at c(g) = 0.
-1, 0, 1, 2
Let k(f) be the first derivative of 20*f**5/7 - 30*f**4/7 - 44*f**3/21 + 24*f**2/7 + 16*f/7 + 2. Solve k(m) = 0.
-2/5, 1
Let w(u) be the third derivative of -1/120*u**5 - 2*u**2 + 0*u + 0*u**3 - 1/48*u**4 + 0 + 1/420*u**7 + 1/240*u**6. Factor w(j).
j*(j - 1)*(j + 1)**2/2
Factor 48 - 192*s - 27/2*s**3 - 105*s**2.
-3*(s + 4)**2*(9*s - 2)/2
Let 0 - 6/5*n**3 + 2*n**4 - 8/5*n - 24/5*n**2 = 0. Calculate n.
-1, -2/5, 0, 2
Suppose -3*q = 2*q - 10. Suppose v = -0*v + q. Factor -1 - r**5 + 0*r**v + 2*r**2 - r - r**4 + 2*r**3 + 0.
-(r - 1)**2*(r + 1)**3
Let a(r) = r**4 - r**3 + r**2 + r. Let n(v) = 2*v**5 - 4*v**4 + 2*v**3 - v**2 - v. Let y(t) = 2*a(t) + 2*n(t). Suppose y(w) = 0. Calculate w.
0, 1/2, 1
Let c(k) = -3*k**2 + 10. Let t(w) = 3*w**2 - 11. Let u(a) = 4*c(a) + 3*t(a). Let b(m) = -6*m**2 + 15. Let d(g) = 4*b(g) - 9*u(g). Factor d(y).
3*(y - 1)*(y + 1)
Let q(j) be the second derivative of -3*j**5/20 + j**4/6 + 5*j**3/6 - j. Let h(y) = y**3 - y. Let o(d) = 4*h(d) + q(d). Find i such that o(i) = 0.
-1, 0
Factor 0*z**2 - 6*z + 13*z**3 + 9*z**2 - 4*z**3 + 9*z**5 - 21*z**4.
3*z*(z - 1)**3*(3*z + 2)
Let 24/11*l + 4/11*l**5 - 53/11*l**2 - 24/11*l**4 + 53/11*l**3 - 4/11 = 0. What is l?
1/2, 1, 2
Let t(y) be the second derivative of y + 1/6*y**3 + 1/60*y**5 + 0 + 1/6*y**2 + 1/12*y**4. Factor t(w).
(w + 1)**3/3
Suppose -5*c - 2*a + 0*a = -169, -2*a = 6. Let s be c/60 - (-3)/4. Suppose 4/3*m + 2/3*m**4 - 2/3 + 0*m**2 - s*m**3 = 0. Calculate m.
-1, 1
Suppose 2*h + 2 - 14 = 4*y, 0 = 5*h + 4*y - 2. Factor -c**2 - c - 2*c**4 + 3*c**h - 3*c**5 + 4*c**5.
c*(c - 1)**3*(c + 1)
Let q = -1/31 - -67/155. Let f(l) be the first derivative of 1/10*l**4 + 1 + 2/5*l + q*l**3 + 3/5*l**2. Find i, given that f(i) = 0.
-1
Let k = -932 + 2800/3. What is a in 4/3*a - 2/3 - 8/3*a**5 + k*a**3 + 16/3*a**2 - 14/3*a**4 = 0?
-1, 1/4, 1
Let x = 215/327 - -1/109. Factor 1/3 + 0*o**2 - x*o**3 - 1/3*o**4 + 2/3*o.
-(o - 1)*(o + 1)**3/3
Let d be (0 + 0 - 0)/(-2). Let b(p) be the third derivative of 0 + 0*p**4 + 0*p + d*p**3 - 4*p**2 + 1/12*p**6 + 1/15*p**5. Determine f so that b(f) = 0.
-2/5, 0
Let d(h) be the third derivative of -h**8/168 + h**6/20 + h**5/15 + 8*h**2. Factor d(g).
-2*g**2*(g - 2)*(g + 1)**2
Suppose 0 = 3*r - 12, -28 = -5*w - r - 4. Let l - 4*l**2 + 20*l**5 - l - 2*l**w - 14*l**3 = 0. Calculate l.
-1/2, -2/5, 0, 1
Suppose d = -3*d + 24. Let g(b) be the first derivative of 1/8*b**4 + 1 + 0*b**2 + 2/5*b**5 - 1/4*b**d - 1/3*b**3 + 0*b. Factor g(h).
-h**2*(h - 1)**2*(3*h + 2)/2
Suppose -3*k = 2*x - 3*x - 12, -5*k = x - 28. Factor -d**x + 3*d**4 - 6*d**3 + 27*d**2 + 6 - 6*d**3 - 21*d - 2*d**3.
3*(d - 2)*(d - 1)**3
Let j(u) = u**3 + 8*u**2 + u + 10. Let s = 12 + -20. Let o be j(s). Let 12*v**3 - 6*v**4 + 2*v + 2*v**5 - o*v**4 - 7*v**2 - v**2 = 0. Calculate v.
0, 1
Let 8/19 + 2/19*r**3 + 10/19*r**2 + 16/19*r = 0. Calculate r.
-2, -1
Let l be ((-20)/(-8) + -3)*6. Let u be (-5)/25*5/l. Factor u - 5/6*o + 1/2*o**3 - 2/3*o**2.
(o - 2)*(o + 1)*(3*o - 1)/6
Let n(w) be the third derivative of w**9/22680 - w**7/1260 - w**6/540 - w**4/8 - 7*w**2. Let h(r) be the second derivative of n(r). Suppose h(l) = 0. What is l?
-1, 0, 2
Let x = 34651 + -3222463/93. Let m = x + -6/31. Let 2/3*p**3 - 2/3*p + m*p**2 - 2/3 = 0. Calculate p.
-1, 1
Let v be (-6)/(-2) + -1 + 0. Suppose -4*q = -0*q. Factor j**2 + q*j**2 + j**4 + 3*j**3 + j**5 + v*j**4.
j**2*(j + 1)**3
Let k(m) be the second derivative of m**6/30 + m**5/10 - m**3/3 - m**2/2 + 11*m. Determine f, given that k(f) = 0.
-1, 1
Let t(n) be the second derivative of -n**6/60 - 11*n**5/80 + 7*n**4/48 + n**3/4 + 6*n + 1. Determine j, given that t(j) = 0.
-6, -1/2, 0, 1
Let z(g) be the first derivative of -3/20*g**4 + 6/25*g**5 + 0*g**2 + 8 - 1/5*g**3 + 0*g. Solve z(b) = 0 for b.
-1/2, 0, 1
Let x(l) be the second derivative of -2*l - 1/21*l**3 - 1/70*l**5 - 1/2*l**2 + 1/21*l**4 + 0. Let n(v) be the first derivative of x(v). Factor n(s).
-2*(s - 1)*(3*s - 1)/7
Let z(v) = -v**3 - 7*v**2 - 7*v + 5. Let n be z(-6). Let d = -6 + n. Factor d*y**2 + 2*y - y - 4*y**2.
y*(y + 1)
Let f(o) = -o**2 - 3*o + 18. Let c be f(-6). Let m(b) be the second derivative of 1/14*b**4 + 0*b**2 + 2/21*b**3 + 0*b**5 - 1/105*b**6 + 2*b + c. Factor m(t).
-2*t*(t - 2)*(t + 1)**2/7
Let r(m) be the first derivative of 1/5*m**5 + 1/2*m**3 - 1 + 0*m + 3/2*m**2 + 1/2*m**4. Let z(t) be the second derivative of r(t). Factor z(q).
3*(2*q + 1)**2
Let d(j) be the second derivative of -j**7/252 + j**6/60 - j**5/60 - j**4/36 + j**3/12 - j**2/12 - 7*j. Factor d(s).
-(s - 1)**4*(s + 1)/6
Let f(q) be the first derivative of -2*q**3/5 - 12*q**2/5 - 17. Determine i, given that f(i) = 0.
-4, 0
Let x be (72/(-33) - -2) + 3672/2772. Suppose 96/7*k**2 + 184/7*k**3 - x + 36/7*k**5 + 136/7*k**4 + 4/7*k = 0. What is k?
-1, 2/9
Let g(o) = o**4 + 4*o**3 - o**2 - 4. Suppose 2*d - 2 = 2. Let t(s) = 0 + d*s**4 - s**4 - s**2 - 3 + 3*s**3. Let y(x) = 3*g(x) - 4*t(x). Factor y(z).
-z**2*(z - 1)*(z + 1)
Solve -5*l**5 + 15*l**3 + 10*l**2 + 12 - 9 - 3 = 0 for l.
-1, 0, 2
Let t(g) be the second derivative of -1/10*g**3 - 1/20*g**4 - 1/10*g**2 - 1/100*g**5 - 3*g + 0. Factor t(i).
-(i + 1)**3/5
Let k(t) be the third derivative of -1/21*t**3 - 2*t**2 - 1/42*t**4 - 1/210*t**5 + 0*t + 0. Factor k(a).
-2*(a + 1)**2/7
Let j = 104 - 104. Let b(m) be the first derivative of 4/15*m**3 - 3/20*m**4 - 4 + j*m - 1/10*m**2. Solve b(k) = 0 for k.
0, 1/3, 1
Let j = 65 - 389/6. Let x(b) be the first derivative of 0*b**5 + 1/4*b**4 + 0*b + 0*b**3 - 2 - j*b**6 + 0*b**2. Factor x(d).
-d**3*(d - 1)*(d + 1)
Let i(z) = -z + 13. Let g be i(0). Determine x so that -3*x - 15*x**2 - 4 + g*x**2 - 3*x = 0.
-2, -1
Let p(s) = 3*s**3 + 14*s**2. Let o(f) = -3*f**3 - 15*f**2. Let w(v) = -2*o(v) - 3*p(v). Factor w(r).
-3*r**2*(r + 4)
Let i(x) = 7*x**2 + 6*x - 5. Let s(h) be the first derivative of -2*h**3 - 3*h**2 + 4*h + 4. Let v(z) = -4*i(z) - 5*s(z). Factor v(k).
2*k*(k + 3)
Let p(y) be the third derivative of 0*y + 4*y**2 - 2/33*y**3 - 1/132*y**4 + 1/330*y**5 + 0. Suppose p(i) = 0. What is i?
-1, 2
Factor 2*r**2 - 21*r + 11*r + 3*r + r**3 + 8*r.
r*(r + 1)**2
Let h be (5 - (-2 - -6))/((-2)/(-8)). Let x(c) be the third derivative of 0*c**3 + 0*c - 1/60*c**5 + 0 + 1/12*c**h - c**2. Factor x(d).
-d*(d - 2)
Let x(k) be the second derivative of 3*k**5/20 - 3*k**4/4 + 3*k**3/2 - 3*k**2/2 - 6*k. Factor x(a).
3*(a - 1)**3
Let i(m) be the third derivative of -m**7/147 + m**6/140 + 2*m**5/35 + m**4/21 + 17*m**2. Suppose i(w) = 0. Calculate w.
-1, -2/5, 0, 2
Let p(g) be the first derivative of 2*g**3/15 - 13*g**2/5 + 24*g/5 + 27. Factor p(d).
2*(d - 12)*(d - 1)/5
Let c(l) be the second derivative of l**6/90 + l**5/10 + 5*l**4/36 - 23*l. Let c(f) = 0. Calculate f.
-5, -1, 0
Let q be ((-640)/576)/(10/(-12)). What is y in 1/6 - q*y + 8/3*y**2 = 0?
1/4
Find h, given that -12*h + 3/2*h**4 - 9*h**3 + 18*h**2 + 0 = 0.
0, 2
Let l be (-8)/(-6)*135/36. Let a(c) be the first derivative of 2 + 1/6*c + 1/30*c**l - 1/9*c**3 + 0*c**4 + 0*c**2. Factor a(r).
(r - 1)**2*(r + 1)**2/6
Let 8/7 - 2/7*i**2 - 2/7*i**3 + 8/7*i = 0. What is i?
-2, -1, 2
Let x(p) = p**3 - 6*p**2 + p - 1. Suppose -2*a = 3*a - 30. Let r be x(a). Determine g so that 0*g - 7*g**3 - r*g**2 + 2*g + 0*g**3 = 0.
-1, 0, 2/7
Let s be (44/297)/((-2)/(-3)). Factor 2/9*g**2 + s*g + 0.
2*g*(g + 1)/9
Suppose 0 - 7 = j. Let d = -4 - j. Factor -2*w**3 + 2*w**3 + 2*w + 2*w**5 - 4*w**d.
2*w*(w - 1)**2*(w + 1)**2
Let x(q) be the second derivative of 1/14*q**7 - 5/6*q**4 + 4/15*q**6 + q**2 + 0*q**5 + 0 - 1/2*q**3 + 2*q. What is y in x(y) = 0?
-2, -1, 1/3, 1
Let c(t) be the second derivative of 0*t**4 + 1/330*t**5 + 1/6*t**3 - 2*t - 1/1980*t**6 + 0 + 0*t**2. Let q(f) be the second derivative of c(f). Factor q(n).
-2*n*(n - 2)/11
Let k(o) = -7*o - 40. Let v be k(-6). Let a(s) be the second derivative of -2*s**v - s - 8/3*s**3 - 7/12*s**4 + 0. Find x such that a(x) = 0.
-2, -2/7
Let x(s) be the second derivative of -s**6/270 + s**5/60 - s**4/36 + s**3/54 - 13*s. Determine r, given that x(r) = 0.
0, 1
Let x(b) be the second derivative of b**4/6 + b**3 + 4*b. Find t such that x(t) = 0.
-3, 0
Let v be (9/12)/(2/(-8)). Let y be ((-6)/(0 - v))/(-6). Factor -y*q**3 + 1/3*q - 1/3 + 1/3*q**2.
-(q - 1)**2*(q