 - 16)**2/5
Let g(b) be the first derivative of -24*b**5 + 93*b**4/2 + 55*b**3 - 123*b**2/2 + 18*b - 153. Suppose g(l) = 0. What is l?
-1, 1/4, 3/10, 2
Let o(y) be the first derivative of -y**6/2880 - 11*y**5/960 + 16*y**3 + 1. Let r(w) be the third derivative of o(w). What is u in r(u) = 0?
-11, 0
Let t(w) = w**4 - w**3 + w**2 + 1. Let m(p) = -5*p**4 + 4*p**3 + 7*p**2 - 18*p + 4. Let g(y) = 3*m(y) + 12*t(y). Factor g(z).
-3*(z - 2)*(z - 1)**2*(z + 4)
Suppose 53 = 3*k - 4*w + 49, 2*k - 2*w = 2. Factor 0 - 1/6*z**4 + 1/6*z**2 + 0*z + k*z**3.
-z**2*(z - 1)*(z + 1)/6
Let c(y) be the first derivative of -2*y**5/5 + y**4/2 + 2*y**3 - y**2 - 4*y - 36. Solve c(a) = 0 for a.
-1, 1, 2
Let o = -12457 - -12457. Factor 6/11*y**2 - 4/11*y + o - 2/11*y**4 + 0*y**3.
-2*y*(y - 1)**2*(y + 2)/11
Let f(k) be the first derivative of 33 + 0*k**2 + 4/5*k**5 + 0*k**3 + 0*k**4 + 0*k + 2/3*k**6. Let f(m) = 0. Calculate m.
-1, 0
Factor -22/3*z + 4 + 4*z**2 - 2/3*z**3.
-2*(z - 3)*(z - 2)*(z - 1)/3
Suppose 6*l - 5*l = -5. Let q(z) = -17*z**2 - 59*z + 43. Let d(n) = -9*n**2 - 29*n + 21. Let m(x) = l*d(x) + 3*q(x). Solve m(o) = 0.
-6, 2/3
Let u(d) = -10*d**2 + 1626*d + 1108. Let o(x) = -3*x**2 + 542*x + 370. Let l(j) = -8*o(j) + 3*u(j). Suppose l(r) = 0. Calculate r.
-2/3, 91
Let y(m) = 13*m**2 + 39*m - 10. Let f(c) = 52*c**2 + 157*c - 42. Let v(a) = 2*f(a) - 9*y(a). Let v(w) = 0. Calculate w.
-3, 2/13
Let m(i) = -8*i + 42. Let c be m(5). Factor -159*q**2 + 160*q**2 + q**3 + 2*q - c*q.
q**2*(q + 1)
Factor 2/3*k**2 - 140/3*k - 142/3.
2*(k - 71)*(k + 1)/3
Let l be (-3)/33*(-143)/52*(-24)/(-5). Factor l + 2/5*i**2 - 2*i + 2/5*i**3.
2*(i - 1)**2*(i + 3)/5
Factor 18*t + t**2 + 3*t - 10 - 24*t.
(t - 5)*(t + 2)
Let h(l) be the first derivative of 5*l**3 - 20*l + l**5 - 25/2*l**2 + 5 + 25/4*l**4. Factor h(i).
5*(i - 1)*(i + 1)**2*(i + 4)
Let s be ((-6)/4)/3*-8. Factor 0*n**4 - 6*n**4 + 2*n**4 - n**s + 5*n**3.
-5*n**3*(n - 1)
Let a(i) be the second derivative of -4/5*i**2 + 11/15*i**3 + 9*i + 1/75*i**6 + 0 - 3/10*i**4 + 1/50*i**5. Factor a(q).
2*(q - 1)**3*(q + 4)/5
Suppose 5*p - 12 = 4*p - 2*m, m = -3*p + 31. Let t be p*((-6)/(-2) + 63/(-56)). Factor -5/2*u**4 + 2*u**2 - t*u**5 + 0*u + 7*u**3 + 0.
-u**2*(3*u - 2)*(5*u + 2)**2/4
Let f = -2488/55 + 612/11. Let q = f + -458/45. Factor -q*m + 2/9*m**2 - 4/9.
2*(m - 2)*(m + 1)/9
Let c(l) be the second derivative of -3*l**5/20 + 7*l**4/2 - 11*l - 1. Solve c(b) = 0.
0, 14
Let b(f) = -3*f - 3. Let r be b(-2). Let m = 23148 + -23148. Factor -6/19*s**4 + 4/19*s**r + 0*s**2 + m*s + 0.
-2*s**3*(3*s - 2)/19
Let u be ((-31626)/840 - -42)*(7 - -1). Determine d so that -u*d**2 - 6*d**5 - 402/5*d**3 + 8*d + 24/5 - 242/5*d**4 = 0.
-6, -1, -2/5, 1/3
Let t(h) be the second derivative of h**4/28 - 5*h**3/14 + 279*h. Find p, given that t(p) = 0.
0, 5
Let r(c) = c**2 + 7*c + 9. Let j be r(-6). Let z be (4/14)/(j/21). Factor -4*g + 7 - 2*g**2 + 3*g**z + 0*g - 4.
(g - 3)*(g - 1)
Let i = -39/10 - -821/210. Let k(w) be the third derivative of 0*w + 2/21*w**3 + 1/84*w**4 + 0 - 4*w**2 - 1/420*w**6 - i*w**5. What is o in k(o) = 0?
-2, -1, 1
Let t(q) be the first derivative of 2*q**5/35 - 6*q**3/7 + 488. Factor t(g).
2*g**2*(g - 3)*(g + 3)/7
Let m(s) be the second derivative of -s**4 + 2*s**3/15 + s - 7. Factor m(t).
-4*t*(15*t - 1)/5
Let a(g) be the first derivative of -3*g**4/28 + 9*g**3/7 - 3*g**2 + 38. Find b, given that a(b) = 0.
0, 2, 7
Let b(o) be the third derivative of -o**5/20 + 29*o**4/2 + 75*o**2 - o. Find y, given that b(y) = 0.
0, 116
Let r(z) be the second derivative of 1/30*z**6 + 11/12*z**4 + 0*z**2 + z**3 + 3/10*z**5 + 2 - 10*z. Factor r(c).
c*(c + 1)*(c + 2)*(c + 3)
Let b(m) = m. Let c be (-2)/(-9) + 306/81. Let x be b(c). Factor k**x + 45*k**2 - 45*k**2.
k**4
Find n, given that 800/7 + 80/7*n + 2/7*n**2 = 0.
-20
Suppose -3*p = -4*o - 9, -o + 9 = 3*p - 0. Factor 5/2*y**p - 2 - 17/2*y**2 + 8*y.
(y - 2)*(y - 1)*(5*y - 2)/2
Find y such that 22/3 - 86/3*y + 14/3*y**4 + 124/3*y**2 - 76/3*y**3 + 2/3*y**5 = 0.
-11, 1
Let b(i) = i - 13. Let d be b(15). Solve 8*t**2 + d*t**3 - 3*t**3 - 20*t + 0*t**3 + 16 = 0 for t.
2, 4
Let w(r) = -r**3 + r. Let t(d) = -2*d**3 - 4*d**2 + 6*d. Let y = 27 + -23. Let k(h) = y*w(h) - t(h). Suppose k(i) = 0. What is i?
0, 1
Let w be 1 - (12/28 + (-4)/(-7)). Let g(j) be the second derivative of 1/2*j**2 - 4*j + 0 + w*j**3 - 1/12*j**4. What is p in g(p) = 0?
-1, 1
Let x(k) be the second derivative of -1/12*k**4 + 5/6*k**3 + 0 - 1/20*k**5 - 3/2*k**2 + 18*k. Determine c, given that x(c) = 0.
-3, 1
Let n = -5334 + 5336. Factor -25/4 - 11/4*c**n + 35/4*c + 1/4*c**3.
(c - 5)**2*(c - 1)/4
Suppose -4*c + 0*c - 5*k = -18, 0 = -5*c + 5*k. Factor -c*s**2 - 3*s**2 - 7*s + 17*s.
-5*s*(s - 2)
Let m = -202431/41 - -4938. Let z = m - -972/205. Factor -51/5*n + z*n**3 + 9/5 + 63/5*n**2.
3*(n + 3)*(3*n - 1)**2/5
Solve 22*o + 1150*o**2 - 82*o - 1147*o**2 = 0.
0, 20
Let l(f) = f**3 + 9*f**2 + 3*f + 30. Let q be l(-9). Solve -8/3*z**q + 0 - 16/9*z**4 - 4/9*z**5 - 16/9*z**2 - 4/9*z = 0 for z.
-1, 0
Let s(c) be the first derivative of -c**6/10 - 3*c**5/20 + 2*c**4 + 6*c**3 - 33*c - 20. Let z(r) be the first derivative of s(r). Solve z(p) = 0.
-2, 0, 3
Let z(c) = -3*c + 3. Let b be z(-18). Solve -160*h + 5*h**4 - 8*h**4 - 36*h**3 - 20*h - 138*h**2 - b - 18 = 0 for h.
-5, -1
Let z be (4/(-216))/(14/6 + -4). Let q(p) be the third derivative of -1/9*p**3 - z*p**6 + 1/18*p**4 + 2*p**2 + 0 + 0*p + 1/90*p**5. Solve q(x) = 0.
-1, 1/2, 1
Let o(w) be the third derivative of -w**6/600 - 13*w**5/300 - 2*w**4/5 - 6*w**3/5 - 2*w**2 + 2*w. Determine y so that o(y) = 0.
-6, -1
Let k(j) be the third derivative of 1/12*j**4 + 0*j**3 + 0*j - 1/180*j**6 + 1/36*j**5 + 5*j**2 + 0 - 1/630*j**7. Suppose k(p) = 0. What is p?
-3, -1, 0, 2
Let k(j) be the second derivative of -64/9*j**3 + 8/15*j**5 - 4/3*j**4 - 3*j - 16/3*j**2 + 0 + 7/45*j**6. Find s, given that k(s) = 0.
-2, -2/7, 2
Let q be (-20)/8*(-8)/10. Suppose -q*x = -38 + 14. Factor -4*u - 2*u**2 - x*u**4 + u + 3*u**3 + 15*u**4 - u**2.
3*u*(u - 1)*(u + 1)**2
Let w(n) be the second derivative of 0*n**2 + 25*n + 0*n**3 + 5/42*n**7 - 1/4*n**5 - 5/6*n**4 + 0 + 1/3*n**6. Suppose w(i) = 0. Calculate i.
-2, -1, 0, 1
Let h(d) = 7*d - 40. Let c be h(6). Solve -2/5*g**c - 4/5 + 6/5*g = 0.
1, 2
Let d(v) = v**3 - 27*v**2 + 81*v - 79. Let w(j) = 0*j - 16*j**3 + 0*j - 1 + 17*j**3. Let c(f) = d(f) + 2*w(f). What is h in c(h) = 0?
3
Suppose -3*z = -5*n + 10, 0*z + 3*z + n = 20. Factor 6*m**3 + 4*m**5 + 13 - 7 + 20*m**2 - 26*m**4 + 6*m**z + 6*m**3 - 22*m.
2*(m - 1)**3*(m + 1)*(5*m - 3)
Solve -205*f**3 + 60*f**4 + 237*f + 207*f**2 - 390*f**2 - 5*f**5 + 193*f**2 + 663*f - 1000 = 0.
-2, 2, 5
Let f(j) be the second derivative of j**8/3360 + j**7/720 + j**6/1080 + 2*j**3/3 - 9*j. Let t(c) be the second derivative of f(c). What is a in t(a) = 0?
-2, -1/3, 0
Let m(x) be the second derivative of x**7/105 + x**6/60 - 12*x**2 + 7*x. Let g(b) be the first derivative of m(b). What is u in g(u) = 0?
-1, 0
Let f(y) be the second derivative of y**8/20160 + y**7/1890 + y**6/720 - y**4/12 - 15*y. Let z(n) be the third derivative of f(n). Factor z(i).
i*(i + 1)*(i + 3)/3
Let n(w) be the first derivative of 4*w**5/5 - 2*w**4 - 16*w**3/3 + 4*w**2 + 12*w + 90. Determine p so that n(p) = 0.
-1, 1, 3
Suppose 3/5*x**2 + 9/5*x - 12/5 = 0. What is x?
-4, 1
Suppose -4*n - 4 = -16. Let l be (-98)/(-24) - (-211)/(-2532). What is g in 13/4*g**n + 3*g**l + 1/4*g + g**5 + 3/2*g**2 + 0 = 0?
-1, -1/2, 0
Let q(c) be the third derivative of c**7/210 - 11*c**6/120 + 23*c**5/60 + 11*c**4/24 - 4*c**3 + 120*c**2 + 3. Suppose q(l) = 0. What is l?
-1, 1, 3, 8
Suppose -25 = -0*d - d. Factor 192*q - d*q**4 - 3125 - 250*q**3 - q**5 - 2408*q - 1575*q + 666*q - 1250*q**2.
-(q + 5)**5
Let i = 1334 + -1334. Let q(g) be the third derivative of 0 + 0*g**3 - 5*g**2 + 0*g**4 - 1/120*g**5 + i*g. Find r such that q(r) = 0.
0
Let r be (-2512)/1336*(-1)/10. Let z = 2/167 + r. Factor -1/5*x + z*x**3 - 2/5*x**2 + 2/5.
(x - 2)*(x - 1)*(x + 1)/5
Let u be -4 - (4 + 3 + -3). Let x = 10 + u. Factor -2/3*b**5 - 4/3*b**4 + 14/3*b + 16/3*b**x + 4/3 + 4/3*b**3.
-2*(b - 2)*(b + 1)**4/3
Suppose -11*n = -4*n - 329. Let h = -93/2 + n. What is g in 0*g + 0 - h*g**2 = 0?
0
Let v be (-13)/(-21) - (-1