*6/630 + s**4/12 + s**2. Let w(f) be the second derivative of i(f). Find t such that w(t) = 0.
0, 2
Let w(z) be the second derivative of z**6/30 + 7*z**5/30 + 17*z**4/36 + z**3/3 - 9*z. Factor w(g).
g*(g + 1)*(g + 3)*(3*g + 2)/3
Let y(q) = 32*q - 15*q - 19*q. Let r be y(-1). Factor -2/5 - 2/5*k**r - 4/5*k.
-2*(k + 1)**2/5
Suppose 4*r = 3*r + 5*t + 91, -3*r = -4*t - 284. Factor 0*i**2 + 4 + 3*i - r*i**3 + 21*i + 64*i**4 + 4*i**2.
4*(i - 1)**2*(4*i + 1)**2
Factor -2*a + 0*a**2 + 1/2*a**3 + 0.
a*(a - 2)*(a + 2)/2
Let b be 10/20 - 3/22. Find d, given that -10/11*d**3 - 6/11*d**2 + b*d + 0 = 0.
-1, 0, 2/5
Let q(r) = 3*r**2 - r - 14. Let y(g) = 3*g**2 - 15. Let a(s) = -6*q(s) + 5*y(s). Let a(v) = 0. Calculate v.
-1, 3
Let s(t) = 2*t**2 - 8*t + 3. Let z(o) = 1. Let x(b) = 2*s(b) + 6*z(b). Factor x(m).
4*(m - 3)*(m - 1)
Let a be 16/(0 + -1)*-2. Let c be a/(-12) + 3 - 0. What is i in -c*i**2 + 1/3*i**3 - 1/3*i + 1/3 = 0?
-1, 1
Let s(p) = -p + 3. Let m be s(-3). Let u be ((-3)/(-2))/(3/m). Find i, given that 3 + 0*i**2 + 2*i**4 + 2*i**2 + 4*i**u - 3 = 0.
-1, 0
Let d = -21 - -24. Factor 13*n**4 + 6*n**5 - 3*n**2 + 3*n**5 + 2*n**4 + d*n**3.
3*n**2*(n + 1)**2*(3*n - 1)
Let z(k) be the third derivative of k**9/60480 + k**8/20160 - k**7/5040 - k**6/720 - k**5/60 - k**2. Let r(w) be the third derivative of z(w). Factor r(u).
(u - 1)*(u + 1)**2
Let g be 68/170*(0 - -5). Factor 16/5 - 56/5*w + 49/5*w**g.
(7*w - 4)**2/5
Let b = 0 + 0. Let o = -34 + 69/2. Solve b*z + 0 - o*z**2 = 0.
0
Let f(z) be the second derivative of z**10/13440 - z**9/20160 - z**8/4480 - z**4/4 + z. Let x(a) be the third derivative of f(a). Factor x(r).
3*r**3*(r - 1)*(3*r + 2)/4
Let y(i) be the third derivative of i**8/840 - i**7/525 - i**6/50 - i**5/75 + i**4/12 + i**3/5 + 16*i**2. Find l such that y(l) = 0.
-1, 1, 3
Let s(a) be the second derivative of -a**5/35 - 3*a**4/7 - 16*a**3/7 - 32*a**2/7 + a - 38. Factor s(j).
-4*(j + 1)*(j + 4)**2/7
Let q(g) = g**2 + g + 4. Let t be q(0). Let n be 10/45 + (-34)/(-90). Factor 6/5*d**3 - n*d + 0*d**2 + 0*d**t - 3/5*d**5 + 0.
-3*d*(d - 1)**2*(d + 1)**2/5
Suppose -2*t + 75 = -91. Let i = t - 55. Factor -i*o**2 + 13*o**3 - 4*o - 61*o**3 - o**3.
-o*(7*o + 2)**2
Let o(v) be the first derivative of -v**4/4 + v**2/2 + 2. Let p(m) = 10*m**3 - 10*m. Let b = 6 + -4. Let i(q) = b*p(q) + 22*o(q). Factor i(t).
-2*t*(t - 1)*(t + 1)
Factor -48*m + 24 - 12*m**3 + 3/2*m**4 + 36*m**2.
3*(m - 2)**4/2
Solve 3/2*a**2 - 9/4*a**5 + 3/4*a**3 - 3*a**4 + 0*a + 0 = 0 for a.
-1, 0, 2/3
Let o(k) = -2*k**2 + 16*k - 24. Let x be o(6). Solve 1/3*m**4 + 0*m**2 - 1/3*m**5 + 0*m + x*m**3 + 0 = 0.
0, 1
Factor 1/2*v**3 + 1/4*v**2 + 0 - 1/2*v - 1/4*v**4.
-v*(v - 2)*(v - 1)*(v + 1)/4
Let b(r) be the first derivative of r**5/240 - r**4/48 + r**3/24 - r**2 + 5. Let j(a) be the second derivative of b(a). Find n such that j(n) = 0.
1
Suppose 4*n = -4*m + 8, 0*n - 2*n - 5*m = -4. What is z in 1 + n*z - 2*z**2 + 4*z**2 - 1 = 0?
-1, 0
Let j(c) be the third derivative of 1/60*c**5 + 0 - 1/6*c**3 + 1/24*c**4 + 4*c**2 + 0*c - 1/120*c**6. Factor j(z).
-(z - 1)**2*(z + 1)
Let m(p) be the first derivative of -p**6/2 + 3*p**4/4 + 2. Factor m(k).
-3*k**3*(k - 1)*(k + 1)
Let q(r) be the second derivative of 1/39*r**3 - 1/39*r**4 + 0 + 6*r + 2/13*r**2 - 1/130*r**5. Factor q(p).
-2*(p - 1)*(p + 1)*(p + 2)/13
Let f(h) be the second derivative of -h**7/147 - h**6/105 + h**5/35 + h**4/21 - h**3/21 - h**2/7 + 9*h. Let f(y) = 0. Calculate y.
-1, 1
Suppose 2834 + 7*d**2 + 2*d**3 + 4*d - 2834 - d**2 = 0. Calculate d.
-2, -1, 0
Let c(n) = -25*n**2 - 15. Let i(l) = l**2 + 1. Let j(h) = c(h) + 20*i(h). Factor j(m).
-5*(m - 1)*(m + 1)
Let s = 15 + -10. Let t(a) be the second derivative of 0*a**2 + 0 - 1/48*a**4 + 1/80*a**s - 2*a + 0*a**3. Determine g so that t(g) = 0.
0, 1
Let j = 66 - 64. Factor 1/3*a**j - 1/3*a + 0.
a*(a - 1)/3
Let u(y) = 2*y + 15. Let w be u(-6). Let d(z) be the first derivative of 2/5*z**5 - w - 2/3*z**6 - 4/3*z**3 + 2*z**4 + 2*z - 2*z**2. What is h in d(h) = 0?
-1, 1/2, 1
Factor -7/3*u + 4/3*u**3 - 2/3 + 5/3*u**2.
(u - 1)*(u + 2)*(4*u + 1)/3
Let b(v) be the second derivative of 16/9*v**3 - 2/3*v**4 - 1/90*v**6 + v + 0 + 2/15*v**5 - 8/3*v**2. Factor b(m).
-(m - 2)**4/3
Determine d, given that -4478 - 750*d**3 - 4897 - 9375*d - 75*d**4 + d**5 - 4*d**5 + 0*d**5 - 3750*d**2 = 0.
-5
Let h be -3 - 136/(-12) - -2. Let l = -10 + h. Factor 1/3*f**3 - l*f + 1/3*f**2 - 1/3.
(f - 1)*(f + 1)**2/3
Factor -205*u**2 + 209*u**2 + 12*u + 0*u + 8.
4*(u + 1)*(u + 2)
Let c(r) be the first derivative of -r**6/3 + r**4 - r**2 - 29. Find l such that c(l) = 0.
-1, 0, 1
Let q(r) = -18*r**3 + 6*r**2 - 24*r - 3. Let m(i) = -i**3 + i**2 - i. Let o(t) = 15*m(t) - q(t). Solve o(k) = 0.
-1
Factor 0 - 8/5*g**2 - 4/5*g - 4/5*g**3.
-4*g*(g + 1)**2/5
Let f(p) be the second derivative of -p**10/7560 - p**9/1890 + p**7/315 + p**6/180 - 2*p**4/3 + 5*p. Let n(t) be the third derivative of f(t). Factor n(v).
-4*v*(v - 1)*(v + 1)**3
Let p(s) be the second derivative of s**7/273 - s**6/65 + s**5/65 + 9*s + 4. Solve p(g) = 0.
0, 1, 2
Factor 1/3*h**5 - 5/3*h - 4/3*h**4 + 4/3*h**3 + 2/3*h**2 + 2/3.
(h - 2)*(h - 1)**3*(h + 1)/3
Let j(q) be the second derivative of q**7/2520 - q**5/120 + q**4/36 - q**3/6 - 4*q. Let v(g) be the second derivative of j(g). Factor v(r).
(r - 1)**2*(r + 2)/3
Let v(u) = -3*u**2 + 4*u + 7. Let x(d) be the second derivative of -1/2*d**2 + 4*d - 1/6*d**3 + 0. Let z(k) = -2*v(k) - 10*x(k). Let z(t) = 0. Calculate t.
-1, 2/3
Let t(q) = q**2 + 4*q + 4. Let c be t(-4). Factor c*d**4 - 4*d**3 + d - 3*d**3 + 4*d**2 + d**5 + 7*d**3 + 6*d**3.
d*(d + 1)**4
Let b(s) be the first derivative of 2*s**6/3 + 4*s**5 + 8*s**4 + 16*s**3/3 - 7. Let b(i) = 0. Calculate i.
-2, -1, 0
Let w(p) be the third derivative of p**7/525 - p**5/150 + 4*p**2. Solve w(q) = 0.
-1, 0, 1
Let u be (-1)/(-6) - (-28)/(-210). Let j(n) be the third derivative of -1/4*n**4 + 0 - u*n**5 - 2/3*n**3 + 3*n**2 + 0*n. Factor j(a).
-2*(a + 1)*(a + 2)
Let z = 4 + -18. Let n(p) = -p**4 + p**2 + p - 1. Let t(b) = b**5 - 3*b**4 + 6*b**3 + 11*b**2 + 8*b - 7. Let y(q) = z*n(q) + 2*t(q). Factor y(w).
2*w*(w + 1)**4
Suppose 9/2*j**4 - 3/2 - 3*j**3 + 9/2*j - 3*j**2 - 3/2*j**5 = 0. Calculate j.
-1, 1
Let p(i) be the second derivative of i**4/72 + i**3/18 + i**2/12 - 5*i. Factor p(d).
(d + 1)**2/6
Let k(o) be the first derivative of -3/35*o**5 + 0*o**2 + 0*o**3 + 3/28*o**4 + 0*o + 5. Factor k(a).
-3*a**3*(a - 1)/7
Let c(k) be the first derivative of 1/25*k**5 + 1/15*k**3 - 1/10*k**4 + 0*k + 0*k**2 - 5. Factor c(o).
o**2*(o - 1)**2/5
Let b = -2 + 19. Factor 29*s + 67*s**2 - 12 + 21*s**4 + 78*s**3 + 14*s**2 - b*s.
3*(s + 1)**2*(s + 2)*(7*s - 2)
Let j(h) be the third derivative of 19/240*h**6 + 2*h**2 + 1/24*h**4 - 11/120*h**5 + 0*h**3 + 0*h + 0 - 13/420*h**7 + 1/224*h**8. Solve j(v) = 0.
0, 1/3, 1, 2
Let c(s) be the third derivative of -s**5/12 - 5*s**4/6 - 19*s**2. Factor c(m).
-5*m*(m + 4)
What is n in 10/7*n**3 + 0*n + 4/7*n**2 + 8/7*n**4 + 2/7*n**5 + 0 = 0?
-2, -1, 0
Factor 47*p + p**4 - 10*p**3 - 128 + 24*p**2 + 27*p - 42*p.
(p - 4)**3*(p + 2)
Suppose 5*j - 12 = -7*l + 3*l, -j = -3*l + 9. Factor 1/2*m**2 - 1/4*m**5 + j + 0*m**4 + 0*m + 3/4*m**3.
-m**2*(m - 2)*(m + 1)**2/4
Let u be ((-1)/21)/(91/(-42) + 2). Factor -4/7 + 0*s**2 - u*s**3 + 6/7*s.
-2*(s - 1)**2*(s + 2)/7
Let v(j) = -j**3 + 8*j**2 + 5*j - 6. Let q(w) = w**3 + w**2 + w. Let o(c) = -2*q(c) + v(c). What is n in o(n) = 0?
-1, 1, 2
Let -k**2 - 8 - 3*k + 3 + 3 = 0. Calculate k.
-2, -1
Suppose -4/9*t + 0 + 2/9*t**2 = 0. Calculate t.
0, 2
Factor -30*c**5 - 6*c**2 + 27*c**5 + 6*c**4 + 0*c**4 + 3*c.
-3*c*(c - 1)**3*(c + 1)
Let m(l) be the first derivative of 0*l + 1/5*l**2 - 1/10*l**4 + 0*l**3 - 5. Factor m(g).
-2*g*(g - 1)*(g + 1)/5
Let l(g) = g**2 + g. Let x(p) = -10*p**2 - 8*p. Let i(s) = -8*l(s) - x(s). Find t such that i(t) = 0.
0
Let r = -38 - -36. Let i = r + 5/2. Suppose -i + 1/4*p + 1/4*p**2 = 0. What is p?
-2, 1
Let z(x) be the third derivative of 7/10*x**7 + 21/4*x**6 - 49/16*x**8 + 0 + 0*x + x**4 + 0*x**3 - x**2 + 19/5*x**5. Determine o, given that z(o) = 0.
-2/7, 0, 1
Let w be (-2 - (-7)/3)*(-8)/(-5). Let j(o) be the first derivative of -o**2 + 2/5*o + w*o**3 + 4. Factor j(n).
2*(n - 1)*(4*n - 1)/5
Let