 2)**3
Let m(a) be the first derivative of 2*a**3 + 0*a + 9/4*a**4 + 3/5*a**5 + 8 + 0*a**2. Factor m(i).
3*i**2*(i + 1)*(i + 2)
Let c(r) be the first derivative of r**3/21 - 2*r**2/7 + 4*r/7 - 119. Factor c(w).
(w - 2)**2/7
Let n(d) = -8*d**3 + 792*d**2 - 31992*d + 31205. Let l(j) = -9*j**3 + 791*j**2 - 31991*j + 31205. Let p(a) = 3*l(a) - 4*n(a). Let p(w) = 0. What is w?
1, 79
Suppose -5*y + 61 = 4*d - 0*d, -2*y = -3*d + 17. Let i be (-15)/10*(-12)/d. Factor -i*v - v + 0*v**2 + 3*v**2.
3*v*(v - 1)
Let j(a) be the third derivative of a**6/40 - a**5/4 - a**4/4 + 12*a**3 - 70*a**2 - 1. Factor j(t).
3*(t - 4)*(t - 3)*(t + 2)
Let c(g) be the second derivative of g**9/7560 - g**7/1260 + 2*g**4/3 + 4*g. Let d(w) be the third derivative of c(w). Factor d(l).
2*l**2*(l - 1)*(l + 1)
Let t be 15 - (-17)/(748/(-539)). Find a, given that 3/2 + 3/2*a**2 - 1/4*a**3 - t*a = 0.
1, 2, 3
Suppose 0*y + 5*y - 4*g = 54, 0 = -y - g + 18. Suppose -18*j = -y*j. Determine b so that 12*b**2 + 16 - b**3 + j*b**3 + 3*b**3 + 24*b = 0.
-2
Factor 50*w + 12*w**3 - 13*w**3 - 27*w**3 - 6*w**4 + 6*w**4 - 55*w**2 - 3*w**4.
-w*(w + 5)**2*(3*w - 2)
Let c(f) be the third derivative of 0 - 1/720*f**6 - 1/90*f**5 + 0*f**3 + 1/1260*f**7 + 1/36*f**4 + 0*f - 16*f**2. Solve c(q) = 0.
-2, 0, 1, 2
Solve -21*y**2 - 24*y**4 + 431*y**5 - 435*y**5 + 5*y**2 - 36*y**3 = 0.
-4, -1, 0
Let j(m) be the third derivative of m**6/1260 + m**5/105 + m**4/21 + 5*m**3/3 + 9*m**2. Let f(c) be the first derivative of j(c). Solve f(s) = 0.
-2
Let j(n) be the first derivative of 6 + 0*n**2 - 1/4*n**4 + 0*n - 1/10*n**5 - 1/6*n**3. Factor j(s).
-s**2*(s + 1)**2/2
Let f(p) be the third derivative of p**5/30 - 8*p**4/3 + 256*p**3/3 - 49*p**2. Determine u, given that f(u) = 0.
16
Solve 20856279 + 6*h**3 + 85450*h - 75463955 - 4*h**3 + 600002*h - 2868*h**2 + 2*h**3 = 0 for h.
239
Find r, given that 7*r**3 + 68*r**2 - 149*r**2 + 2880*r - 3905 - 102*r**2 + 1205 - 4*r**3 = 0.
1, 30
Let i(c) be the second derivative of 1/3*c**4 - 4/3*c**3 + 31*c + 2*c**2 + 0. Factor i(w).
4*(w - 1)**2
Let q(h) = -3*h**3 - 3*h**2 + 45*h - 24. Let o(c) = 20*c**3 + 20*c**2 - 292*c + 156. Let u(v) = 5*o(v) + 32*q(v). Factor u(a).
4*(a - 1)**2*(a + 3)
Let u = 65 + -1. Let z be (u/(-28) - (-3 - -1))*-7. Factor 2/5*n**5 + 0 + 6/5*n**4 + 6/5*n**3 + 2/5*n**z + 0*n.
2*n**2*(n + 1)**3/5
Let l(f) be the third derivative of -f**6/30 - 2*f**5/5 - 3*f**4/2 - 47*f**2. Determine v so that l(v) = 0.
-3, 0
Suppose 4*w = -8 + 12. Suppose 6*k = -w + 13. Let 0 - 2/5*g**3 + 0*g + 0*g**k = 0. Calculate g.
0
Let o = -106/7 - 61/14. Let z = o + 20. Factor 0*x + z - 1/2*x**2.
-(x - 1)*(x + 1)/2
Find v such that -180*v - 32*v**3 - 40 + 18*v**4 + 6*v**4 - 130*v**2 + 77*v**3 + 11*v**4 = 0.
-2, -1, -2/7, 2
Let c(g) be the second derivative of -g**5/110 + 4*g**3/33 - 23*g. Factor c(d).
-2*d*(d - 2)*(d + 2)/11
Let j be (-4288)/864 + (-5)/(-1). Let g(o) be the second derivative of -1/90*o**5 + 0 - j*o**4 + 0*o**2 - 1/27*o**3 - 5*o. Factor g(f).
-2*f*(f + 1)**2/9
Suppose -98*c - 266*c - 33*c**3 + 32*c - 144 - 4*c**4 + 56*c - 11*c**3 - 172*c**2 = 0. What is c?
-4, -3, -1
Factor 1152/5*w**2 + 6/5*w**3 + 73728/5*w + 1572864/5.
6*(w + 64)**3/5
Let l(s) = 10*s**4 - 90*s**3 + 140*s**2 + 10*s. Let g(a) = -5*a**4 + 45*a**3 - 70*a**2 - 6*a. Let z(i) = 5*g(i) + 3*l(i). Determine y so that z(y) = 0.
0, 2, 7
Let w(n) = 26*n**3 - 241*n**2 + 247*n - 38. Let l(c) = 26*c**3 - 240*c**2 + 246*c - 36. Let j(o) = -6*l(o) + 4*w(o). What is s in j(s) = 0?
2/13, 1, 8
Factor 9680 - 4*g**2 - g**5 - 4*g - 9680 + 2*g**4 + 3*g**3.
-g*(g - 2)**2*(g + 1)**2
Let h(b) be the second derivative of b**4/48 + 73*b**3/6 + 5329*b**2/2 - b + 8. Factor h(g).
(g + 146)**2/4
Suppose 91 - 91 = 28*t. Let k(d) be the first derivative of 1/3*d**2 + t*d + 2/3*d**4 - 1/5*d**5 - 7/9*d**3 + 1. Let k(a) = 0. What is a?
0, 2/3, 1
Suppose 20*x = -4*c + 22*x + 10, 0 = -3*c - 3*x + 3. Let q(p) be the first derivative of -2*p**3 + 9*p - 6*p**c + 3*p**4 - 3/5*p**5 - 4. Solve q(i) = 0 for i.
-1, 1, 3
Let p(d) = -4*d**5 + 38*d**4 - 100*d**3 + 26*d**2 + 116*d - 52. Let u(s) = s**4 - s**2 - 2*s - 2. Let h(y) = p(y) + 6*u(y). Solve h(q) = 0 for q.
-1, 1, 2, 8
Let p be (-1)/(-2) + 139/(-278). Let l(k) be the second derivative of -1/24*k**4 + p + 9*k - 4*k**2 - 2/3*k**3. Factor l(d).
-(d + 4)**2/2
Let h = 1/192 + 51/448. Let o(j) be the second derivative of h*j**4 + 4/7*j**2 - 7*j + 0 - 1/70*j**5 - 8/21*j**3. Factor o(q).
-2*(q - 2)**2*(q - 1)/7
Suppose -w + 4 = -4*p, 0*w - 44 = 4*w + 4*p. Let i(m) = m**2 + 9*m + 11. Let u be i(w). Factor -d**3 + 3*d - 5*d**u + d**5 + 2*d**5.
3*d*(d - 1)**2*(d + 1)**2
Let l be 30/(-12)*12/10. Let s be 1 + 4 + l/1. Determine i so that 0*i + 4 - 2*i**s + i - 3*i + 0*i**2 = 0.
-2, 1
Let u(x) = -2*x**2 - 2*x. Let q be u(2). Let o = q + 14. Factor -8*c**2 - c - c**3 + 11*c**2 + 0*c + c**4 - o*c**3.
c*(c - 1)**3
Let r be ((-160)/(-24))/(12/18). Suppose -2*y = -r*y + 24. Let 5/3*c**2 - y*c**3 + 7/3*c**4 - 1/3*c - 2/3*c**5 + 0 = 0. What is c?
0, 1/2, 1
Find p such that 0 - 2/3*p**2 + 2*p = 0.
0, 3
Let c = 1015/4068 - -1/2034. Let 1/4*k**4 - 3/4*k**2 + 1/2 - c*k**3 + 1/4*k = 0. What is k?
-1, 1, 2
Factor -38/9 + 13/3*p - 1/9*p**2.
-(p - 38)*(p - 1)/9
Let d(t) = 125*t**3 + t**2 - 2. Let a be d(-1). Let q = a - -128. Factor -2/13 + 4/13*p - 2/13*p**q.
-2*(p - 1)**2/13
Let w = -273331/30 - -9115. Let d = w + -19/6. Solve -d - 2/5*l**3 + 2/5*l - 2/5*l**4 + 6/5*l**2 = 0.
-2, -1, 1
Suppose k + 1 + 2 = 0. Let s be (-6*k/(-6))/(-1). Suppose -9*v**2 - 6*v**3 - v**3 + 3*v - 4*v**s - v**3 = 0. Calculate v.
-1, 0, 1/4
Let f(g) = -5*g**4 - 35*g**3 + 3*g**2 + 6. Let k(t) = 41*t**4 + 279*t**3 - 25*t**2 - 50. Let u(d) = 50*f(d) + 6*k(d). Factor u(n).
-4*n**3*(n + 19)
Let o = -12 - -24. Let f = -8 + o. Find s, given that 14*s**4 + 8*s**5 - 2*s - 8*s - 14*s**2 + 2*s**3 - 2 + 11*s**4 - 9*s**f = 0.
-1, -1/2, 1
Factor 20 + 11*z + 1/2*z**2.
(z + 2)*(z + 20)/2
Let p(b) = 2*b**3 + 2*b**2 + 6*b + 14. Let o be p(7). Solve 5*u**3 + o*u + 7*u**3 + 3*u**4 - 9 + 6*u**2 - 852*u = 0 for u.
-3, -1, 1
Let n = 5027/25150 - -3/25150. Find z such that -3/5*z**2 + n*z**3 + 0*z + 0 = 0.
0, 3
Let j = 39 - 12. Factor -27 - 4*x + j + 2*x**5 + 6*x**4 - 6*x**2 + 2*x**3.
2*x*(x - 1)*(x + 1)**2*(x + 2)
Suppose 6 = -3*c, 9 + 13 = 3*i - 5*c. Factor i + 19*b**2 + 69*b**3 - b - 50*b**2 - 83*b**3 - 3*b.
-(b + 2)*(2*b + 1)*(7*b - 2)
Suppose 0 = -0*t - 5*t + 10. Factor 28*u**3 + 19*u + 12*u**4 + 6*u**2 - 15*u + 14*u**t.
4*u*(u + 1)**2*(3*u + 1)
Find x, given that -4914*x + 1 + 4904*x + 2 + 5 + 2*x**2 = 0.
1, 4
Let x(p) = p**2 + 3. Let v(z) = -200*z + 1985. Let r(c) = -v(c) - 5*x(c). Factor r(g).
-5*(g - 20)**2
Let t(b) = 3*b**3 + 18*b**2 - 18*b + 3. Let n(r) = r**3 + 17*r**2 - 18*r + 2. Let l(q) = -3*n(q) + 2*t(q). Factor l(k).
3*k*(k - 3)*(k - 2)
Determine v, given that -2*v**2 - 357 + 365 + 0*v**2 = 0.
-2, 2
Suppose 3*y**3 - 3*y + 3/4 - 3/4*y**2 = 0. Calculate y.
-1, 1/4, 1
Let v = 135 - 132. Suppose 5*t = v*t + t. Factor -3/5*k**3 + 0 + 6/5*k**2 + t*k.
-3*k**2*(k - 2)/5
Let d(y) be the second derivative of -y**6/90 - y**5/10 - 2*y**4/9 + y**3/3 + 3*y**2/2 - 106*y. Suppose d(r) = 0. What is r?
-3, -1, 1
Let 2*m**3 - m**3 + 71714 - 4*m**3 - 71714 + 210*m**2 = 0. What is m?
0, 70
Let l**3 + l**4 - 3*l + 4*l**2 + 2*l - 9*l**2 - 5*l**2 + 7*l**2 + 2 = 0. What is l?
-2, -1, 1
Let c(u) = u**4 + 10*u**3 + 14*u**2 - 10*u - 9. Let t(h) = h**4 - h**2 + 1. Let p(w) = -c(w) + 6*t(w). Let p(z) = 0. What is z?
-1, 1, 3
Suppose 421*v = 420*v. Factor -4/3*y**2 + 0*y - 2/9*y**3 + v.
-2*y**2*(y + 6)/9
Let h be (-1260)/(-70) + 32/(-2). Factor -5/7*z**3 + 5/7*z - 4/7 + 3/7*z**h + 1/7*z**4.
(z - 4)*(z - 1)**2*(z + 1)/7
Let l(a) be the first derivative of 2*a**3/15 + 6*a**2/5 + 25. Let l(u) = 0. Calculate u.
-6, 0
What is y in 3/5*y**3 + 189/5 + 153/5*y + 39/5*y**2 = 0?
-7, -3
Let b = 6563 + -72139/11. Let y = b + -140/33. Factor -y + 0*f + 2/3*f**2.
2*(f - 1)*(f + 1)/3
Let c(d) be the first derivative of 2*d**2 + 0*d + 0*d**4 - 31 + 2*d**3 - 2/5*d**5. Solve c(q) = 0 for q.
-1, 0, 2
Suppose 28 = -8*k + 12*k - 2*s, 4*k + 2*s = 20. Determine l, given that 8*l + 15*l + 3*l**3 - 9 + k*l - 15*l**2 - 8*l = 0.
1, 3
Let f(c) be the second derivative of c**5/180 - c**3/54 + 50*c. Suppo