*(w - 1)*(w + 1)*(w + 10)
Factor 19 + 12*x + 4*x**2 + 32 - 43.
4*(x + 1)*(x + 2)
Let v(t) = -4*t**3 - t - 1. Let m be v(-1). Suppose -m*d - 8 = -16. Factor -2*j**2 + 4*j**2 + 2*j**2 - 6*j**d.
-2*j**2
Let h(p) = 3*p**3 + 2*p**2 + 2*p. Suppose -4*k = 6*k + 20. Let c(r) = 16*r**3 + 10*r**2 + 11*r. Let d(n) = k*c(n) + 11*h(n). Let d(x) = 0. Calculate x.
-2, 0
Suppose -z = 33 - 35. Determine f, given that -6 + 0 - f**2 + z*f**2 + 5 = 0.
-1, 1
Let p(u) be the first derivative of -1/6*u**6 - 27*u - 5/2*u**4 + 4 - 7/5*u**5 + 27/2*u**2 + 6*u**3. Solve p(c) = 0.
-3, 1
Let f(o) be the first derivative of 16 + 8/21*o**3 + 1/14*o**4 - 2/35*o**5 - 4/7*o**2 + 0*o. Factor f(y).
-2*y*(y - 2)*(y - 1)*(y + 2)/7
Suppose -5 = 5*f, -5*f = -29*z + 25*z + 5. Let r(p) be the first derivative of 0*p**2 - 1 + 1/10*p**4 + 0*p**3 - 2/25*p**5 + z*p. Factor r(n).
-2*n**3*(n - 1)/5
Let n = 6224 - 24895/4. Suppose 4 = 5*o - 3*o. Determine u, given that -1 - n*u**3 + 0*u + 3/4*u**o = 0.
-1, 2
Let o = 6561/7 - 19613/21. Factor 0*g**2 + 5/3*g**5 + 5/3*g + 0 - o*g**3 + 0*g**4.
5*g*(g - 1)**2*(g + 1)**2/3
What is a in 35*a**3 + 2*a**4 - 2*a**4 + 20*a**2 - 60*a**2 + 5*a**4 = 0?
-8, 0, 1
Let v = 110 + -107. Let k(l) be the first derivative of -1/6*l**v - 4 + 3/2*l + 1/2*l**2. Factor k(u).
-(u - 3)*(u + 1)/2
Let c(k) = -k**2 - 7*k - 4. Let a be c(-6). What is z in -z**2 - 4*z**3 + 6*z**4 + 17*z**a - 8*z + 24*z - 10*z**4 = 0?
-2, -1, 0, 2
Let o(d) be the second derivative of d**7/210 - 2*d**5/15 - 9*d**3/2 - 14*d. Let c(i) be the second derivative of o(i). Let c(q) = 0. Calculate q.
-2, 0, 2
Let o be -4*92/32*-2. Let m = o - 20. Let 2 - 4*b**m - b - 2*b**4 + b + 4*b = 0. What is b?
-1, 1
Let g(j) be the second derivative of j**4/6 - 22*j**3/3 + 62*j + 3. Factor g(x).
2*x*(x - 22)
Let 3969*b + 2079/4*b**2 + 27783/8 + 3/8*b**4 + 24*b**3 = 0. What is b?
-21, -1
Let q(b) be the first derivative of 8/21*b**3 - 11/14*b**4 + 18/35*b**5 - 35 + 3/14*b**2 - 2/7*b - 5/42*b**6. Factor q(y).
-(y - 1)**4*(5*y + 2)/7
Let g = 262/777 - 1/259. Let i(d) be the first derivative of -1/12*d**4 - g*d**3 + 0*d - 2 - 1/3*d**2. Determine k so that i(k) = 0.
-2, -1, 0
Let o(s) be the third derivative of s**7/105 + 3*s**6/20 - 7*s**5/10 + 11*s**4/12 + 191*s**2. Solve o(u) = 0.
-11, 0, 1
Let -12/7*g - 1/7*g**2 + 13/7 = 0. What is g?
-13, 1
Let 4 - 2/9*d**2 - 14/9*d = 0. Calculate d.
-9, 2
Let k = -7091/9 - -788. Solve -k*w**3 - 1/9*w**4 + 1/3*w**2 + 1/9*w - 2/9 = 0 for w.
-2, -1, 1
Let k(g) = g**2 - 13*g - 10. Let d be k(-1). Let f(x) be the first derivative of 0*x - 9/4*x**4 + d + 0*x**2 + 2/3*x**3. Factor f(n).
-n**2*(9*n - 2)
Let v(a) be the first derivative of 9/8*a**3 - 9/16*a**2 + 1/8*a - 27/32*a**4 - 45. Factor v(b).
-(3*b - 1)**3/8
What is v in -86/11*v**2 + 24/11*v**3 + 120/11*v - 2/11*v**4 - 56/11 = 0?
1, 2, 7
Let v be 2/4*(2710/(-5) - -4). Let g = v + 1081/4. Factor -q**2 + 0*q + 0 + 2*q**3 + 1/4*q**5 - g*q**4.
q**2*(q - 2)**2*(q - 1)/4
Let m(o) = 15*o**3 + 38*o**2 + 78*o + 40. Let l(v) = -13*v**3 - 38*v**2 - 79*v - 40. Let i(k) = 6*l(k) + 5*m(k). Let i(w) = 0. What is w?
-10, -2, -2/3
Let i(f) be the first derivative of -f**3/6 - 11*f**2/4 + 21*f + 33. Solve i(x) = 0.
-14, 3
Let p(a) be the second derivative of 10/21*a**7 + 29*a + 3/2*a**6 - 5*a**3 + 0 - 10/3*a**4 - 5/2*a**2 + 1/2*a**5. Determine v, given that p(v) = 0.
-1, -1/4, 1
Let y be 2/(-5)*10/(-8). Let v = 1043/694 - 1/347. Suppose -v*c**3 + y*c**5 + 0 + c + 1/2*c**4 - 1/2*c**2 = 0. What is c?
-2, -1, 0, 1
Let -25 - 2*y**2 - 48*y - 11*y**2 + 9*y**2 - 19 = 0. What is y?
-11, -1
Let y(n) be the second derivative of n**4/12 + 2*n**3 - 43*n**2/2 + 55*n. Let h be y(-15). Factor 9/2*a - 3*a**h + 0.
-3*a*(2*a - 3)/2
Suppose -4*b = -5*k + 12 + 7, 4*k = -3*b + 9. Let f be 0/4*b*1/1. Factor 0 + 6/7*x**4 + 0*x**2 + 8/7*x**5 - 2/7*x**3 + f*x.
2*x**3*(x + 1)*(4*x - 1)/7
Let i(y) = -y - 5. Let s be i(-11). Suppose 0 = d - s*d + 10. Determine r, given that -4 - 2*r - 2*r + 6*r**d - 4*r**2 + 6*r = 0.
-2, 1
Factor -26*a**2 + 5*a**3 + 6*a**2 - 54*a + 69*a.
5*a*(a - 3)*(a - 1)
Let z(g) be the third derivative of -g**7/10 + g**6/8 + 4*g**5/5 + g**4/2 + 2*g**2 - 4. Factor z(w).
-3*w*(w - 2)*(w + 1)*(7*w + 2)
Let c be ((-52)/(-6))/((-9)/27). Let o = 26 + c. Determine i, given that -1/6*i**4 + o*i**2 + 0 + 0*i + 0*i**3 + 1/6*i**5 = 0.
0, 1
Suppose 0 = -5*f + 41*f. Factor -2/11*n**5 + 0*n + f + 0*n**2 - 2/11*n**3 - 4/11*n**4.
-2*n**3*(n + 1)**2/11
Let z(n) = 4*n**2 + 388*n + 8836. Let q(h) = 4*h**2 + 385*h + 8836. Let y(w) = -4*q(w) + 3*z(w). Factor y(d).
-4*(d + 47)**2
Let g(x) = x**2 + 2*x. Let t(l) = 3*l**2 - l + 36. Let c(q) = 4*g(q) - t(q). Factor c(j).
(j - 3)*(j + 12)
Factor 5*g**3 - 3*g**3 + 5046*g - 18*g**2 + 101*g**2 + 91*g**2 + 48778.
2*(g + 29)**3
Factor 2 - 36*c**4 - 144*c - 2 - 12*c**2 + 39*c**3 + 373*c**5 - 369*c**5 + 53*c**3.
4*c*(c - 4)*(c - 3)**2*(c + 1)
Find m such that 3/2*m**3 - 5/3 - 1/6*m**4 + 9/2*m - 25/6*m**2 = 0.
1, 2, 5
Let z(w) be the third derivative of 0 + 7/6*w**4 + 1/2*w**5 - 5*w**2 + 0*w - 1/112*w**8 + 4/3*w**3 + 1/24*w**6 - 4/105*w**7. Solve z(b) = 0.
-2, -1, -2/3, 2
Let p(m) = m**3 - 2*m**2 + m - 2. Let s(h) = -6*h**3 + 10*h**2 - 6*h + 11. Let k(i) = -3*i + 27. Let l be k(20). Let b(r) = l*p(r) - 6*s(r). Factor b(v).
3*v*(v + 1)**2
Suppose 9/7*h**4 + 0 + 9/7*h**2 - 4/7*h**5 + 26/7*h**3 - 4/7*h = 0. What is h?
-1, 0, 1/4, 4
Let g(m) be the third derivative of -m**6/210 + m**5/35 - m**4/14 + 2*m**3/21 + 5*m**2 + 8*m. Factor g(j).
-4*(j - 1)**3/7
Let g(w) be the third derivative of -w**7/70 - w**6/8 + 3*w**5/5 + 10*w**4 + 32*w**3 - 516*w**2. Factor g(d).
-3*(d - 4)*(d + 1)*(d + 4)**2
Let x be 16/(-136) + 432/(-85). Let r = x + 57/10. Factor 1 + 3/2*b + r*b**2.
(b + 1)*(b + 2)/2
Suppose 4*y + a = 17, 0 = -65*y + 62*y - a + 14. Factor 13/4*s + 3/4 + 15/4*s**y + 21/4*s**2 + s**4.
(s + 1)**3*(4*s + 3)/4
Let q(r) be the first derivative of 8*r**5/45 - 31*r**4/18 - 16*r**3/27 - 50. Determine p so that q(p) = 0.
-1/4, 0, 8
Let a(t) = -t**3 + 2*t**2 + 3*t + 5. Let l be a(3). Let g be ((-2)/6)/(l/(-3)). Factor g*s**4 - 2/5*s + 0*s**2 - 1/5 + 2/5*s**3.
(s - 1)*(s + 1)**3/5
Let a = -263/3 - -88. Let y(d) be the first derivative of -a*d**6 - 54*d - 81*d**2 - 23*d**4 + 3 - 60*d**3 - 22/5*d**5. Factor y(u).
-2*(u + 1)**2*(u + 3)**3
Suppose -3*g - 3*w - 3 = 0, 3*w + 8 + 9 = 4*g. Let j(m) = -m. Let b(u) = 0*u**2 - u**2 - 2 + 3*u - 5*u. Let k(o) = g*j(o) + 2*b(o). Factor k(n).
-2*(n + 1)*(n + 2)
Let m = 45 + 19. Factor -4*z**2 + 32*z + 0*z**2 + 4*z**2 - 4*z**2 - m.
-4*(z - 4)**2
Let u = 3041 - 27361/9. Let a be (-10)/2*3/(-5). Let u*n + 8/3*n**2 + 26/9*n**a + 0 + 2/9*n**5 + 4/3*n**4 = 0. Calculate n.
-2, -1, 0
Let j(v) be the first derivative of 5*v**6/3 + 14*v**5/5 + v**4 - 76. Factor j(c).
2*c**3*(c + 1)*(5*c + 2)
Let z(u) = u**5 + u**4 - 2*u**3 - u - 1. Let v(n) = -4*n**5 - n**4 + 5*n**3 + 3*n + 3. Let j(c) = -v(c) - 3*z(c). Factor j(a).
a**3*(a - 1)**2
Let g(l) = -2*l**3 - 5*l**2 - 6*l + 3. Let b(w) = 2*w**3 + 6*w**2 + 7*w - 4. Let s(d) = -6*b(d) - 5*g(d). Factor s(u).
-(u + 3)**2*(2*u - 1)
Let h(j) be the first derivative of 5*j**3/3 - 870*j**2 + 151380*j + 357. Factor h(s).
5*(s - 174)**2
Factor 239 - 1361*g + 1088*g - 3*g**2 - 56 + 93.
-3*(g - 1)*(g + 92)
Let x = 429783/14 + -30733. Let j = -65/2 - x. Factor -18/7*p**4 + 0 - 2/7*p**2 - j*p**3 + 0*p - 8/7*p**5.
-2*p**2*(p + 1)**2*(4*p + 1)/7
Factor -16/7*a**2 - 24/7*a + 0 - 2/7*a**3.
-2*a*(a + 2)*(a + 6)/7
Suppose -391*t = -115*t - 552. Factor 1/2*f + 0 + 1/2*f**t.
f*(f + 1)/2
Let j(i) = -42*i**3 - 3*i**2 - 3*i - 1. Let t be j(-1). Factor 3*l**2 + 0*l - 5*l + 35 - t + 2*l.
3*(l - 2)*(l + 1)
Let o be (2 + -6)*35/14. Let m be -1*((-3)/(-6)*o - -2). Let -5/4*y**m + 5/4*y - 1/2*y**4 + 1/2 + 0*y**2 = 0. What is y?
-2, -1, -1/2, 1
Find n, given that 3/7*n**2 + 396/7*n + 0 = 0.
-132, 0
Let j(v) be the third derivative of v**6/60 + 13*v**5/30 - 43*v**4/6 + 24*v**3 + 395*v**2. Let j(k) = 0. Calculate k.
-18, 1, 4
Let w(z) be the second derivative of 0 + 0*z**2 + 1/12*z**4 + 1/6*z**3 - 6*z. Factor w(x).
x*(x + 1)
Let x(j) be the third derivative of 1/20*j**5 + 17*j**2 + 0 + 2*j**3 + 0*j + 1/2*j**4. Find h such that x(h) = 0.
-2
Let t be 3/12*2*1*8. Let -6*z**3 + 10*z**4 - 3*z**5 - 14*z**4 + 13*z**t =