- 5*n(f). Factor p(c).
-2*c**2*(c + 1)*(c + 3)
Suppose -13*m + 19*m = -18. Let k(i) = 3*i**4 + 12*i**3 + 9*i**2 - 9*i - 9. Let w(j) = -j - 1. Let f(v) = m*w(v) - k(v). Factor f(t).
-3*(t - 1)*(t + 1)*(t + 2)**2
Let g(w) be the first derivative of -2*w**3/27 + 31*w**2/9 + 64*w/9 + 14. Suppose g(a) = 0. What is a?
-1, 32
Let t be (27/(-36))/((-10)/(-8) + -1). Let s be -7 + (-30)/t + 37/5. Solve -4/5 + s*y - 169/5*y**2 = 0.
2/13
Let a(d) = d**3 + 4*d**2 - 6*d - 22. Let i be a(-4). Factor 0 + 3/7*k**3 - 3/7*k + 0*k**i.
3*k*(k - 1)*(k + 1)/7
Determine a so that 6/7*a**2 - 1/7 + 1/7*a = 0.
-1/2, 1/3
Let b(p) = p**2 - 6. Let d be b(-5). Factor -d*x**2 + 2 + 1 - 9*x**3 - 14*x**2 - 3*x + 18*x**2.
-3*(x + 1)**2*(3*x - 1)
What is t in 11/2*t**4 + 25/2*t + 0 - 109/2*t**3 + 265/2*t**2 = 0?
-1/11, 0, 5
Let i(n) be the second derivative of 11*n**7/14 + 12*n**6/5 + 3*n**5/5 + n - 3. Factor i(b).
3*b**3*(b + 2)*(11*b + 2)
Let h = 361 + -356. Let f(s) be the first derivative of 3 + 1/9*s**2 - 2/45*s**h + 0*s - 1/18*s**4 + 2/27*s**3. Factor f(x).
-2*x*(x - 1)*(x + 1)**2/9
Let z = 16 + -9. Let a be z/(-28) + (-17)/(-4). Factor 18 + a*x**2 + 5*x - 2 + 10*x + 5*x.
4*(x + 1)*(x + 4)
What is c in -1/2*c**2 - 7 - 15/2*c = 0?
-14, -1
Suppose 315 = 29*d + 76*d. Let t(i) be the second derivative of -2*i**2 - 11*i - 1/6*i**4 - i**d + 0. Factor t(b).
-2*(b + 1)*(b + 2)
Let d(p) be the first derivative of 5/3*p**3 + 10*p - 15/2*p**2 - 15. Factor d(k).
5*(k - 2)*(k - 1)
Factor 24/5*x**2 + 4/5*x**3 + 0 + 32/5*x.
4*x*(x + 2)*(x + 4)/5
Let g(m) be the first derivative of -3*m**4/4 + 112*m**3 + 339*m**2/2 - 232. Suppose g(s) = 0. What is s?
-1, 0, 113
Let p(a) be the first derivative of 31 - 2*a**2 + 2*a**5 + 4*a**4 + 0*a + 2/3*a**3. Factor p(f).
2*f*(f + 1)**2*(5*f - 2)
Suppose 6*p - 2*p = 0. Let m(x) = x**2 + 5. Let b be m(p). What is l in -12 - 25*l**4 + 72*l - 32*l**4 + 29*l**4 - 171*l**2 + 201*l**3 + 27*l**b - 89*l**4 = 0?
2/3, 1
Let r(z) = -z**3 + 3*z**2 + 5*z. Let b be r(4). Suppose -o - 8 + 19 = 0. Factor o*j**3 + 27*j + 45*j**2 - 8*j**3 + 3*j**b + 18*j**3.
3*j*(j + 1)*(j + 3)**2
Factor -1/4*v**5 + 9/4*v - 2*v**3 + 1/2*v**2 - 3/2*v**4 + 1.
-(v - 1)*(v + 1)**3*(v + 4)/4
Let b(p) = -p - 1. Let f(g) = -2*g**2 - 85*g + 5. Let a(c) = -5*b(c) - f(c). Let a(w) = 0. What is w?
-45, 0
Let p(w) be the first derivative of -3*w**5/40 - w**4/2 - w**3 - 4*w + 17. Let y(i) be the first derivative of p(i). Factor y(t).
-3*t*(t + 2)**2/2
Suppose -184*v + 312*v - 60 - 40 + 5*v**3 - 233*v = 0. What is v?
-4, -1, 5
Let y(m) = 2*m**3 + m**2 - 3*m + 2. Let w be y(1). Let v(x) be the first derivative of 0*x + 2/5*x**w - 1 - 14/15*x**3. Solve v(t) = 0 for t.
0, 2/7
Let t be (-3)/(-2)*(3 - 1). Let -39*m**2 + 4*m**3 - t*m**3 + 37*m**2 = 0. Calculate m.
0, 2
Let w = -159 + 141. Let t be 12/w*30/(-5). Factor -8/3*b + 4/3*b**2 + 8/3*b**3 - 4/3*b**t + 0.
-4*b*(b - 2)*(b - 1)*(b + 1)/3
Solve 1/2*d**2 + 8 - 5*d = 0.
2, 8
Let m be (-4 + 13)*17/3. Suppose 5*b - 54 = m. Determine d so that 6*d**2 + b*d - 17*d + 2*d**2 + 4*d**3 = 0.
-1, 0
Suppose -2*r - 11 + 33 = 4*y, 3*r = -3*y + 21. Find d such that -4/7*d**4 + 0*d + 0*d**2 + 0 - 12/7*d**r = 0.
-3, 0
Let a(g) be the second derivative of 0 + 1/4*g**2 + 1/72*g**4 + 17*g + 1/9*g**3. Determine f, given that a(f) = 0.
-3, -1
Let y(g) = -g**2 + 2*g - 1. Let k(u) = -2*u**2 - 2*u + 4. Let f(q) = k(q) - y(q). Find s such that f(s) = 0.
-5, 1
Solve -95*k**3 + 10*k**4 + 10*k**4 - 24*k - 20*k**2 - 4*k**5 + 123*k**3 = 0 for k.
-1, 0, 1, 6
Let x(f) be the first derivative of f**4/36 + 20*f**3/27 + 19*f**2/18 - 241. Factor x(j).
j*(j + 1)*(j + 19)/9
Suppose 2*l = -q + 3, l + 8 - 32 = -5*q. Suppose -4 = -q*z + 16. Factor -3*r**z - 7*r**4 - 4*r**3 - 5*r + 5*r**4 - 11*r**3 - 15*r**2.
-5*r*(r + 1)**3
Let t(j) be the third derivative of j**8/7840 + j**7/882 + j**6/2520 - j**5/70 - j**4/2 - 10*j**2. Let l(p) be the second derivative of t(p). Factor l(m).
2*(m + 1)*(m + 3)*(3*m - 2)/7
Let n(m) be the second derivative of -2*m**7/315 - m**6/270 - m**3/2 - 3*m. Let c(b) be the second derivative of n(b). Let c(u) = 0. Calculate u.
-1/4, 0
Let j(y) be the first derivative of 5*y**6/6 + y**5 - 5*y**4/2 - 10*y**3/3 + 5*y**2/2 + 5*y - 6. Factor j(v).
5*(v - 1)**2*(v + 1)**3
Let l(k) be the second derivative of 0*k**3 + 0 + 0*k**2 - 11*k + 0*k**4 + 0*k**5 + 1/15*k**6 - 1/21*k**7. Determine a, given that l(a) = 0.
0, 1
Factor 43*p**2 - 32*p - 22*p**2 - 25*p**2.
-4*p*(p + 8)
Let -10/3*h**4 - 25/3*h + 8*h**3 + 1/3*h**5 + 10/3*h**2 + 0 = 0. Calculate h.
-1, 0, 1, 5
Factor 2*b**5 - 17785*b - 8*b**3 + 17785*b.
2*b**3*(b - 2)*(b + 2)
Let k(l) be the first derivative of l**3/21 + l**2 + 24*l/7 - 71. Factor k(c).
(c + 2)*(c + 12)/7
Let c be (6/4)/((-3)/(-4)). Let n be c/(-2) - (-15)/5. Solve k**2 - 2 - 1 + 2*k**n = 0 for k.
-1, 1
Let z(l) be the first derivative of -5*l**4/4 - 145*l**3 - 12615*l**2/2 - 121945*l + 17. Factor z(o).
-5*(o + 29)**3
Suppose -x - 33 = -56. Suppose -13 - x = -9*m. Let 0 + 2/11*u**m - 6/11*u**3 + 6/11*u**2 - 2/11*u = 0. Calculate u.
0, 1
Let j(m) be the second derivative of -m**8/336 - 17*m**7/504 - m**6/36 - 19*m**4/12 + m**2 - 35*m + 1. Let q(y) be the third derivative of j(y). Factor q(i).
-5*i*(i + 4)*(4*i + 1)
Let s(p) be the second derivative of -p**3/3 + 3*p**2/2 + 7*p. Let f be s(-2). Find y such that -2*y**2 + 0*y - 3*y**2 + f*y - 2*y = 0.
0, 1
Factor -1/4*m**4 - 1/4 - 1/2*m**3 + 1/4*m**5 + 1/2*m**2 + 1/4*m.
(m - 1)**3*(m + 1)**2/4
Let s be ((-11)/(-231) - -3) + (-1 - 2). Let b(q) be the second derivative of 7*q - 1/7*q**2 - s*q**3 + 1/42*q**4 + 0 + 1/70*q**5. Solve b(j) = 0.
-1, 1
Let s(r) be the second derivative of -r**8/840 + r**7/210 - r**6/180 - 13*r**3/6 - 2*r. Let w(g) be the second derivative of s(g). Factor w(v).
-2*v**2*(v - 1)**2
Factor 93*r**3 + 4*r**4 - 93*r**2 - 224 - 97*r**3 - 304*r - 27*r**2.
4*(r - 7)*(r + 2)**3
Let g(a) = 2*a**3 - a**2 - a. Let m(l) = -36*l**4 + 352*l**3 + 108*l**2 - 204*l + 36. Let i(d) = 20*g(d) - m(d). Factor i(z).
4*(z - 9)*(z + 1)*(3*z - 1)**2
Let k(v) be the third derivative of -1/135*v**5 - 1/108*v**4 + 4*v**2 + 0*v**3 - 1/540*v**6 + 0*v + 0. Factor k(u).
-2*u*(u + 1)**2/9
Let 8/3*j**2 + j - 5/3 = 0. What is j?
-1, 5/8
Let b(r) = r**2 + 10*r + 18. Let f be b(-8). Suppose -f*p = -6*p. Factor p*s**5 + s**3 + 3*s**5 - 5*s**3 + s**3.
3*s**3*(s - 1)*(s + 1)
Let k(q) = 105*q**4 - 690*q**3 - 465*q**2 + 258*q + 18. Let j(s) = -30*s**4 + 197*s**3 + 133*s**2 - 74*s - 5. Let n(o) = -18*j(o) - 5*k(o). Factor n(b).
3*b*(b - 7)*(b + 1)*(5*b - 2)
Suppose 66*p - 70*p + 5*i = 19, 0 = 5*i - 35. Let 4/3 - 10/3*u**3 - 14/3*u + 2/3*u**p + 6*u**2 = 0. Calculate u.
1, 2
Let v be 37*2/91 - (-12)/(-28). Let k(m) be the first derivative of 1/39*m**6 + 5/13*m**4 - 20/39*m**3 - 2/13*m + v*m**2 + 7 - 2/13*m**5. Factor k(s).
2*(s - 1)**5/13
Let o(g) be the first derivative of -g**5/90 - g**4/36 + 13*g**2/2 + 10. Let j(m) be the second derivative of o(m). What is s in j(s) = 0?
-1, 0
Let a = -8476/5 - -8504/5. Factor 4/5*m**3 + a*m - 12/5 - 4*m**2.
4*(m - 3)*(m - 1)**2/5
Suppose -5*x = 20, -2*u - 4*x - 15 + 3 = 0. Determine z, given that -3*z**u + 0*z**2 - 10*z + 13*z = 0.
0, 1
Let i be (-2)/(-140)*58 - (-172)/(-430). Factor i*p**2 + 18/7 - 15/7*p.
3*(p - 3)*(p - 2)/7
Let g(f) be the second derivative of -16*f**2 - 20*f - 28/3*f**3 + 17/3*f**4 + 0 + f**5. Factor g(b).
4*(b - 1)*(b + 4)*(5*b + 2)
Let m(k) = 2*k**2 - 5*k + 4. Let r be m(2). Factor -7*c**2 - r*c**3 + 16 + c**2 - c + 13*c.
-2*(c - 2)*(c + 1)*(c + 4)
Let r be (-1*(0 + 1))/(2/(-6)). Let x(y) be the second derivative of -3/20*y**5 + r*y + 1/10*y**6 + 1/16*y**4 + 0*y**2 + 0 + 0*y**3. Factor x(q).
3*q**2*(2*q - 1)**2/4
Suppose 0 = 4*n - 2 - 6. Determine k so that -7*k**n + 9*k**3 - 30*k**4 + 6*k**4 + 9*k**4 + k**5 + 2*k + 10*k**4 = 0.
0, 1, 2
Determine r, given that 4 - 22/5*r + 2/5*r**2 = 0.
1, 10
Suppose -52 - 61 - 22*k - 45 + 134 + 2*k**2 = 0. What is k?
-1, 12
Suppose 2*j = 0, 4*q = -5*j + 49 - 41. Let o(w) be the first derivative of 4*w - 10 - 23/5*w**5 + 35/4*w**4 + 5/6*w**6 - 17/3*w**3 - q*w**2. Factor o(h).
(h - 2)*(h - 1)**3*(5*h + 2)
Let c(a) be the second derivative of -a**9/30240 - a**8/13440 + a**7/5040 + a**6/1440 + a**4/6 + 5*a. Let r(z) be the third derivative of c(z)