*n**3 - 4*n - n.
5*n*(n - 1)*(n + 1)
Determine k so that 2*k**4 - k**3 - 9*k**2 - 2*k**3 + 13*k**2 - 6 - 5*k**3 + 8*k = 0.
-1, 1, 3
Let k(j) be the first derivative of 7*j**4/16 + j**3/6 - 7*j**2/8 - j/2 + 53. Factor k(w).
(w - 1)*(w + 1)*(7*w + 2)/4
Suppose -4*d - d + 5 = 0. Let a be (0*(-1 + 0))/d. Solve -2/5*z**2 + 0*z + 2/5*z**4 + 0*z**3 + a = 0.
-1, 0, 1
Let r(m) be the second derivative of m**4/4 - m**3 - 12*m**2 + 24*m + 2. Find q, given that r(q) = 0.
-2, 4
Factor 92*n**2 - 264*n - 500*n**3 + 433*n**2 + 36 + 353*n**3.
-3*(n - 3)*(7*n - 2)**2
Let c(g) = 12*g**4 - 225*g**3 + 963*g**2 + 9. Let q(z) = 3*z**4 - 56*z**3 + 241*z**2 + 2. Let p(j) = -2*c(j) + 9*q(j). Let p(s) = 0. Calculate s.
0, 9
Suppose 0 = 6*z - 2*z - 16. Let q(v) be the first derivative of -1/5*v**5 - 3/4*v**z + 1 - v**3 - 1/2*v**2 + 0*v. Factor q(k).
-k*(k + 1)**3
Let i(z) be the first derivative of 4*z**6/51 + 2*z**5/5 + 14*z**4/17 + 44*z**3/51 + 8*z**2/17 + 2*z/17 - 36. Factor i(t).
2*(t + 1)**4*(4*t + 1)/17
Let w be 138/184*((-2)/6)/(-1). Factor w*j**3 + 3/4*j + 1/4 + 3/4*j**2.
(j + 1)**3/4
What is u in -10/13*u**2 + 2/13*u**4 + 2/13*u**5 - 6/13*u**3 - 4/13*u + 0 = 0?
-1, 0, 2
Suppose g = 8*g - 21. Let r(c) be the first derivative of 1/4*c**2 + 0*c**g - 1/20*c**5 + 1/4*c - 1/8*c**4 - 4. Solve r(i) = 0 for i.
-1, 1
Let t(m) = m - 3. Let z be t(4). Let s(o) = 5*o**4 - 2*o**3 - 3*o**2 + 4. Let j(r) = r**4 - r**2 + 1. Let h(w) = z*s(w) - 4*j(w). Let h(d) = 0. What is d?
0, 1
Let m = -324 - -324. Factor 2/7*f**3 + m*f**2 + 0*f + 0.
2*f**3/7
Suppose a + 1 = d, 2*d + 3*d + 5 = -5*a. Let o(j) be the second derivative of -3*j + 0 + 1/30*j**6 + d*j**2 + 0*j**3 + 1/12*j**4 - 1/10*j**5. Factor o(v).
v**2*(v - 1)**2
Let o = 13 - 9. Let j = -1 + o. Factor -2/5*r**5 + 0 - 2/5*r + 4/5*r**j + 0*r**4 + 0*r**2.
-2*r*(r - 1)**2*(r + 1)**2/5
Let m(x) = x + 1. Let h(w) = w**2 + 3*w + 4. Let y(u) = h(u) + 3*m(u). Let p be y(-5). Let 3*d**3 + 0*d**2 + 3*d**2 - d**p = 0. What is d?
-2/3, 0
Suppose 2*n - 3 = n. Let v be n/(-6) + (-7)/(-6). Factor -8/3*c**2 - 8/3*c**4 + 4*c**3 + v*c**5 + 0 + 2/3*c.
2*c*(c - 1)**4/3
Let o be (-3 + (-2 - -8))*1. Suppose -15*y**2 - 8*y**3 + y**o - 6*y + 2*y - y**4 - 5*y = 0. Calculate y.
-3, -1, 0
Let l(w) = -w**2 + 2*w. Let f(m) = 14*m**2 - 4*m. Let o(u) = -f(u) - 12*l(u). Solve o(s) = 0 for s.
-10, 0
Factor 1/2*p**4 + 1 + 1/2*p**3 - 1/2*p - 3/2*p**2.
(p - 1)**2*(p + 1)*(p + 2)/2
Let x(f) = -8*f**3 + 8*f**2 - 4*f. Let w(c) = -7*c**3 + 9*c**2 - 5*c. Let z(u) = 4*w(u) - 3*x(u). Factor z(t).
-4*t*(t - 2)*(t - 1)
Let l(f) be the third derivative of 1/30*f**5 + 0*f - f**2 + 4/3*f**3 + 0 - 5/12*f**4. Factor l(x).
2*(x - 4)*(x - 1)
Let i = -3387/2840 - -90/71. Let m(z) be the third derivative of 1/100*z**5 + 0*z + 1/5*z**3 - 4*z**2 - i*z**4 + 0. What is y in m(y) = 0?
1, 2
Suppose 18 = -4*z + 5*z. Let c = z + -18. Find d, given that 4/3*d**4 + c + 0*d**2 - 2/3*d**5 - 2/3*d**3 + 0*d = 0.
0, 1
Find k such that -3/8*k**4 + 0*k**2 + 0*k - 1/2*k**3 + 1/8*k**5 + 0 = 0.
-1, 0, 4
Let v = 9 + -4. Suppose -v = -5*l, -3*h - l + 11 = 4*l. Solve 0*m**h - 2*m - m**2 - m**2 = 0.
-1, 0
Let b(d) = d**3 - d**2 - 3*d**3 - d + 3*d**3 + 3. Let h be b(0). Let -h*k**5 - 6*k**3 + 4*k**4 + 2*k**5 + 4*k**2 - k + 0*k = 0. What is k?
0, 1
Factor -8/9*s - 2/9*s**4 + 4/9*s**3 - 8/9 + 2/3*s**2.
-2*(s - 2)**2*(s + 1)**2/9
Factor 0 - 5/2*b + 5/2*b**2.
5*b*(b - 1)/2
Let i(z) = -z**2 - 1. Let a(q) = 2*q**3 + 4. Let j(m) = a(m) + 4*i(m). Factor j(p).
2*p**2*(p - 2)
Let s(d) be the third derivative of -d**9/30240 - d**8/5040 + d**5/20 - d**2. Let x(o) be the third derivative of s(o). Factor x(j).
-2*j**2*(j + 2)
Let y(v) be the third derivative of -v**5/6 - 13*v**4/36 + 2*v**3/9 - 8*v**2. Solve y(h) = 0.
-1, 2/15
Factor 0*j - 1/3 + 1/3*j**2.
(j - 1)*(j + 1)/3
Let t = -58 + 62. Let s(l) be the second derivative of -1/3*l**3 - 1/12*l**t + 4*l - 1/2*l**2 + 0. Let s(i) = 0. Calculate i.
-1
Let v(h) = 5*h**3 + 4*h**2 + h + 2. Let p(o) = o**3 - o. Let f(k) = -k + 7. Let n be f(3). Let a(u) = n*p(u) - v(u). Factor a(g).
-(g + 1)**2*(g + 2)
Let k(n) = -18*n + 38. Let s be k(2). Let r = -98/3 + 33. Let -a + r*a**s + a**3 - 2/3 + 1/3*a**4 = 0. What is a?
-2, -1, 1
Suppose 3*j = 5*i - 7, 11*i - 4*j + 10 = 14*i. Factor 2/13*o**3 + 8/13 + 16/13*o + 10/13*o**i.
2*(o + 1)*(o + 2)**2/13
Let v(s) be the third derivative of 0*s**3 - 3*s**2 + 0*s + 0 + 0*s**5 - 1/72*s**4 + 1/360*s**6. Find a, given that v(a) = 0.
-1, 0, 1
Factor 0 + 4/7*m + 0*m**2 - 8/7*m**3 + 4/7*m**5 + 0*m**4.
4*m*(m - 1)**2*(m + 1)**2/7
Let q(x) be the third derivative of x**5/70 + 9*x**4/56 + 2*x**3/7 - 6*x**2. Factor q(r).
3*(r + 4)*(2*r + 1)/7
Let g be ((-1)/(-2))/((-1)/22). Let b = g + 15. Solve -b*r**5 + 3*r**3 + 17/3*r**4 + 2/3 - 19/3*r**2 + r = 0.
-1, -1/4, 2/3, 1
Let p(l) = -l**4 + 6*l**3 - 6*l**2 + 6. Let k(h) = -2*h**4 + 7*h**3 - 7*h**2 + 7. Let b(z) = 6*k(z) - 7*p(z). Let b(y) = 0. What is y?
0
Let w(l) = l**4 - l**3 - l**2 - l - 1. Let q(a) = -3*a**4 + 9*a**3 + 3*a**2 + 3*a + 6. Let b be 3 - (-1 + (-6)/(-2)). Let c(y) = b*q(y) + 6*w(y). Factor c(s).
3*s*(s - 1)*(s + 1)**2
Suppose 3*x - 24 = -2*x - 4*w, -5*w = 3*x - 17. Suppose -x*n + 15*n**4 - 9*n**2 - 7*n**4 + n**2 + 0*n + 4*n**5 = 0. Calculate n.
-1, 0, 1
Let i = -7/33 - -25/66. Let y(w) be the third derivative of 0 + 0*w - 3*w**2 - 1/60*w**5 - 1/12*w**4 - i*w**3. Factor y(d).
-(d + 1)**2
Let k(t) be the first derivative of -5*t**3/3 - 10*t**2 - 15*t + 6. Factor k(i).
-5*(i + 1)*(i + 3)
Find w such that -17*w**4 - 38*w**3 - 17*w**4 - 36*w - 64*w**2 - 18*w**3 - 4*w**5 - 8 + 10*w**4 = 0.
-2, -1
Let y(k) = -k**5 - k**4 - k**3. Let g(n) = -2*n**5 - 8*n**4 - 4*n**3 + 4*n**2 - 2*n. Let t(b) = g(b) - 4*y(b). Factor t(p).
2*p*(p - 1)**3*(p + 1)
Let a(m) be the first derivative of -m**5/30 + m**4/24 + m**3/18 - m**2/12 - 7. Factor a(j).
-j*(j - 1)**2*(j + 1)/6
Let l(j) be the first derivative of -5/9*j**2 + 4 - 16/9*j**5 + 16/27*j**6 + 25/18*j**4 - 2/9*j + 10/27*j**3. Factor l(k).
2*(k - 1)**3*(4*k + 1)**2/9
Let j = 8 - -13. Let c = j - 19. Suppose 0 + 7/2*n**3 + n + 9/2*n**c = 0. Calculate n.
-1, -2/7, 0
Let c = 1 + -7. Let k = c - -10. Factor 4*a**3 + 0*a**3 + 6*a**k + 0*a**3.
2*a**3*(3*a + 2)
Let g(r) be the second derivative of -2/3*r**2 - 1/5*r**5 + 0 + 2/3*r**3 - 5/36*r**4 + 7*r + 1/10*r**6. Factor g(c).
(c - 1)*(c + 1)*(3*c - 2)**2/3
Factor 10*s**3 + 12*s**2 - 13*s**3 - 7*s + 6 - 8*s.
-3*(s - 2)*(s - 1)**2
Factor 4*z**2 + 2*z**2 - 6*z**4 - 3*z**5 + 2 - 2 + 3*z.
-3*z*(z - 1)*(z + 1)**3
Let l(z) = -4*z + 47. Let o be l(11). Factor 2/11*m**o - 6/11*m**2 - 2/11 + 6/11*m.
2*(m - 1)**3/11
Let n be (-2 - 16/(-12))*-3. Factor -1 - 1 + l - l**5 + 2*l + 4*l**n + 2*l**3 - 4*l - 2*l**4.
-(l - 1)**2*(l + 1)**2*(l + 2)
Let m(v) = v + 1. Let p(y) = -2*y**2 - y - 9. Let i(s) = -6*m(s) - p(s). Factor i(j).
(j - 1)*(2*j - 3)
Let x(c) = -25*c**4 + 23*c**3 - 8*c**2 - 5. Let m(q) = q**4 + q**3 + 1. Let k(n) = -5*m(n) - x(n). Factor k(d).
4*d**2*(d - 1)*(5*d - 2)
Let o(p) be the third derivative of -p**10/151200 + 7*p**5/60 + 8*p**2. Let l(y) be the third derivative of o(y). Find a such that l(a) = 0.
0
Let l(q) be the second derivative of -q**4/36 + 2*q**2/3 + 4*q. Factor l(r).
-(r - 2)*(r + 2)/3
Factor 2*k**3 + 10/7*k + 22/7*k**2 + 2/7*k**4 + 0.
2*k*(k + 1)**2*(k + 5)/7
Let v(o) = -2*o - 2. Let d be v(-1). Let y(c) be the second derivative of c + 0*c**3 + d*c**4 + 0*c**2 + 0 + 1/10*c**5. Solve y(z) = 0.
0
Let f(a) = 8*a**4 - 8*a**3 + 3*a**2 - 5*a + 2. Let h(q) = -q**4 + q**3. Let t(j) = 2*f(j) + 18*h(j). Factor t(r).
-2*(r - 1)**3*(r + 2)
Let v = -18 + 20. Suppose -2*h = -0*h - v, -3*l + 10 = h. Suppose -m + m**2 + 1/3 - 1/3*m**l = 0. Calculate m.
1
Let x be (21/12 + 2)*-36. Let i = 947/7 + x. Factor i + 0*v - 2/7*v**2.
-2*(v - 1)*(v + 1)/7
Let b(n) be the second derivative of -n**5/60 + 2*n**2 + 2*n. Let u(m) be the first derivative of b(m). Factor u(k).
-k**2
Let -3/7 + 1/7*m**4 + 0*m**3 - 8/7*m - 6/7*m**2 = 0. What is m?
-1, 3
Let p(k) be the second derivative of -k**4/8 - k**3/4 - 38*k. Factor p(z).
-3*z*(z + 1)/2
Let c(d) be the third derivative of -1/20*d**5 - 1/12*d**3 + 1/12*d**4 + 0*d + d**2 + 1/60*d**6 + 0 - 1/420*d**7. Factor c(o).
-(o - 1)**4/2
Let s(w) = 3*w**4 - 9*w**3 + 5*w**2 + 3*w - 8. Let y(