t t(z) = 3*z**3 - 15*z**2 - 12*z + 51. Let g(x) = c*t(x) + 3*o(x). Factor g(w).
-3*(w - 3)**2*(w + 2)
Let i(c) be the third derivative of -1/36*c**5 + 0*c**3 + 0 - 21*c**2 + 1/120*c**6 + 1/36*c**4 + 0*c. What is w in i(w) = 0?
0, 2/3, 1
Let t = -12 + 15. Factor -p**2 - 9*p + p**3 - t*p**2 + 13*p.
p*(p - 2)**2
Let r(g) = 2*g**2 - 9*g + 13. Let u = 30 + -28. Let a be r(u). Let 1/2*q - 3/2*q**2 + 0 - 1/2*q**4 + 3/2*q**a = 0. Calculate q.
0, 1
Let m = 11419/45740 - -4/11435. Factor -f**2 + m*f**3 - 11/4*f - 3/2.
(f - 6)*(f + 1)**2/4
Let i(g) = 316*g**2 + 24*g. Let s(y) = 105*y**2 + 8*y. Let k(c) = 3*i(c) - 8*s(c). Suppose k(r) = 0. What is r?
-2/27, 0
Let g = -2559/46 + -43/23. Let q = 60 + g. Factor q*d**4 + 9/2*d**2 - 1/2*d + 13/2*d**3 - 1.
(d + 1)**3*(5*d - 2)/2
Let w(n) be the second derivative of -25/4*n**5 + 40/3*n**3 - 10*n**2 - 5*n + 0 - 25/12*n**4. Factor w(o).
-5*(o + 1)*(5*o - 2)**2
Let z(x) be the first derivative of 1/2*x**2 - 1/24*x**3 - 1/48*x**4 - 1/240*x**5 + 0*x - 4. Let v(a) be the second derivative of z(a). Factor v(k).
-(k + 1)**2/4
Let m = 153296/1085 + 68/217. Let z = m + -141. Factor 3/5*h**4 - 9/5*h**2 + 6/5 + z*h - 3/5*h**3.
3*(h - 2)*(h - 1)*(h + 1)**2/5
Let t(k) be the first derivative of -3*k**5/40 + 189*k**4/16 - 4093*k**3/8 + 5859*k**2/4 - 2883*k/2 + 41. Find d such that t(d) = 0.
1, 62
Let i(m) = 2*m**3 - 4*m**2 + 3*m - 2. Let q be i(2). Factor 5*z**4 + 5*z**5 - 13*z**2 - 20*z**3 + 4*z**4 - q*z**4 - 7*z**2.
5*z**2*(z - 2)*(z + 1)*(z + 2)
Let s(x) = -6*x**3 - 252*x**2 + 8184*x - 15374. Let t(p) = -22*p**3 - 756*p**2 + 24552*p - 46121. Let n(c) = -7*s(c) + 2*t(c). Factor n(g).
-2*(g - 62)**2*(g - 2)
Let v(r) be the third derivative of 5/84*r**8 - 9*r**2 - 1/10*r**6 - 22/105*r**7 + 0*r + 0 + 0*r**3 - 1/3*r**4 + 11/15*r**5. Determine o, given that v(o) = 0.
-1, 0, 1/5, 1, 2
Let d(i) be the third derivative of 5*i**8/21 + 3*i**7/2 + 5*i**6/2 - i**5/3 + 389*i**2. Factor d(v).
5*v**2*(v + 2)**2*(16*v - 1)
Let d(n) = -4*n**4 - 17*n**3 - 3*n**2 + 3*n - 7. Let s(x) = -3*x**4 - 12*x**3 - 2*x**2 + 2*x - 5. Let y(j) = -5*d(j) + 7*s(j). Suppose y(f) = 0. What is f?
-1, 0, 1
Let c = -20284/3 - -6765. Find m such that -3*m**2 - 2/3 + c*m = 0.
2/9, 1
Let k(b) be the first derivative of -2*b**5 + b**4/2 - 8*b + 44. Let t(o) = o**4 - o**3 + o + 1. Let s(z) = -k(z) - 8*t(z). Factor s(v).
2*v*(v - 1)*(v + 2)**2
Let -339*v - 16*v**3 - v**4 + 241*v - 78*v**2 + v**2 = 0. What is v?
-7, -2, 0
Let s = 269 - 269. Let z(n) be the third derivative of 1/30*n**5 + 0 + s*n + 1/60*n**4 + 2/75*n**6 + 0*n**3 + 5*n**2 + 4/525*n**7. Factor z(b).
2*b*(b + 1)*(2*b + 1)**2/5
Suppose -13 = -3*y - 3*l + 2, -y - 3*l + 11 = 0. Factor -1/3*x**5 + 0 - 5/3*x**4 - 3*x**3 - 2/3*x - 7/3*x**y.
-x*(x + 1)**3*(x + 2)/3
Suppose -y = y + 10, 3*l - 2*y = 91. Find z, given that 2*z**2 - 4*z**2 + 29*z - l*z + 0*z**2 = 0.
0, 1
Let q(k) be the third derivative of k**8/16 + 72*k**7/175 + 19*k**6/25 - 2*k**4/5 - 14*k**2 - 2. Determine t so that q(t) = 0.
-2, -2/5, 0, 2/7
Suppose 5*b - 21 = -6. Factor -4*l**b + 3 + 5 + 9*l + 3*l.
-4*(l - 2)*(l + 1)**2
Let w = -20 - -23. Let k be ((-1)/w)/((-2)/18). Determine b, given that -2*b - 2*b**2 + 3*b**2 + 4*b**k - b**3 - 2*b**3 = 0.
-2, 0, 1
Let t(w) be the first derivative of w**4/20 + 2*w**3/15 - 3*w**2/2 - 36*w/5 - 112. Factor t(h).
(h - 4)*(h + 3)**2/5
Let d(k) be the third derivative of -k**9/7560 + k**8/1120 + k**7/1260 - k**6/120 - 5*k**4/12 + 7*k**2. Let p(w) be the second derivative of d(w). Factor p(g).
-2*g*(g - 3)*(g - 1)*(g + 1)
Let k = -121/85 - -65/17. Factor -k*h**2 + 3/5*h**3 + 3*h - 6/5.
3*(h - 2)*(h - 1)**2/5
Solve 70/3*h - 31*h**4 + 27*h**2 - 175/6*h**3 + 4 + 35/6*h**5 = 0.
-1, -2/5, -2/7, 1, 6
Suppose -16 = 4*r - 2*s - 36, 2*s = -2*r + 4. Let a(i) be the third derivative of 1/90*i**5 + r*i**2 + 0*i + 1/6*i**4 + i**3 + 0. Find n such that a(n) = 0.
-3
Suppose 2*k + 3*k = 20. Find s such that 0*s**3 - s**3 - s**3 + k*s**2 - 2*s + 0*s = 0.
0, 1
Let x be 1/(-56)*((-176)/24 - -6). Let n(z) be the second derivative of -x*z**4 + 1/21*z**3 + 0*z**2 - 3*z + 0. Suppose n(g) = 0. What is g?
0, 1
Let q = 136 + -134. Let f(n) be the second derivative of 0 + 10*n**4 - q*n + 24*n**3 + 7/5*n**5 + 16*n**2. Factor f(u).
4*(u + 2)**2*(7*u + 2)
Let i(c) = 5*c - 22. Let k be -2 - (-1 - (-21)/(-3)). Let g be i(k). Determine j, given that -8*j + 7*j + 10*j**2 + g - 23*j = 0.
2/5, 2
Let t(s) be the third derivative of 49*s**7/300 - 1127*s**6/400 + 518*s**5/25 - 1264*s**4/15 + 1024*s**3/5 - 520*s**2. Factor t(z).
(z - 3)*(7*z - 16)**3/10
Let p = -69 - -71. Let -3*x - 31*x**p + 3*x + 35*x**2 - x**4 = 0. Calculate x.
-2, 0, 2
Let t(p) be the first derivative of -25*p**4/12 - 35*p**3/9 - 5*p**2/3 - 145. Factor t(r).
-5*r*(r + 1)*(5*r + 2)/3
Let f(i) = i**2 - 6*i. Let n(t) = 2*t**2 + 72*t - 2025. Let r(g) = 12*f(g) - 4*n(g). Factor r(a).
4*(a - 45)**2
Let b(z) be the second derivative of 2*z**6/15 + 7*z**5/5 + 11*z**4/3 + 10*z**3/3 - 446*z. Let b(x) = 0. Calculate x.
-5, -1, 0
Let b(q) be the third derivative of 1/540*q**6 - q**2 - 1/90*q**5 + 3*q + 0 - 1/27*q**3 + 1/36*q**4. Find t, given that b(t) = 0.
1
Let j(p) be the second derivative of p**7/70 + 7*p**6/50 + 39*p**5/100 + p**4/20 - 7*p**3/5 - 12*p**2/5 - 419*p. Let j(o) = 0. What is o?
-4, -2, -1, 1
Let m(k) be the second derivative of -7*k - 1/160*k**5 + 1/80*k**6 + 1/48*k**3 - 1/32*k**4 + 0*k**2 + 0. What is t in m(t) = 0?
-1, 0, 1/3, 1
Factor -23120 - 680*y - 3309*y**2 + 1651*y**2 + 1653*y**2.
-5*(y + 68)**2
Let y be (-6)/(-36) + (-519)/9. Let r = 58 + y. Factor -1/2 + 1/2*x**3 - r*x + 1/2*x**2.
(x - 1)*(x + 1)**2/2
Let g be (3/(-27))/(7/(-21)). What is y in -y**2 + g*y - 1/3*y**3 + 1/3 + 2/3*y**4 = 0?
-1, -1/2, 1
Let x(w) be the second derivative of -w**6/30 + 11*w**5/20 + 13*w**4/4 + 41*w**3/6 + 7*w**2 + 34*w - 1. Factor x(d).
-(d - 14)*(d + 1)**3
Let y(j) = j**3 - 7*j**2 + 10*j - 12. Let n be y(5). Let x be ((-8)/14)/(n/42). Factor 1/4*u + 0*u**x - 1/4*u**3 + 0.
-u*(u - 1)*(u + 1)/4
Suppose 6 = 9*r - 6*r. Let m(y) = -3*y**3 - 10*y**2 + 5*y + 8. Let z(t) = t**3 - 1. Let u(d) = r*z(d) - m(d). Factor u(s).
5*(s - 1)*(s + 1)*(s + 2)
Factor -84*h**2 - 5*h**4 - 138*h**2 + 240*h + 50*h**2 - 112 + h**4 + 48*h**3.
-4*(h - 7)*(h - 2)**2*(h - 1)
Let t(h) be the first derivative of -h**6/20 - 3*h**5/40 + 11*h + 6. Let n(s) be the first derivative of t(s). What is r in n(r) = 0?
-1, 0
Let j = 4 + 2. Suppose -5*r + 16 = j. Factor -7*h**r + 3*h**3 + 2*h**2 + 2*h**2.
3*h**2*(h - 1)
Let s = 3689 + -3687. Determine k, given that -96/7*k**4 - 9/7*k - 144/7*k**5 - 6/7 + 102/7*k**s + 153/7*k**3 = 0.
-1, -2/3, -1/4, 1/4, 1
Let f(o) be the third derivative of -o**5/90 - 5*o**4/36 - 4*o**3/9 + 301*o**2. Let f(w) = 0. Calculate w.
-4, -1
Suppose 5*r - 4*u - 19 = -u, -3*r = -5*u - 21. Factor r*i**2 + 11*i - i**2 + 8 - 2 - 3*i**2.
-(i - 6)*(2*i + 1)
Let i(q) = 4*q - 15. Let z be i(-6). Let r = z + 41. Find m such that 3*m**2 + r*m - 4*m**2 + m + 0*m = 0.
0, 3
Let b(n) be the third derivative of 2*n**7/105 - n**6/5 + 11*n**4/3 + 10*n**3 + 71*n**2. Find w, given that b(w) = 0.
-1, 3, 5
Let y be 24/48 - (-1 - 3/2). Suppose c = -q + 3 + 1, -y*q - c + 8 = 0. Determine r so that 2/9*r + 4/3*r**q - 4/9 = 0.
-2/3, 1/2
What is v in 0 + 48*v**5 - 3*v - 81*v**3 + 48*v**4 + 57/2*v**2 = 0?
-2, 0, 1/4, 1/2
Let t(d) be the second derivative of -1/8*d**4 + 0*d**3 + 1/80*d**5 + 0*d**2 + d - 2. Suppose t(z) = 0. What is z?
0, 6
Let p(l) be the third derivative of -1/240*l**6 - 1/360*l**5 + 1/48*l**4 + 0*l + 0 + 1/18*l**3 - 1/1260*l**7 + 8*l**2. Factor p(y).
-(y - 1)*(y + 1)**2*(y + 2)/6
Find r such that -40/13*r - 2/13*r**2 + 42/13 = 0.
-21, 1
Let t = 229/965 - -70/193. Factor -t*m - 1/5*m**2 + 0.
-m*(m + 3)/5
Let p = 121 - 119. Let t(h) be the second derivative of 1/10*h**6 + 0 + 9/20*h**5 + h + 0*h**p + 1/2*h**3 + 3/4*h**4. Suppose t(s) = 0. Calculate s.
-1, 0
Let z(i) be the first derivative of -i**8/10080 + i**7/1680 - i**6/1080 - 4*i**3 - 12. Let h(w) be the third derivative of z(w). Factor h(q).
-q**2*(q - 2)*(q - 1)/6
Let h(y) be the second derivative of y**6/6 + 23*y**5/2 - 235*y**4/12 + 328*y. Factor h(v).
5*v**2*(v - 1)*(v + 47)
Let z = 43 + -30. Let r be 370/130 - (-2)/z. Suppose 0*a + 115*a**3 - 6*a - 125*a**r