9*p - 9. Let c(m) = -2*m**3 - 54*m**2 - 50*m - 6. Let l(g) = 3*c(g) - 2*z(g). Factor l(t).
-4*t*(t + 1)*(t + 13)
Let g(d) be the third derivative of 0*d + 0*d**3 - 1/8*d**4 + 1/30*d**5 + 0 + 29*d**2. Suppose g(b) = 0. What is b?
0, 3/2
Suppose 55 - 25 = 15*s. Let o(j) be the first derivative of -4/35*j**5 + 0*j**3 - 1/14*j**4 + 0*j**s + 5 + 0*j + 1/7*j**6. Determine x, given that o(x) = 0.
-1/3, 0, 1
Let y(v) be the second derivative of -v**6/195 - v**5/13 - 6*v**4/13 - 18*v**3/13 - 27*v**2/13 + 34*v. Solve y(t) = 0 for t.
-3, -1
Let n(b) be the second derivative of 2*b + 0*b**4 + 0 + 2*b**2 - 1/180*b**6 + 0*b**3 + 1/90*b**5. Let z(v) be the first derivative of n(v). Factor z(f).
-2*f**2*(f - 1)/3
Find b such that -549*b**2 - 5*b**3 + 8*b + 539*b**2 + 7*b = 0.
-3, 0, 1
Let z(n) = 9*n - 42. Let s be z(5). Find w such that -18*w - 37*w**2 - 10*w**4 - 44*w**s - w**4 - 11*w**2 - 5*w**4 - 2*w**5 = 0.
-3, -1, 0
Let a(p) be the second derivative of 3/4*p**2 + 1/4*p**4 + 3/4*p**3 - 3/20*p**6 + 5*p + 0 - 3/20*p**5 - 1/28*p**7. Determine m, given that a(m) = 0.
-1, 1
Let h(r) be the second derivative of -r**6/70 - 81*r**5/140 - 66*r**4/7 - 544*r**3/7 - 2304*r**2/7 + 2*r - 66. Factor h(w).
-3*(w + 3)*(w + 8)**3/7
Factor -57*d**2 + 4*d**3 + 215*d - d**3 - 161*d.
3*d*(d - 18)*(d - 1)
Factor 96 - 35*l + 33*l - 5*l**2 - 20*l**3 - 3*l**2 + 49*l + 33*l - 4*l**4.
-4*(l - 2)*(l + 2)**2*(l + 3)
Let t(x) be the first derivative of x**5/70 - x**4/42 - 2*x**3/21 - 16*x + 11. Let f(b) be the first derivative of t(b). Factor f(z).
2*z*(z - 2)*(z + 1)/7
Factor -12 - 122*a**4 - 2*a**3 + 250*a**4 - 7*a**2 + 20*a - 127*a**4.
(a - 2)**2*(a - 1)*(a + 3)
Factor -56/13 - 2/13*h**2 + 22/13*h.
-2*(h - 7)*(h - 4)/13
Let m(c) be the second derivative of c**4/2 + 3*c**3/2 - 3*c**2 - 186*c. Factor m(x).
3*(x + 2)*(2*x - 1)
Let p(y) be the second derivative of y**4/36 + y**3 - 19*y**2/6 - 7*y + 1. Factor p(c).
(c - 1)*(c + 19)/3
Suppose -5*s + 15 = 4*k - 11, 5*s - 5*k = -10. Let o(t) be the first derivative of 12*t**s + 3/8*t**4 - 4*t**3 - 8 + 0*t. What is z in o(z) = 0?
0, 4
Suppose 19 - 4 = -5*t. Let s be 4 + -1 + 2 + t. Factor 6*z - 127*z**s + 183*z**2 + 22*z**5 + 28*z**5 + 140*z**4 + 2*z + 138*z**3.
2*z*(z + 1)**2*(5*z + 2)**2
Let t(x) be the second derivative of -x**5/5 - 4*x**4 - 6*x**3 + 44*x**2 + 55*x + 1. Factor t(i).
-4*(i - 1)*(i + 2)*(i + 11)
Let m(z) be the first derivative of -z**4/36 - 8*z**3/27 - 2*z**2/3 - 109. Determine s so that m(s) = 0.
-6, -2, 0
Let g(d) be the first derivative of d**4/8 + d**3/2 - 5*d**2/2 - 423. Factor g(s).
s*(s - 2)*(s + 5)/2
Let r = 53 - 51. Factor -562 + 562 + 2*p**2 + r*p**3.
2*p**2*(p + 1)
Let f = 30251 - 30248. Find g, given that 2/5*g + 0 + 1/5*g**2 - 1/5*g**f = 0.
-1, 0, 2
Let z = 2251 + -2247. Find d such that -6*d**2 - 10/3*d**3 - 4/3 - 2/3*d**z - 14/3*d = 0.
-2, -1
Suppose 10*z = 7*z + 381. Let y = 131 - z. Suppose 6/5*k**4 - 12/5*k + 2/5 - y*k**3 + 24/5*k**2 = 0. Calculate k.
1/3, 1
Let p(m) be the second derivative of m**7/1260 + m**6/144 + m**5/60 - 7*m**4/12 + 43*m. Let v(o) be the third derivative of p(o). Factor v(y).
(y + 2)*(2*y + 1)
Let z be (10 - 80/12) + -3. Let -2/3*g + z + 1/3*g**2 = 0. What is g?
1
Let s(k) be the third derivative of 0*k**3 - 1/20*k**5 + 0*k**4 - 1/112*k**8 + 0 - 3/40*k**6 - 3/70*k**7 + 0*k - 10*k**2. Factor s(d).
-3*d**2*(d + 1)**3
Let i(c) = -c**3 - c**2 - c + 2. Let m(a) = -4*a**3 - 28*a**2 - 48*a + 29. Let o(z) = 3*i(z) - m(z). Let x be o(-23). Let 1/4*b + x + 1/4*b**2 = 0. Calculate b.
-1, 0
Suppose 2/17*v**2 + 18/17*v + 40/17 = 0. What is v?
-5, -4
Let j(o) = o**3 + 21*o**2 + 102*o + 58. Let l be j(-14). Factor 4/11*y**l + 6/11*y + 0 - 2/11*y**3.
-2*y*(y - 3)*(y + 1)/11
Let n = 25 + -22. Let d(j) be the third derivative of 1/60*j**5 - 1/60*j**6 + 0*j + 1/210*j**7 + 0*j**n + 0 + 0*j**4 - 4*j**2. Factor d(b).
b**2*(b - 1)**2
Let k(h) be the first derivative of 3/5*h**4 - 8/15*h**3 - 2/5*h**2 - 23 + 0*h. Factor k(q).
4*q*(q - 1)*(3*q + 1)/5
Let j(z) be the third derivative of -z**5/60 - 5*z**4/24 - 3*z**2. Let a be j(-4). Find i, given that 3*i**a + 0*i**5 - 6*i**4 + i**4 - 2*i**5 = 0.
-1, 0
Suppose 3*u - 14 = u. Factor 3 + 2 - 6 + 2*i - 6*i**5 - u*i**4 + 8*i**2 + 2*i**5 + 2*i**3.
-(i - 1)*(i + 1)**3*(4*i - 1)
Let -2/7*c**3 - 74/7*c**2 - 78/7 + 22*c = 0. What is c?
-39, 1
Factor 5*o**2 + 18*o**2 - 391*o + 7*o**2 + 215*o + 26 + 2*o**3 + 230*o.
2*(o + 1)**2*(o + 13)
Let s = 29 + -56. Let w = s - -29. Factor 5*y**2 + y**3 - 6*y**w - 9*y**3 + 8*y - y**2 + 2.
-2*(y - 1)*(y + 1)*(4*y + 1)
Let g = 1395 + -1391. Let v(k) be the second derivative of 1/78*k**4 - 1/13*k**2 + 0 + g*k - 1/130*k**5 + 1/39*k**3. Factor v(r).
-2*(r - 1)**2*(r + 1)/13
Let v(f) be the second derivative of f**7/1260 - f**6/108 - 10*f**3/3 + 7*f. Let x(c) be the second derivative of v(c). Factor x(i).
2*i**2*(i - 5)/3
Let x(j) = -16*j**2 + 76*j - 244. Let w(h) = -4*h**2 - 3 + 3*h**2 + h + 4. Let i(m) = 12*w(m) - x(m). Solve i(t) = 0.
8
Let t(d) be the third derivative of 1/17*d**4 + 1/510*d**5 + 0*d + 0 + 12/17*d**3 + 15*d**2. Suppose t(m) = 0. What is m?
-6
Factor -1/8*b**2 - 35/8*b + 9/2.
-(b - 1)*(b + 36)/8
Factor 573*q - 540 + 366*q - 24*q**2 - q**2 + 421*q.
-5*(q - 54)*(5*q - 2)
Let i(s) be the second derivative of s**5/20 - s**4/3 + s**3/6 + 3*s**2 + 362*s. Suppose i(z) = 0. Calculate z.
-1, 2, 3
Let d be (-3)/(-36)*(23 - 19). Suppose d*f**2 + 4/3*f + 1 = 0. What is f?
-3, -1
Let g(o) = o**3 - o**2 - 60. Let w be g(0). Let y = w + 303/5. Let 3/5*i + y*i**2 - 6/5 = 0. What is i?
-2, 1
Suppose 9 = -68*i - 8 + 153. Factor 2/5*p + 0 + 2/5*p**i.
2*p*(p + 1)/5
Suppose -2*h = -2, 243*w - 3*h - 6 = 240*w. Let -26/9*r**4 + 0 + 2/9*r**5 + 40/3*r**w - 224/9*r**2 + 128/9*r = 0. Calculate r.
0, 1, 4
Let r(a) be the third derivative of a**8/1344 - a**7/280 - a**6/480 + 11*a**5/240 - a**4/8 + a**3/6 + 49*a**2. Find g such that r(g) = 0.
-2, 1, 2
Suppose 25 = 2*d + 19. Solve 62 - 62 + 14*g**2 - 6*g - 10*g**d + 2*g**4 = 0 for g.
0, 1, 3
Let x = -6 + 11. Suppose -2*b = y - 9, 5*b - 3*y = -2*y + 12. Solve 4*l**2 + 13 - x - 2*l**2 - 5*l - b*l = 0 for l.
2
Let u(k) be the first derivative of -2*k**3/27 + 8*k**2/9 - 8*k/3 - 62. Factor u(x).
-2*(x - 6)*(x - 2)/9
Factor 0 + 1/3*h**2 + 19/3*h.
h*(h + 19)/3
Let b(l) be the third derivative of 61*l**5/60 + 23*l**4/8 + 4*l**3/3 + 16*l**2. Let d(i) = -15*i**2 - 17*i - 2. Let m(r) = -4*b(r) - 18*d(r). Factor m(n).
2*(n + 1)*(13*n + 2)
Let i = -1580 - -1582. Determine n, given that 4/3 + 32/3*n**2 + 70/9*n - i*n**3 = 0.
-1/3, 6
Let t(x) be the first derivative of -x**6/360 - x**2 - 5*x + 4. Let p(r) be the first derivative of t(r). Let j(i) be the first derivative of p(i). Factor j(w).
-w**3/3
Let h(y) be the first derivative of 2*y**5/35 - 5*y**4/7 + 26*y**3/21 + 60*y**2/7 + 72*y/7 + 40. Factor h(d).
2*(d - 6)**2*(d + 1)**2/7
Let u(m) be the first derivative of m**5 - 5*m**3 + 5*m**2 + 44. Factor u(w).
5*w*(w - 1)**2*(w + 2)
Let p(u) be the third derivative of -2*u**5/135 - 71*u**4/108 + 2*u**3/3 - 2*u**2 + 41. Factor p(v).
-2*(v + 18)*(4*v - 1)/9
Let y(p) = -6*p**3 - 42*p**2 - 39*p + 87. Let f(z) = -7*z**3 - 41*z**2 - 40*z + 88. Let i(n) = 3*f(n) - 4*y(n). Let i(h) = 0. What is h?
-14, -2, 1
Let b(k) be the first derivative of -2/15*k**5 - 12 + 0*k**4 + 0*k**2 + 0*k + 0*k**3 + 1/9*k**6. Determine i, given that b(i) = 0.
0, 1
Let d(b) be the third derivative of b**10/40320 - b**9/10080 + b**7/1680 - b**6/960 + 3*b**4/8 + 6*b**2. Let o(w) be the second derivative of d(w). Factor o(u).
3*u*(u - 1)**3*(u + 1)/4
Let g(m) be the first derivative of -2*m**5/15 - m**4/6 + 4*m**3/9 + 87. Suppose g(u) = 0. Calculate u.
-2, 0, 1
Let i(u) be the second derivative of -5*u**4/4 + 335*u**3/3 - 220*u**2 + 239*u. Factor i(o).
-5*(o - 44)*(3*o - 2)
Let s be 6/((3 - 11)/(-4)). Let 1592*m**2 + 2156*m**5 + 32 - 184*m - 185*m - 128*m - 1624*m**4 - 1756*m**s + 97*m = 0. Calculate m.
-1, 2/11, 2/7, 1
Let m be (-2)/(-11) - 602/(-77). Suppose 6*h - 2*h = m. Factor 2*b + h*b**2 + 2*b**2 + 0*b.
2*b*(2*b + 1)
Suppose 11*z - 16*z = -100. Suppose -2*y - 10 = -s, 0 = -7*s + 4*s - 4*y - z. Factor 10*c**5 + 28/5*c**3 + 13*c**4 + 4/5*c**2 + 0*c + s.
c**2*(2*c + 1)*(5*c + 2)**2/5
Let p(t) = t**3 + 7*t**2 - t - 5. Let n be p(-7). Let u b