + 3*f + 4. Let w(r) = r**2 - 4*r - 5. Let b(m) = d*w(m) + 4*k(m). Let b(t) = 0. Calculate t.
-1, 1
Let u be (-5 - (-4 - 1))/(-4). Let h(d) be the third derivative of -1/240*d**5 - 1/840*d**7 - 2*d**2 + u + 0*d**3 - 1/240*d**6 + 0*d + 0*d**4. Factor h(i).
-i**2*(i + 1)**2/4
Let t(g) be the first derivative of -5*g**3/3 - 15*g**2/2 + 20*g + 11. Factor t(f).
-5*(f - 1)*(f + 4)
Determine t so that 5/3*t**3 + 0 - t**2 - 1/3*t**4 - 3*t = 0.
-1, 0, 3
Let j(g) = -3*g**3 - g**2. Let i(y) = -y**5 - y**4 - y**3 - y**2. Let b(x) = -4*i(x) + 4*j(x). Factor b(s).
4*s**3*(s - 1)*(s + 2)
Let c be (-6)/15 + (-136)/(-90). Let d = 125/603 - -1/67. Let -8/9*r**2 + c*r - d = 0. What is r?
1/4, 1
Let q = 12721/3 - 4317. Let l = -76 - q. Factor 1/6*v**2 + l + 2/3*v.
(v + 2)**2/6
Let z(l) be the first derivative of -1/8*l**2 - 1 + 1/12*l**3 + 0*l. Suppose z(d) = 0. What is d?
0, 1
Suppose -4/7*l**3 + 0 + 2/7*l**2 + 2/7*l**4 + 0*l = 0. What is l?
0, 1
Suppose 5*g - 2*t + 0 = 82, -5*t + 43 = 3*g. What is q in -6*q**2 + g*q**2 - 8*q**2 = 0?
0
Suppose -f - 2 = -4. What is p in 24*p - 5*p**f + 12 + 9*p**2 - 8*p = 0?
-3, -1
Find t, given that -1/2 + 9/4*t + 13/4*t**3 + 6*t**2 = 0.
-1, 2/13
Factor 0*l**5 + 0*l**4 - l**5 - l**3 + 2*l**4.
-l**3*(l - 1)**2
Factor 0 - 6/5*n - 9/5*n**2 - 3/5*n**3.
-3*n*(n + 1)*(n + 2)/5
Let o = -519/70 + 54/7. Let v(k) be the second derivative of 0 + 3/10*k**6 - 3/2*k**2 - 1/2*k**4 - 1/14*k**7 - 3*k + 3/2*k**3 - o*k**5. Let v(b) = 0. What is b?
-1, 1
Let w(n) be the third derivative of n**5/210 - n**4/6 + 7*n**3/3 + 9*n**2. Let w(g) = 0. What is g?
7
Let f = -156 - -784/5. Let -f - 6/5*x**2 - 2*x = 0. Calculate x.
-1, -2/3
Let f be -2*6*3/(-12). What is y in -20*y**4 - 2*y**2 + 32*y**f - 6*y - 14*y**2 + 4*y**5 + 6*y = 0?
0, 1, 2
Let h(i) be the second derivative of -i**6/240 + i**5/160 - 3*i. Suppose h(x) = 0. What is x?
0, 1
Let d(y) be the third derivative of y**6/660 + y**5/330 - 2*y**2 + 17. Let d(s) = 0. Calculate s.
-1, 0
Let o(u) be the third derivative of u**8/504 - u**6/60 + u**5/45 - 12*u**2. Suppose o(j) = 0. Calculate j.
-2, 0, 1
Suppose -t + d = 62, 2*d - 186 = 3*t - 0*t. Let x = -245/4 - t. Factor x*r**2 - 3/4 + 3/4*r**3 - 3/4*r.
3*(r - 1)*(r + 1)**2/4
Let h(c) be the third derivative of 0*c**5 + 0*c**3 + 0*c + 0*c**6 - 1/84*c**8 + 4/105*c**7 - 3*c**2 + 0 + 0*c**4. Factor h(m).
-4*m**4*(m - 2)
Let o(l) = -l**2 + 14*l - 10. Let j be o(13). Determine z, given that 0 + 0*z + 1/4*z**j + 1/4*z**2 = 0.
-1, 0
Factor -13*y**3 + 20 + 44*y + 17*y**3 + 11*y**2 + 17*y**2.
4*(y + 1)**2*(y + 5)
Factor -84*x + 4*x**5 + 24*x**3 - 8*x**5 - x**4 + 36 + 40*x**2 - 11*x**4.
-4*(x - 1)**3*(x + 3)**2
Let g(f) = f**3 + 2*f**2 - 3*f - 4. Let s be