ctor v(u).
2*u**2
Let h(o) = o**4 + 12*o**3 - 11*o**2 - 32*o + 22. Let f(z) = 12*z**3 - 12*z**2 - 33*z + 21. Let d(n) = 2*f(n) - 3*h(n). Solve d(j) = 0 for j.
-4, -2, 1
Let a(j) be the first derivative of -1/3*j**2 - 4/9*j**3 + 0*j - 1/6*j**4 - 4. Suppose a(o) = 0. Calculate o.
-1, 0
Factor -z**5 + 40*z**3 + 20*z + 40*z**2 + 20*z**4 + 4 + z**5 + 4*z**5.
4*(z + 1)**5
Let i(q) be the second derivative of 0 + 8/9*q**3 + 5/18*q**4 + 1/30*q**5 + 4/3*q**2 + 3*q. Factor i(j).
2*(j + 1)*(j + 2)**2/3
Let t(y) be the first derivative of -4*y**6/3 + 26*y**5/5 - 11*y**4/2 + 4*y**3/3 + 4. Suppose t(g) = 0. What is g?
0, 1/4, 1, 2
Let d(n) be the third derivative of n**6/360 + n**5/45 + n**4/18 + 42*n**2. Find a such that d(a) = 0.
-2, 0
Let q = 11 - 7. Let b(p) be the first derivative of 2*p**5 - 17/2*p**q + 4*p - 11*p**2 - 2 + 14*p**3. Suppose b(r) = 0. Calculate r.
2/5, 1
Let n(w) be the first derivative of w**8/560 - w**7/280 - w**6/120 + w**5/40 - w**3 + 1. Let t(h) be the third derivative of n(h). Find u such that t(u) = 0.
-1, 0, 1
Let k(z) = -19*z**2 + 51*z - 19. Let b(d) = 6*d**2 - 17*d + 6. Let u(p) = 14*b(p) + 4*k(p). Factor u(j).
2*(j - 4)*(4*j - 1)
Let o = 32 + -18. Let i(w) be the first derivative of 5*w**3/3 + 3*w**2/2 - 2*w + 4. Let s(a) = 2*a**2 + a - 1. Let n(l) = o*s(l) - 6*i(l). Factor n(q).
-2*(q + 1)**2
Let j(y) be the third derivative of y**6/80 + y**5/24 - y**4/24 + 13*y**2. Factor j(r).
r*(r + 2)*(3*r - 1)/2
Let c(x) be the first derivative of -2*x**3/27 - 2*x**2/9 - 2*x/9 + 9. Factor c(r).
-2*(r + 1)**2/9
Let s be 2/7 + 0/5. Factor -4/7*z**3 + 0*z - 2/7*z**2 - s*z**4 + 0.
-2*z**2*(z + 1)**2/7
Let g(k) be the third derivative of k**8/16800 - k**7/3150 + k**6/1800 + k**4/6 - 3*k**2. Let v(t) be the second derivative of g(t). Factor v(w).
2*w*(w - 1)**2/5
Suppose -4*h = -0*h. Let u(c) be the third derivative of h*c**5 + 0 + 1/60*c**6 + 2*c**2 + 0*c**3 + 0*c - 1/72*c**4 + 4/315*c**7 + 1/336*c**8. Factor u(z).
z*(z + 1)**3*(3*z - 1)/3
Let o(s) = -2*s + 8. Let i be o(4). Let l(t) be the first derivative of -1/3*t**6 + i*t**2 + 0*t + 0*t**4 - 2/5*t**5 + 0*t**3 - 2. Factor l(j).
-2*j**4*(j + 1)
Let f(i) be the first derivative of i**4/6 - i**2 + i - 2. Let w(o) be the first derivative of f(o). Factor w(p).
2*(p - 1)*(p + 1)
Let z(q) be the second derivative of 1/147*q**7 - 1/7*q**2 - 1/35*q**5 - 5*q - 1/105*q**6 + 0 + 1/21*q**3 + 1/21*q**4. Suppose z(w) = 0. What is w?
-1, 1
Let x(a) = -2*a**2 - 100*a - 500. Let t(n) = 5*n**2 + 200*n + 1000. Let r(z) = 3*t(z) + 5*x(z). Factor r(s).
5*(s + 10)**2
Let z be (-2)/(-4) + 2/(-4). Let y = 2 + z. Factor 2 - g**2 + g**3 - y.
g**2*(g - 1)
Let z(d) = 7*d**2 + 12*d + 4. Let f(n) = -n**2 + 0*n - n + 0*n. Let l(i) = 4*f(i) + z(i). Factor l(g).
(g + 2)*(3*g + 2)
Let q(h) be the first derivative of -h**6/4 + 7*h**5/10 - h**4/4 - h**3 + 5*h**2/4 - h/2 + 25. Solve q(o) = 0.
-1, 1/3, 1
Factor -3/2*r**2 - 3/8 + 15/8*r.
-3*(r - 1)*(4*r - 1)/8
Let h = -224/9 + 457/18. Factor 1/2 - h*o**2 + 0*o.
-(o - 1)*(o + 1)/2
Suppose 17*m = 22*m. Factor 3/2*h**2 + m + 3*h - 3/2*h**3.
-3*h*(h - 2)*(h + 1)/2
Factor 24/7*a**3 + 0 + 0*a + 4/7*a**4 + 36/7*a**2.
4*a**2*(a + 3)**2/7
Suppose 5*y - 3*c - 38 = 0, -3*y = -6*y + c + 22. Factor -5*m + 4*m + 5 - y*m + 2*m**2 + 3.
2*(m - 2)**2
Let t be 6/4*4/18. Suppose -3*z - 2*g - 5 = -g, 5*g + 25 = -4*z. Find f, given that z*f + 1/3 - t*f**2 = 0.
-1, 1
Let q = -64 + 67. Suppose 2/7*y**4 + 0 + 6/7*y**q + 6/7*y**2 + 2/7*y = 0. What is y?
-1, 0
Let s(w) be the second derivative of w**8/3360 + w**7/5040 - w**6/360 - w**5/240 + w**4/12 + w. Let r(j) be the third derivative of s(j). Factor r(t).
(t - 1)*(t + 1)*(4*t + 1)/2
Let i(n) be the first derivative of 2/3*n**3 + 4*n + 3*n**2 - 4. Determine y, given that i(y) = 0.
-2, -1
Let u = -6299/36 + 175. Let o(c) be the second derivative of u*c**4 + 0*c**2 + 0 - 1/18*c**3 - c. Factor o(g).
g*(g - 1)/3
Let y(l) be the second derivative of -l**9/1680 + l**8/560 + l**7/840 - l**6/120 + l**4/30 + l**3/2 - l. Let j(s) be the second derivative of y(s). Factor j(f).
-(f - 1)**3*(3*f + 2)**2/5
Let b(p) = -2*p**2 + 6*p - 4. Let o = 2 + 1. Let q(a) = -4*a**3 - 7*a**2 - 12 + o*a**3 + 18*a + 2*a**3. Let w(n) = -7*b(n) + 2*q(n). Factor w(l).
2*(l - 1)**2*(l + 2)
Determine v, given that -16/5*v + 2/5*v**2 + 32/5 = 0.
4
Let v = 20 + -18. Let a(h) be the third derivative of 0*h**4 + 1/105*h**7 + 1/168*h**8 - 1/30*h**5 + 0*h + h**v + 0 + 0*h**3 - 1/60*h**6. Factor a(z).
2*z**2*(z - 1)*(z + 1)**2
Let z(h) be the first derivative of -h**6/40 + h**5/20 + h**4/8 - h**3/2 + h**2/2 + 5. Let b(t) be the second derivative of z(t). Factor b(l).
-3*(l - 1)**2*(l + 1)
Let w be (3/(-378))/(6/(-9)). Let n(t) be the third derivative of 2*t**2 + 1/735*t**7 + w*t**4 - 1/210*t**5 + 0 + 0*t + 0*t**3 - 1/420*t**6. Factor n(p).
2*p*(p - 1)**2*(p + 1)/7
Let h(m) be the second derivative of -m**10/75600 - m**9/37800 + m**8/16800 + m**7/6300 + m**4/12 - m. Let x(y) be the third derivative of h(y). Factor x(w).
-2*w**2*(w - 1)*(w + 1)**2/5
Let x = 2/61 + 179/122. Let l(p) be the first derivative of 9*p**3 + 33/5*p**5 + x*p**6 + 45/4*p**4 + 1 + 3*p**2 + 0*p. Find m such that l(m) = 0.
-1, -2/3, 0
Suppose 5*k - k + 3*p - 18 = 0, -3*p = -3*k + 3. Find j, given that 2/5*j**4 + 6/5*j**k + 0 + 6/5*j**2 + 2/5*j = 0.
-1, 0
Suppose 6*m**2 - 35*m**4 + 59 - 5*m - 49 - 48*m**2 - 33*m**2 - 95*m**3 = 0. Calculate m.
-1, 2/7
Factor 2/15*n - 4/5 + 2/15*n**2.
2*(n - 2)*(n + 3)/15
Suppose 0 = -3*m + 5 + 4. Factor -m*p**2 - 7*p + 8*p - 4*p.
-3*p*(p + 1)
Determine y so that -5/3*y**4 + 5/3*y**3 + 0*y**2 + 0*y + 0 = 0.
0, 1
Let k be 90/4*8/6. Solve -32 - 4*v + v**2 + k - 3*v**2 = 0 for v.
-1
Let r(u) be the second derivative of -u**7/8820 + u**6/1260 - u**5/420 + u**4/3 + 2*u. Let f(n) be the third derivative of r(n). Find q, given that f(q) = 0.
1
Factor 1/3*n**4 + 36*n + 4*n**3 + 27 + 18*n**2.
(n + 3)**4/3
Let f(j) be the first derivative of -45*j**4/4 - 10*j**3/3 + 45*j**2/2 + 10*j - 4. What is r in f(r) = 0?
-1, -2/9, 1
Let n = 1 - -1. Factor 0 + r**2 + 0 - 3*r**n - 2*r**3.
-2*r**2*(r + 1)
Let a(w) = -3*w**4 - 16*w**3 + 7*w**2 + 5*w + 7. Let i(q) = -q**4 - 5*q**3 + 2*q**2 + 2*q + 2. Let g(y) = 6*a(y) - 21*i(y). Factor g(k).
3*k*(k - 1)*(k + 2)**2
Let h(z) be the second derivative of z**5/15 - 2*z**4/9 - 2*z**3/9 + 4*z**2/3 + 6*z. Factor h(t).
4*(t - 2)*(t - 1)*(t + 1)/3
Let j be 10/15 + (-4)/(-3). Suppose 4*o - 6 = j. Solve 0 + 0*r + 2/3*r**o = 0.
0
Let m = 5 + -5. Let a(o) = o**2 + o + 2. Let g be a(m). Solve -g*s**3 - 2*s**5 + s**4 + s**3 - 3*s**4 + s**5 = 0.
-1, 0
Let y = -6 - -12. Suppose 3*w + 3 = -3*f, -y*f + 2*f - 4 = 5*w. Factor 7*t + t + w*t**2 + 2*t**2 + 8.
2*(t + 2)**2
Let q(j) be the third derivative of 1/735*j**7 + j**2 + 1/420*j**6 - 1/105*j**5 + 0 + 0*j + 0*j**3 + 0*j**4. Factor q(o).
2*o**2*(o - 1)*(o + 2)/7
Factor 0 + 0*w - 4/3*w**3 - 8/3*w**2 + 4/3*w**4.
4*w**2*(w - 2)*(w + 1)/3
Let u be -1 + 30 + (-3)/3. Suppose -4*b = -4*d - u, -3*d = 3*b - 0*b + 9. Determine p so that -b*p + 2*p + p**3 = 0.
0
Let y be (-8)/(-15)*(-6 + 495/60). Factor -y*m**2 - 2/5 - 8/5*m.
-2*(m + 1)*(3*m + 1)/5
Let p(s) be the first derivative of 1 - 3/4*s**4 - 2/3*s**3 + 1/2*s**2 + 0*s. Determine y so that p(y) = 0.
-1, 0, 1/3
Factor -2*h - 2*h**2 + 3*h**2 + h.
h*(h - 1)
Let p(s) be the third derivative of 1/6*s**3 - 6*s**2 + 1/12*s**4 + 1/60*s**5 + 0 + 0*s. Determine l, given that p(l) = 0.
-1
Let h(b) = -3*b**4 - 6*b**3 + 27*b**2 - 21*b + 9. Let f(s) = -s**5 + s**4 + s**2 + 1. Let g(l) = -3*f(l) + h(l). Factor g(t).
3*(t - 1)**4*(t + 2)
Let o be 18/(-70) + 3/(-21). Let r = o + 24/35. Solve 0*b**4 + 0*b**2 + 2/7*b**5 + 0*b - r*b**3 + 0 = 0 for b.
-1, 0, 1
Let q(i) = -2*i**3. Let k be q(-1). Solve k*x**2 - 1 - x**4 + 3*x**5 - x - 3*x**5 + 2*x**3 - x**5 = 0.
-1, 1
Factor 4/5 + 2/5*c**3 - 6/5*c**2 - 2/5*c + 2/5*c**4.
2*(c - 1)**2*(c + 1)*(c + 2)/5
Let k be -3 + (-2 - (-3 - 5)). Factor 1/4*v**k + 1/4 - 1/4*v - 1/4*v**2.
(v - 1)**2*(v + 1)/4
Let r be (10/4 - 3)*0. Let f(s) be the third derivative of 0*s**5 + 0 + 3*s**2 + r*s - 1/300*s**6 + 0*s**4 + 0*s**3. Factor f(m).
-2*m**3/5
Suppose 0*k = k - 4. Suppose -k*q + i = -5, -q + 6*i + 25 = i. Determine u so that 0*u - 2/9*u**3 - 2/9*u**2 + q = 0.
-1, 0
Let r be (-