erivative of d**8/3360 - d**7/1260 + d**4/6 - 2*d**2. Let v(t) be the second derivative of n(t). Let v(b) = 0. Calculate b.
0, 1
Let d(o) be the second derivative of -o**7/42 - o**6/3 - 33*o**5/20 - 10*o**4/3 - 8*o**3/3 + 3*o + 4. Determine h, given that d(h) = 0.
-4, -1, 0
Let u(q) be the first derivative of -5*q**5/66 + 5*q**4/22 - 3*q**3/11 + 2*q**2 - 1. Let g(n) be the second derivative of u(n). Factor g(p).
-2*(5*p - 3)**2/11
Let r(t) be the second derivative of -t**7/1260 + t**6/720 + t**5/120 - t**4/3 + 3*t. Let o(z) be the third derivative of r(z). Factor o(c).
-(c - 1)*(2*c + 1)
Let t = 279 - 555/2. Determine h so that 0 - 3/2*h**4 + t*h**2 + 9/2*h**3 - 9/2*h = 0.
-1, 0, 1, 3
Let b(i) = -49*i - 338. Let l be b(-7). Factor -1/2*x**4 + 1/2*x + 1/2*x**l - x**3 - 1/2 + x**2.
(x - 1)**3*(x + 1)**2/2
Let p(l) be the second derivative of -l**4/48 + l**2/8 - 6*l. Factor p(x).
-(x - 1)*(x + 1)/4
Let m(n) be the first derivative of -2*n**3/3 - n**2 - 26. Factor m(a).
-2*a*(a + 1)
Let w(b) = -3*b**4 + 2*b**3 + 9*b**2 + 9. Let o(g) = g**4 - g**2 - 1. Let j(i) = 18*o(i) + 2*w(i). Factor j(c).
4*c**3*(3*c + 1)
Let b be (8/320)/(21/2). Let a(l) be the third derivative of 0*l**3 - 1/105*l**5 - l**2 - b*l**6 + 0 + 0*l - 1/84*l**4. Solve a(c) = 0.
-1, 0
Let v = 11 + -9. Let w(s) be the first derivative of 0*s**v + 0*s - 3 + 1/12*s**6 + 1/6*s**3 - 1/8*s**4 - 1/10*s**5. Factor w(f).
f**2*(f - 1)**2*(f + 1)/2
Let j = 251 - 7529/30. Let x(z) be the third derivative of 0*z**3 - j*z**5 + 0*z + 0 - 4*z**2 - 1/12*z**4. Suppose x(n) = 0. Calculate n.
-1, 0
Suppose 0 = -2*d + d. Factor 6*t**2 + 4 + d*t - 4*t**2 + 2*t - 4*t**2.
-2*(t - 2)*(t + 1)
Suppose -52 = -4*m + u - 32, 4*m - 2*u - 24 = 0. Factor 0*x**3 + 0 + 2/9*x**m - 2/3*x**2 - 4/9*x.
2*x*(x - 2)*(x + 1)**2/9
Let d(t) be the third derivative of 1/120*t**6 + t**2 + 0*t - 1/8*t**4 + 1/3*t**3 + 0 + 0*t**5. Factor d(w).
(w - 1)**2*(w + 2)
Let n(h) = h**3 + 8*h**2 + 6*h - 6. Let k be n(-7). Let q be k/(-2) - (-5 + 3). Factor -p**2 - q*p - 1/2.
-(p + 1)*(2*p + 1)/2
Factor 3*o**3 + 0*o**2 + o**3 + 4*o + 8*o**2.
4*o*(o + 1)**2
Suppose -4/3*x - 1/3*x**3 + 0 - 4/3*x**2 = 0. Calculate x.
-2, 0
Let r(l) = 2. Let i(x) = -3*x + 10*x - 8*x - 5 + 2*x**2 - x**2. Let p(g) = -2*i(g) - 5*r(g). Determine z so that p(z) = 0.
0, 1
Let u(b) be the first derivative of 5*b**4/4 + 35*b**3/3 + 75*b**2/2 + 45*b + 13. Suppose u(l) = 0. What is l?
-3, -1
Let w be (10/(-6))/(5/(-15)). Suppose -4*h + 18 + 3 = -w*s, -5*h + 19 = s. Factor -6*r**3 + 3*r**3 - 14*r + 16*r**2 - 3*r**3 + h.
-2*(r - 1)**2*(3*r - 2)
Let g(w) = 2*w**3 - 2*w**2 - 4*w + 2. Let z(l) = 10*l**3 - 11*l**2 - 21*l + 11. Let o(s) = -22*g(s) + 4*z(s). Suppose o(f) = 0. What is f?
-1, 0, 1
Let k(j) = -j**2 + 6*j - 2. Let r be k(5). Factor v - 2 - 4*v**3 + 2 + 3*v**r - v**4 + v**2.
-v*(v - 1)*(v + 1)**2
What is r in -r**3 + 2*r - 3*r**3 + 2*r**4 + 2*r**3 + 4*r**2 - 6*r**2 = 0?
-1, 0, 1
Let o(w) be the first derivative of -2*w**5/45 - 2*w**4/9 - 10*w**3/27 - 2*w**2/9 - 6. Factor o(c).
-2*c*(c + 1)**2*(c + 2)/9
Suppose 0*y - 3*y = -3*c - 39, 38 = 4*y + 3*c. Let r = y + -8. Factor -r*l**3 + 0*l**2 - 3*l**3 - 2*l**2 + 4*l**3.
-2*l**2*(l + 1)
Let r = 1/1488 + 24799/1488. Let 10/3*p**2 - r*p**3 + 32/3*p + 8/3 = 0. Calculate p.
-2/5, 1
Let k(j) = -j**2 + 7*j + 3. Let v be k(4). Factor -15*f - 16*f**2 + v*f - 4*f**3.
-4*f**2*(f + 4)
Let j(t) be the third derivative of 1/240*t**6 + 0*t - 1/1344*t**8 - 1/24*t**3 + 1/120*t**5 - 1/840*t**7 - t**2 + 0 - 1/96*t**4. Determine i so that j(i) = 0.
-1, 1
Let f(h) be the first derivative of 7*h**6/540 - h**5/36 - h**4/18 + 8*h**3/3 + 3. Let a(i) be the third derivative of f(i). Factor a(x).
2*(x - 1)*(7*x + 2)/3
Let b(o) be the second derivative of -1/90*o**5 + 2/9*o**3 - o**2 - 1/36*o**4 + 0 - o. Let a(f) be the first derivative of b(f). Solve a(v) = 0.
-2, 1
Factor 3*z**3 - 5*z**4 + 3*z**4 - z**5 - 12*z + 8*z + 4*z**2.
-z*(z - 1)**2*(z + 2)**2
Let t(a) be the third derivative of -a**6/120 + a**5/20 + 4*a**2. Factor t(f).
-f**2*(f - 3)
Factor 225/8*q + 3/8*q**3 - 45/8*q**2 - 375/8.
3*(q - 5)**3/8
Suppose d + 3*d**3 + 8*d + 83 + 15*d**2 - 110 = 0. Calculate d.
-3, 1
Let d(a) be the first derivative of 2*a + 1/2*a**4 + 2 - 2/3*a**3 - a**2. Factor d(r).
2*(r - 1)**2*(r + 1)
Let r(z) be the third derivative of -z**5/240 + z**4/24 - z**3/6 + 15*z**2. Factor r(p).
-(p - 2)**2/4
Let c(y) = y**3 + 2*y**2 - 2*y - 4. Let n be c(-2). Determine h so that -2/5*h**2 + n + 4/5*h = 0.
0, 2
Let w(x) = x**3 + 3*x**2 - 1. Let t be w(-2). Suppose -44*o + 12*o + 128 = 0. Let -2/9*h**t + 10/9*h + 2/9*h**o - 4/9 - 2/3*h**2 = 0. Calculate h.
-2, 1
Suppose 0 = -5*k + 8*k - 2*d + 2, -3*k + 5*d = 5. Factor -3/5 + 6/5*b**3 + k*b**2 - 6/5*b + 3/5*b**4.
3*(b - 1)*(b + 1)**3/5
Factor 11*s**2 + 2*s**3 - 2*s**2 - 7*s**2 + 0*s**3 - 2*s - 2.
2*(s - 1)*(s + 1)**2
Suppose 2*c - 32 = -c + 4*b, 0 = 4*b + 20. Factor k + 0*k - 2*k**2 - k**2 + c*k**2.
k*(k + 1)
Let x be (-7)/3 - ((2 - 9) + 4). Factor -x*a**2 + 0 - 4/3*a.
-2*a*(a + 2)/3
Factor 24/5 + 18/5*x**2 - 3/5*x**3 - 36/5*x.
-3*(x - 2)**3/5
Let y(s) be the third derivative of s**9/60480 + s**8/20160 - s**7/5040 - s**6/720 - s**5/12 + s**2. Let a(z) be the third derivative of y(z). Factor a(r).
(r - 1)*(r + 1)**2
Let d(j) = -2*j**2 - 2*j + 11. Let l = -8 + 4. Let a(x) = -x**2 - x + 4. Let s(r) = l*d(r) + 11*a(r). Factor s(p).
-3*p*(p + 1)
Suppose -8 = -4*j - 0*j. Suppose 0*v - j = -v. Factor -v*f**5 + 8 + 3*f**3 - 5*f**3 - 8 - 4*f**4.
-2*f**3*(f + 1)**2
Let v(r) be the second derivative of -15*r**4/4 - 10*r**3 - 10*r**2 - 4*r. Suppose v(t) = 0. What is t?
-2/3
Let o(v) be the second derivative of v**9/1008 - 3*v**7/280 + v**6/60 + v**3/6 - 3*v. Let c(l) be the second derivative of o(l). Factor c(p).
3*p**2*(p - 1)**2*(p + 2)
Let s = -12 - -9. Let m be (s/(-2))/((-6)/(-8)). Factor 3/5*f**m - 3/5 - 3/5*f**3 + 3/5*f.
-3*(f - 1)**2*(f + 1)/5
Let l(q) be the second derivative of q**10/20160 + q**9/7560 - q**8/13440 - q**7/2520 + q**4/6 + 3*q. Let s(v) be the third derivative of l(v). Factor s(b).
b**2*(b + 1)**2*(3*b - 2)/2
Suppose -4*i + 8 = -3*r, -2*r + i = r + 2. Suppose -10 = -5*z - r*z. Factor -5/2*h - z*h**2 - 1 - 1/2*h**3.
-(h + 1)**2*(h + 2)/2
Let c(z) be the third derivative of z**9/5040 - z**8/2240 - 5*z**4/24 - 4*z**2. Let p(n) be the second derivative of c(n). Factor p(w).
3*w**3*(w - 1)
Let r(u) be the first derivative of u**6/6 + u**5/5 - 9*u**4/4 + 11*u**3/3 - 2*u**2 - 18. Suppose r(w) = 0. What is w?
-4, 0, 1
Let b = 30 + -30. Factor -1/2*j + b + 1/2*j**2.
j*(j - 1)/2
Let o(y) = -3*y**5 + 15*y**4 - 12*y**3 + 2*y**2. Let i(w) = 5*w**5 - 30*w**4 + 25*w**3 - 5*w**2. Let b(q) = 2*i(q) + 5*o(q). Factor b(s).
-5*s**3*(s - 2)*(s - 1)
Let j(v) = -10*v**4 + 50*v**3 - 90*v**2 + 74*v - 20. Let u(l) = -9*l**4 + 49*l**3 - 91*l**2 + 74*l - 20. Let h(t) = 3*j(t) - 4*u(t). Factor h(y).
2*(y - 5)*(y - 1)**2*(3*y - 2)
Suppose -3*p - 2*k + 2 = -1, k + 9 = 2*p. Factor 2/5*t**p + 0*t**2 + 0 - 2/5*t.
2*t*(t - 1)*(t + 1)/5
Let 2/5*y**4 + 12/5 + 2/5*y - 2/5*y**3 - 14/5*y**2 = 0. What is y?
-2, -1, 1, 3
Let c(v) = v**3 + 3*v**2 - 14*v + 29. Let n be c(-6). Factor -1/2*l**3 - 1/4 - 1/4*l**n + 3/4*l + 3/4*l**4 - 1/2*l**2.
-(l - 1)**4*(l + 1)/4
Let r(a) be the first derivative of -a**3/9 - a**2/2 - 2*a/3 + 3. Suppose r(h) = 0. Calculate h.
-2, -1
Let a(c) = -c**3 - c - 1. Let p(s) = 3*s**3 + 14*s**2 - 56*s + 76. Let q(i) = -4*a(i) - p(i). Solve q(d) = 0.
2, 6
Let f = -8 - -4. Let z(l) = l**2. Let h(m) = m**2 + m + 1. Let k(y) = f*h(y) + 3*z(y). Factor k(d).
-(d + 2)**2
Let x = 20 - 14. Suppose 4*a = 2 + x. What is z in -z**4 + 2*z**a + 2*z - z - z**3 - z**2 = 0?
-1, 0, 1
Suppose -5 + 2 = -3*m. Let t be m/45 - 8/(-40). Find n, given that -2/9 + 4/9*n**3 - 2/9*n**4 - t*n + 4/9*n**2 - 2/9*n**5 = 0.
-1, 1
Let w(f) be the third derivative of f**8/5040 + f**7/420 + f**6/90 + f**5/45 + f**3/3 - 8*f**2. Let i(r) be the first derivative of w(r). Factor i(c).
c*(c + 2)**3/3
Let o(r) be the second derivative of r**8/2520 + r**7/630 - r**5/90 - r**4/36 + 2*r**3/3 - 3*r. Let f(d) be the second derivative of o(d). Factor f(y).
2*(y - 1)*(y + 1)**3/3
Suppose -410*p = -415*p. Factor -4/7*s**2 + 0*s - 2/7*s**3 + p.
-2*s**2*(s + 2)/7
Let o(x) be the first deri