k(b) be the third derivative of b**8/120 + 6074*b**7/525 + 655333*b**6/150 - 1509016*b**5/75 + 138649*b**4/4 - 25230*b**3 + 1917*b**2. Solve k(g) = 0.
-435, 2/7, 1
Let a(m) = 4*m**2 - 77*m + 21. Suppose 10*g + 4 = 194. Let p be a(g). Let 18/5*x - 10*x**4 - p*x**3 + 42/5*x**2 + 0 = 0. What is x?
-3/5, 0, 1
Let k(w) be the first derivative of 1/6*w**4 + 50/9*w**3 + 18*w - 53/3*w**2 - 23. Find l, given that k(l) = 0.
-27, 1
Let x(y) be the third derivative of -9*y**8/112 - 104*y**7/35 - 181*y**6/8 - 143*y**5/2 - 199*y**4/2 - 36*y**3 + 2056*y**2. Solve x(m) = 0.
-18, -2, -1, -1/9
Let q be (-1)/(-15) - 18/(-855). Let o = 67/114 - q. Determine i, given that -o*i**2 + 1/2 - 1/4*i**3 + 1/4*i = 0.
-2, -1, 1
Let v(j) be the third derivative of 7/15*j**5 - 25/3*j**3 + 0 + j**2 + 28*j - 55/24*j**4 - 1/40*j**6. Let v(z) = 0. What is z?
-2/3, 5
Suppose -448*b = -447*b + 517. Let j = -514 - b. Factor 0*n**2 + 3/2*n**j + 0 - 3/2*n.
3*n*(n - 1)*(n + 1)/2
Let u be (16 - 5249/87) + 46. Find t, given that -u*t**4 + 13/3*t**2 - 28/3*t - 1/3*t**5 + 3*t**3 + 4 = 0.
-6, -2, 1
Let d(m) be the second derivative of -m**6/1440 + m**5/30 - 41*m**3/3 + 3*m**2/2 - 237*m. Let x(s) be the second derivative of d(s). Factor x(n).
-n*(n - 16)/4
Let z(t) = 3*t + 65. Let j be z(-6). Let r = j - 44. Factor -2/7*x**r - 16/7*x**2 - 12/7 - 26/7*x.
-2*(x + 1)**2*(x + 6)/7
Let t = 266 - 261. Suppose t - 1 = 2*q. Factor -1/3*u**3 + 1/3*u**q + 0 + 0*u.
-u**2*(u - 1)/3
Let w = -16815484/9 + 1868388. Determine s so that -w + 2*s**2 + 32/9*s = 0.
-2, 2/9
Factor -200*k**2 - 903*k**5 + 899*k**5 + 32*k**4 - 8*k**3 - 7*k**3 - 5*k**3.
-4*k**2*(k - 5)**2*(k + 2)
Factor 10170*a - 2490084 - 4*a**2 - 1494*a - 2364*a.
-4*(a - 789)**2
Let v be (-10)/65 + 123/39. Suppose -v*t - 1 = 4*w + 5, 5*t + w = 7. Factor 30*i**2 - 3 + 38*i**t - 3 - 71*i**2 - 11*i.
-(i + 3)*(3*i + 2)
Let u(a) = -8*a**4 - 43*a**3 - 13*a**2 + 152*a - 5. Let i(x) = 11*x**4 + 64*x**3 + 19*x**2 - 228*x + 7. Let r(h) = 5*i(h) + 7*u(h). Factor r(q).
-q*(q - 19)*(q - 2)*(q + 2)
Let b be 4 + ((-2)/(-5))/((-2)/(-30)). Suppose 11*l = -b + 43. Determine o, given that -3/2*o**4 + 9/2*o**2 - 1/2*o**l - 3/2*o - 1 = 0.
-2, -1/3, 1
Find a, given that -4261*a**2 + 4915*a**2 + 484 + 3476*a + 20*a**5 + 5290*a**2 - 296*a**4 + 3416*a**3 + 780*a**4 = 0.
-11, -1, -1/5
Let o(g) = 15*g**2 + 5*g + 2. Let x(h) = h**2 + 15*h + 55. Let u be x(-7). Let c be o(u). Factor -19*d - 5*d + 1 - c*d**2 + 37 - 6 + 4*d**3.
4*(d - 4)*(d - 1)*(d + 2)
Let m(k) be the third derivative of -k**5/12 + 1725*k**4/4 - 1785375*k**3/2 + 101*k**2 + 6*k + 1. Factor m(n).
-5*(n - 1035)**2
Suppose 2*d - 5*d + 31 = 5*p, -d = -p + 3. Suppose -6*c = -14 + d. Factor -2*j**2 + j**2 - 3*j**3 - c*j**2 + 6*j.
-3*j*(j - 1)*(j + 2)
Suppose -2*r - 4*l + 12 = 0, 23 - 9 = 5*r + 2*l. Suppose r = -k + 3*t, -t = -4*k - 3*t + 6. What is i in 3*i**2 - 2 - 21*i - i**3 - k + 22*i = 0?
-1, 1, 3
Solve -131/3*q**2 + 49/3*q**4 + 168*q + 208/3 - 210*q**3 = 0.
-4/7, 1, 13
Solve 2/3*d**3 - 20/3 - 8*d**2 + 14*d = 0.
1, 10
Let r(i) = i**2 - 24*i + 79. Let o be r(16). Let u be -3 + (-77)/o + 2. What is k in -8/7*k**3 + 0 - 10/7*k**2 - 2/7*k**4 - u*k = 0?
-2, -1, 0
Suppose -11*p + 188 = -10*p. Let c = 190 - p. Factor -21/2*x - 9/2 - 15/2*x**c - 3/2*x**3.
-3*(x + 1)**2*(x + 3)/2
Suppose -7*g - 472 = -1193. Factor -3*n**4 - g*n + 99*n**2 - 20*n - 27*n**3 + 18*n + 36.
-3*(n - 1)**3*(n + 12)
Factor -1116 - 4885*h - 10*h**3 + 8731*h - 180 + 164*h**2 - 4368*h.
-2*(h - 9)**2*(5*h + 8)
Let l be 70/2250 - ((-15)/(-10) + 1580/(-1000)). Factor 1/9*c**3 + 20/9 - 16/9*c + l*c**2.
(c - 2)**2*(c + 5)/9
Let b(p) be the third derivative of -p**5/120 - 343*p**4/24 - 117649*p**3/12 - 2*p**2 - 851. Factor b(z).
-(z + 343)**2/2
Let n(d) be the second derivative of d**5/20 - 7*d**4/2 + 7*d**3 - 39*d**2/2 + 106*d. Let q be n(41). Solve -a**q - 1 - 10/3*a = 0 for a.
-3, -1/3
Let c(d) be the third derivative of -d**6/40 + 17*d**5/2 + 173*d**4/8 - 171*d**3 - 6338*d**2. Solve c(g) = 0 for g.
-2, 1, 171
Let b be ((-7)/(-14))/((-3)/(-24)). Factor -r**2 + b*r**2 + 5*r - 18 + 7*r + 3*r.
3*(r - 1)*(r + 6)
Solve -44*f**2 - 2/5*f**3 + 44 + 2/5*f = 0 for f.
-110, -1, 1
Let r(o) be the second derivative of o**4/12 + 2*o**3 - 25*o**2/2 + 8*o. Let a be r(-14). Factor 3*n - 2*n**3 + 4*n**a + 2 - 6*n - n**3.
(n - 1)**2*(n + 2)
Let k(g) be the second derivative of -g**5 - 25/126*g**7 + 320/9*g**3 + 23/18*g**6 - 100/9*g**4 - 75 - 2*g - 40*g**2. Determine p so that k(p) = 0.
-2, 3/5, 2
Find y, given that 84 - 96*y + 48*y**4 + 13*y**3 - 17*y**4 - 37*y**2 + 38*y**3 - 3*y**5 - 16*y**4 - 14*y**2 = 0.
-2, 1, 7
Let a(g) be the second derivative of 7*g**5/80 + 121*g**4/16 + 195*g**3 - 169*g**2/2 + 3478*g. Solve a(t) = 0.
-26, 1/7
Let u(i) = i**2 - 270*i + 3344. Let q be u(13). Let s = 1168/77 + -148/11. Factor -6/7 + 16/7*j + 0*j**q - s*j**2 + 2/7*j**4.
2*(j - 1)**3*(j + 3)/7
Let m(j) = -2163 - 8*j**3 + 3982 + 572*j - 92*j**2 - 2291. Let g(y) = y**3 - 1. Let w(n) = 12*g(n) + m(n). Suppose w(h) = 0. What is h?
1, 11
Let v be -19 + 33 + -20 + 9. Let t(h) be the first derivative of 0*h**2 - 15 + 0*h**v + 1/12*h**4 + 3/10*h**5 + 0*h. Factor t(f).
f**3*(9*f + 2)/6
Let o be ((15/(-80))/((-3)/(-26)))/(-6 + 2033/342). Find g, given that -7/4*g**2 - o*g + 17/2 = 0.
-17, 2/7
Let q(u) be the second derivative of u**7/1260 + u**6/180 + u**5/60 + 13*u**4/4 + u**3/6 - 52*u. Let n(t) be the third derivative of q(t). Solve n(s) = 0.
-1
Let k(r) be the third derivative of r**8/1680 - r**7/75 + 23*r**6/200 - 37*r**5/75 + 7*r**4/6 - 8*r**3/5 + 2733*r**2. Determine i, given that k(i) = 0.
1, 2, 4, 6
Factor -740662 - 29929*q**2 - 39630*q**2 - 952*q**3 - 2047048*q - 6281*q**2 - 4*q**4 - 1231494.
-4*(q + 1)*(q + 79)**3
Let t(x) be the second derivative of 121*x**6/15 + 132*x**5/5 + 83*x**4/3 + 8*x**3 + x**2 + x - 496. Suppose t(b) = 0. Calculate b.
-1, -1/11
Let w(r) = -13*r**2 + 901*r - 2611. Let m(k) = -7*k**2 + 451*k - 1305. Let v(s) = -5*m(s) + 3*w(s). Find h such that v(h) = 0.
3, 109
Let o be (-1916)/(-20)*4/(-12). Let i = o + 163/5. Determine d so that 0 + i*d - d**3 - 1/3*d**4 + 1/3*d**5 + 1/3*d**2 = 0.
-1, 0, 1, 2
Let q(r) be the first derivative of -3*r**5/5 + 123*r**4/16 - 87*r**3/4 - 6*r**2 + 87*r + 4270. Suppose q(w) = 0. What is w?
-1, 2, 29/4
Let z(f) be the third derivative of 0*f**4 + 1/540*f**6 + 0*f + 8 + 10*f**2 + 0*f**3 + 0*f**5 + 1/945*f**7. Factor z(y).
2*y**3*(y + 1)/9
Let a(m) = 5*m**4 + m**3 - 22*m**2. Let w(k) = -14*k**4 - 4*k**3 + 64*k**2. Let y(x) = 8*x + 124. Let h be y(-15). Let g(l) = h*w(l) + 11*a(l). Factor g(z).
-z**2*(z - 2)*(z + 7)
Let h(p) be the first derivative of 3*p**5/5 - 6*p**4 - 28*p**3 + 120*p**2 - 1805. Suppose h(r) = 0. Calculate r.
-4, 0, 2, 10
Factor -533/3*g**2 + 1681/9*g - 9*g**3 - 1/9*g**4 + 0.
-g*(g - 1)*(g + 41)**2/9
Let i(p) be the first derivative of 0*p**3 - p**2 + 19 + 0*p + 1/2*p**4. Let i(l) = 0. What is l?
-1, 0, 1
Let m(i) be the second derivative of -5/21*i**3 + 249*i + 0 - 6/7*i**2 - 1/42*i**4. Find w, given that m(w) = 0.
-3, -2
Factor 1/9*o**4 - 64/3*o**2 + 0 - 7/9*o**3 - 76*o.
o*(o - 19)*(o + 6)**2/9
Let t(c) be the first derivative of -5/3*c**3 - 13/2*c**2 - 191 + 6*c. Factor t(g).
-(g + 3)*(5*g - 2)
Let j = 784 - -707. Let x = j + -7449/5. What is f in 1/5*f**3 - 2/5*f**2 + x - f = 0?
-2, 1, 3
Let k be ((-32)/(-72))/((-2)/(-36)*4). What is w in 0*w**2 + 3*w**3 + 14*w**4 - 9*w**4 + w**5 - 7*w**2 + 0*w**k - 2*w**2 = 0?
-3, 0, 1
Factor 2/7*z**2 + 916/7*z + 0.
2*z*(z + 458)/7
Let x(o) be the second derivative of -o**5/70 + 37*o**4/21 + 157*o**3/7 + 720*o**2/7 + 8547*o. Factor x(n).
-2*(n - 80)*(n + 3)**2/7
Let n(g) = 3*g**2 - 25*g - 18. Let f be n(9). Let d be (-5 - f) + -2 - -10. Factor 8/7*y + 16/21 + 4/7*y**2 + 2/21*y**d.
2*(y + 2)**3/21
Factor -8*q**2 + 2*q**2 + 12*q**2 - 10*q**2 - 2202256 + 5936*q.
-4*(q - 742)**2
Let s = -3 + 9. Let z = 423 + -420. Let q(o) = -o**4 - o**3 + o**2 + 1. Let g(d) = 3*d**4 + d**3 - 3*d**2 + d - 2. Let r(n) = s*q(n) + z*g(n). Factor r(t).
3*t*(t - 1)**2*(t + 1)
Factor 1/7*p**2 + 54 + 191/7*p.
(p + 2)*(p + 189)/7
Let l be (-8)/(-3) - (-8)/(-12). Let x = 84 - 62. Factor 8 - 15*b + x*b**l + 4 - 63*b**2 - 22*b**2.
-3*(3*b - 1)*(7*b + 4)
Let v(x) = -2*x + 7. Let b(l) = -l + 4. Let t(y) = 5*b