2*(l - 2)*(l + 6)
Let k(q) be the first derivative of q**3/3 - q**2/2 - 56*q - 2109. Solve k(c) = 0.
-7, 8
Let w = 1384 - 668. Let c = w - 713. What is q in -1/3*q**2 + 0*q + 0 + 2/3*q**c = 0?
0, 1/2
Let a(o) be the first derivative of o**5/12 + o**4/2 + 7*o**3/18 - o**2 - 56*o + 14. Let t(v) be the first derivative of a(v). Suppose t(w) = 0. What is w?
-3, -1, 2/5
Let u(a) = 18*a + 21. Let h be u(-1). Let r(x) be the second derivative of 2/45*x**h - 1/18*x**4 + 0*x**2 - 3*x + 0. Find d such that r(d) = 0.
0, 2/5
Let l(i) be the first derivative of -i**4/7 + 116*i**3/21 - 1451. Suppose l(u) = 0. Calculate u.
0, 29
Let o = -2190 + 32851/15. Let z(s) be the third derivative of 0 + 0*s**3 + 1/12*s**4 - 4*s**2 + 1/60*s**6 - o*s**5 + 0*s. Factor z(l).
2*l*(l - 1)**2
Suppose 19 = 2*z - 5*o + 5, 2*z - 2*o - 8 = 0. Suppose 11 - 4 = d - 2*j, -3*d + 5 = z*j. Factor -3/4*c**5 - 15/4*c**d + 3*c**4 + 3/2*c**2 + 0*c + 0.
-3*c**2*(c - 2)*(c - 1)**2/4
Let f = 48576/565981 + -10/3349. Let z = 451/676 + f. Let 441*b - 63/2*b**2 + z*b**3 - 2058 = 0. Calculate b.
14
Determine y, given that 5/3*y**4 + 28/3*y - 1/3*y**5 - y**3 - 17/3*y**2 - 4 = 0.
-2, 1, 2, 3
Let o = -3/321443 - -17357943/2250101. Let 282/7*t**2 - 75/7*t**3 - 12/7*t**4 - 141/7*t - o = 0. Calculate t.
-9, -1/4, 1, 2
Let g(q) be the third derivative of -q**7/30 - 2*q**6/45 + 29*q**3/3 - 2*q**2 - 9. Let s(t) be the first derivative of g(t). Suppose s(k) = 0. What is k?
-4/7, 0
Let k(m) be the first derivative of 32/3*m**3 + 0*m - 8*m**2 - 5*m**4 - 100 + 4/5*m**5. Factor k(q).
4*q*(q - 2)**2*(q - 1)
Factor 104/17*v**3 - 12480/17*v - 872/17*v**2 - 2/17*v**4 - 28800/17.
-2*(v - 30)**2*(v + 4)**2/17
Let u(v) be the third derivative of -v**5/270 - 37*v**4/36 - 728*v**3/27 - 1079*v**2 - 2. Factor u(b).
-2*(b + 7)*(b + 104)/9
Let b be 537 + ((-54)/(-36))/((-1)/(-2)). Let c be 40/b - 2/27. Factor 20/3*s**3 - 50/3*s**2 - 2/3*s**4 + c + 0*s.
-2*s**2*(s - 5)**2/3
Let n = 773/47 + -7939/517. Determine m so that 0*m - 62/11*m**3 - 8/11*m**5 + 0 - n*m**2 - 58/11*m**4 = 0.
-6, -1, -1/4, 0
Let f(s) = 3*s - 51. Let c be f(17). Let o be 2 - c*(4 + (-45)/12). Factor -31*i**2 - 5*i**o - 4*i**4 - 36*i + 16 + 28*i - 22*i**3.
-2*(i + 2)**3*(2*i - 1)
Let b = -205151/3 + 67816. Let k = 569 + b. Factor -4/3*u + 8/3 - 5/2*u**2 + k*u**3 - 1/6*u**4.
-(u - 4)**2*(u - 1)*(u + 1)/6
Suppose 2/3*h**5 - 22/3*h**3 + 128/3*h - 52/3*h**2 - 64/3 + 8/3*h**4 = 0. What is h?
-4, 1, 2
Let m = 1364 - 1364. Let y(l) be the first derivative of 6 + 5/4*l**3 + 3/8*l**4 - 9/8*l**2 + m*l. Factor y(n).
3*n*(n + 3)*(2*n - 1)/4
Let f = -64 + 69. Suppose -f*m = -2*m - 3, m - 11 = -5*r. Find i, given that 33*i**2 - i - i - 31*i**r = 0.
0, 1
Suppose -4*i + 84 - 68 = 0. Let x be i/(-2) - -2 - -353. Factor 3*l**4 + 3*l**2 - x*l + 353*l - 6*l**3.
3*l**2*(l - 1)**2
Let p be 44 - 50 - (1 - 837/117). Factor 6/13*q**3 + 0*q + p*q**4 + 0*q**2 + 0.
2*q**3*(q + 3)/13
Let c(x) be the third derivative of 145*x**8/504 + 589*x**7/630 + x**6/8 - 499*x**5/180 - 227*x**4/72 + x**3 + 1196*x**2. Find r, given that c(r) = 0.
-1, 2/29, 9/10
Let k = -492978 - -81834613/166. Let x = k - 8/83. Suppose 1/2*l**2 + 0 + x*l = 0. Calculate l.
-3, 0
Determine z so that -24*z + 22/3*z**3 + 16*z**2 + 2/3*z**4 + 0 = 0.
-6, 0, 1
Let a = -1/300 + 13/150. Let p(l) be the first derivative of 0*l**2 + 0*l**3 - a*l**4 + 0*l + 1/30*l**5 - 10. Solve p(u) = 0.
0, 2
Suppose 6*g - 44*g + 118 = 21*g. Let k(q) be the third derivative of -1/3*q**4 - 1/15*q**5 + 0 + 0*q - 2/7*q**3 - 7*q**g + 2/105*q**6. Factor k(t).
4*(t - 3)*(t + 1)*(4*t + 1)/7
Let k(l) be the first derivative of 3*l**4/16 + 71*l**3/6 + 185*l**2/8 + 23*l/2 - 727. Factor k(t).
(t + 1)*(t + 46)*(3*t + 1)/4
Let j(d) = 21*d + 52 - 5 - 26*d. Let u be j(9). What is r in -3817*r**u + 2*r + 9*r**4 - 2*r**4 - 2*r**3 + 3810*r**2 = 0?
-1, 0, 2/7, 1
Let i(x) = -2*x**3 - 5*x**2 + 2*x + 5. Let t(s) = 5*s**3 + 11*s**2 - 5*s - 11. Let b be (0 - 4/(-4))*7. Let p(j) = b*i(j) + 3*t(j). What is n in p(n) = 0?
-1, 1, 2
Let b(g) be the second derivative of g**4/6 - 276*g**3 + 171396*g**2 + 2*g - 401. Factor b(t).
2*(t - 414)**2
Let w(u) be the third derivative of 0*u**4 - 1/360*u**5 + 0 + 0*u**3 + 50*u**2 + 0*u - 1/720*u**6. Suppose w(i) = 0. Calculate i.
-1, 0
Suppose -2*m - 8 = -6*m. Let t(f) = 3*f + 30. Let o be t(-7). Factor -o*z**m - 2*z**2 + 25*z + 15 + z**2.
-5*(z - 3)*(2*z + 1)
Factor 819/2 + 3/2*p**3 + 9/2*p**2 - 327/2*p.
3*(p - 7)*(p - 3)*(p + 13)/2
Let r(n) be the third derivative of -n**8/84 - 2*n**7/15 - 13*n**6/30 - n**5/15 + 7*n**4/3 + 16*n**3/3 + 943*n**2. Suppose r(k) = 0. What is k?
-4, -2, -1, 1
Factor -6*h**3 + 5138 - 8*h**2 + 5146 - h**4 + 6*h - 10275.
-(h - 1)*(h + 1)*(h + 3)**2
Let p(w) = 44*w**2 - 2938*w - 668. Let m be p(67). Factor 41/8*d + 1/2 + 5/4*d**m.
(d + 4)*(10*d + 1)/8
Let x(b) be the first derivative of b**3/24 - 133*b**2/16 + 131*b/4 - 4185. Suppose x(f) = 0. What is f?
2, 131
Let t be (8 - 60/8)*4. Factor 5*p**3 + 3*p + 3*p - 41 + 1 + 25*p**t + 0*p**3 + 4*p.
5*(p - 1)*(p + 2)*(p + 4)
Let g be -38 + 55 + (1 - 16). Factor -j + 3/2*j**g + 0 - 3/2*j**4 + j**3.
-j*(j - 1)*(j + 1)*(3*j - 2)/2
Factor 1/3*l**3 - 700/3*l + 0 + 31*l**2.
l*(l - 7)*(l + 100)/3
Let b(g) be the first derivative of 2/39*g**3 + 2/13*g**5 + 0*g + 0*g**2 - 81 + 2/39*g**6 + 2/13*g**4. Factor b(y).
2*y**2*(y + 1)**2*(2*y + 1)/13
Let t(n) be the second derivative of 32*n**6/105 + 24*n**5/35 - 5*n**4/7 + 4*n**3/21 + 43*n + 2. Factor t(a).
4*a*(a + 2)*(4*a - 1)**2/7
Suppose -w - 644 = -5*g, -5*g + 2*w = -4 - 639. Suppose -3*b + 141 - g = 0. Factor 7/4*r**b - 1/2*r**3 + 0 - 7/4*r**2 + 1/2*r.
r*(r - 1)*(r + 1)*(7*r - 2)/4
Let j(q) be the first derivative of q**5/180 - q**4/24 + q**3/9 - 4*q**2 - 4*q - 41. Let o(v) be the second derivative of j(v). Factor o(f).
(f - 2)*(f - 1)/3
Let h be (-4)/(((-18)/45)/(3/15)). Determine l so that -3/4*l**2 + h - 3/2*l + 1/4*l**3 = 0.
-2, 1, 4
Let a(h) be the second derivative of -1/50*h**6 + 1/10*h**4 + 0*h**3 + 0 - 3/10*h**2 + 0*h**5 + 13*h. Determine q so that a(q) = 0.
-1, 1
Let v(r) be the third derivative of r**5/60 + 95*r**4/24 - 97*r**3/3 + 1369*r**2. Determine q, given that v(q) = 0.
-97, 2
Let p(k) be the third derivative of 0*k**3 - 1/15*k**5 + 0*k + 0 - 16*k**2 + 1/2*k**4. Let p(n) = 0. Calculate n.
0, 3
Let l(v) = v**3 + 14*v**2 + 17*v - 4. Let t be l(-12). Find c, given that t + 13*c - 4*c**2 + 7*c + 4*c - 28*c = 0.
-5, 4
Suppose -2*h = 2*h - 8. Let m be (0 - -2)*(2 - (-216)/48). Factor 8*g - m*g**2 + 5*g**3 - h*g - 17*g**2 + 39*g.
5*g*(g - 3)**2
Let l(t) = -5*t**3 + 7*t**2 + 8*t + 2. Let r be l(0). Factor -1/2*f**r - 5/2 - 3*f.
-(f + 1)*(f + 5)/2
Let v(i) = -87*i**2 + 27*i + 26. Let a(p) = 8*p**2 - p - 1. Let r(q) = -22*a(q) - 2*v(q). Factor r(o).
-2*(o + 1)*(o + 15)
Let b(o) be the first derivative of -4*o + 0*o**2 - 29 + 4/3*o**3. Factor b(t).
4*(t - 1)*(t + 1)
Let g(l) be the second derivative of -l**7/70 - 23*l**6/50 - 9*l**5/5 - 6226*l. Find r such that g(r) = 0.
-20, -3, 0
Suppose -14*z**3 + 154*z**3 - 1440*z**2 - 53*z**3 + 5580*z + 63*z**3 - 1260*z - 5*z**4 = 0. What is z?
0, 6, 12
Let z(w) be the first derivative of -2*w**5/5 - 23*w**4/3 - 154*w**3/3 - 136*w**2 - 224*w/3 - 7552. Solve z(l) = 0 for l.
-7, -4, -1/3
Let b(v) = -v**2 + 7*v - 4. Let z be b(13). Let f = z - -89. Factor -15*t**4 + 36*t**5 - 31*t**5 - 15*t + 5 + 3*t**3 + f*t**3 + 10*t**2.
5*(t - 1)**4*(t + 1)
Let c = 1214/3199 - -2/1371. Let q(j) be the second derivative of -13*j + c*j**3 + 1/42*j**4 + 0 + 16/7*j**2. Factor q(k).
2*(k + 4)**2/7
Let m(c) be the second derivative of c**5/10 + c**4/2 - 3*c**3 + 5*c**2 + 9615*c. Factor m(i).
2*(i - 1)**2*(i + 5)
Let z(q) be the third derivative of -5*q**8/672 + 3*q**7/70 + q**6/24 - q**5/2 - 5*q**4/48 + 7*q**3/2 + 2*q**2 + 31*q + 34. Solve z(y) = 0 for y.
-7/5, -1, 1, 2, 3
Suppose 16*t - 45 = 131. Factor -24*a**2 - 32 + t*a**3 - 7*a**3 - 8*a**3 - 48*a.
-4*(a + 2)**3
Let k be (-4 + 44/10)/(5/200). Let r be (2 + -6)/k + 596/32. Let -27/2*s - r*s**4 - 327/8*s**2 - 189/4*s**3 - 3/2 = 0. Calculate s.
-1, -2/7
Let i = -3418560/427 - -8006. Let h = 1714/1281 - i. Factor 8/3 - 4/3*d - h*d**2.
-4*(d - 1)*(d + 2)/3
Let q be 8 + (-1 - 2)/3 - 1. Suppose 0 = -2*t - 2 + q. Factor 15*g**3 - 2*g**t + 8*g**3 - 2