1
Let m(y) be the third derivative of -y**8/5040 - 2*y**7/315 - 4*y**6/45 + y**5/20 + y**2. Let p(i) be the third derivative of m(i). Let p(b) = 0. Calculate b.
-4
Let c(d) = d**2 + 4*d + 3. Let z = -10 + 6. Let t be c(z). Factor -f + 7/3*f**t - f**4 + 2/3 - f**2.
-(f - 1)**3*(3*f + 2)/3
Determine x so that -6*x**3 + 10*x**2 + 0 + 2/3*x**4 + 50/3*x = 0.
-1, 0, 5
What is a in 2/7*a + 0 + 0*a**2 - 2/7*a**3 = 0?
-1, 0, 1
Let m be (-2)/(-4)*(-5 + 11). Suppose 0*l**3 + 2*l**m - 6*l**2 + 5*l**2 - l**4 = 0. What is l?
0, 1
Let b(c) be the first derivative of 3/10*c**2 + 0*c + 2/15*c**3 - 2. Factor b(o).
o*(2*o + 3)/5
Let c = 29/6 + -13/3. Let l - 1/2*l**3 - c*l**2 + 0 = 0. What is l?
-2, 0, 1
Let l be (-2*5/(-60))/((-5)/(-3)). Let d(x) be the first derivative of 2/15*x**3 + 0*x + l*x**4 - 2 + 0*x**2. Solve d(p) = 0 for p.
-1, 0
Let h = -2 - 1. Let z = 7 + h. Let n(a) = a**5 - 5*a**4 + a**3 + a**2 - 2*a + 4. Let i(p) = -p**4 + p**3 - p**2 + 1. Let b(f) = z*i(f) - n(f). Factor b(q).
-q*(q - 1)**3*(q + 2)
Let f(a) be the second derivative of -a**7/84 + a**6/10 - 13*a**5/40 + a**4/2 - a**3/3 + 6*a. Factor f(t).
-t*(t - 2)**2*(t - 1)**2/2
Let u(z) be the first derivative of 4*z**5/5 - z**4/2 - 4*z**3/3 + z**2 + 22. Let u(l) = 0. Calculate l.
-1, 0, 1/2, 1
Factor 5*k**2 + 20*k - 650 + 650.
5*k*(k + 4)
Let a(b) be the second derivative of -b**7/840 + b**6/360 + b**5/120 - b**4/24 - b**3/6 - b. Let f(m) be the second derivative of a(m). Factor f(v).
-(v - 1)**2*(v + 1)
Let p(d) be the first derivative of d**5 + 15*d**4/4 + 5*d**3/3 - 15*d**2/2 - 10*d + 6. Let p(f) = 0. What is f?
-2, -1, 1
Let k(a) = -a**3 - 9*a**2 - 8*a - 5. Let o be k(-8). Let p = o + 9. Factor -p*v**2 + 2*v**4 - 5*v + 5*v + 2.
2*(v - 1)**2*(v + 1)**2
Let k(u) = u**3 + u**2 + 2*u. Let i(r) = -7*r - 4*r**2 - 2*r**3 - r**3 + 0*r**3. Let y(z) = -6*i(z) - 21*k(z). Factor y(h).
-3*h**2*(h - 1)
Let h(j) be the first derivative of j**4/90 + j**3/45 + j - 10. Let l(p) be the first derivative of h(p). Suppose l(m) = 0. What is m?
-1, 0
Factor -4/3 + 7/3*w + 2/3*w**2.
(w + 4)*(2*w - 1)/3
Let u = 12001/48 + -250. Let h(n) be the second derivative of 0 + u*n**4 - n + 1/2*n**2 + 1/6*n**3. Factor h(z).
(z + 2)**2/4
Let w(a) be the first derivative of -a**6/15 + 2*a**5/25 + a**4/2 - 2*a**3/3 - 4*a**2/5 + 8*a/5 + 16. Solve w(q) = 0.
-2, -1, 1, 2
Solve -8*m**2 + 16*m**3 - 3*m**4 - 6*m**5 + 0*m**2 + 0*m**4 + m**4 = 0.
-2, 0, 2/3, 1
Let s(m) = 6*m**2 + 26*m**2 - 3 + 3*m + 49*m**4 + 0 + 74*m**3 - 2*m. Let p(g) = -98*g**4 - 147*g**3 - 64*g**2 - g + 7. Let z(b) = 3*p(b) + 7*s(b). Factor z(t).
t*(t + 1)*(7*t + 2)**2
Let u(s) = 2*s**3 + s - 1. Suppose -5*p = 17 - 22. Let a be u(p). Factor -8/3*o**a + 10/3*o - 2/3.
-2*(o - 1)*(4*o - 1)/3
Let m be -1 + 1 + (-12 - -4 - -8). Factor 1/6*x**3 + 0*x**2 + 0 + m*x.
x**3/6
Let n(k) be the second derivative of -k**6/120 + 7*k**3/6 + 7*k. Let w(f) be the second derivative of n(f). Solve w(l) = 0.
0
Factor -6/5*d**3 - 6/5*d**4 + 6/5*d**2 + 0 + 6/5*d.
-6*d*(d - 1)*(d + 1)**2/5
Let h = 192 + -383/2. Let o(u) be the second derivative of -h*u**3 + 0 + 1/4*u**4 + 1/2*u**2 - 1/20*u**5 + u. Factor o(b).
-(b - 1)**3
Let z(s) be the third derivative of s**5/20 - 3*s**4/8 - 9*s**2. Find x, given that z(x) = 0.
0, 3
Let l(y) be the second derivative of y**4/18 - y**3/9 + 7*y. Factor l(d).
2*d*(d - 1)/3
Let f(g) be the third derivative of g**8/112 + g**7/35 - g**5/10 - g**4/8 - 2*g**2. Factor f(n).
3*n*(n - 1)*(n + 1)**3
Let m = -2/23 + 41/207. Let p(l) be the second derivative of -l + 0 + 1/135*l**6 - m*l**2 + 0*l**4 + 1/45*l**5 - 2/27*l**3. What is y in p(y) = 0?
-1, 1
Find z such that -12*z - 2 - 7*z**2 + 6*z - 2*z**3 + z**2 = 0.
-1
Let t(f) be the third derivative of -f**5/12 - 5*f**4/6 - 5*f**3/2 - f**2. Determine l so that t(l) = 0.
-3, -1
Factor -3/2*u**2 - 3 + 21/4*u - 3/4*u**3.
-3*(u - 1)**2*(u + 4)/4
Suppose 13 = 2*q + 3. Suppose y - 1 = 4*c, 5*y = 4*c - 2 + 7. Factor 0*z - 1/2*z**q + c + 0*z**3 + 0*z**2 + 1/4*z**4.
-z**4*(2*z - 1)/4
Let d(w) be the third derivative of 5*w**8/336 - w**7/42 - w**6/8 + w**5/12 + 5*w**4/12 - 14*w**2. Solve d(v) = 0 for v.
-1, 0, 1, 2
Let -11*s**2 + 5*s + 4*s + 7*s**2 - s = 0. What is s?
0, 2
Let g be (-15)/20 + (-9)/(-12). Let r(m) be the first derivative of -4/27*m**3 - 2 + 0*m - 1/18*m**4 + g*m**2. What is u in r(u) = 0?
-2, 0
Let u(l) = -l**3 + l**2 + l. Let h be 1 + 1/((-2)/(-2)). Let o = 5 - h. Let f(q) = 2*q**4 - 5*q**3 + q**2 + 5*q. Let y(c) = o*u(c) - f(c). Factor y(r).
-2*r*(r - 1)**2*(r + 1)
Factor -4/7 - 2*r - 10/7*r**3 - 18/7*r**2 - 2/7*r**4.
-2*(r + 1)**3*(r + 2)/7
Let y(p) be the second derivative of -p**7/168 + 3*p**5/40 + p**4/6 + p**3/8 + 5*p. Factor y(o).
-o*(o - 3)*(o + 1)**3/4
Suppose 6 = 6*a - 4*a. Determine o, given that 2*o**4 + 2*o**5 + 0*o**3 + o**3 - a*o**4 + o**2 - 3*o**5 = 0.
-1, 0, 1
Let z = 19 - 21. Let v be 7/6 + z/3. Factor -k + v*k**2 + 1/2.
(k - 1)**2/2
Let o(d) be the first derivative of d**8/4200 - d**6/300 + d**5/150 - 2*d**3/3 - 4. Let q(x) be the third derivative of o(x). Suppose q(y) = 0. What is y?
-2, 0, 1
Let h(v) be the first derivative of -v**5/5 + v**4/2 + v**3/3 - v**2 - 5. Factor h(l).
-l*(l - 2)*(l - 1)*(l + 1)
Let v(r) be the first derivative of -3*r**5/40 + r**3/4 - 3*r/8 - 3. Factor v(m).
-3*(m - 1)**2*(m + 1)**2/8
Determine s, given that 15/4*s**3 + 5*s - 5/4*s**5 + 0 + 10*s**2 - 5/2*s**4 = 0.
-2, -1, 0, 2
Suppose -3*r - 7*f = -3*f - 2, -5 = -r + 3*f. Let o(v) be the first derivative of -1/7*v**r + 2/21*v**3 + 2 - 4/7*v. Suppose o(c) = 0. What is c?
-1, 2
Suppose -3*d + 3 = 0, -4*d + 9 - 3 = w. Solve r**3 + w*r**3 - 3*r + 2*r - 2*r = 0 for r.
-1, 0, 1
Let u(y) be the third derivative of -y**8/336 + y**6/30 - y**5/30 - y**4/8 + y**3/3 + 2*y**2. Factor u(q).
-(q - 1)**3*(q + 1)*(q + 2)
Let t be (-10)/(-5) - 19*-1. Suppose t + 14 = 5*q. Solve -q*b**3 + 0 + 4*b - 2 + 0*b**4 + 2*b**4 + 3*b**3 = 0 for b.
-1, 1
Suppose -3*a - 4*h = 4, a - h - 2*h - 3 = 0. Factor -1/2*d + a + d**2 - 1/2*d**3.
-d*(d - 1)**2/2
Let h(m) be the first derivative of 2*m**6/3 - 13*m**5/5 + 11*m**4/4 - 2*m**3/3 - 24. Let h(j) = 0. Calculate j.
0, 1/4, 1, 2
Let v(d) be the second derivative of d**4/42 + 5*d**3/21 - 4*d. Solve v(a) = 0 for a.
-5, 0
Let g(x) = -x + 3. Let d be g(0). Let u be (-8)/(-12) + 4/d. Determine v so that -5*v**2 + 9*v**5 - 6*v**4 - 5*v**3 - 16*v**3 - v**u = 0.
-1, -1/3, 0, 2
Solve -3/5*i**3 + 6/5*i**2 - 3/5*i + 0 = 0.
0, 1
Let a(w) = 8*w**2 + 11 + 16*w**2 + 13*w**2 - 29*w. Let l = -1 - 5. Let i(g) = -18*g**2 + 14*g - 5. Let n(y) = l*a(y) - 14*i(y). Factor n(p).
2*(3*p - 1)*(5*p - 2)
Let w(z) be the second derivative of 3*z**4/20 + 2*z**3/5 - 6*z**2/5 - 6*z + 4. Find k, given that w(k) = 0.
-2, 2/3
Let g be 2*(-2 + (-1)/(-2)). Let z be (-2)/g - 2/3. Factor -1/3*s - 1/3*s**5 + z - 2*s**3 + 4/3*s**4 + 4/3*s**2.
-s*(s - 1)**4/3
Let k(r) = -r + 10. Let c be k(8). Let -c*m**5 + 4*m**3 - m**4 + 2*m**5 + 5*m**4 + m**5 = 0. What is m?
-2, 0
Let q = 43 - 40. Let h(i) be the second derivative of 0 - 3*i - i**2 + 2/3*i**4 - i**q. Factor h(n).
2*(n - 1)*(4*n + 1)
Let z(m) be the second derivative of -m**6/255 + m**4/51 - m**2/17 - 10*m. Factor z(p).
-2*(p - 1)**2*(p + 1)**2/17
Let s(q) be the second derivative of -q**6/15 + q**5/2 - 4*q**4/3 + 4*q**3/3 + 3*q. Factor s(r).
-2*r*(r - 2)**2*(r - 1)
Let d(y) be the first derivative of -y**7/280 - y**6/80 + y**5/80 + y**4/16 - y**2 - 4. Let j(r) be the second derivative of d(r). Factor j(a).
-3*a*(a - 1)*(a + 1)*(a + 2)/4
Let x(z) be the third derivative of -z**8/504 - z**7/630 + 7*z**6/360 + 7*z**5/180 - z**4/72 - z**3/9 + 12*z**2. Solve x(u) = 0 for u.
-1, 1/2, 2
Let i(s) be the third derivative of -s**6/600 + s**5/300 + s**4/60 + 3*s**2. Factor i(u).
-u*(u - 2)*(u + 1)/5
Suppose 0 = l - z - 2, z = -4*l - 21 + 34. Factor -3/2*s + 3/2*s**2 - 3/2 + 3/2*s**l.
3*(s - 1)*(s + 1)**2/2
Let r be 154/49 + 2/(-14). Factor -12*v + 10*v - 2*v**r - 7*v**3 - 2*v**4 - 6*v**2 + 3*v**3.
-2*v*(v + 1)**3
Suppose x + 6 = 4*d - x, 5*d = -x + 18. Let g = 6 - 1. Solve -3/5*c**d + 0*c + 0 + 3/5*c**4 + 1/5*c**2 - 1/5*c**g = 0 for c.
0, 1
Let y(k) be the first derivative of k**6/1440 - k**5/240 + k**3/3 + 5. Let c(j) be the third derivative of y(j). Determine i, given that c(i) = 0.
0, 2
Let 