Let r(s) be the first derivative of -s**4/2 - 8*s**3/3 - 5*s**2 - 4*s - 8. Factor r(g).
-2*(g + 1)**2*(g + 2)
Let y(r) = r**2 - 4*r - 9. Let l(s) = 3*s**2 - 15*s - 36. Let c(m) = -2*l(m) + 9*y(m). Solve c(k) = 0.
-1, 3
Factor 5/4*s**3 + 0*s - 5*s**2 + 0.
5*s**2*(s - 4)/4
Let q(f) be the first derivative of f**4/12 + 2*f**3/5 + 2*f**2/5 + 3*f - 3. Let y(b) be the first derivative of q(b). Let y(u) = 0. Calculate u.
-2, -2/5
Let y(s) be the first derivative of 9*s**4/4 + 2*s**3 - 9*s**2/2 - 6*s - 32. Factor y(q).
3*(q - 1)*(q + 1)*(3*q + 2)
Let j(h) be the second derivative of h**5/30 + 2*h**4/9 + h**3/3 + 8*h. Let j(x) = 0. Calculate x.
-3, -1, 0
Let l(c) = 0 + 5*c - 2*c**2 - 7*c**4 - 9*c**3 + 0. Let r(h) = -3*h**4 - 4*h**3 - h**2 + 2*h. Let x(g) = -6*l(g) + 15*r(g). Factor x(m).
-3*m**2*(m + 1)**2
Let r(j) = j**2 - j + 3. Let o be r(-4). Let 0 - 12*c + 14*c**2 - o*c**2 + 12 = 0. What is c?
-2, 2/3
Let z(n) be the second derivative of 4/3*n**2 - 3*n + 1/18*n**4 + 0 - 4/9*n**3. Find j such that z(j) = 0.
2
Let m(y) be the second derivative of -y**5/20 - y**4/12 + y**3/3 + 3*y. Solve m(k) = 0.
-2, 0, 1
Let s(f) = 42*f**4 - 143*f**3 + 31*f**2 + 168*f - 53. Let k(y) = -21*y**4 + 71*y**3 - 16*y**2 - 84*y + 26. Let l(n) = -5*k(n) - 2*s(n). What is r in l(r) = 0?
-1, 2/7, 2
Let b(a) be the third derivative of a**5/60 - a**4/8 + a**2. Factor b(x).
x*(x - 3)
Let q(c) be the second derivative of 3*c**5/40 - 5*c**4/24 + c**3/12 + c**2/4 - c. Factor q(s).
(s - 1)**2*(3*s + 1)/2
Let i be (5/(-15))/(-1 - 48/(-63)). Determine r so that i*r**3 - 7/5*r + 2/5*r**2 - 2/5 = 0.
-1, -2/7, 1
Let r(g) be the second derivative of -g**7/63 + g**5/15 - g**3/9 - 2*g. Determine x so that r(x) = 0.
-1, 0, 1
Suppose -o - 2*s = -2*o - 4, 4*o = 4*s - 8. Suppose -4*u - 4*q = -48, o*u - 2*q = -4*u + 36. Factor -2*l + 7*l**3 - 4*l**2 + 3*l**5 + 0*l + u*l**4 - 2*l.
l*(l + 1)**2*(l + 2)*(3*l - 2)
Suppose -5*p - 3*o = -3*p - 22, -3*o = 4*p - 32. Let f(i) be the third derivative of 0*i - 1/18*i**3 + 0 + 2*i**2 - 1/60*i**p + 1/18*i**4. Solve f(w) = 0.
1/3, 1
Let y be (1 - 1)*(-11 - -5)/6. Factor -4/3 + 1/3*g**2 + y*g.
(g - 2)*(g + 2)/3
Let c be (-8 + 1)*60/(-140). Find a such that 2/3*a**c - 5/3*a**5 + 0 + 0*a + 0*a**2 - a**4 = 0.
-1, 0, 2/5
Let h(j) be the first derivative of j**6/51 - j**4/34 - 14. Factor h(c).
2*c**3*(c - 1)*(c + 1)/17
Suppose 0*u = u - 5*s + 1, 5*u - 4*s = 100. Let v be ((-8)/(-30))/(u/20). Factor -4/9*k**3 + v*k**5 - 4/9*k**2 + 2/9 + 2/9*k**4 + 2/9*k.
2*(k - 1)**2*(k + 1)**3/9
Suppose 0 = 31*h - 32*h. Factor 2/7*x**2 + h - 4/7*x.
2*x*(x - 2)/7
Let u be (-1 - 0) + 2 + -1. Let t(c) be the third derivative of 1/6*c**4 + 1/30*c**5 + 1/3*c**3 + 0*c + u + c**2. Factor t(f).
2*(f + 1)**2
Let i(y) be the third derivative of -y**10/3780 + y**9/1512 - y**8/3360 - y**4/24 + 2*y**2. Let l(p) be the second derivative of i(p). Factor l(c).
-2*c**3*(c - 1)*(4*c - 1)
Suppose 2*o - 4*b = 106, -o + 63 + 4 = 5*b. Solve 3*a + 54*a**5 - 3/2*a**2 + 3/2*a**4 + 0 - o*a**3 = 0.
-1, -1/4, 0, 2/9, 1
Let c(s) be the first derivative of -s**6/30 + s**5/5 - 5*s**4/12 + s**3/3 + s + 1. Let q(h) be the first derivative of c(h). Solve q(o) = 0.
0, 1, 2
Let w(i) = -i**5 - i**3 - i**2 - i - 1. Let d(m) = -7*m**5 - m**4 - 6*m**3 - 6*m**2 - 6*m - 6. Let k(j) = -d(j) + 6*w(j). Solve k(b) = 0 for b.
-1, 0
Factor -1/4*y**4 + y + 1/4*y**2 + 0 - y**3.
-y*(y - 1)*(y + 1)*(y + 4)/4
Let n(b) = -4*b**5 + 17*b**3 + 5*b. Let y(h) be the third derivative of -h**8/336 + h**6/30 + h**4/24 - 6*h**2. Let f(m) = 4*n(m) - 18*y(m). Factor f(o).
2*o*(o - 1)**2*(o + 1)**2
Let d(n) be the second derivative of 0*n**2 + 2*n + 1/24*n**4 + 0 + 1/12*n**3. Let d(l) = 0. What is l?
-1, 0
Let z(w) be the third derivative of -w**9/540 + w**8/105 - 11*w**7/630 + w**6/90 + w**4/12 - 2*w**2. Let h(p) be the second derivative of z(p). Factor h(t).
-4*t*(t - 1)**2*(7*t - 2)
Let n = 9 + -9. Let c be (-80)/(-36) + 4/(-18). Determine u so that 2/3*u**c + 0*u + n - 2/3*u**4 + 0*u**3 = 0.
-1, 0, 1
Let v(k) be the first derivative of -1/21*k**3 + 0*k**2 + 3*k + 1/70*k**5 + 0*k**4 - 3. Let b(u) be the first derivative of v(u). Factor b(q).
2*q*(q - 1)*(q + 1)/7
Let y(u) be the first derivative of 9*u**5/10 - 21*u**4/4 + 25*u**3/6 - u**2 - 8. Determine l so that y(l) = 0.
0, 1/3, 4
Suppose 5*f - 12 = -3*g, -5*f + 0*f + 3*g - 12 = 0. Let y(b) be the second derivative of -3*b - b**2 + 1/6*b**4 + f + 0*b**3. Solve y(d) = 0 for d.
-1, 1
Let t(q) = 3*q**4 + 2*q**3 - 3*q**2 - 6*q + 4. Let a(y) = -8*y**4 - 6*y**3 + 8*y**2 + 17*y - 11. Let n(o) = 4*a(o) + 11*t(o). Solve n(h) = 0.
-1, 0, 1, 2
Let v be ((-7)/(-3) + -2)*2. Let r(f) be the first derivative of 1/3*f**6 + 0*f**2 - 6/5*f**5 + 0*f - v*f**3 + 3/2*f**4 + 2. Factor r(b).
2*b**2*(b - 1)**3
Let m(n) = 2*n + 5. Let l be m(-4). Let f = l - -3. Factor f*a - 2/9*a**3 + 2/9*a**2 + 0.
-2*a**2*(a - 1)/9
Suppose -22/9*s**2 + 70/9*s - 50/9 + 2/9*s**3 = 0. Calculate s.
1, 5
Find w, given that 53 + 11 - 32*w + 8*w**2 - 4*w**2 = 0.
4
Suppose 0 = -4*h, -5*d = 3*h + 3 - 8. Suppose d = 2*i - 7. Solve -1/4*p**i + 0*p**2 + 3/4*p**3 - p + 0 = 0.
-1, 0, 2
Let g(n) = -5*n**2 - 4*n**3 - 3 + 0 + 3*n + 8*n**2. Let h(b) = -b**3 + b**2 + b - 1. Let j(x) = -g(x) + 3*h(x). Find z such that j(z) = 0.
0
Let a(k) = -7*k**3 - 24*k**2 - 59*k - 26. Let p(x) = -48*x**3 - 168*x**2 - 411*x - 183. Let z(r) = 27*a(r) - 4*p(r). Factor z(h).
3*(h + 1)*(h + 2)*(h + 5)
Let l(j) be the third derivative of -j**7/315 - j**6/45 - j**2 - 18. Factor l(c).
-2*c**3*(c + 4)/3
Let d(k) = -k**2 - k + 1. Let h = -11 - -2. Let r = h - -27. Let s(m) = 10*m**2 + 10*m - 11. Let z(a) = r*d(a) + 2*s(a). Factor z(i).
2*(i - 1)*(i + 2)
Let u(y) be the first derivative of y**4/2 + 4*y**3 + 12*y**2 + 16*y + 8. Let u(n) = 0. Calculate n.
-2
Determine m so that -m - 8*m + 33*m**3 + 3*m**2 - 24*m**3 - 3*m**4 = 0.
-1, 0, 1, 3
Suppose o - 3*s - 4 = 0, -5*s + 4*s - 4 = -3*o. Suppose 7 + o = 4*h. Factor 0 - 2/7*v**3 + 0*v - 2/7*v**h.
-2*v**2*(v + 1)/7
Suppose 2*q**3 + 3*q - 3*q**2 - 3*q**3 + 3*q**4 - 2*q**3 = 0. What is q?
-1, 0, 1
Let s be ((-342)/(-627) - 19/(-66))/5. Factor -1/2*i + s*i**2 + 1/3.
(i - 2)*(i - 1)/6
Suppose -z + 39 = 37. What is n in 2/7*n**3 + 2/7*n**z + 0*n + 0 = 0?
-1, 0
Suppose f - 46 = -y - 0*f, 2*f - 215 = -5*y. Let t = y + -81/2. Factor 0 + 0*u**3 - t*u**5 + u**4 + 1/2*u - u**2.
-u*(u - 1)**3*(u + 1)/2
Let a(p) be the first derivative of -p**6/33 + 2*p**5/55 + p**4/22 - 2*p**3/33 + 8. Factor a(x).
-2*x**2*(x - 1)**2*(x + 1)/11
Let -3/4*w**4 - 3/4*w**5 + 3/4*w**2 + 0 - 3/2*w + 9/4*w**3 = 0. Calculate w.
-2, -1, 0, 1
Let m = 11 - 7. Solve l**m + l**5 - l**2 - 2*l**3 - 2*l**3 + 3*l**3 = 0 for l.
-1, 0, 1
Determine b, given that 0 - 4/5*b**2 + 16/5*b = 0.
0, 4
Let c = 22 - 20. Let j(u) be the second derivative of 1/3*u**c + u + 1/30*u**5 - 1/18*u**4 - 1/9*u**3 + 0. Let j(f) = 0. Calculate f.
-1, 1
Let k(p) = -123*p. Let c be k(-2). Let o = -2704/11 + c. Factor 0 - o*i**2 + 0*i - 2/11*i**3.
-2*i**2*(i + 1)/11
Let r = 63 - 43. Let o = r - 17. Solve 0 + 2/3*a**2 + 1/3*a**o + 0*a = 0 for a.
-2, 0
Let l = -7 + 21. Let x be (-4)/l + 200/210. Factor x*v**2 - 2/3*v**3 - 2/3*v**4 + 0 + 2/3*v.
-2*v*(v - 1)*(v + 1)**2/3
Let y be -6 - -2 - (-7802)/470. Suppose -51/5*n**3 + 6/5 + 3*n**4 + y*n**2 - 33/5*n = 0. Calculate n.
2/5, 1
Let o be 526/(-6) + (-2)/2. Let g = 90 + o. Factor 2/3 + 2/3*l**2 + g*l.
2*(l + 1)**2/3
Let r(d) be the second derivative of -4*d**6/45 - d**5/2 - 2*d**4/3 + 4*d**3/9 - 4*d. Suppose r(x) = 0. What is x?
-2, 0, 1/4
Let t(j) be the first derivative of 1/2*j - 1/8*j**4 - 3 - 1/6*j**3 + 1/4*j**2. Suppose t(n) = 0. What is n?
-1, 1
Let o(u) be the third derivative of u**5/12 + u**4/8 + u**3/3 + 3*u**2. Let l(b) = 26*b**2 + 15*b + 11. Let z(k) = 2*l(k) - 11*o(k). Factor z(d).
-3*d*(d + 1)
Suppose 4*f - i - 11 = 0, -4*i + 7 - 19 = 0. Let x(s) = -s**2 - s - 2. Let r(z) = -5*z**2 - 4*z - 9. Let l(d) = f*r(d) - 9*x(d). Factor l(w).
-w*(w - 1)
Factor 2*k**2 + 317*k**4 - 5*k**2 - 314*k**4.
3*k**2*(k - 1)*(k + 1)
Let t(v) be the third derivative of -v**7/105 + v**6/30 + v**5/10 - v**4/3 - 4*v**3/3 - 4*v**2. Factor t(f).
-2*(f - 2)**2*(f + 1)**2
Let k(u) be the first derivative of u**3/15 - 4*u**2/5 + 16*u/5 - 5. Solve k(z) = 0 for z.
4
Facto