rd derivative of -p**7/210 - p**6/40 - p**5/20 - p**4/24 - 13*p**2. Factor g(a).
-a*(a + 1)**3
Let s be (-150)/(-25)*2/((-40)/(-18)). Suppose -3/5*o**2 - s + 18/5*o = 0. What is o?
3
Factor 1/2*n**3 + 1/2*n**2 - 1/2*n - 1/2.
(n - 1)*(n + 1)**2/2
Suppose 3*n = 5*s + 31, -2*n - 3 = s - 2. Let r(o) be the first derivative of -1/3*o**3 + 1/10*o**5 + 1/2*o + 1 - 1/12*o**6 - 1/4*o**n + 1/4*o**4. Factor r(v).
-(v - 1)**3*(v + 1)**2/2
Suppose 2 = 3*x + 8. Let d be x/4 - 3/6. Let n(v) = 81*v**2 - 38*v + 4. Let w(s) = s. Let y(g) = d*n(g) - 2*w(g). Factor y(l).
-(9*l - 2)**2
Let 2/13*s**2 - 60/13*s + 450/13 = 0. Calculate s.
15
Let m(k) be the second derivative of k**5/5 - 2*k**4/3 - 2*k**3/3 + 4*k**2 - 14*k. Suppose m(u) = 0. What is u?
-1, 1, 2
Let a(s) be the first derivative of -5 + 117/2*s**2 + 6*s + 324/5*s**5 + 999/2*s**4 + 265*s**3 - 540*s**6. Find i such that a(i) = 0.
-2/5, -1/6, 1
Let a(b) = -200*b**4 + 116*b**3 + 176*b**2 - 116*b + 20. Let d(y) = -199*y**4 + 115*y**3 + 177*y**2 - 115*y + 19. Let x(l) = 3*a(l) - 4*d(l). Factor x(h).
4*(h - 1)*(h + 1)*(7*h - 2)**2
Let d(r) be the third derivative of r**8/1680 - 2*r**7/525 + r**6/120 - r**5/150 + 8*r**2. Factor d(n).
n**2*(n - 2)*(n - 1)**2/5
Let q(d) = 4*d**5 - 2*d**4 + 4*d**3 - 3*d + 3. Let s(l) = -l**5 - l**3 + l - 1. Let g(k) = 5*q(k) + 15*s(k). What is m in g(m) = 0?
0, 1
Let g(n) be the first derivative of -n**8/840 - 2*n**7/525 - n**6/300 - 2*n**2 - 8. Let o(x) be the second derivative of g(x). Determine w, given that o(w) = 0.
-1, 0
Let a(x) be the first derivative of -x**4/6 - 10*x**3/9 - 4*x**2/3 - 29. Find c such that a(c) = 0.
-4, -1, 0
Let q(n) be the second derivative of -n**5/20 - n**4/2 - n**3/3 - 9*n**2/2 + n. Let o be q(-6). Factor 0 - 1/2*g**o - 1/4*g**4 - 1/4*g**2 + 0*g.
-g**2*(g + 1)**2/4
Suppose 0*n = 4*n - 60. Suppose 0 = 2*l - 5*v, l + 0*l + 5*v = n. Factor -2*g**5 - 4*g**2 + g**l - 5*g**4 + g**4 - 4*g**3 - g - 2*g**3.
-g*(g + 1)**4
Let n(g) = 3 + 1 - 2 - 6*g + 4 + 2*g**2. Let s(m) = 2*m**2 - 6*m + 7. Let o(c) = -3*n(c) + 2*s(c). What is a in o(a) = 0?
1, 2
Let c(n) be the first derivative of 0*n - 2/27*n**3 + 4 + 0*n**2. Factor c(j).
-2*j**2/9
Solve -16*x**3 + 3*x**4 - 2 + 10 + 16*x - 2*x**2 - 10*x**4 + x**4 = 0 for x.
-2, -1, -2/3, 1
Let k(f) be the third derivative of -f**8/168 + 4*f**7/105 - f**6/12 + f**5/15 + 3*f**2. Factor k(r).
-2*r**2*(r - 2)*(r - 1)**2
Let p(l) be the first derivative of -l**6/6 - 3*l**5/5 - l**4/2 + 2*l**3/3 + 3*l**2/2 + l - 5. Factor p(c).
-(c - 1)*(c + 1)**4
Suppose -5 = -3*v + k, 5*k - 5 = 5*v - 0*k. Let l be 1*(v + 1)/12. Factor c**2 + c + 1/3 + l*c**3.
(c + 1)**3/3
Let q be (-2)/(-3)*(-30)/4. Let x(z) = -z**5 - z**4 - z**2 - z. Let i(l) = -8*l**5 + 3*l**4 - 7*l**3 - 3*l**2 - 5*l. Let p(u) = q*x(u) + i(u). Factor p(t).
-t**2*(t - 1)**2*(3*t - 2)
Let i(j) be the first derivative of -j**4/6 + j**3/3 - 6*j - 4. Let l(d) be the first derivative of i(d). Suppose l(n) = 0. What is n?
0, 1
Suppose m + 6 - 8 = 0. Solve 4*a**3 + 5*a**2 + a**4 + a + a**m + a - a**2 = 0 for a.
-2, -1, 0
Let w(y) be the second derivative of -y**6/240 - y**5/120 + y**4/48 + y**3/12 + y**2 - y. Let d(u) be the first derivative of w(u). Factor d(b).
-(b - 1)*(b + 1)**2/2
Let o(a) = -a. Let s be o(-5). Suppose 15*c**3 + 16*c**s + 0*c**5 + 48*c**4 + 11*c**5 - 6*c**2 = 0. Calculate c.
-1, 0, 2/9
Let z = -1 + 2. Suppose z + 2*r - 6 + 0*r + 1 + 2*r**2 = 0. What is r?
-2, 1
Suppose -3*p - 5 = -4*x, -3*x + 3 = -p - 2. Let h be -6*(3/2)/(-3). Determine s, given that -x*s**3 + 13*s - 11*s + h - 1 - 2*s**2 = 0.
-1, 1
Solve 196/3*z**3 - 70/3*z**4 - 50*z**5 + 6 - 26*z + 20/3*z**2 = 0.
-1, 1/3, 3/5
Suppose -11 = -3*a + 16. Let w be (-1)/((-3)/(a/1)). Solve -2*l + l - 2*l**3 + w*l = 0.
-1, 0, 1
Let z be 21/4 - (-1)/(-4). Find r such that 3*r**3 + 2 - 3*r**5 + 2*r**4 - 4*r + 2*r**z - 4*r**2 - 2 = 0.
-1, 0, 2
Let s = 36069910/201 + -179451. Let t = 3/67 + s. What is n in -8/3*n**5 - 2/3*n**2 + 0 - t*n**3 + 0*n + 14/3*n**4 = 0?
-1/4, 0, 1
Let d(m) be the first derivative of 27*m + 27/2*m**2 + 1/4*m**4 + 3*m**3 - 3. Factor d(q).
(q + 3)**3
Let y be (4/10)/((-3)/(-15)). Let t(u) = u**4 - u**3 - 2*u**2 + 2*u - 2. Let f(i) = 2*i**4 - i**3 - 3*i**2 + 3*i - 3. Let a(z) = y*f(z) - 3*t(z). Factor a(h).
h**3*(h + 1)
Let d(q) = -14*q**4 - 11*q**3 + 14*q**2 - 7*q. Let x(p) = p**4 + p**3 - p**2 + p. Let j = 6 - 4. Let n(b) = j*d(b) + 18*x(b). Factor n(g).
-2*g*(g - 1)*(g + 1)*(5*g + 2)
Let 1/3*i**3 - 1/3 - i**2 + i = 0. Calculate i.
1
Let p = -653/7 + 36569/392. Let m(n) be the third derivative of -p*n**8 + 0*n**3 + 0 - 1/35*n**6 + 2/147*n**7 + 1/35*n**5 + n**2 + 0*n - 1/84*n**4. Factor m(h).
-2*h*(h - 1)**3*(3*h - 1)/7
Let b(w) be the second derivative of -2*w**6/3 + 12*w**5/5 - 3*w**4 + 4*w**3/3 - 9*w. Factor b(r).
-4*r*(r - 1)**2*(5*r - 2)
Suppose q = -0*q + 4*l + 10, 11 = -4*q - l. Let x(b) = 3*b**2 + 3*b + 4. Let y(g) = -7*g**2 - 6*g - 9. Let f(r) = q*y(r) - 5*x(r). Determine n so that f(n) = 0.
-2, -1
Let k(r) be the second derivative of -r**5/30 - r**4/12 + r**2 - 3*r. Let m(f) be the first derivative of k(f). Factor m(t).
-2*t*(t + 1)
Let h(l) be the third derivative of -l**5/270 + l**4/36 - 2*l**3/27 - 8*l**2. Factor h(i).
-2*(i - 2)*(i - 1)/9
Let t(l) be the first derivative of l**8/1176 + 2*l**7/735 + l**6/420 - 3*l**2/2 - 3. Let r(p) be the second derivative of t(p). Factor r(w).
2*w**3*(w + 1)**2/7
Suppose -3*h - 5*k = -11, -k - k - 8 = -5*h. Determine p so that 10*p**3 + 14*p - 2 - 3*p**4 + 6 + 5*p**4 + 18*p**h = 0.
-2, -1
Factor -2/3 + 200/3*o**3 - 38/3*o - 160/3*o**2.
2*(o - 1)*(10*o + 1)**2/3
Let i be -2 + 1 + (-145)/295. Let h = 1/118 - i. Find z such that 3/2*z - h*z**2 + 0 = 0.
0, 1
Let t be 6/10 - 69/15. Let j be 2/t*(-10 + 6). Let 0*k**j + 1/2*k**4 + 0 + 0*k + 1/2*k**3 = 0. What is k?
-1, 0
Suppose 4 - 16 = -4*k + 3*o, -5*o = 5*k - 50. Suppose -4*i + i = -k. Suppose 2*r**2 - 3*r**2 - i*r - 3*r**2 = 0. Calculate r.
-1/2, 0
Let 3*v**3 - 9*v**2 + 3*v**2 + 8 - 8 = 0. Calculate v.
0, 2
Suppose -6 = -2*s, -3 = -2*k - s - 0*s. Factor 5 - 4*l - 4 + l**2 + 2 + k*l**2.
(l - 3)*(l - 1)
Let a be -1 + 3 - (17 - 17). Let y(o) be the second derivative of 0*o**2 - 1/12*o**4 - a*o + 1/30*o**6 + 0*o**3 + 0 + 0*o**5. Let y(x) = 0. What is x?
-1, 0, 1
Factor -2/5*a**2 - 2/5*a**4 + 0 - 4/5*a**3 + 0*a.
-2*a**2*(a + 1)**2/5
Let f = 1422/71 - 124840/781. Let r = 140 + f. Suppose r*m**2 - 4/11*m + 0 = 0. What is m?
0, 2
Let h(y) be the third derivative of -3*y**6/40 + 13*y**5/20 - 5*y**4/3 + 2*y**3 - 7*y**2. Factor h(n).
-(n - 3)*(3*n - 2)**2
Let l = 15 + -27/2. Factor 0 + 3*c**2 - l*c**3 - 2*c + 1/4*c**4.
c*(c - 2)**3/4
Suppose 0 = -x + v - 3, 4*x + 3*v + 3 = 26. Factor 16*m**x + 9*m - 4*m + 7*m**3 + 2 + 6*m.
(m + 1)**2*(7*m + 2)
Let h(s) be the second derivative of s**7/56 + s**6/20 + 3*s**5/80 + 20*s. Factor h(d).
3*d**3*(d + 1)**2/4
Determine g, given that -2 + 10/3*g - 2/3*g**3 - 2/3*g**2 = 0.
-3, 1
Let p be (-3)/18 + 43/6. Let l = p + -7. Factor 1/4*c**2 - 1/4*c**3 + 1/4*c**5 + 0 - 1/4*c**4 + l*c.
c**2*(c - 1)**2*(c + 1)/4
Let h(v) be the third derivative of v**5/20 + v**4/2 + 2*v**3 - 6*v**2. Factor h(t).
3*(t + 2)**2
Let l(r) = 2*r**2 - 5. Let u be l(2). Suppose 5*s = s. Factor 0*h + 2/11*h**5 + 0*h**u + 0 + s*h**2 - 2/11*h**4.
2*h**4*(h - 1)/11
Let f(w) = -66*w**4 - 78*w**3 + 27*w. Let o(c) = 5*c**4 + 6*c**3 - 2*c. Let q be 27 + -1*0/4. Let x(t) = q*o(t) + 2*f(t). Factor x(k).
3*k**3*(k + 2)
Determine y so that -24*y + 15*y**2 + 63*y - 1 - 17 = 0.
-3, 2/5
Let v(o) be the third derivative of 3*o**5/20 - 7*o**4/24 - o**3/3 - 35*o**2. Determine k so that v(k) = 0.
-2/9, 1
Let s(q) be the third derivative of -1/12*q**4 + 0 + 1/60*q**6 + 0*q**3 + 1/30*q**5 + 0*q - 2*q**2 - 1/105*q**7. Solve s(a) = 0 for a.
-1, 0, 1
Factor -3/5*r**2 + 1/5*r**4 + 0*r**3 + 0 - 2/5*r.
r*(r - 2)*(r + 1)**2/5
Let z(c) = 2*c**2 + 4*c. Let g(k) = 4*k**2 + 8*k - 1. Let f(i) = -2*g(i) + 5*z(i). Factor f(h).
2*(h + 1)**2
Let k be -1 + 2/(-6) + (-20)/(-6). Find v such that 0*v - 2/7*v**4 + 0*v**k + 2/7*v**3 + 0 = 0.
0, 1
Let 9*g**3 + 3*g - g + 0*g**3 + 3*g + 16*g**2 - 2 = 0. What is g?
-1, 2/9
Let v = 9439/7 + -1345. Factor v*g**3 - 2*g**2 + 0 + 2/7*g.
2*g*(3*g - 1)*(4*g - 1)/7
Suppose 0 = -2*p + 1 + 5. Suppose 0 = -u + p