first derivative of t**8/1344 + t**7/840 - t**6/480 - t**5/240 - 3*t**2/2 + 2. Let d(n) be the second derivative of q(n). Factor d(r).
r**2*(r - 1)*(r + 1)**2/4
Let r = 12 - 5. Let k = -4 + r. What is z in 4 + k*z - z**2 + 7*z**2 - 4*z**2 + 3*z = 0?
-2, -1
Let o(j) be the third derivative of j**5/60 + j**4/24 - 2*j**3/3 + 2*j**2. Let v be o(-3). Factor -4/3*l**2 - 4/3*l**3 - 2/3*l**5 + v*l**4 - 2/3 + 2*l.
-2*(l - 1)**4*(l + 1)/3
Let b(j) be the second derivative of -j**9/13608 + j**8/7560 + j**7/3780 - j**6/1620 + j**3/2 + 5*j. Let i(o) be the second derivative of b(o). Factor i(q).
-2*q**2*(q - 1)**2*(q + 1)/9
Let j(t) be the third derivative of t**5/270 - 4*t**4/27 + 64*t**3/27 - 3*t**2. Let j(c) = 0. What is c?
8
Let p = 3 + 0. Let o(i) be the first derivative of -1 - 2/9*i**2 - 10/27*i**p + 0*i - 1/6*i**4. Suppose o(k) = 0. What is k?
-1, -2/3, 0
Let q(y) be the second derivative of -y**6/540 - y**5/90 - y**4/36 + y**3/3 + 2*y. Let s(a) be the second derivative of q(a). Factor s(g).
-2*(g + 1)**2/3
Factor -s**3 + 0 + 0*s + 0*s**2 - 1/3*s**5 - 4/3*s**4.
-s**3*(s + 1)*(s + 3)/3
Let k(v) = -11*v**4 - 7*v**3 - 3*v**2 + 7*v - 7. Let f(x) = 5*x**4 + 3*x**3 + x**2 - 3*x + 3. Let p(q) = -7*f(q) - 3*k(q). Suppose p(r) = 0. What is r?
-1, 0, 1
Let u(a) be the third derivative of -8*a**2 + 0*a + 0 + 1/84*a**4 + 1/42*a**3 + 1/420*a**5. Suppose u(v) = 0. Calculate v.
-1
Let t = 49 - 146/3. Determine b, given that t*b**2 + 2/3*b + 1/3 = 0.
-1
Suppose -4*u = 12*u - 3*u. Factor -2/3*a**2 + u - 2/3*a.
-2*a*(a + 1)/3
Let o(v) be the first derivative of v**8/504 + 2*v**7/315 - v**5/45 - v**4/36 - 3*v**2 - 4. Let f(x) be the second derivative of o(x). Factor f(i).
2*i*(i - 1)*(i + 1)**3/3
Let d = 4 - 2. Let a be 1/(-2) + (-7)/(-2). Factor 2*k**3 - 3*k**4 - 4*k**5 - a*k + 2*k**d + k**5 + 4*k**5 + 1.
(k - 1)**4*(k + 1)
Let r(x) be the first derivative of -x**8/1512 - 2*x**7/945 - x**6/540 - 3*x**2 - 4. Let c(a) be the second derivative of r(a). Factor c(l).
-2*l**3*(l + 1)**2/9
Let d(u) = u**2 - 7*u + 3. Let m be d(7). Suppose q - 6 = -m. Determine y, given that q*y + 2*y**3 + 6*y**2 + 13*y - 16*y**2 - 8 = 0.
1, 2
Let g(s) be the second derivative of 0 - 8/27*s**3 + 0*s**2 - 1/135*s**6 - s - 1/15*s**5 - 2/9*s**4. Factor g(a).
-2*a*(a + 2)**3/9
Let t(f) = -36*f - 100. Let n(r) = r**2 + 37*r + 100. Let j(x) = 4*n(x) + 3*t(x). Factor j(k).
4*(k + 5)**2
Let a(y) = -3*y**3. Let r be a(-1). Let f(j) be the first derivative of -1/2*j - 5/12*j**r + 7/8*j**2 - 3. Factor f(x).
-(x - 1)*(5*x - 2)/4
Let q = 0 + 6. Let u(m) = -m + 10. Let b be u(q). Suppose -2*v**3 + 4 + 2*v - 4 - v**b + 1 = 0. What is v?
-1, 1
Let b(g) = 4*g**2 - 6*g + 4. Let l(v) = v**2 - 2*v + 1. Let o = 6 + -4. Let x = 1 + -8. Let p(k) = o*b(k) + x*l(k). Find q, given that p(q) = 0.
-1
Let h(j) = 484*j**2 - 528*j + 141. Let p(m) = 1. Let l(v) = -h(v) - 3*p(v). Let l(x) = 0. Calculate x.
6/11
Let y(g) be the first derivative of 5*g**4/12 + 5*g**3/3 - 4. Determine r, given that y(r) = 0.
-3, 0
Suppose 0*m = -m + 7. Suppose 3*c - 2*o - 8 = 0, 3*c - m*c = 2*o - 6. Factor 0 - 2/3*d**3 + 2/3*d**c + 0*d.
-2*d**2*(d - 1)/3
Let o(s) be the first derivative of -1/6*s**4 - 1/3*s**2 + 4/9*s**3 + 0*s + 4. Let o(f) = 0. Calculate f.
0, 1
Solve -5*q**2 - q**2 + 4*q**3 - 2*q**2 + 4*q**2 = 0 for q.
0, 1
Let g = -1 + 1. Suppose 0 = b + 4*w - 21, -5*b + 17 = -2*w - g*w. Let -3*q**2 + b*q**2 + 0 - 2 = 0. What is q?
-1, 1
Let w(x) be the first derivative of -x**5/10 - 2*x**4/3 - 4*x**3/3 + 7*x - 4. Let s(q) be the first derivative of w(q). Let s(b) = 0. What is b?
-2, 0
Let v be 399/9 + 1/3. Let y = 45 - v. Find r such that y*r**2 + 0 + 0*r = 0.
0
Let s(f) be the first derivative of 1/7*f**2 + 0*f + 1 + 2/21*f**3. Let s(h) = 0. Calculate h.
-1, 0
Factor 0*o**3 - 3/4*o**2 + 1/4*o**4 - 1/2*o + 0.
o*(o - 2)*(o + 1)**2/4
Let a(x) be the second derivative of 8*x**6/75 + 6*x**5/25 + 3*x**4/20 + x**3/30 - 11*x. Suppose a(v) = 0. Calculate v.
-1, -1/4, 0
Let z(y) be the first derivative of 1 + 0*y**3 - 1/8*y**2 + 3*y + 1/48*y**4. Let c(m) be the first derivative of z(m). Factor c(q).
(q - 1)*(q + 1)/4
Let u be ((27/(-12))/(-3))/(-8 - -23). Let n(r) be the second derivative of 1/2*r**3 + 0*r**4 + r - r**2 - u*r**5 + 0. What is j in n(j) = 0?
-2, 1
Let j(h) = -41*h**3 + 72*h**2 - 49*h + 3. Let y(c) = 62*c**3 - 108*c**2 + 74*c - 4. Let s(d) = -8*j(d) - 5*y(d). What is k in s(k) = 0?
1/3, 2/3, 1
Let y(i) = 18*i + 55. Let a be y(-3). What is o in -a - 1/4*o**2 + o = 0?
2
Suppose 15 = -4*u + 3*i, -6*u - i = -4*u - 5. Let n(p) be the first derivative of 0*p + u*p**3 - 2 - 1/16*p**4 + 1/8*p**2. Factor n(m).
-m*(m - 1)*(m + 1)/4
Let b(y) be the third derivative of y**7/6300 - y**6/900 + y**5/300 - y**4/12 + y**2. Let k(d) be the second derivative of b(d). Find m such that k(m) = 0.
1
Factor -v - 5*v + 2*v**4 + 4*v**3 - v + 3*v - 2*v**2.
2*v*(v - 1)*(v + 1)*(v + 2)
Let z(f) be the first derivative of -f**3/6 + f**2/4 - 9. Factor z(p).
-p*(p - 1)/2
Let t(i) be the third derivative of 0*i**4 + 9*i**2 + 1/84*i**8 + 0*i + 0*i**3 + 1/6*i**6 + 0 - 2/15*i**5 - 8/105*i**7. Let t(x) = 0. Calculate x.
0, 1, 2
Suppose -20 = -2*m - 0*m. Solve 14 - 4*a + 2*a**2 - m - a**2 = 0 for a.
2
Determine d, given that 0*d**3 - 2/9 - 2/9*d**4 + 4/9*d**2 + 0*d = 0.
-1, 1
Suppose 2*t = 5*i - 21, -7*t + 3*t + i = -3. Factor 1/3*b**t - 2/3*b + 1/3.
(b - 1)**2/3
Factor -10*f - 15*f**2 - 5/2*f**4 - 10*f**3 - 5/2.
-5*(f + 1)**4/2
Let j(h) = 10*h**4 - 2*h**3 - 25*h**2 + 8*h + 9. Let g(l) = -9*l**4 + l**3 + 26*l**2 - 8*l - 10. Let i(w) = -6*g(w) - 7*j(w). Solve i(y) = 0 for y.
-1, -1/4, 3/4, 1
Let w(v) = v**3 - v**2 + v. Let s = 9 + -4. Let i(z) = 3*z**4 - 5*z**3 + 2*z**2 - 5*z. Let n(r) = s*w(r) + i(r). Factor n(b).
3*b**2*(b - 1)*(b + 1)
Let v = 33 - 30. Let d(x) be the third derivative of 0*x + 3/10*x**5 + 7/60*x**6 + v*x**2 + 1/6*x**4 + 0*x**3 + 0. Factor d(o).
2*o*(o + 1)*(7*o + 2)
Determine l, given that 18/5*l**4 - 54/5 + 2/5*l**5 - 54/5*l + 52/5*l**3 + 36/5*l**2 = 0.
-3, -1, 1
Let t(y) be the second derivative of -5*y**7/56 + y**6/24 + 3*y**5/8 - 5*y**4/24 - 5*y**3/8 + 5*y**2/8 - 10*y. Determine k, given that t(k) = 0.
-1, 1/3, 1
Let q(b) be the second derivative of -b**5/20 + b**4/6 + 7*b**3/6 + 2*b**2 - 13*b. What is c in q(c) = 0?
-1, 4
Let i be -4 + (-7)/(-35) + 4. Factor -i*k**2 + 2/5*k + 0.
-k*(k - 2)/5
Factor 2/7 - 2/7*y**3 - 6/7*y + 6/7*y**2.
-2*(y - 1)**3/7
Let q = -41 - -44. Solve -4/9*g**q - 2/9 + 0*g**2 + 4/9*g + 2/9*g**4 = 0.
-1, 1
Let o = 1003/804 + 1/402. Factor -5*f - 3/2*f**2 + 13/4*f**3 + o*f**4 + 2.
(f - 1)*(f + 2)**2*(5*f - 2)/4
Let x(i) be the second derivative of i**7/14 + i**6/3 + 3*i**5/5 + i**4/2 + i**3/6 + 9*i. Factor x(t).
t*(t + 1)**3*(3*t + 1)
Suppose -3*h - 4*h = h. Factor h + a**4 - 1/5*a**5 + 7/5*a**2 - 2/5*a - 9/5*a**3.
-a*(a - 2)*(a - 1)**3/5
Suppose -4*z + 6 = -6. Determine t so that -18*t - 21*t**3 + 6*t**z + 5*t**3 - 12*t**3 + 6*t**4 + 30*t**2 + 4 = 0.
2/3, 1
Let v(y) = -12*y**4 + 28*y**3 - 20*y**2 + 4. Let t(h) = 49*h**4 - 113*h**3 + 81*h**2 - h - 16. Let f(i) = -4*t(i) - 18*v(i). Let f(w) = 0. What is w?
-2/5, 1
Let y(w) be the third derivative of -w**7/840 - w**6/540 + w**5/360 + w**3/3 - 6*w**2. Let h(m) be the first derivative of y(m). Factor h(x).
-x*(x + 1)*(3*x - 1)/3
Let y be 10/(-25)*(6 + (-47)/7). Factor -2/7*g**3 + 2/7*g + 0 - 2/7*g**4 + y*g**2.
-2*g*(g - 1)*(g + 1)**2/7
Let a = -57 + 57. Factor 6/5*n**3 - 3/5*n**4 + 0 + a*n - 3/5*n**2.
-3*n**2*(n - 1)**2/5
Let m(w) = 2*w - 2. Let c be m(2). Let u(g) be the first derivative of 0*g - 1/6*g**6 + 1/4*g**4 + 0*g**3 + c + 0*g**2 + 0*g**5. Suppose u(n) = 0. What is n?
-1, 0, 1
Let r(t) = -t**3 - t**2 + 2. Let w be r(0). Factor -4*b**w - b + 0*b + 3*b**2.
-b*(b + 1)
Let l = -1 - -3. Let q(p) be the first derivative of 0*p - 1/5*p**l + 2 - 1/15*p**3. What is u in q(u) = 0?
-2, 0
Let w(p) be the first derivative of -p**7/1680 + 2*p**3/3 + 1. Let d(n) be the third derivative of w(n). Suppose d(j) = 0. What is j?
0
Let n(r) = -r**2 - 12*r - 9. Let o be n(-11). Factor 12 + 11*b + 3*b**2 - 5*b**o + 6*b**2 - 27*b.
4*(b - 3)*(b - 1)
Solve 1/3*y**2 - y + y**3 + 0 - 1/3*y**4 = 0.
-1, 0, 1, 3
Let s(d) = 7*d**2 + 23*d + 9. Let g(q) = -2*q**2 - 6*q - 2. Let w(l) = -9*g(l) - 2*s(l). 