i**3. Factor a(f).
2*f*(f - 2)
Let h(f) be the third derivative of -3/10*f**5 + 1/12*f**4 + 2/3*f**3 + 0 - 13/60*f**6 - 1/21*f**7 + 3*f + 3*f**2. Factor h(p).
-2*(p + 1)**3*(5*p - 2)
Let w(k) = 9*k**4 + 3*k**3 + 7*k**2 - 19*k + 10. Let z(n) = -7*n**4 - 2*n**3 - 8*n**2 + 18*n - 9. Let i(t) = -4*w(t) - 5*z(t). Factor i(v).
-(v - 1)**3*(v + 5)
Suppose -105*g - 8*g + 656658 + 2405*g + 2*g**2 = 0. What is g?
-573
Find l such that 1/10*l**5 + 57/10*l**3 + 3*l + 0 + 73/10*l**2 + 3/2*l**4 = 0.
-10, -3, -1, 0
Let g(m) be the first derivative of -5*m**4/4 + 65*m**3/3 + 45*m**2 - 1800*m - 2574. What is p in g(p) = 0?
-5, 6, 12
Suppose -24 = -3*i + 30. Suppose -i*m + 5 = -17*m. Factor 0*o + 0*o**2 + 0 + 0*o**3 - 3/2*o**m - 3/2*o**4.
-3*o**4*(o + 1)/2
Factor -12*z + 0 - 1/3*z**4 + 9*z**2 + 10/3*z**3.
-z*(z - 12)*(z - 1)*(z + 3)/3
Let t = -1306 + 1309. Let q(d) be the third derivative of -1/60*d**6 - 1/30*d**5 + 0 + 0*d**t + 8*d**2 + 0*d + 0*d**4. Determine o, given that q(o) = 0.
-1, 0
Let i(w) be the third derivative of 72*w**2 + 1/720*w**6 + 0*w + 49/18*w**3 + 2/45*w**5 + 77/144*w**4 + 0. Factor i(p).
(p + 2)*(p + 7)**2/6
Let n = 38 - 264/7. Let w be (36/294)/((-4)/84*-3). Solve 8/7*d - w - n*d**2 = 0 for d.
1, 3
Let m(q) be the second derivative of -q**5/50 + 7*q**4/15 + 24*q**3/5 + 10043*q. Factor m(b).
-2*b*(b - 18)*(b + 4)/5
Let h(o) = -o**3 + 2*o**2 - 2*o. Let j(s) = 4*s**4 + 96*s**3 - 2252*s**2 - 77444*s - 550256. Let f(m) = 4*h(m) + j(m). Determine l so that f(l) = 0.
-17, 28
Let w(z) be the second derivative of -5*z**7/42 - 73*z**6/6 - 1627*z**5/4 - 18285*z**4/4 - 24480*z**3 - 69120*z**2 + 49*z + 18. Factor w(y).
-5*(y + 3)**3*(y + 32)**2
Factor 3/5*g**2 - 96/5*g + 693/5.
3*(g - 21)*(g - 11)/5
What is c in 10176*c + 999*c**3 + 7192*c**2 - 1152 + 38*c**4 + 232*c**3 - 106*c**3 - 141*c**3 = 0?
-12, -2, 2/19
Let k(g) = -5*g - 99. Let r be k(-19). Let o(d) = 8*d**3 - 15*d**2 + 17*d - 2. Let j(q) = -7*q**3 + 14*q**2 - 14*q + 1. Let h(v) = r*j(v) - 3*o(v). Factor h(z).
(z - 2)*(z - 1)*(4*z + 1)
Suppose -1987*b + 1393 = -4568. Determine y, given that -135*y**4 - 3441/4*y**b + 18 - 585/2*y**2 + 57*y = 0.
-6, -2/5, -2/9, 1/4
Let s be ((-59136)/2310)/(4 + (-3882)/960). Solve 4/7*z**2 + s + 256/7*z = 0.
-32
Suppose -19*u = -20*u + 45. Suppose -3*v + 20*v**4 + 15*v**2 + 39*v**3 - 17*v + u*v**2 + 36*v**3 = 0. Calculate v.
-2, 0, 1/4
Suppose 392*v + 966*v = 0. Suppose -22/3*y**2 + 0 - 2/3*y**4 - 8*y**3 + v*y = 0. What is y?
-11, -1, 0
Let c(a) = 481*a + 32231. Let u be c(-67). Suppose -100/9*z**2 + 0 - 4/9*z**u + 0*z - 40/9*z**3 = 0. Calculate z.
-5, 0
Let a(x) be the second derivative of 1/3*x**4 - 16/3*x**3 + 0*x**2 + 67*x + 0. Factor a(b).
4*b*(b - 8)
Let w be ((-2883)/912)/(-4 - 36/8). Let k = 1/323 + w. Solve 3/2*d - 15/8 + k*d**2 = 0.
-5, 1
Let j(k) be the first derivative of k**3 + 27*k**2/2 + 20*k - 251. Let q(y) = y**2 - y. Let z(n) = j(n) + 2*q(n). Factor z(p).
5*(p + 1)*(p + 4)
Suppose 141*j = 385*j. Solve j + 3/2*n**2 - 39/2*n = 0 for n.
0, 13
Let o(v) = v**3 + 18*v**2 - 9*v - 18. Let c be o(-21). Let u = c - -1767. Factor -2*k**4 + 2*k**3 + 2*k**2 - 2*k + 0*k**3 + 615 - u.
-2*k*(k - 1)**2*(k + 1)
Let k be (0 - 8/(-10)) + -42*(-64)/(-20160). Find j, given that -8*j**2 + 0*j + 0 + k*j**3 = 0.
0, 12
Let n be (-405)/(-54) + (234/(-8))/13*(-8)/(-3). What is y in 36 + n*y**4 - 27/2*y**3 + 45*y**2 - 66*y = 0?
2, 3
Let l be ((-70)/28)/((-2)/4). Factor -5*q + 10*q**2 + 3726 - l*q**3 - 3726.
-5*q*(q - 1)**2
Let p be (-190)/(-2 + 12) - 8806/(-374). Determine m, given that -30/11*m - 18/11*m**2 - 2/11*m**3 + p = 0.
-5, 1
Suppose -14*r**2 + 186516 - 186516 - 18*r**2 - 98*r**4 + 112*r**3 = 0. What is r?
0, 4/7
Let g(u) be the third derivative of u**8/504 + 13*u**7/1260 + 11*u**6/720 + u**5/180 - 995*u**2. Solve g(k) = 0.
-2, -1, -1/4, 0
Suppose 25*t**2 - 5*t**2 + 5159 + 8839*t - 34047*t + 4921 = 0. Calculate t.
2/5, 1260
Let t = -43 - -34. Let h be (-15)/t - (-7)/21. Factor 1024 + 1024*b + 64*b**3 + 42*b**2 + 4*b**4 + 227*b**2 + 115*b**h.
4*(b + 4)**4
Let v(a) = 7*a**3 - 41*a**2 - 243*a - 307. Let j(y) = -y**3 + 3*y - 1. Let x(c) = -40*j(c) - 5*v(c). Find i, given that x(i) = 0.
-35, -3
Let n(t) = 20*t**2 - 69*t + 49. Let o(b) be the first derivative of 5*b**3/3 - 17*b**2/2 + 12*b + 13. Let u(m) = -2*n(m) + 9*o(m). Solve u(a) = 0 for a.
1, 2
Factor 1083/8*u**2 + 0*u + 57/4*u**3 + 0 + 3/8*u**4.
3*u**2*(u + 19)**2/8
Suppose 2*d + 5 - 8 = 3*v, 0 = d + 2*v + 2. Let -5*n**2 + d*n - n**2 + 2*n**3 + 6*n - 2*n = 0. Calculate n.
0, 1, 2
Let t(j) be the second derivative of -j**6/1800 + j**5/50 + 13*j**4/120 + 18*j**3 + 12*j - 2. Let s(g) be the second derivative of t(g). Factor s(l).
-(l - 13)*(l + 1)/5
Let n(i) be the third derivative of i**8/504 + 13*i**7/315 - 13*i**6/36 + 17*i**5/30 + i**2 - 93*i + 1. Let n(m) = 0. Calculate m.
-17, 0, 1, 3
Let s(d) be the first derivative of d**4/16 + 65*d**3/6 + 257*d**2/8 + 32*d + 2364. Factor s(v).
(v + 1)**2*(v + 128)/4
Suppose 16*q + 1277 + 3987 = 0. Let m = -1643/5 - q. Factor -m*a**2 - 8/5 + 2*a.
-2*(a - 4)*(a - 1)/5
Let b(k) be the first derivative of -k**3/18 - 29*k**2 - 5046*k - 4755. Factor b(i).
-(i + 174)**2/6
Let w(q) = q**2 - 2*q + 2. Let s be w(-8). Suppose -5*c = 3*n - 136, -c + s = 2*c + 2*n. Factor 5*z**3 + 2*z**2 + c - 20 - 14 - 28*z + 2*z**3.
(z - 2)*(z + 2)*(7*z + 2)
Let d = -179 - -185. Factor -7*j**4 - 4*j**3 + 4*j + 10*j**3 - d*j**2 + 5*j**4 - 2*j.
-2*j*(j - 1)**3
Let t(s) = -328*s**3 - 476*s**2 + 468*s + 316. Let l(q) = 47*q**3 + 68*q**2 - 67*q - 45. Let y(d) = 20*l(d) + 3*t(d). Factor y(z).
-4*(z - 1)*(z + 2)*(11*z + 6)
Let y = 18828/955 - 22/191. Let x(r) = -1934*r - 25137. Let n be x(-13). Determine s, given that -266/5*s + 212/5*s**2 - 22/5*s**4 - 2/5*s**n + y - 4*s**3 = 0.
-7, 1
Let y(u) be the first derivative of 0*u**2 - 2 + 1/4*u**3 - 3*u. Solve y(s) = 0 for s.
-2, 2
Let f(d) be the first derivative of 18*d**5 + 55/2*d**4 - 15/2*d**2 + 25/6*d**6 + 213 - 10*d + 40/3*d**3. Factor f(b).
5*(b + 1)**4*(5*b - 2)
Let m be 0/(-2 + 3 - 3). Suppose k + k + 8 = m, k = -5*u + 36. Determine n so that 4 - 6*n + n**2 - u - 3*n**2 - n + n**3 = 0.
-1, 4
Let w(i) = i**3 - 21*i**2 + 26*i + 19. Let q be w(23). Let t = q + -1672. Factor 0 + 14/3*o**2 + 2/3*o**4 + 10/3*o**t + 2*o.
2*o*(o + 1)**2*(o + 3)/3
Factor -104*f**3 - 536*f + 61*f**3 + 146 + 6 + 51*f**3 - 290*f**2.
2*(f - 38)*(f + 2)*(4*f - 1)
Suppose -1/3*z**4 + 2860*z + 44*z**3 - 4225/3 - 4486/3*z**2 = 0. What is z?
1, 65
Let h = 50 + -42. Factor 4*j**2 - j**4 - 5*j + h*j**3 - 21*j**2 + 7*j + 8*j.
-j*(j - 5)*(j - 2)*(j - 1)
Suppose -5*r + 90 = 2*u, 21*r - 72 = 17*r - 2*u. Factor 10*n**2 + 26*n - r*n**2 + 0*n**3 - 42*n - n**3.
-n*(n + 4)**2
Let c be -32 + 1116/(80 - 49). Find p such that 0 - 2/3*p**c - 30*p**2 + 8*p**3 + 100/3*p = 0.
0, 2, 5
Let c(m) be the first derivative of -m**5/80 + 5*m**4/48 - m**3/3 + m**2/2 - 48*m - 27. Let b(t) be the first derivative of c(t). Determine k so that b(k) = 0.
1, 2
Suppose 12*p + 5*p = -102. Let y be p/(-7)*(-54)/(-36). Determine v, given that -12/7 + y*v + 3/7*v**2 = 0.
-4, 1
Let m = -107 - -113. Let i be (191 + 1)/m*(-2)/(-10). Find h such that 14/5*h**2 + 24/5 - 2/5*h**3 - i*h = 0.
2, 3
Let v be 6/(7 + -15 - -14). Find h such that -1 + 72*h + 3*h**2 + 57*h + 2 - v = 0.
-43, 0
Let n be 0 - ((-12)/3 + 21 + -20 + 242/88). Suppose n*m**2 + 15 + 8*m = 0. What is m?
-30, -2
Let q be 132/176*(-1 + -3). Let n be q - 8/(-40)*23. Factor 4/5*u**2 + 12/5*u + n.
4*(u + 1)*(u + 2)/5
Let k(r) be the first derivative of -15*r**4/4 + 2335*r**3/3 + 7935*r**2/2 + 2385*r + 3987. Factor k(p).
-5*(p - 159)*(p + 3)*(3*p + 1)
Let x be 6/(-33) + 888/44. Let l be x/(-15)*3/(-2). Suppose -44*o + 16 + 33*o**2 + l - 5*o - 56*o = 0. Calculate o.
2/11, 3
Let k(i) = -51*i + 100*i - 7*i**2 - 47*i - 9. Let x(f) = -6*f**2 + f - 8. Let z(o) = -5*k(o) + 6*x(o). Suppose z(p) = 0. Calculate p.
-3, -1
Let v = -740 - -402. Let a = 340 + v. Factor -4/5 - 8/5*c + c**a.
(c - 2)*(5*c + 2)/5
Solve -512/5 - 1628/5*j**3 - 5056/5*j - 6176/5*j**2 + 38/5*j**4 + 34/5*j**5 = 0 for j.
-4, -1, -2/17, 8
Let u = 27998 + -27995. Suppose 0*o**2 - 1/2 - 3/4*o + 1/4*o**u = 0. What is o?
-1, 2
Suppose -13*c = -16*c + 6. Let a be (23/c - 8) + -2. Determine m so that 10/3*m - a*m*