 n(r) be the first derivative of -r**6/2 - 33*r**5/5 - 129*r**4/4 - 73*r**3 - 84*r**2 - 48*r + 6. Factor n(w).
-3*(w + 1)**3*(w + 4)**2
Let c(q) be the first derivative of -3/14*q**4 - 1/7*q**2 + 0*q - 2/7*q**3 - 2/35*q**5 + 3. Factor c(i).
-2*i*(i + 1)**3/7
Suppose -32*r = -34*r. Let i(h) be the second derivative of r + 1/3*h**3 + h - 1/6*h**4 + 2*h**2. Suppose i(n) = 0. Calculate n.
-1, 2
Let g(m) be the second derivative of 0 - 3*m - 2/5*m**2 - 27/20*m**4 + 6/5*m**3. Find k such that g(k) = 0.
2/9
Let i(l) be the first derivative of -4*l**5/25 + 3*l**4/5 - 8*l**2/5 - 1. Factor i(v).
-4*v*(v - 2)**2*(v + 1)/5
Let l = 65/228 + -2/57. Solve 1/2*y**3 + 0 + 0*y**2 - 1/4*y + 0*y**4 - l*y**5 = 0.
-1, 0, 1
Let z(o) be the second derivative of -o**7/315 - o**6/180 + o**5/90 + o**4/36 - 2*o**2 + 2*o. Let u(y) be the first derivative of z(y). Factor u(p).
-2*p*(p - 1)*(p + 1)**2/3
Let b = 24 - 16. Factor b*r**4 - 2*r**3 - r**4 - 9*r**4 + 4*r**5.
2*r**3*(r - 1)*(2*r + 1)
Let w(s) be the third derivative of -1/150*s**5 + 5*s**2 - 1/10*s**4 - 3/5*s**3 + 0*s + 0. Find b such that w(b) = 0.
-3
Let l(k) be the first derivative of 25*k**3/18 - 5*k**2/3 + 2*k/3 - 4. Solve l(f) = 0.
2/5
Let y(d) = 4*d + 37. Let w(c) = c + 12. Let k(p) = 7*w(p) - 2*y(p). Let t be k(6). Factor -2 + t*x**2 + x + 5 + 8*x - 1.
(x + 2)*(4*x + 1)
Let i(q) = -2*q**3 + 7*q**2 + 3*q + 6. Let d be i(4). Let -1/5*k**d + 1/5*k + 0 = 0. Calculate k.
0, 1
Let c(m) = -m**2 - 5*m - 17. Let f be c(7). Let u = -503/5 - f. Factor -1/5*y - 1/5*y**2 + u.
-(y - 1)*(y + 2)/5
Let w(r) be the first derivative of -4/3*r**3 + 0*r**2 - 1/3*r**6 + r + 3/5*r**5 + 2 + 1/2*r**4. Solve w(p) = 0.
-1, -1/2, 1
Let m(z) be the third derivative of z**8/84 + 2*z**7/35 + z**6/30 - z**5/5 - z**4/3 - 3*z**2. Solve m(r) = 0 for r.
-2, -1, 0, 1
Let r(h) be the second derivative of 14/3*h**7 - 40*h**3 + 84/5*h**6 - 6*h - 118/3*h**4 + 0 - 16*h**2 + 11/5*h**5. Determine w, given that r(w) = 0.
-2, -1, -2/7, 1
Suppose 147 + 3 = -5*i. Let o = i + 32. Suppose 1/4*u**3 + u**o + 0 - u**4 - 1/4*u = 0. What is u?
-1, 0, 1/4, 1
Factor 0*s - 3*s**2 - s**2 + 2*s - 6*s.
-4*s*(s + 1)
Let p(d) be the second derivative of d**4/6 + 4*d**3/3 + 4*d**2 + 14*d. Factor p(f).
2*(f + 2)**2
Let q(z) = -11*z + 14. Let o(t) = 5*t - 7. Let m(g) = 7*o(g) + 3*q(g). Let h be m(5). Factor 5*v**2 - 3*v - h*v**2 + v.
2*v*(v - 1)
Find t such that 514*t + 54*t**2 - 224*t - 6*t**3 + 1458 + 196*t + 8*t**3 = 0.
-9
Let n(s) be the second derivative of 1/21*s**3 - s + 2/7*s**2 - 1/42*s**4 + 0. Let n(p) = 0. What is p?
-1, 2
Let x(r) = 2*r**2 - 4*r + 3. Let v be x(2). Suppose 2*a - 4*a = -6. Determine s, given that a*s + 0*s**3 - 2*s**v - s = 0.
-1, 0, 1
Let p(y) be the third derivative of y**8/1008 - y**7/630 - y**6/360 + y**5/180 + 8*y**2. Factor p(f).
f**2*(f - 1)**2*(f + 1)/3
Solve 0*h + 0 + 0*h**3 + 0*h**2 + 3/7*h**5 + 6/7*h**4 = 0 for h.
-2, 0
Let p = -8 - -44. Let n be (-2)/(-18) + 8/p. Factor 4/3*d**3 + 2*d + 3*d**2 + n.
(d + 1)**2*(4*d + 1)/3
Let -n**3 + 1046*n - 12*n**2 - 1030*n - 3*n**3 = 0. Calculate n.
-4, 0, 1
Let w(v) = 2*v**3 - 7*v**2 - v + 3. Let o(s) = -s**2 - s + 1. Let q(d) = 6*o(d) - 2*w(d). What is g in q(g) = 0?
0, 1
Let x(z) be the first derivative of z**3/27 - z**2/6 - 18. Suppose x(a) = 0. Calculate a.
0, 3
Let t be (21/6)/((-3)/(-30)). Let v = t + -104/3. What is l in 1/3*l + 0 + v*l**2 = 0?
-1, 0
Let 0*n + 0 - 3/4*n**3 - 1/4*n**5 + 1/4*n**2 + 3/4*n**4 = 0. What is n?
0, 1
Let b(k) be the third derivative of -k**5/360 - k**4/72 - k**3/36 - 2*k**2. Factor b(o).
-(o + 1)**2/6
Let p = 2746/3 - 910. Factor -p*j + 8*j**2 + 2/3*j**4 - 4*j**3 + 0.
2*j*(j - 2)**3/3
Let k(o) be the first derivative of -o**8/6720 - o**7/840 - o**6/288 - o**5/240 + 2*o**3 + 2. Let g(r) be the third derivative of k(r). Let g(n) = 0. What is n?
-2, -1, 0
Factor 0*d**2 - 3*d**2 - 10*d**4 + 13*d**4.
3*d**2*(d - 1)*(d + 1)
Let k be 30/9 + 4/6. Let z = 7 - k. Find y such that -2 - 7*y**2 - z*y + 12*y**2 - 6*y**2 = 0.
-2, -1
Suppose 2*r + 7 = 33. Determine m, given that 13*m - m**2 + m**3 - r*m = 0.
0, 1
Let o(p) = -2*p - 7. Let v be o(-5). Factor -4*a**2 - 9*a**v - 2*a**2 - 3*a**4 + 0*a**2 + 0*a**4.
-3*a**2*(a + 1)*(a + 2)
Let q = 2/57 - -47/285. Factor q*a**2 + 0 - 1/5*a.
a*(a - 1)/5
Let l(r) be the second derivative of 2/9*r**3 + 0 - 1/18*r**4 - 3*r - 1/3*r**2. Factor l(n).
-2*(n - 1)**2/3
Let n(c) be the third derivative of 0 + 3/2*c**4 - 4*c**3 + 0*c + 1/40*c**6 - 3/10*c**5 + c**2. Solve n(i) = 0 for i.
2
Let z(c) = c**3 - 6*c**2 + 6*c - 7. Let j(o) = -o**3 + 5*o**2 - 5*o + 6. Let s(l) = 3*j(l) + 2*z(l). Let x(n) be the first derivative of s(n). Factor x(q).
-3*(q - 1)**2
Find b, given that -1/5*b + 1/5*b**4 - 1/5*b**2 + 1/5*b**3 + 0 = 0.
-1, 0, 1
Let v(b) be the first derivative of b**4/4 + 2*b**3/3 - 7*b**2/2 + 4*b - 47. Factor v(c).
(c - 1)**2*(c + 4)
Let y(j) be the third derivative of -1/175*j**7 + 0*j**5 - 6*j**2 - 1/150*j**6 + 0*j + 0*j**3 + 0*j**4 - 1/840*j**8 + 0. Let y(w) = 0. Calculate w.
-2, -1, 0
Let d(r) = -r**2 - 5*r - 4. Let w be (-2 + 0)*(-3)/(-2). Let j be d(w). Factor g + g**j + 5*g**3 + g**2 - 4*g**3.
g*(g + 1)**2
Let c(z) = z**3 + 7*z**2 + 4*z - 8. Let i be c(-6). Determine a so that 2*a**3 - 5*a**3 + 2*a**i - 4*a**4 + a**3 = 0.
-1, 0
Let h(q) be the second derivative of q**6/90 - q**4/6 - 4*q**3/9 - q**2/2 + 12*q. What is a in h(a) = 0?
-1, 3
Let i(x) be the third derivative of 5*x**2 + 0 + 1/30*x**5 + 1/12*x**4 + 0*x + 0*x**3. Factor i(t).
2*t*(t + 1)
Let o(h) be the second derivative of h**5/45 - h**4/9 + 9*h**2/2 + 2*h. Let m(n) be the first derivative of o(n). What is f in m(f) = 0?
0, 2
Let h(s) be the second derivative of 0*s**5 + 1/15*s**4 + 0 + 0*s**2 + 1/15*s**3 - 1/105*s**7 - 2/75*s**6 + 3*s. Let h(l) = 0. Calculate l.
-1, 0, 1
Let m(d) = 52*d**3 + 136*d**2 - 32*d + 32. Let q(t) = 8*t**3 + 21*t**2 - 5*t + 5. Let y(a) = 5*m(a) - 32*q(a). Let y(s) = 0. What is s?
-2, 0
Let c(k) be the second derivative of k**6/25 + 2*k**5/25 - k**4/30 - 2*k**3/15 - 11*k. Factor c(o).
2*o*(o + 1)**2*(3*o - 2)/5
Let w(n) = n - 1. Let i(z) = -3*z**3 + 6*z**2 + 5*z + 4. Let g(p) = i(p) + 4*w(p). Factor g(h).
-3*h*(h - 3)*(h + 1)
Let z(o) = o**3 + o**2 + 2. Let i(x) = 9*x**3 + 7*x**2 + x + 17. Let u(a) = -6*i(a) + 51*z(a). Solve u(v) = 0.
0, 1, 2
Let v(j) be the third derivative of -j**8/84 - 2*j**7/105 + j**6/30 + j**5/15 - 2*j**2. Factor v(n).
-4*n**2*(n - 1)*(n + 1)**2
Suppose j + 5 = 2*d, -3*d - 2*d + j + 20 = 0. Suppose -2*o + 13 = d*f, 4*f - 3*o + 2*o = 13. Suppose -2*c**f - 2/3*c - 2/3*c**4 - 2*c**2 + 0 = 0. Calculate c.
-1, 0
Suppose 0 = -g - 3*g - 4*w + 616, -w - 764 = -5*g. Let u = -104 + g. Determine p, given that -35*p**2 + 7*p**2 + p - 5*p - u*p**3 = 0.
-2/7, 0
Let o = -408 + 411. Factor -11/5*g + 7/5*g**5 + 16/5*g**4 - 2/5 + 4/5*g**o - 14/5*g**2.
(g - 1)*(g + 1)**3*(7*g + 2)/5
What is y in -2*y + 2 + 1/2*y**2 = 0?
2
Suppose 4*t = 2*t + 10. Factor 3*r**t - 3*r**3 + r**2 - 3*r**4 - 2*r**2 + 4*r**2.
3*r**2*(r - 1)**2*(r + 1)
Suppose 2*b + 153 + 47 = 0. Let a be ((-208)/b + -2)*5. Find o, given that 6/5*o + a*o**2 - 6/5*o**3 - 4/5 + 2/5*o**4 = 0.
-1, 1, 2
Let s(z) be the first derivative of 1/6*z**3 - 2 - 1/24*z**6 + 1/5*z**5 + 0*z - 5/16*z**4 + 0*z**2. Factor s(y).
-y**2*(y - 2)*(y - 1)**2/4
Let i be 10/(-95) + 6/57. Factor i + 0*x + 2/13*x**3 + 4/13*x**2.
2*x**2*(x + 2)/13
Let m(l) be the second derivative of l**4/12 + 2*l**3 - 4*l. Let a be m(-12). Suppose 0*o**2 - 7/5*o**5 + 0*o + a - 2/5*o**4 + 0*o**3 = 0. Calculate o.
-2/7, 0
Factor -1/4*g**2 - 1/2 + 3/4*g.
-(g - 2)*(g - 1)/4
Let l be 35/15*1*36/42. Solve 9/2*p**l + 0 + 3*p = 0 for p.
-2/3, 0
Let v(c) be the third derivative of -3*c**7/70 - c**6/20 + c**5/4 + c**4/2 + 36*c**2. Determine x so that v(x) = 0.
-1, 0, 4/3
Let w(s) be the third derivative of s**6/40 - s**5/4 + s**4 - 2*s**3 - 23*s**2. Find o, given that w(o) = 0.
1, 2
Suppose 2*i + 18 = -0*i. Let l(m) = m**3 + 10*m**2 + 8*m - 7. Let f be l(i). Factor f*u**2 + u - u.
2*u**2
Let j be (-26)/(-7) + 12/42. Factor -11*g**4 + 5*g**j + 7*g**4.
g**4
Let o(w) = -w**3 - 6*w**2 - 10*w - 22. Let b be o(-5). Let 14/13*j**b + 24/13*j**2 + 6/13*j - 4/13 = 0. Calculate j.
-1, 2/7
Let x = 404/633 - -6/211. Factor -2/3*d**3 - 2/3 + x*d**2 + 2/3*