o(-7). Suppose 4*k - 5*z = 23, -2*k - 2*z - 4 + 2 = 0. Factor 4*t**2 + 2*t + 3*t**3 + t + d*t**k.
3*t*(t + 1)**2
Let z(j) be the third derivative of -j**6/30 + j**4/2 - 4*j**3/3 - 35*j**2. Solve z(p) = 0.
-2, 1
Let u(z) be the second derivative of z**9/1512 + z**8/480 + z**7/630 - 5*z**4/12 - 6*z. Let b(f) be the third derivative of u(f). Factor b(x).
2*x**2*(x + 1)*(5*x + 2)
Let w(p) be the third derivative of -p**8/504 + 2*p**7/315 - p**6/180 - 6*p**2. Determine s, given that w(s) = 0.
0, 1
Let p = 70 + -139/2. Factor -1/2 - 3/2*n**2 + p*n**3 + 3/2*n.
(n - 1)**3/2
Suppose v = -1 - 0, 4*r = 2*v + 2. Let n(i) be the first derivative of 0*i**3 - 1/5*i**5 - 1/4*i**4 + r*i**2 + 2 + 0*i. Let n(y) = 0. What is y?
-1, 0
Factor -1/2*a**2 + 3/2 + a.
-(a - 3)*(a + 1)/2
Let y(t) be the third derivative of -1/40*t**6 - 1/336*t**8 + 0*t**4 + t**2 + 0 + 0*t + 0*t**3 + 1/60*t**5 + 1/70*t**7. What is p in y(p) = 0?
0, 1
Solve 4/3 + 28/9*g**4 + 88/9*g**2 + 8*g**3 + 52/9*g + 4/9*g**5 = 0 for g.
-3, -1
Let r(l) be the first derivative of l**6/2 - 9*l**4/4 + 2*l**3 - 8. Factor r(g).
3*g**2*(g - 1)**2*(g + 2)
Let j be (-8)/(-12) - (-30)/9. Let v be (-6)/(-8) - 3/j. Factor 0*p**2 + 0*p + v - 1/4*p**3.
-p**3/4
Let d be 8788/40 - 6/(-4). Let q = d - 220. Suppose 2/5 + 2/5*v**3 + 6/5*v + q*v**2 = 0. Calculate v.
-1
Let d be 1 + -1 + 5 - (1 - -1). Let g(o) be the third derivative of -1/9*o**4 + 0*o + 4/45*o**5 - 2*o**2 + 0 + 1/18*o**d. Factor g(c).
(4*c - 1)**2/3
Let d(h) be the third derivative of h**5/20 + 9*h**4/8 - 5*h**3 - 28*h**2. Solve d(w) = 0.
-10, 1
Let k(l) = 8*l**2 - 3*l + 2. Let s be k(1). Let z = 9 - 6. Factor -14*b + s*b**3 + z*b**3 + 4 + 4*b**3 + 0*b**3 - 4*b**2.
2*(b - 1)*(b + 1)*(7*b - 2)
Suppose v**4 - v + 8918 - 8918 + v**3 - v**2 = 0. Calculate v.
-1, 0, 1
Suppose -18 = 14*l - 23*l. Find w, given that 0 - 1/6*w - 1/6*w**l = 0.
-1, 0
Suppose 6/5*x + 2/5*x**3 - 2/5 - 6/5*x**2 = 0. What is x?
1
Let q be 133/21 - (-4)/6. Let h(t) be the third derivative of 0*t - 1/90*t**6 + 0*t**5 + 0 + 0*t**3 + 0*t**q + 1/36*t**4 - t**2 + 1/504*t**8. Factor h(f).
2*f*(f - 1)**2*(f + 1)**2/3
Let f(x) = x**2 + x. Let z(t) = 3*t**2 + 3*t. Let o(c) = -12*f(c) + 5*z(c). Factor o(n).
3*n*(n + 1)
Factor 2/5*c**2 - 16/5 + 14/5*c.
2*(c - 1)*(c + 8)/5
Let m(j) = -j**2 - 32*j + 35. Let x be m(-33). Let i(s) be the first derivative of 1/2*s**x - 1/2*s + 0*s**3 + 2 - 1/4*s**4 + 1/10*s**5. Factor i(a).
(a - 1)**3*(a + 1)/2
Let l = -880/17 + 211217/4080. Let q(r) be the third derivative of -1/96*r**4 + 2*r**2 - l*r**5 + 1/24*r**3 + 0 + 0*r + 1/480*r**6. Factor q(t).
(t - 1)**2*(t + 1)/4
Find c such that 0 + 0*c - 4/7*c**4 + 4/7*c**3 + 8/7*c**2 = 0.
-1, 0, 2
Let z(c) = -4*c - 26. Let n be z(-7). Let j(f) be the first derivative of -5/2*f**4 - 1/15*f**6 + 76/15*f**3 + 16/5*f - 28/5*f**n + 1 + 16/25*f**5. Factor j(r).
-2*(r - 2)**3*(r - 1)**2/5
Let c(m) be the second derivative of m**6/60 - 4*m**5/45 + 7*m**4/36 - 2*m**3/9 - m**2/2 - 3*m. Let n(t) be the first derivative of c(t). Solve n(f) = 0.
2/3, 1
Suppose 0 = -3*t - 2*r + r + 7, 4*r + 2 = -2*t. Let y(s) be the first derivative of -2 + 0*s + 0*s**2 - 1/9*s**t. Let y(w) = 0. Calculate w.
0
Let j(b) be the third derivative of b**5/100 - 3*b**4/20 + 9*b**3/10 + 6*b**2. Factor j(w).
3*(w - 3)**2/5
Suppose 8*k = 14*k. Factor -8/3*u**2 + 2/3*u**3 + k + 8/3*u.
2*u*(u - 2)**2/3
Let r(p) = 6*p**5 + 15*p**4 - 6*p**3 + 15. Let f(s) = s**5 + 2*s**4 - s**3 + 2. Let l(m) = -15*f(m) + 2*r(m). Factor l(j).
-3*j**3*(j - 1)*(j + 1)
Let c(d) be the third derivative of 2*d**7/21 - 5*d**6/24 - d**5/4 + 25*d**4/24 - 5*d**3/6 - 22*d**2. Suppose c(p) = 0. Calculate p.
-1, 1/4, 1
Let m(r) be the second derivative of -r**6/6 - 3*r**5/4 + 5*r**4/6 + 10*r**3 + 20*r**2 - 4*r - 2. Factor m(v).
-5*(v - 2)*(v + 1)*(v + 2)**2
Suppose -4*a - 19 = 13. Let r = a + 13. Determine y so that -1/6*y**r + 0 + 0*y**3 - 1/3*y**4 + 1/6*y + 1/3*y**2 = 0.
-1, 0, 1
Factor -25*y - 6 - 17*y**2 - 5*y**2 + 14*y**2 - 4*y**2 + 7*y**3.
(y - 3)*(y + 1)*(7*y + 2)
Suppose 3*n - 2*d = 2*d + 6, 0 = n - 2*d. Find s such that -3*s - n*s**2 + 3*s + 3*s**3 + 3*s**4 = 0.
-2, 0, 1
Let f be 2/9 - (-1477)/(-6930). Let o(v) be the second derivative of -1/33*v**3 + 2/11*v**2 - 3*v + 0 - 1/33*v**4 + f*v**5. Factor o(g).
2*(g - 2)*(g - 1)*(g + 1)/11
Let a be (-1*(-4)/(-10))/((-7)/35). Let h(v) be the first derivative of 2/5*v**5 + 0*v**2 + 0*v - 2/3*v**3 - 1/2*v**4 + 1/3*v**6 + a. Solve h(p) = 0 for p.
-1, 0, 1
Let z be ((-39)/(-156))/((-2)/(-4)). Factor 1/4*r**4 + 5/4*r**2 - r**3 - z*r + 0.
r*(r - 2)*(r - 1)**2/4
Let c be 9/6 + 8/((-96)/18). Factor c*o + 9/4*o**3 + 0 - 3/4*o**2 - 9/4*o**4 + 3/4*o**5.
3*o**2*(o - 1)**3/4
Suppose 5*b = -2*d - 19, -2*b + 5*b = -3*d - 6. Factor 0*l + 1/3*l**4 + 0 - 1/3*l**2 + 0*l**d.
l**2*(l - 1)*(l + 1)/3
Let i(x) be the second derivative of x**8/2520 + x**7/630 - x**6/540 - x**5/90 - 5*x**3/6 - 9*x. Let w(z) be the second derivative of i(z). Solve w(c) = 0.
-2, -1, 0, 1
Let f = 46/3 - 44/3. Let a be (6/(-27))/(1/(-3)). Factor f - 4/3*x + a*x**2.
2*(x - 1)**2/3
Let p(u) be the second derivative of -u**5/2 - u**4/6 + 5*u**3/3 + u**2 + 3*u. Solve p(v) = 0.
-1, -1/5, 1
Let k(t) = 2*t**2 - 6*t - 6. Let i(o) = o**2 - 5*o - 5. Let d(n) = -3*i(n) + 2*k(n). Let z be d(-3). Suppose 4*y**2 - y**3 + 4*y**z - 5*y**2 = 0. What is y?
0, 1/3
Let c = -19 - -19. Factor c - 2/13*y - 8/13*y**3 - 10/13*y**2.
-2*y*(y + 1)*(4*y + 1)/13
Factor 0 + 48*i - 54*i**4 + 6 + 132*i**4 + 2 + 134*i**3 + 18*i**5 + 114*i**2.
2*(i + 1)**3*(3*i + 2)**2
Suppose 2/5*j**2 - 4/5*j + 2/5*j**3 + 0 = 0. What is j?
-2, 0, 1
Let n(x) be the first derivative of 2*x**5/35 + x**4/7 - 2*x**3/21 - 2*x**2/7 - 1. Factor n(l).
2*l*(l - 1)*(l + 1)*(l + 2)/7
Let -32/17 - 48/17*o - 18/17*o**2 - 2/17*o**3 = 0. Calculate o.
-4, -1
Let w(g) be the second derivative of -5*g**7/42 + g**6 - 9*g**5/4 - 17*g. Factor w(h).
-5*h**3*(h - 3)**2
Let i(n) = n**2 - 8. Let j be i(6). Let m be j/8 + 3/(-1). Factor -c + 1/2*c**2 + m.
(c - 1)**2/2
Suppose 0*g + 3*g = 0. Let y = 2 - -1. Factor g*l**y + 5*l**3 - 5*l**3 + l**3.
l**3
Factor 6*p**2 + 15 + 2*p**3 + 2*p**2 - 15 - 2*p**4 - 8*p.
-2*p*(p - 2)*(p - 1)*(p + 2)
Let b(s) be the second derivative of 27*s**5/5 + 19*s**4/4 - 15*s**3/2 + 3*s**2 + 5*s. What is m in b(m) = 0?
-1, 2/9, 1/4
Let z(j) = 37*j**4 - 10*j**3 - 37*j**2 + 17*j - 7. Let t(v) = 19*v**4 - 5*v**3 - 19*v**2 + 9*v - 4. Let g(q) = -7*t(q) + 4*z(q). Find d, given that g(d) = 0.
-1, 0, 1/3, 1
Let a(i) be the second derivative of i**10/105840 + i**9/17640 + i**8/7840 + i**7/8820 + i**4/6 + 3*i. Let x(o) be the third derivative of a(o). Factor x(h).
2*h**2*(h + 1)**3/7
Let k(b) = b**3 - b + 1. Let q be (-3)/(3/(-2)) + 0. Let j(w) = 0*w + 4 + 0*w - 2*w**q + 5*w - 5*w**3. Let m(r) = j(r) - 2*k(r). Find l such that m(l) = 0.
-1, -2/7, 1
Let w(u) be the first derivative of -u**6/3 - 6*u**5/5 + 35. Factor w(r).
-2*r**4*(r + 3)
Factor 2*w**2 - w + 11*w - w**2 - 15*w.
w*(w - 5)
Let i = -637/165 + 58/15. Let d = i + 107/495. Find b, given that d*b**2 + 0 - 2/9*b**3 + 0*b = 0.
0, 1
Let o(p) be the second derivative of -p**9/60480 - p**8/8960 - p**7/3360 - p**6/2880 + p**4/4 + 4*p. Let y(b) be the third derivative of o(b). Factor y(v).
-v*(v + 1)**3/4
Suppose 3*b = 8*b. Let z(w) be the second derivative of 1/21*w**7 + 0*w**3 - 2*w + 0*w**4 + b*w**6 + 0*w**5 + 0 + 0*w**2. Find q such that z(q) = 0.
0
Let w(o) = o**3 + 7*o**2 + 5*o - 1. Let v be w(-4). Find a such that 0*a + 12*a**4 - v*a**3 - 6*a + 3*a + 18*a**2 = 0.
0, 1/4, 1
Let c be (-3 - -1) + 318/(-12). Let f = c + 30. Factor -f*b**3 + 0 - 3*b**2 - 3/2*b.
-3*b*(b + 1)**2/2
Let n(i) be the second derivative of 0 - 1/20*i**5 + 0*i**3 + 0*i**2 + 1/12*i**4 - 2*i. Factor n(g).
-g**2*(g - 1)
Let s(j) = 4*j**2 - 26*j - 56. Let a(f) = 3*f**2 - 25*f - 55. Let q(g) = -6*a(g) + 5*s(g). What is w in q(w) = 0?
-5
Let -a**3 + 4*a**3 + 36*a**2 - 2*a**3 - 35*a**2 - 2*a = 0. Calculate a.
-2, 0, 1
Let x = 37/45 - 3/5. Let 8/9*i**4 + x*i**5 + 8/9*i**3 - 4/9*i**2 - 10/9*i - 4/9 = 0. What is i?
-2, -1, 1
Let k(v) be the second derivative of v**7/70 - v**6/40 - v**5/20 + v**4/8 - 4*v**2 + 6*v. Let t(c) be the first derivative of k(c). Factor t(m).
3*m*(m - 1)**2*(m + 1)
Suppose -3*h + 4*h + 2 = 0. Let n(d) 