 t(o) be the third derivative of o**8/168 - o**7/105 - o**6/20 + o**5/30 + o**4/6 - 20*o**2. Find w such that t(w) = 0.
-1, 0, 1, 2
Let o(c) be the first derivative of 0*c**2 + 1/60*c**5 + 1/18*c**3 - 1 - 2*c - 1/18*c**4. Let s(a) be the first derivative of o(a). Solve s(t) = 0.
0, 1
Let y = -1 - -3/2. Let q = 11/4 - y. Determine l so that -5/4*l**3 - 7/4*l**4 + q*l**2 + 5/4*l - 1/2 = 0.
-1, 2/7, 1
Suppose 4 - 3 = v. Let i = -1 + 3. What is u in 5*u + 4*u**3 - 3*u**2 - 8*u**i - v + 3*u**2 = 0?
1/2, 1
Let i(t) be the second derivative of -t**6/60 - t**5/20 + t**3/6 + t**2/4 - t. Solve i(u) = 0 for u.
-1, 1
Let f(i) be the first derivative of -i**5/35 + i**4/14 - i**2/7 + i/7 + 12. Factor f(b).
-(b - 1)**3*(b + 1)/7
Factor 2*b**2 + 4*b - 1633*b**3 + 1632*b**3 - 4*b - b**4.
-b**2*(b - 1)*(b + 2)
Let z be (1 + (-2 - -1))*(3 - 2). Let u(p) be the second derivative of 0*p**2 - p - 1/12*p**4 + 1/20*p**5 - 1/6*p**3 + 1/30*p**6 + z. Factor u(a).
a*(a - 1)*(a + 1)**2
Let j be (-33)/(-11) - 6*1. Let m be (-18)/(-54) + 1/j. Factor 2/3*g**2 + 0*g + m.
2*g**2/3
Let l be 33/(-12) - 15/(-20). Let x be (24 + -16)/((-12)/l). Factor -4/3 + x*g**2 + 2/3*g**3 - 2/3*g.
2*(g - 1)*(g + 1)*(g + 2)/3
Suppose -3*d - 32 = -5*x, 3*d + 2*d + 3*x = -8. Let o = d - -6. Factor -2/7*n + 0 - 2/7*n**o.
-2*n*(n + 1)/7
Let w(y) be the first derivative of y**5/5 - y**4 + y**3 - 3. Factor w(x).
x**2*(x - 3)*(x - 1)
Let y(m) = -m**2 - 6*m - 3. Let u be y(-5). Suppose 4*j - u*j = 2*x + 8, -17 = -4*j + 3*x. Factor j*t + t**2 - 1 + 0*t**2 - 5*t**2.
-(t - 1)*(4*t - 1)
Let g(i) = -4*i**3 + 5*i**2 + 2*i + 3. Let w(s) = 7*s**3 - 10*s**2 - 3*s - 5. Let a(k) = 11*g(k) + 6*w(k). Determine y, given that a(y) = 0.
-3, -1/2, 1
Let u(k) be the third derivative of k**7/385 + k**6/660 - k**5/66 - k**4/132 + 2*k**3/33 - 4*k**2. Solve u(i) = 0.
-1, 2/3, 1
Let m(f) = -3*f**2 - 9*f. Let q(k) = -5*k**2 - 17*k - 1. Let z be 18/12 + 25/(-2). Let o(i) = z*m(i) + 6*q(i). Factor o(u).
3*(u - 2)*(u + 1)
Let z(f) be the third derivative of -f**8/1848 - 2*f**7/1155 + f**5/165 + f**4/132 - f**2. Factor z(t).
-2*t*(t - 1)*(t + 1)**3/11
Suppose -p + x - 9 = -4*p, 2*x = 4*p - 12. Solve 0*a + 4*a**2 + 2*a + a**4 - 2*a**4 - p*a**4 - 2*a**5 = 0 for a.
-1, 0, 1
Let n(a) be the first derivative of -a**4/10 + 2*a**3/3 - 7*a**2/5 + 6*a/5 + 6. Factor n(g).
-2*(g - 3)*(g - 1)**2/5
Let w(n) be the second derivative of -n**4/114 + 14*n**3/57 - 13*n**2/19 + 46*n. Factor w(a).
-2*(a - 13)*(a - 1)/19
Let q(b) = 2*b**3 + b**2 + 4*b - 4. Let t(w) = -5*w**3 - 3*w**2 - 11*w + 11. Let y(g) = 8*q(g) + 3*t(g). Factor y(n).
(n - 1)**2*(n + 1)
Let k(l) be the second derivative of 11*l**4 - 6*l + 21/2*l**5 + 0 + 4*l**3 + 5/2*l**6 + 0*l**2. Find n such that k(n) = 0.
-2, -2/5, 0
Let t(u) be the third derivative of u**9/1120 - 3*u**8/1120 + u**7/280 - u**6/360 - u**5/60 - u**2. Let z(g) be the third derivative of t(g). Factor z(s).
2*(3*s - 1)**3
Let i(c) = 12*c**2 - 38*c - 22. Let t(r) = 4*r**2 - 13*r - 7. Let l(w) = -5*i(w) + 14*t(w). Factor l(z).
-4*(z - 3)*(z + 1)
Let z = -10 - -12. Factor r**2 - 2*r**2 + 0*r**3 + 3*r**2 - z + 2*r**3 - 2*r.
2*(r - 1)*(r + 1)**2
Let w(u) be the third derivative of -u**5/180 - u**4/24 - u**3/9 + 3*u**2. Factor w(n).
-(n + 1)*(n + 2)/3
Suppose 0*v - 4/5*v**4 + 0*v**2 - 4/5*v**3 + 0 = 0. What is v?
-1, 0
Suppose -5*v = -20, 3*v + 2*v - 20 = 5*x. Suppose x + 2/11*h**3 - 2/11*h**2 - 4/11*h = 0. What is h?
-1, 0, 2
Solve 0 + 10/9*c**3 - 2*c - 2/9*c**4 - 2/3*c**2 = 0.
-1, 0, 3
Let l(n) be the third derivative of -n**7/210 - n**6/60 + n**4/12 + n**3/6 - 5*n**2. Determine r, given that l(r) = 0.
-1, 1
Let n(b) = -b**3 - 6*b**2 - 7*b - 6. Let y be n(-5). Determine l, given that 6*l**4 + 0*l**3 - 6*l**2 + 4*l**4 - 3*l**3 + 3*l**5 - 4*l**y = 0.
-2, -1, 0, 1
Find a, given that 9/7 - 3*a + 15/7*a**2 - 3/7*a**3 = 0.
1, 3
Let x(t) = t**2 - 3*t - 4. Let i be x(4). Let z be (3 - 1) + i/1. Solve -7 + 2 + 0 - 2*m**z - 3 + 8*m = 0.
2
Determine a, given that -57*a**2 + 3*a - 12*a**4 + 25*a**2 - 21*a**3 + 26*a**2 = 0.
-1, 0, 1/4
Let j(i) = i**2 + 3*i - 3. Let w(k) = -k**2 - 4*k + 4. Let t(s) = 4*j(s) + 3*w(s). Let p(r) = -3*r**3 - 15*r**2 + 12. Let h(u) = p(u) + 6*t(u). Factor h(d).
-3*(d - 1)*(d + 2)**2
Let q(i) be the second derivative of -3*i**5/20 + 3*i**4/4 - 6*i**2 + 13*i. Factor q(u).
-3*(u - 2)**2*(u + 1)
Let d(b) be the third derivative of -b**6/40 - b**5/20 + 13*b**2. Factor d(c).
-3*c**2*(c + 1)
Let i(n) be the third derivative of 0*n + 0*n**5 + 1/210*n**7 + 0*n**6 + 0*n**3 + 0*n**4 + 0 + 1/336*n**8 + 3*n**2. Factor i(y).
y**4*(y + 1)
Let t(g) = g. Let n(a) = -2*a**2 - 12*a + 4. Let z(j) = n(j) + 10*t(j). Let b(s) = 3*s**2 - 4 + 1 - 2 + 2*s. Let c(l) = -4*b(l) - 5*z(l). Solve c(h) = 0.
0, 1
Let m(h) be the third derivative of -h**8/84 - h**7/35 + 31*h**6/480 + 11*h**5/120 - 5*h**4/32 + h**3/12 + 2*h**2. What is y in m(y) = 0?
-2, -1, 1/4, 1
Suppose 6 = 3*s - 21. Suppose -s = 3*c - 6*c. Find j such that 9*j - 3*j**5 - 3*j**2 - 9*j**4 - 9*j**3 + 5*j**2 + 3 + 4*j**2 + c*j**3 = 0.
-1, 1
Let f(y) be the third derivative of y**8/2016 + y**7/315 + y**6/120 + y**5/90 + y**4/144 - 5*y**2. Factor f(a).
a*(a + 1)**4/6
Let h(f) = f**3 - 6*f**2 + 3*f - 6. Let b be h(7). Let z = b + -574/9. Factor z*g**2 - 2/9*g + 0.
2*g*(g - 1)/9
Let p(u) = -u + 1. Let r be p(6). Let t(z) = -z**3 - 4*z**2. Let d(k) = k**3 + 5*k**2. Let l(m) = r*t(m) - 4*d(m). What is f in l(f) = 0?
0
Let n(c) = 21*c**2 + 12*c - 15. Let v(b) = 5*b**2 + 3*b - 4. Let u(p) = 2*n(p) - 9*v(p). Suppose u(q) = 0. Calculate q.
-2, 1
Let h(k) be the first derivative of k**5/15 + 5*k**4/3 + 50*k**3/3 + 250*k**2/3 + 625*k/3 - 7. Factor h(t).
(t + 5)**4/3
Solve -4*r**3 + 1 + 4*r - 4*r**4 - 1 + 4*r**2 = 0 for r.
-1, 0, 1
Factor 16/7*n - 4/7*n**2 - 12/7.
-4*(n - 3)*(n - 1)/7
Suppose -t + 2*o - 5 = -0, 0 = -o + 4. Let m = -15 + 17. Determine b, given that 4*b - 6*b**t - m + 2*b**2 + 0 + 2 = 0.
-2/3, 0, 1
Let s(r) = r**3 - 8*r**2 + 5*r + 17. Let i be s(7). Let g(z) be the second derivative of -i*z + 1/60*z**5 + 0*z**2 + 0 + 0*z**3 - 1/36*z**4. Factor g(n).
n**2*(n - 1)/3
Let k = -326 - -330. Find n such that 15/2*n**2 - 9/2*n - 3/2 + 9/2*n**3 - 6*n**k = 0.
-1, -1/4, 1
Let v = -42 + 45. Let y(x) be the first derivative of -3/2*x**4 + 3/2*x**2 + 2/5*x**5 - 4/3*x**v - 2 + 2*x + 1/2*x**6. Let y(f) = 0. What is f?
-1, -2/3, 1
Factor -5*p**4 - 10 - 45*p**2 - 10*p**3 - 10*p + 45*p + 16*p**3 + 19*p**3.
-5*(p - 2)*(p - 1)**3
Determine p so that 0*p**4 - 8*p**3 - 6*p**4 + 8*p**4 - 20*p**2 - 2*p**2 - 12*p = 0.
-1, 0, 6
Let s(q) be the second derivative of 3*q**5/20 - q**4/2 + q**3/2 - q. What is n in s(n) = 0?
0, 1
Let f = 514 + -2562/5. Factor 16/5*u + f + 2/5*u**3 + 2*u**2.
2*(u + 1)*(u + 2)**2/5
Let m(g) = 11*g**3 - 5*g**2 + 19*g - 11. Let p(o) = 10*o**3 - 6*o**2 + 18*o - 10. Let u(c) = 6*m(c) - 7*p(c). Factor u(x).
-4*(x - 1)**3
Let l(x) be the third derivative of 1/480*x**6 + 0*x + 0 - 1/240*x**5 + 1/24*x**3 - 1/96*x**4 - 3*x**2. Factor l(y).
(y - 1)**2*(y + 1)/4
Let k = -1/23 + 26/69. Let j(m) be the second derivative of -k*m**3 + 2*m + 1/6*m**4 + 0*m**2 + 0. Let j(n) = 0. Calculate n.
0, 1
Let c be (-8)/(-3)*3/2. Suppose -c*k - 1 = -9. Factor 0 - 2/3*d**k + 2/3*d**3 + 0*d.
2*d**2*(d - 1)/3
Factor -2/9*n**4 - 2/9*n**3 + 0*n + 0 + 2/9*n**2 + 2/9*n**5.
2*n**2*(n - 1)**2*(n + 1)/9
Suppose 5*l + 10 = -5*b, l = 6*l + 5. Let m = 6 + b. Factor 4*s**2 - 2*s**2 - s**m - 2*s**4 + 2*s**3 - s**5.
-2*s**2*(s - 1)*(s + 1)**2
Let v(k) = 21*k**2 - 31*k + 7. Let s(z) = 104*z**2 - 156*z + 36. Let x(p) = 3*s(p) - 16*v(p). What is j in x(j) = 0?
1/6, 1
Factor 0*p - 3/7*p**3 + 3/7*p**2 + 0.
-3*p**2*(p - 1)/7
Let b = 824/21 - -128/21. Let p = -45 + b. Let 4/3 + p*u**2 - 4/3*u = 0. What is u?
2
Suppose 0*z + 2*z = -20. Let i = z - -14. Factor 3*r**2 + 4*r - r**2 - 12*r**3 - 14*r**5 - 11*r**3 + 38*r**i - 7*r**3.
-2*r*(r - 1)**3*(7*r + 2)
Let k(r) be the first derivative of 0*r**3 + 4/35*r**5 - 1/21*r**6 + 4 + 0*r + 0*r**2 - 1/14*r**4. Find b, given that k(b) = 0.
0, 1
Let z(b) be the third derivative of -b**8/11760 - b**7/2940 - b**6/2520 + b**3/6 + 4*b**2. Let x(i) be the first derivative of z(i). Factor x(t).
-t**2*(t + 1)**2/7
Factor -1/7*z - 2/7 + 1/7*z**2.
(z - 2)*(z + 1)/7
Let c = -3167/15 - -1109