*5 + 8*y**2 + 0 + 5/56*y**4 - 1/7*y**3 + 0*y. Factor d(o).
3*(o + 2)*(3*o - 1)/7
Let k(u) be the third derivative of 2*u**7/525 + 9*u**2. Factor k(o).
4*o**4/5
Let k = -15 + 15. Let w(t) be the second derivative of 0 - 1/48*t**4 + k*t**2 + 1/80*t**5 + t + 0*t**3. Factor w(p).
p**2*(p - 1)/4
Let c be (3*-1)/3*(-32)/24. Let 2/3*p**2 + 0 - c*p = 0. What is p?
0, 2
Let f(g) be the third derivative of -g**7/1260 + g**5/60 - g**4/3 + 2*g**2. Let w(z) be the second derivative of f(z). What is i in w(i) = 0?
-1, 1
Factor -3*y**2 + 4*y**2 - y + y**2 - y.
2*y*(y - 1)
Let s(q) = -q**2 - q + 3*q**3 - 4*q**3 - 5*q**3 + 1 + 7*q**3. Let l(f) = 3*f**5 + 12*f**4 + 12*f**3 + 18*f**2 + 9*f - 6. Let c(p) = -l(p) - 6*s(p). Factor c(g).
-3*g*(g + 1)**4
Let h(k) be the second derivative of k**5/30 - 4*k**4/9 + 13*k**3/9 - 2*k**2 + 8*k + 4. Factor h(l).
2*(l - 6)*(l - 1)**2/3
Let x be 65/15 + 2 + (-2 - 4). Determine s, given that x*s**3 - 1/6*s**5 - 1/3*s**2 + 1/6*s**4 - 1/6*s + 1/6 = 0.
-1, 1
Let c(t) be the second derivative of -7*t**6/240 - t**5/60 - t**2/2 + 3*t. Let f(u) be the first derivative of c(u). Determine l, given that f(l) = 0.
-2/7, 0
Let q(v) = -v**2 - 7*v + 10. Let m be q(-8). Factor -p**4 + 8*p**3 + 8*p - p**2 + 5*p**4 - 2*p**4 + 13*p**m + 2.
2*(p + 1)**4
Let u(y) = -5*y**2 - 9*y + 11. Let x(l) = -l**2 - 2*l + 2. Let f(t) = 2*u(t) - 11*x(t). Determine w so that f(w) = 0.
-4, 0
Suppose c + 3*c + 3*j - 12 = 0, -4*c = 4*j - 16. Find p such that -3*p**3 + c + 2/3*p**2 + 0*p = 0.
0, 2/9
Let o(k) = -k**3 - 2*k**2 + 2*k + k**2 - k - 1. Let f(t) = -7 - 5*t**2 + 9*t - 5*t**3 + 4*t**2 - 8*t**2. Let z(a) = f(a) - 6*o(a). Factor z(r).
(r - 1)**3
Suppose -5*f + 1 + 4 = 0. Suppose -a + f + 2 = 0. Suppose 0*w - 2/3*w**a + 2/9*w**4 + 0 + 4/9*w**2 = 0. Calculate w.
0, 1, 2
Let m be 0*(-3 + 2 + 2). Let t(d) be the second derivative of 0 + 4/9*d**3 + m*d**2 + 0*d**4 - 49/30*d**5 - d. Suppose t(z) = 0. What is z?
-2/7, 0, 2/7
Let a be 10*24/40*4/54. Factor a*c**3 - 2/3*c**4 + 2/9 - 2/3*c + 2/9*c**5 + 4/9*c**2.
2*(c - 1)**4*(c + 1)/9
Let l(a) be the first derivative of a**7/280 - 5*a**2/2 - 3. Let q(p) be the second derivative of l(p). Suppose q(o) = 0. Calculate o.
0
Let q(o) = -o**3 + o - 60. Let i be q(0). Let t be ((-18)/i)/((-2)/(-8)). Determine b so that 0 - 3*b**4 - t*b**2 + 0*b - 21/5*b**3 = 0.
-1, -2/5, 0
Suppose -1/3*b**2 + 1/3*b + 2/3 = 0. Calculate b.
-1, 2
Let u(g) be the third derivative of g**8/294 - 3*g**7/245 + g**6/70 - g**5/210 - g**2. Let u(c) = 0. Calculate c.
0, 1/4, 1
Let o = -5999/20 - -300. Let d(r) be the second derivative of -1/120*r**6 + 0 - 1/8*r**2 - 1/8*r**4 + r + o*r**5 + 1/6*r**3. Factor d(x).
-(x - 1)**4/4
Let r(c) be the third derivative of -c**7/168 + 15*c**2. Suppose r(u) = 0. What is u?
0
Let j(m) be the first derivative of -m**6/1440 + 4*m**3/3 - 2. Let g(r) be the third derivative of j(r). Factor g(d).
-d**2/4
Let f = 22 - 3. Suppose -3*w = 10 - f. Factor -45/2*g**3 - 33/2*g**4 + 0 - 27/2*g**2 - w*g - 9/2*g**5.
-3*g*(g + 1)**3*(3*g + 2)/2
Let q(j) = -9*j**3 + 8*j**2 - 5*j - 2. Let f(y) = y**4 + 45*y**3 - 39*y**2 + 26*y + 11. Let i(r) = 6*f(r) + 33*q(r). Factor i(n).
3*n*(n - 3)*(n - 1)*(2*n - 1)
Let a(h) = h**2 + 4*h + 2. Let q be a(-4). Let d be 1*(6/q + 13). Solve -d*r + 1 + 2*r**2 - 5 + 18*r = 0 for r.
-2, 1
Let f = 5/3 - 7/6. Let t(c) be the first derivative of -1 + 0*c - 1/4*c**4 + f*c**2 + 1/3*c**3 - 1/5*c**5. Let t(n) = 0. What is n?
-1, 0, 1
Let p(a) be the third derivative of a**6/40 - 11*a**5/40 + 3*a**4/4 + 9*a**3/4 + 23*a**2. Factor p(o).
3*(o - 3)**2*(2*o + 1)/2
Let g be (-1)/5 - 48/(-15). Factor -3 + 1 - 6*h**3 + 3*h**3 + g*h**2 - h**2 + 3*h.
-(h - 1)*(h + 1)*(3*h - 2)
Let f(d) = d + 10. Let k be f(-7). Suppose -k*q = -q. Determine p, given that -3*p**3 + q*p**2 + 2*p + p**3 + 2*p**2 - 2 = 0.
-1, 1
Let y(z) be the first derivative of 1/20*z**4 + 1/30*z**6 + 0*z + 4 - 3/25*z**5 - 1/5*z**2 + 1/5*z**3. Let y(g) = 0. Calculate g.
-1, 0, 1, 2
Let b(d) be the third derivative of -d**6/30 + 4*d**5/5 - 8*d**4 + 128*d**3/3 - 3*d**2. Suppose b(y) = 0. Calculate y.
4
Suppose 2*a = -c, 7*a - 3*a = 5*c. Let 2/9*p**4 + 0*p + c*p**2 + 0 - 2/9*p**3 = 0. Calculate p.
0, 1
Let -8/5*i**3 + 4/5*i**4 + 2/5*i**5 + 0 + 6/5*i - 4/5*i**2 = 0. Calculate i.
-3, -1, 0, 1
Let o(i) be the first derivative of i**6/540 + i**5/54 + i**4/36 - i**3/3 + 3*i**2/2 + 2. Let g(j) be the second derivative of o(j). Factor g(h).
2*(h - 1)*(h + 3)**2/9
Let m(n) be the second derivative of 2*n + 1/18*n**3 + 1/36*n**4 + 0*n**2 + 0. Factor m(l).
l*(l + 1)/3
Let 12*v**5 + 8*v - 30*v**3 - 10*v**3 - 2*v**2 - 28*v**2 + 2*v**4 + 8 = 0. Calculate v.
-1, -2/3, 1/2, 2
Solve -12*j**2 - 5*j**3 - j + j**3 + j = 0.
-3, 0
Let f(b) be the third derivative of -b**5/12 - 5*b**4/8 + 10*b**3/3 - 2*b**2. Factor f(z).
-5*(z - 1)*(z + 4)
Let k(h) be the third derivative of -h**6/40 + 3*h**4/8 - h**3 - 4*h**2. Find t, given that k(t) = 0.
-2, 1
Factor 0 + 0*l + 2/11*l**4 - 6/11*l**3 + 0*l**2.
2*l**3*(l - 3)/11
Let u(l) be the second derivative of -l**8/3360 + l**7/840 - l**6/720 - l**3/3 + l. Let t(g) be the second derivative of u(g). Factor t(h).
-h**2*(h - 1)**2/2
Let o(s) be the first derivative of 4 + s + 8/11*s**2 + 1/11*s**4 + 1/110*s**5 + 4/11*s**3. Let b(c) be the first derivative of o(c). Factor b(l).
2*(l + 2)**3/11
Factor 1/4*r**2 + 0*r - 1.
(r - 2)*(r + 2)/4
Let c(l) be the third derivative of -l**5/140 + 5*l**4/56 - 2*l**3/7 + 29*l**2. Find f such that c(f) = 0.
1, 4
Suppose -5*u - 40 = -125. Let g = 38 + -36. Find s such that 21*s**4 - u*s**g + 2 - 3 - 5*s**4 + 2 = 0.
-1, -1/4, 1/4, 1
Let g(o) be the third derivative of 0 + 0*o**3 - 1/16*o**8 + o**2 + 1/5*o**5 - 19/70*o**7 - 1/5*o**6 + 0*o + 0*o**4. Solve g(i) = 0.
-2, -1, 0, 2/7
Let j(l) = 2*l**3 + 6*l**2 + l + 7. Let s(c) be the second derivative of c**3/6 - c**2/2 - 3*c. Let z(x) = j(x) + 5*s(x). Factor z(n).
2*(n + 1)**3
Let o be 20/75*(-100)/(-8). Solve -2/3*d - 2*d**3 + o*d**2 - 2/3 = 0 for d.
-1/3, 1
Let q = -3 + 4. Let h be 4 - (-2 + 3)/q. Solve b + 4*b**h + 2*b - b**3 - 5*b - b**2 = 0.
-2/3, 0, 1
Let y(i) be the second derivative of -2*i**6/135 - i**5/45 - 34*i + 2. Find a such that y(a) = 0.
-1, 0
Let y = -34 + 34. Let j(f) be the third derivative of -1/42*f**4 + 1/735*f**7 + 0*f + 0*f**3 - f**2 - 1/105*f**6 + 1/42*f**5 + y. Suppose j(g) = 0. What is g?
0, 1, 2
Determine x, given that 27*x + 2 + 5*x**2 + 2 - 19*x + x**3 = 0.
-2, -1
Let o = -2 + 2. Suppose 3*q + j - 6 - 2 = o, -5*q + j = -24. Find n, given that 6/5*n**q + 4/5*n**3 - 2/5*n**2 + 0 + 0*n = 0.
-1, 0, 1/3
Factor -2/9*i**4 - 4/9*i - 8/9*i**3 + 0 - 10/9*i**2.
-2*i*(i + 1)**2*(i + 2)/9
Factor 8*i**3 - 3/2*i**4 + 8/3*i - 26/3*i**2 + 0.
-i*(i - 4)*(3*i - 2)**2/6
Factor -24/13*o**2 + 0 + 72/13*o + 2/13*o**3.
2*o*(o - 6)**2/13
Let u = -15 - -25. Let d(j) = 10 + 0 - j - 17 + j**2. Let t(x) = 1. Let q(w) = u*t(w) + 2*d(w). Let q(p) = 0. What is p?
-1, 2
Let h(v) be the first derivative of -v**3/15 + v**2/5 - 2. Factor h(g).
-g*(g - 2)/5
Let i be ((-687)/(-75) - 9)/((-4)/(-30)). Factor 0 + 2/5*h**3 + 4/5*h - i*h**2.
2*h*(h - 2)*(h - 1)/5
Let g(h) be the first derivative of -h**3 - 2*h**2 - 3*h**4 + 8*h**2 + 4*h + 6 - 7*h + 2*h**3. Factor g(d).
-3*(d - 1)*(d + 1)*(4*d - 1)
Suppose -138*f = -134*f - 16. Find b such that 26/7*b + 4/7 + 2*b**f + 54/7*b**2 + 46/7*b**3 = 0.
-1, -2/7
Let q(w) be the third derivative of w**6/30 - w**5/5 + w**4/2 - 2*w**3/3 - 44*w**2. Factor q(b).
4*(b - 1)**3
Let p be (57/(-209))/(4/(-22)). Factor p*s**3 + 2*s**2 - 2*s + 0.
s*(s + 2)*(3*s - 2)/2
Suppose 68 = 4*i - 0*i. Let j be -18 + i + (-22)/(-4). Factor 7/2*v + j*v**2 - 1.
(v + 1)*(9*v - 2)/2
Suppose 4*i = 2*u - 22, 8*u - 4*u - 8 = -4*i. Suppose -2*j - u*h = j + 11, -10 = -2*j + h. Factor 3*c**4 + 3*c**4 + c**3 + j*c**3.
2*c**3*(3*c + 2)
Let b = 10 + -10. Let z(n) be the second derivative of -2/3*n**2 - 2*n - 1/18*n**4 + b - 1/3*n**3. Find m, given that z(m) = 0.
-2, -1
Let x(p) be the third derivative of -p**7/840 + 7*p**4/24 - 2*p**2. Let f(m) be the second derivative of x(m). Find v, given that f(v) = 0.
0
Suppose 8*s = 3*s - 4*l + 26, l = 4. Factor -2*d + d**s - 38 - 3*d**2 + 42.
-2*(d - 1)*(d + 2)
Let a(x) be the second derivative of 5*x**7/14 - 2*x**6/5 - 39*x**5/50 + 3*