o) = -g(o) - 6*u(o). Factor i(w).
3*(w - 14)*(w - 6)
Let q = 175 - 177. Let c(w) = -8*w**2 + 6*w - 2. Let g(v) = -11*v**2 + 7*v - 3. Let j(f) = q*g(f) + 3*c(f). Factor j(z).
-2*z*(z - 2)
Determine f, given that 27/5*f**3 + 87/5*f**2 - 108/5*f - 12/5*f**4 - 156/5 = 0.
-2, -1, 2, 13/4
Suppose 4*k = -3967 + 3975, -k - 1 = -t. Let c(d) be the first derivative of -35/3*d**t + 5/4*d**4 + 15 + 80*d + 20*d**2. Factor c(h).
5*(h - 4)**2*(h + 1)
Let t(a) be the first derivative of a**6/2 + 48*a**5/5 + 207*a**4/4 + 90*a**3 + 6806. Factor t(l).
3*l**2*(l + 3)**2*(l + 10)
Let b(u) = -2*u**2 - 168*u + 176. Let c(v) = v**2 + 168*v - 174. Let j(n) = 5*b(n) + 6*c(n). Factor j(h).
-4*(h - 41)*(h - 1)
Factor 228099131 - 367225*z + 3*z**3 - 212322*z + 27*z**3 + 1833*z**2 - 31*z**3 - 540416*z.
-(z - 611)**3
Let n(m) be the first derivative of m**6/280 - m**5/14 - 11*m**4/56 + 89*m**2 + 85. Let l(u) be the second derivative of n(u). Determine g so that l(g) = 0.
-1, 0, 11
Let k = 9596/3 - 3187. Let s(d) be the first derivative of -45/4*d**4 - 5*d**2 - 5/6*d**6 + 0*d + 5*d**5 + 16 + k*d**3. Factor s(b).
-5*b*(b - 2)*(b - 1)**3
Let f(l) be the first derivative of -3*l**5/70 - 5*l**4/42 + 26*l**3/21 - 8*l**2/7 - 136*l + 14. Let j(t) be the first derivative of f(t). Factor j(o).
-2*(o - 2)*(o + 4)*(3*o - 1)/7
Let f be (((-2700)/(-40))/15)/30. Let q(h) be the first derivative of 0*h - 30 + 1/30*h**3 - f*h**2. Find b, given that q(b) = 0.
0, 3
Let x(m) be the third derivative of -m**6/180 - 17*m**5/30 + 35*m**4/12 + 2*m**3/3 + 36*m**2. Let r(j) be the first derivative of x(j). Solve r(c) = 0 for c.
-35, 1
Let r(t) be the third derivative of t**6/480 - 17*t**5/120 + 271*t**4/96 + 51*t**3/4 - 1845*t**2. Factor r(w).
(w - 18)*(w - 17)*(w + 1)/4
Let g be (-2)/(-6)*(-1)/(-3). Let z(u) be the first derivative of 1/3*u + g*u**3 - 10 + 1/3*u**2. Factor z(k).
(k + 1)**2/3
Suppose 3*t + h + h = 14, 3*h - 12 = 0. Suppose 3*j + q + t = 0, -j - 2*q + 5*q = -6. Find s such that 0*s**2 + j + 0*s + 4/11*s**5 + 2/11*s**3 + 6/11*s**4 = 0.
-1, -1/2, 0
Let b be -3 - 0 - 152/(-40). Let v = 16925 + -16923. Factor b*n**3 + 0*n + 3/5*n**v + 1/5*n**4 + 0.
n**2*(n + 1)*(n + 3)/5
Let j(y) = -3*y**2 + 2724*y - 618376. Let x(g) = g**2 - 908*g + 206124. Let h(l) = -2*j(l) - 7*x(l). What is v in h(v) = 0?
454
Factor -9*o**5 + 83/3*o**4 - 2/3*o + 11*o**2 + 0 - 29*o**3.
-o*(o - 1)**3*(27*o - 2)/3
Let h(y) be the first derivative of -y**4/28 + 6*y**2/7 - 16*y/7 + 216. Suppose h(n) = 0. Calculate n.
-4, 2
Let n(l) = -7*l + 4*l + 4*l. Let g(i) = 32*i**5 - 240*i**4 + 386*i**3 + 240*i**2 + 50*i. Let w(f) = -2*g(f) + 36*n(f). Determine p, given that w(p) = 0.
-1/4, 0, 4
Let w be 116/(-87)*((-38)/2 - (-2)/14). Suppose 4/7*t**2 + w*t + 1936/7 = 0. Calculate t.
-22
Determine c, given that -40*c**2 + 640/3 - 50/3*c**3 + 160/3*c - 5/3*c**4 = 0.
-4, 2
Let a(f) be the first derivative of -f**5/30 + 5*f**4/2 - 53*f**3/18 - 59*f**2/2 - 8810. Find s such that a(s) = 0.
-2, 0, 3, 59
Factor -18*q + 59 - 18*q - 8*q - 25 + 4*q**2 + 6.
4*(q - 10)*(q - 1)
Let r(b) be the second derivative of b**4/30 + 26*b**3/5 - 79*b**2/5 - 172*b. Suppose r(g) = 0. Calculate g.
-79, 1
Factor 5271616/5 + 2/5*z**5 + 2308/5*z**4 + 796256*z**2 + 672752/5*z**3 + 7925792/5*z.
2*(z + 2)**3*(z + 574)**2/5
Let s(m) be the first derivative of m**5/30 + m**4/6 - m**3/9 - m**2 - 73*m + 33. Let f(z) be the first derivative of s(z). Factor f(r).
2*(r - 1)*(r + 1)*(r + 3)/3
Let q(t) = 16*t**3 - 172*t**2 - 32*t + 4. Let j(m) = -17*m**3 + 173*m**2 + 33*m - 3. Let b(u) = 4*j(u) + 3*q(u). Find s, given that b(s) = 0.
-1/5, 0, 9
Let k(w) = 11*w - 7. Let x be k(1). Suppose y = x*y. Factor 3 + y - 4 + g**2 + 7*g - 7.
(g - 1)*(g + 8)
Let p(q) = -q. Let f(m) = m**2 + 5*m + 12. Let n(z) = -f(z) + 6*p(z). Let i be n(-9). Factor -6 - 2*s**2 - i + 12.
-2*s**2
Factor 45*p**2 - 220*p - 5/3*p**3 - 1900/3.
-5*(p - 19)*(p - 10)*(p + 2)/3
Let a(j) be the third derivative of -4/3*j**3 + 0*j**7 + 10*j + 0 - 2/15*j**6 + 2/15*j**5 + 1/2*j**4 - j**2 + 1/84*j**8. Suppose a(v) = 0. Calculate v.
-2, -1, 1
Let -109*i**3 - 12*i**2 + i**4 + i + 64 + 105*i**3 + 20*i + 11*i = 0. What is i?
-2, 4
What is b in -77/3*b + 3*b**2 - 12 = 0?
-4/9, 9
Suppose 2*x = 3*y - 9, 2*x - 7*y + 19 = -2*y. Suppose -5*a**x + 206*a**2 + 2*a**3 - 10404*a + 117912 + 100*a**2 = 0. Calculate a.
34
Factor -9/2*b**2 + 309/4 - 1851/4*b.
-3*(b + 103)*(6*b - 1)/4
Suppose c = 5*y + 90, 1049*y = -4*c + 1052*y + 54. Find r, given that 4*r + c + 1/4*r**4 + 7/2*r**3 - 31/4*r**2 = 0.
-16, 0, 1
Suppose 105*a**3 - 10*a + 1484879 + 125*a**4 - 1484879 + 45*a**5 + 15*a**2 = 0. What is a?
-1, 0, 2/9
Let w(y) = -y**3 + 31*y**2 - 41*y + 333. Let t be w(30). Factor -5/3*v - 2 - 1/3*v**4 + 7/3*v**2 + 5/3*v**t.
-(v - 6)*(v - 1)*(v + 1)**2/3
Let o(s) be the second derivative of 3*s**5/140 + 97*s**4/28 - s**3/14 - 291*s**2/14 - 2*s - 167. Find g such that o(g) = 0.
-97, -1, 1
Let h(g) = g**2 + 11*g**2 - 120 + 93*g - 18*g**2. Let k(y) = y**2 - 18*y + 24. Let f(j) = -4*h(j) - 21*k(j). Factor f(p).
3*(p - 2)*(p + 4)
Let d(j) be the second derivative of 5*j**7/42 + j**6/2 - j**5/4 - 5*j**4/4 - 5*j + 165. Factor d(f).
5*f**2*(f - 1)*(f + 1)*(f + 3)
Let f(t) = -t - 2. Let x be f(-9). Determine n, given that -2*n**2 + x*n**3 - 5*n**3 - n**3 - 3*n = 0.
-1, 0, 3
Let s(n) be the third derivative of -3645/2*n**4 - 1/24*n**6 + 27/2*n**5 + 131220*n**3 + 0 - 109*n**2 - 2*n. Factor s(l).
-5*(l - 54)**3
Let r = -10 - -15. What is i in i**2 - 13*i - 10*i + 24*i - r*i = 0?
0, 4
Factor 1/3*b**2 + 19200 + 160*b.
(b + 240)**2/3
Let h(c) be the second derivative of 41/2*c**3 + 2 + 30*c**2 - 15*c - 3/20*c**5 - 1/10*c**6 + 21/4*c**4. Find w, given that h(w) = 0.
-4, -1, 5
Let l(c) be the first derivative of 20 + 4/9*c**3 + 124/9*c + 188/9*c**2. Factor l(a).
4*(a + 31)*(3*a + 1)/9
Let z(k) be the first derivative of 2/3*k**2 + 2/5*k**5 + 1/18*k**6 + 4/3*k**3 + 0*k + 13/12*k**4 - 47. Let z(m) = 0. What is m?
-2, -1, 0
Suppose -2*n**2 - 1875*n + 0*n**2 + 50 + 32768938*n**3 - 32768863*n**3 = 0. Calculate n.
-5, 2/75, 5
Let t(u) be the first derivative of -129 + 108/11*u**3 - 1344/11*u**2 - 5/22*u**4 + 1024/11*u. Find k such that t(k) = 0.
2/5, 16
Factor 68/7*l**2 - 3/7*l**3 + 50/7 + 173/7*l.
-(l - 25)*(l + 2)*(3*l + 1)/7
Suppose 5*n - s = -12, 24*n = 23*n + 3*s - 8. Let h be ((-48)/(-64))/((-75)/(-24) + n). Let -10/3*a + h*a**2 + 8/3 = 0. Calculate a.
1, 4
Let i(o) be the second derivative of 5/6*o**3 + 1/48*o**4 + 0 + 25/2*o**2 - 35*o. Factor i(k).
(k + 10)**2/4
Let d be ((8 - 5) + -3)/2. Let u(f) be the third derivative of -10*f**2 + d + 2/25*f**5 - 2/15*f**4 + 0*f + 0*f**3 + 1/525*f**7 - 1/50*f**6. Factor u(t).
2*t*(t - 2)**3/5
Let u(r) = r**3 - r**2 + 2*r. Let w be -4 - 3/((-12)/8). Let v(h) = -7*h**3 + 2*h**2 + 16*h. Let o(z) = w*u(z) - v(z). Factor o(s).
5*s*(s - 2)*(s + 2)
Let i be (-1080)/(-504) + (-12)/(-336)*-4. Suppose 0*c**3 - 6/7*c**i + 3/7*c**4 + 0*c + 3/7 = 0. What is c?
-1, 1
Let g(n) = 19*n**2 + 4*n - 31. Let d be g(5). Solve 226*k**5 - d*k**5 - 20*k**2 + 75*k**4 - 60*k**3 + 218*k**5 = 0 for k.
-1/4, 0, 2
Let j(r) be the first derivative of r**6/39 + 6*r**5/5 - 41*r**4/13 + 4*r**3/39 + 81*r**2/13 - 82*r/13 + 1147. Let j(o) = 0. What is o?
-41, -1, 1
Let w(f) = -f**2 - 40*f - 40. Let r be w(-19). Let k = 359 - r. Find h, given that 0*h**4 + k + 4/15*h**2 - 2/5*h**3 + 2/15*h**5 + 0*h = 0.
-2, 0, 1
Let s(q) = -2*q + 10. Let v be s(11). Let i be (-4 - 0) + 8*(-9)/v. Factor 1/3*r**i + 1/3*r + 0.
r*(r + 1)/3
Let t(h) be the first derivative of -9/4*h**4 - 13/8*h**2 + 1/4*h + 108 + 4*h**3. What is w in t(w) = 0?
1/6, 1
Determine h, given that 1/3*h**2 + 334668 + 668*h = 0.
-1002
Let h(u) be the first derivative of u**5 + 15*u**4/4 - 5*u**3 - 55*u**2/2 - 30*u - 298. Factor h(c).
5*(c - 2)*(c + 1)**2*(c + 3)
Suppose -7*c + 20 = 3*c. Factor -c*d**2 + 0*d**2 + 2 - 62 - 3*d**2 + 101*d - 61*d.
-5*(d - 6)*(d - 2)
Let h(u) be the third derivative of -5/8*u**4 + 0*u + 0 + 1/24*u**6 + 1/3*u**5 - 15*u**3 - 23*u**2. Find i such that h(i) = 0.
-3, 2
Find p such that -569 - 75 - 178*p - 84 + p**2 = 0.
-4, 182
Let s be (21/399)/(12/76). Let x(a) be the second derivative of 0 - 18*a - 3/2*a**2 + 1/90*a**6 + 1/10*a**5 + 2/9*a**4 - s*a**3. Factor x(u).
(u - 1)*(u +