ctor m(r).
(r - 3)**3*(r + 1)/6
Let v(m) be the second derivative of 0 + 0*m**2 - m + 2/3*m**4 + 1/10*m**6 - 11/20*m**5 + 2/3*m**3. Factor v(f).
f*(f - 2)**2*(3*f + 1)
Let g(u) = -7*u**4 - 4*u**3 - 7*u**2 - 5*u. Let b(x) = -x**4 - x**2 - x. Let q(k) = 5*b(k) - g(k). Factor q(o).
2*o**2*(o + 1)**2
Let f(p) = -3*p**3 - p**2 + 1. Let j(l) = 12*l**3 + 3*l**2 - l - 3. Let m(n) = -4*n - 10. Let v be m(-8). Let g(c) = v*f(c) + 6*j(c). Factor g(x).
2*(x - 1)*(x + 1)*(3*x - 2)
Determine n, given that 1/3*n - 1/2*n**2 + 1/2*n**4 - 1/6*n**5 + 0 - 1/6*n**3 = 0.
-1, 0, 1, 2
Let k = 1 + -1. Let m = -63/10 - -13/2. Factor k + m*x**3 - 1/5*x + 0*x**2.
x*(x - 1)*(x + 1)/5
Let i(q) be the first derivative of -2/5*q + 0*q**2 - 1 + 2/15*q**3. Determine o, given that i(o) = 0.
-1, 1
Factor -15*c**3 + 21*c + c**4 + 26*c**3 - 9 - 10*c**2 - 17*c**3 + c**5 + 2*c**4.
(c - 1)**3*(c + 3)**2
Let l(h) be the second derivative of -h**3 - 5/2*h**2 - 2*h + 5/12*h**4 + 0 + 1/20*h**5. Let y(u) = -5*u**2 + 5*u + 4. Let x(m) = 4*l(m) + 5*y(m). Factor x(p).
p*(p - 1)*(4*p - 1)
Let c(w) = w**3 - 9*w**2 + 8*w + 10. Let z be c(8). Let y be (-4)/z - 17/(-5). Find k such that -4/5 + 8/5*k - k**2 + 1/5*k**y = 0.
1, 2
Suppose 5*x = 10 + 10. Let j(m) be the second derivative of -2*m - 1/36*m**x + 0 - 1/6*m**2 + 1/9*m**3. Factor j(h).
-(h - 1)**2/3
Determine v so that -34/3*v**3 - 8/3*v**4 + 8/3 + 34/3*v + 0*v**2 = 0.
-4, -1, -1/4, 1
Let b(v) = v**4 - v**3 + v**2 - 1. Let a(d) = d**3 - 2*d**2 + 2. Suppose 2*z - 9 = -z. Let s(f) = z*a(f) + 6*b(f). Solve s(k) = 0.
0, 1/2
Suppose 4*y - 4*z - 20 = 0, 5*y + 5*z - 7 = z. Let m(t) = 2*t - 24. Let u be m(13). Factor 2*x**y + 4*x - 2*x - u*x**2 + 6*x**2.
2*x*(x + 1)**2
Let t(r) = -6*r**2 - 12*r + 11. Let n be ((-22)/(-6))/((-1)/3). Let a(j) = -2*j**2 - 4*j + 4. Let i(y) = n*a(y) + 4*t(y). Suppose i(q) = 0. What is q?
-2, 0
Suppose 4*r + 0 - 20 = 0. Let w = 9 - r. Find c such that -4*c - 6*c**3 + 2*c + 0*c**4 - 6*c**2 - 2*c**w = 0.
-1, 0
Let m = 104/5 - 3026/145. Let t = m + 64/87. Suppose 4/3*u**2 - t*u + 0 - 2/3*u**3 = 0. What is u?
0, 1
Let k(f) be the third derivative of 0*f + 0 + 1/840*f**8 + 6*f**2 + 0*f**3 + 1/75*f**5 + 0*f**6 - 2/525*f**7 - 1/60*f**4. What is v in k(v) = 0?
-1, 0, 1
Suppose q**2 + 5*q**4 - 6*q**2 - 8*q**3 + 13*q**3 - 5*q**5 = 0. Calculate q.
-1, 0, 1
Let i(v) = 2*v**2 + 4*v. Let z(f) = -2*f**2 - 5*f. Let g(x) = -5*i(x) - 4*z(x). Factor g(n).
-2*n**2
Suppose -156/5*p - 3/5*p**5 - 111/5*p**3 - 192/5*p**2 - 48/5 - 6*p**4 = 0. What is p?
-4, -2, -1
Factor 8*u + 8*u - 4*u**2 - u**2 + 9*u**2.
4*u*(u + 4)
Find b, given that 12/13*b**2 - 18/13*b + 0 - 2/13*b**3 = 0.
0, 3
Let b(p) be the third derivative of -p**7/336 - 13*p**6/960 + p**5/80 + 5*p**4/48 - p**3/6 - 21*p**2. Find n, given that b(n) = 0.
-2, 2/5, 1
Suppose -y = -240 - 104. Let s = 2416/7 - y. Find r such that 22/7*r**2 - 50/7*r**4 - 24/7*r - s + 60/7*r**3 = 0.
-2/5, 1
Factor 0*b**2 + 1/6*b**3 + 1/6*b**5 + 0*b + 0 - 1/3*b**4.
b**3*(b - 1)**2/6
Let p(g) = g**2 + 10*g + 3. Let h be p(-10). Let t(v) be the first derivative of 0*v**2 + 0*v - 2/5*v**5 - 1/2*v**4 + 0*v**3 - h. Factor t(s).
-2*s**3*(s + 1)
Solve 1/4*d**3 - d**2 + 0 + 0*d = 0 for d.
0, 4
Factor 37*n**3 + 5*n**2 + 4*n**5 + 20*n**4 - 41*n**2 - 25*n**3.
4*n**2*(n - 1)*(n + 3)**2
Factor 2 - 1/2*i**3 + 7/2*i + i**2.
-(i - 4)*(i + 1)**2/2
Suppose m + 5 = 2*m. Suppose -5*v = 3*n - 0*n - 70, m*n - 3 = 2*v. Factor -10*o**2 - 4 + v*o - 7*o + 10*o.
-2*(o - 1)*(5*o - 2)
Let s be (-10)/(-25) + (-26)/(-10). Factor 2*i**4 - 2*i**3 + 5*i**3 - 3*i**3 + 2*i**s.
2*i**3*(i + 1)
Let s(n) be the first derivative of -n**5/90 + n**4/18 + 3*n**2 + 4. Let l(h) be the second derivative of s(h). Suppose l(z) = 0. What is z?
0, 2
Let t(b) = b**2 - 4*b + 2. Let q be t(5). Let f = -4 + q. Let d**3 + 2*d - 2*d**f - d = 0. What is d?
-1, 0, 1
Let d(i) be the first derivative of -i**6/9 + 2*i**5/15 + 2*i**4/3 - 8*i**3/9 + 29. What is x in d(x) = 0?
-2, 0, 1, 2
Let s(n) be the first derivative of n**6/180 + n**5/60 - n**4/6 + 2*n**3/3 - 3. Let i(f) be the third derivative of s(f). What is y in i(y) = 0?
-2, 1
Let j(h) be the first derivative of h**6/2 + 6*h**5 + 99*h**4/4 + 40*h**3 + 24*h**2 - 3. Factor j(l).
3*l*(l + 1)**2*(l + 4)**2
Factor -6*s**2 - 3*s**4 + 2*s**4 + 4*s**2 + 3*s**2.
-s**2*(s - 1)*(s + 1)
Let g(z) be the first derivative of z**6/3 + 4*z**5/5 + z**4/2 - 15. Factor g(s).
2*s**3*(s + 1)**2
Let x = -51 + 53. Determine v, given that -2/3*v**5 - 8/3*v**4 - 8/3*v**x + 0 - 2/3*v - 4*v**3 = 0.
-1, 0
Let o = 75 + -70. Let f(m) be the first derivative of 0*m**3 + 0*m**2 + 4 + 1/16*m**4 + 0*m - 1/20*m**o. Suppose f(l) = 0. What is l?
0, 1
Suppose 0 = 3*c - 44 + 32. Factor 0 - 1/3*u**2 + 1/3*u**c - 2/3*u + 2/3*u**3.
u*(u - 1)*(u + 1)*(u + 2)/3
Suppose -v - 14 = -3*r, -2*v + 24 = 4*r + 2*v. Suppose -4*o**3 + o - 2*o**4 - 2*o**5 - 2 + 3*o + 4*o**2 - 2*o + 4*o**r = 0. What is o?
-1, 1
Let g(r) be the first derivative of r**5/40 + r - 3. Let v(t) be the first derivative of g(t). Find b such that v(b) = 0.
0
Let l(r) be the third derivative of -1/240*r**6 + 0*r**4 - 3*r**2 + 0*r + 0*r**5 + 0 + 0*r**3. Find p such that l(p) = 0.
0
Let t = 23 + -21. Let x(n) be the third derivative of 0*n**3 + 0*n + 0*n**4 + 1/60*n**5 + 0 - 1/120*n**6 - 2*n**t. What is k in x(k) = 0?
0, 1
Let r(p) be the first derivative of 0*p + 1 + 0*p**2 + 2/15*p**5 + 1/3*p**4 + 2/9*p**3. Determine z so that r(z) = 0.
-1, 0
Factor 7*r + 6 + 5*r - 6 + 4*r**2.
4*r*(r + 3)
Suppose 5*l = y - 4, 0*l + 2*l - 2*y = -8. Factor 0 + l*m + 2/11*m**2 + 2/11*m**3.
2*m**2*(m + 1)/11
Let l(x) be the first derivative of -5 + 1/24*x**6 + 1/12*x**3 + 0*x - 1/16*x**4 + 0*x**2 - 1/20*x**5. Factor l(m).
m**2*(m - 1)**2*(m + 1)/4
Suppose -24/7*z + 8/7 + 10/7*z**2 = 0. What is z?
2/5, 2
Let z be 10/(-45)*(-12)/8. Factor z*w**5 - 2/3*w**2 - w - 1/3 + w**4 + 2/3*w**3.
(w - 1)*(w + 1)**4/3
Let -2/3*l**2 + 2/3*l**4 + 0 + 0*l + 0*l**3 = 0. Calculate l.
-1, 0, 1
Let k(t) be the third derivative of -t**5/20 - 7*t**4/8 + 4*t**3 - 15*t**2. Find p, given that k(p) = 0.
-8, 1
Let d(v) = -v**3 - v**2 - 1. Let x(q) = 39*q**3 + 67*q**2 - 16*q + 3. Let c(z) = -3*d(z) - x(z). Let c(u) = 0. What is u?
-2, 0, 2/9
Factor 1/3*x**3 + 36*x + 6*x**2 + 72.
(x + 6)**3/3
Find f such that -3*f**2 + 1/4*f**4 - 4*f + 0*f**3 + 0 = 0.
-2, 0, 4
Let n(c) be the third derivative of -c**7/525 - c**6/100 - 4*c**2. Factor n(m).
-2*m**3*(m + 3)/5
Let c be 10/6 + ((-222)/36 - -6). Factor v**2 - 3/2*v**4 + 1/2 - 1/2*v**5 + c*v - v**3.
-(v - 1)*(v + 1)**4/2
Let -162/7 - 108/7*o**2 - 2/7*o**4 - 24/7*o**3 - 216/7*o = 0. What is o?
-3
Factor 75/4*m**4 + 138*m**2 - 72*m - 90*m**3 + 12.
3*(m - 2)**2*(5*m - 2)**2/4
Let b = -9 + 3. Let d be (16/b - -3) + 1. Solve 2*w**2 + 0 - 2*w**4 - d*w**3 + 4/3*w = 0 for w.
-1, -2/3, 0, 1
Let t(j) be the second derivative of 6*j + 3/4*j**4 - 3/4*j**2 + 21/80*j**5 + 3/8*j**3 + 0. Suppose t(o) = 0. Calculate o.
-1, 2/7
Suppose -20/3*z**4 + 8/3*z**3 - 4/3 - 4*z**5 + 8*z**2 + 4/3*z = 0. What is z?
-1, 1/3, 1
Let q be 2 - (-2)/(-24)*20. Let -1/3*d**2 + q*d + 2/3 = 0. Calculate d.
-1, 2
Let y(h) be the first derivative of -5*h**4/4 - 5*h**3 + 27. Determine c so that y(c) = 0.
-3, 0
Factor 2*x**4 + 2*x**3 + 26*x**2 - 26*x**2.
2*x**3*(x + 1)
Factor -3/2*v - v**2 + 1/2*v**5 + 3/2*v**4 + v**3 - 1/2.
(v - 1)*(v + 1)**4/2
Let o(j) be the second derivative of -j**5/10 - 7*j**4/12 - 2*j**3/3 + j**2/2 - j. Let s(k) be the first derivative of o(k). Determine p, given that s(p) = 0.
-2, -1/3
Find o, given that -2*o + 8/3*o**3 + 2/3 + 0*o**2 = 0.
-1, 1/2
Let t(o) be the first derivative of -o**3/3 + 5*o**2/2 - 4*o - 32. Factor t(a).
-(a - 4)*(a - 1)
Suppose -5*c + 8 = -c. What is z in -2*z**2 - 5*z + c*z + z = 0?
-1, 0
Let a(p) be the third derivative of p**6/2160 + p**5/360 - p**4/48 - p**3/6 - 10*p**2. Let k(q) be the first derivative of a(q). Factor k(u).
(u - 1)*(u + 3)/6
Find n, given that -3/4*n**4 + 0*n - 1/4*n**2 - 3/4*n**3 - 1/4*n**5 + 0 = 0.
-1, 0
Suppose -10*u + 21 = -19. Solve 2/13*j**3 + 0*j**2 - 2/13*j**u + 0*j + 0 = 0 for j.
0, 1
Let -10*m - 15*m - 50*m**3 - 5*m**4 - 4*m**4 - 50*m**2 - 5*m**5 - 16*m**4 - 5 = 0. What is m?
-1
Let f = -20 + 43/2. Let x = 31/2 + -15. Factor f*w**3 + 0 - w**2 - x*w.
w*(w - 1)*(3*w