r + 1)*(r + 251)
Let x(g) be the first derivative of g**5/270 + 5*g**4/108 - 2*g**3/9 + 47*g**2 - 12. Let o(m) be the second derivative of x(m). Factor o(k).
2*(k - 1)*(k + 6)/9
Determine v so that 0*v - 106*v**4 + 28*v**3 - 100*v + 55*v**4 - 71*v**2 + 50*v**4 = 0.
-1, 0, 4, 25
Let m(l) be the third derivative of -l**7/70 + l**6/20 + 21*l**5/20 + 9*l**4/4 - 462*l**2 + 3*l. Factor m(f).
-3*f*(f - 6)*(f + 1)*(f + 3)
Suppose -4377 = 5*p + 4*c - 4329, -3*p - 5*c - 60 = 0. Factor 3/4*n**3 + 0 + p*n - 3/4*n**4 - 1/4*n**2 + 1/4*n**5.
n**2*(n - 1)**3/4
Let x(y) = 64*y**2 - 1496*y + 557. Let j be x(23). Factor -98/5*k**j + 0*k + 104/5*k**3 + 0 + 16/5*k**2 + 28*k**4.
-2*k**2*(k - 2)*(7*k + 2)**2/5
Let l(v) be the second derivative of 63*v**5/4 + 733*v**4/4 - 427*v**3 + 24*v**2 - 8085*v. Suppose l(g) = 0. What is g?
-8, 2/105, 1
Let u(w) = -5*w**2 - 2*w. Let t(d) = 4*d**2 + 2*d. Suppose 23 = 3*c - 1. Suppose -c*y = -12*y - 20. Let o(b) = y*u(b) - 6*t(b). Suppose o(g) = 0. What is g?
0, 2
Let s(y) be the third derivative of -7/15*y**4 - y**3 + 1/525*y**7 + 0 + 0*y + 1/75*y**6 - 142*y**2 - 1/15*y**5. Factor s(j).
2*(j - 3)*(j + 1)**2*(j + 5)/5
Let b(l) be the first derivative of -l**4/2 + 86*l**3 + 528*l**2 + 1064*l + 143. Determine t, given that b(t) = 0.
-2, 133
Let q = 10349/765 + -1131/85. Factor -16 + 20/9*y**2 - 8/3*y - q*y**3.
-2*(y - 6)**2*(y + 2)/9
Find a such that 26/5*a**3 - 2/5*a**4 - 104/5*a - 36/5*a**2 + 176/5 = 0.
-2, 2, 11
Let c(s) be the first derivative of -5/12*s**6 - 110 - 5/2*s**2 + 15/8*s**4 - 5/6*s**3 + 0*s + 1/2*s**5. Find k, given that c(k) = 0.
-1, 0, 1, 2
Find i, given that -2*i**3 - 18*i**2 - 186426 + 44*i + 186426 = 0.
-11, 0, 2
Let x(d) be the third derivative of d**5/60 - 281*d**4/24 - 47*d**3 - 126*d**2 + 2. Factor x(n).
(n - 282)*(n + 1)
Let r(b) = -b**3 - 3*b**2 + b + 8. Let u be r(-3). Let k be -5 - (-2 + -1 - u). Let -2*n**k + 2 + n + n**5 + 2*n**4 - 1 + 1 - 4*n**2 = 0. What is n?
-2, -1, 1
Factor -s - 1/3*s**3 + 5/3*s**2 - 3.
-(s - 3)**2*(s + 1)/3
Let t(y) be the first derivative of -81*y**5/10 - 45*y**4/8 + 97*y**3/3 - 19*y**2 + 4*y - 1917. Determine z, given that t(z) = 0.
-2, 2/9, 1
Let q be (-37)/(-13) + (96/(-52) - -2). Suppose s + 72 = 10*s. Factor 3*h**q - s*h + 6*h**3 + 73*h**5 - 3*h**3 - 8*h**2 + 8*h**4 - 71*h**5.
2*h*(h - 1)*(h + 1)*(h + 2)**2
Suppose 4 = o, -497*p + 4*o = -502*p + 16. Let w(h) be the third derivative of 1/60*h**6 + 0*h**3 + p*h**5 - 32*h**2 + 0*h - 3/4*h**4 + 0. Factor w(u).
2*u*(u - 3)*(u + 3)
Suppose -4*p - 60*p + 256 = 0. Factor -3*f**p - 60*f + 2*f**4 + 45 + 20*f**3 - 223*f**2 + 213*f**2 + 6*f**4.
5*(f - 1)**2*(f + 3)**2
Let p(v) be the third derivative of 0 + 1/660*v**6 + 0*v + 2/11*v**4 + 7*v**2 + 3/110*v**5 + 20/33*v**3. Suppose p(c) = 0. What is c?
-5, -2
Find f, given that -52*f**3 - 162/7 - 14*f**4 - 522/7*f - 10/7*f**5 - 636/7*f**2 = 0.
-3, -9/5, -1
Factor 2*g**3 + 39*g - 208*g + 180 - 2*g - 95*g + 116*g**2 - 32*g**2.
2*(g - 2)*(g - 1)*(g + 45)
Let q(l) = l**3 - 7*l**2 + 17*l - 116. Suppose 3*k + a - 7 = 12, -3*k + a = -23. Let x be q(k). Factor f**2 + 3/2*f - 3/2*f**x - 1.
-(f - 1)*(f + 1)*(3*f - 2)/2
Suppose 3*u + 2*q - 82 = 0, 2*u + 2*u - 108 = -3*q. Suppose 13 - 3 - 96*n + u + 86*n - 5*n**2 = 0. What is n?
-4, 2
Let w(a) = 7*a**2 - 22*a + 60. Let s(f) = -11*f**2 + 33*f - 90. Let g(t) = 5*s(t) + 8*w(t). Let x be g(7). Factor d + 17*d**x - 11*d - 15*d**2.
2*d*(d - 5)
Factor -68/7*u**2 - 164/7*u + 4/7*u**3 + 228/7.
4*(u - 19)*(u - 1)*(u + 3)/7
Let d(l) be the third derivative of l**5/5 + 2281*l**4/6 + 1520*l**3/3 - 7513*l**2. What is a in d(a) = 0?
-760, -1/3
Let r(g) = -g**2 + 127*g + 5032. Let j(o) = 10*o**2 - 1395*o - 55350. Let l(w) = 4*j(w) + 45*r(w). Factor l(x).
-5*(x - 48)*(x + 21)
Let u be 13 - (-5)/((-6)/60 + (-42)/105). Determine a so that 102/5 - 3/5*a - 102/5*a**2 + 3/5*a**u = 0.
-1, 1, 34
Suppose f = -2*f + 12*f. Suppose f = c + 3*c. Suppose 4/5*i**3 + 0*i + 1/5*i**4 + c + 0*i**2 = 0. What is i?
-4, 0
Factor 2/15 + 10416/5*b**2 - 502/15*b + 10584/5*b**3.
2*(b + 1)*(126*b - 1)**2/15
Let p(k) be the second derivative of -3*k**7/14 + 7*k**6/10 + 21*k**5/20 - 3*k**4/4 + 3095*k. What is r in p(r) = 0?
-1, 0, 1/3, 3
Factor -84/5*a**2 + 672/5 - 152/5*a + 4*a**3.
4*(a - 4)*(a - 3)*(5*a + 14)/5
Let g be (-4*(-3 + 2))/(-12 + 14). What is h in -28 - 158*h + 27*h**2 - 14*h**2 - 22*h**2 - 13*h**g = 0?
-7, -2/11
Let k = 454 + -498. Let b(y) = 10*y**3 + 5*y**2 - 11. Let l(o) = 2*o**3 - 1. Let c(w) = k*l(w) + 4*b(w). Factor c(s).
-4*s**2*(12*s - 5)
Factor 18 + 25409*y**3 - 4*y**2 - 25410*y**3 - 21*y + 12*y**2.
-(y - 3)**2*(y - 2)
Suppose -18 = -q - 17. Find x such that x**5 - 11*x**5 + 32*x**4 - 26*x**4 + 17 - q + 146*x**2 + 94*x**3 + 84*x = 0.
-1, -2/5, 4
Let l(v) = -79*v - 7266. Let q be l(-92). Let k(c) be the first derivative of 0*c - 3/2*c**q + 2 - 1/5*c**3. Suppose k(u) = 0. What is u?
-5, 0
Let n(u) = 13*u**2 - 29*u + 9. Let x(a) = 37*a**2 - 85*a + 26. Let f(m) = 8*n(m) - 3*x(m). Let z be f(3). Find o such that 0 - 1/8*o**2 + z*o = 0.
0
Let f(c) be the second derivative of 11*c**5/100 + c**4/40 + 59*c**2/2 - 30*c. Let o(w) be the first derivative of f(w). Factor o(a).
3*a*(11*a + 1)/5
Let t(b) = b**3 + 10*b**2 - 1001*b - 72. Let u be t(-37). Let -58*s**4 + 0*s - 18*s**5 + 0 - 560/9*s**3 - 200/9*s**u = 0. Calculate s.
-10/9, -1, 0
Let l(b) be the first derivative of 0*b + 5*b**2 + 5/6*b**3 + 1/300*b**5 + 1/12*b**4 + 6. Let o(g) be the second derivative of l(g). Factor o(j).
(j + 5)**2/5
Let z = 58967309/13 - 4533789. Let v = z + -2154. Suppose -2/13*r**2 - v + 20/13*r = 0. Calculate r.
5
Let c(g) be the third derivative of g**8/2240 - g**7/168 - 7*g**6/120 + g**4/3 + 7*g**3/6 - 243*g**2. Let q(k) be the second derivative of c(k). Factor q(h).
3*h*(h - 7)*(h + 2)
Let n(y) be the first derivative of 1/12*y**4 + 8/3*y**2 + 63 + 7/9*y**3 + 4*y. Suppose n(h) = 0. Calculate h.
-3, -2
Solve 2744/5 + 38/5*a**4 + 2618/5*a**2 + 1/5*a**5 + 980*a + 499/5*a**3 = 0 for a.
-14, -7, -2, -1
Factor -2/3*c**2 + 76/3*c + 160/3.
-2*(c - 40)*(c + 2)/3
Let h(a) = 11*a**3 - a**2 - 59*a + 49. Let d(y) = 18 - 29*y + 7*y**3 - y**2 - 2*y**3 + 7. Let t(x) = -5*d(x) + 2*h(x). Solve t(i) = 0.
-3, 1, 3
Let k(h) be the third derivative of -h**5/300 + 461*h**4/60 - 212521*h**3/30 + h**2 + 509. Factor k(b).
-(b - 461)**2/5
Let d(k) = 33731*k + 101195. Let z be d(-3). What is b in 5/2*b - 2 - 1/2*b**z = 0?
1, 4
Determine p, given that 4 - 2*p**3 - 22/3*p - 40/3*p**2 = 0.
-6, -1, 1/3
Let i(x) be the second derivative of -5/2*x**2 - 5 + 65/6*x**3 - 25*x**4 - 32/3*x**6 + 28*x**5 + 12*x. Factor i(v).
-5*(v - 1)*(4*v - 1)**3
Let r(g) be the third derivative of -g**6/90 + 29*g**5/15 + 124*g**4/3 + 3040*g**3/9 - 14*g**2 - g + 3. Let r(w) = 0. What is w?
-4, 95
Let 188/3*r + 78/5*r**2 + 14/15*r**3 - 96/5 = 0. What is r?
-9, -8, 2/7
Let q = -34 - -64. Let d = q + 39. Solve d - 5*n**2 - 69 = 0.
0
Suppose -5*o + 9*s = 20, 3*o + 2*s - 18 = 7. Let l(u) be the third derivative of 0*u**3 - 1/70*u**o + 0 + 14*u**2 + 0*u + 5/28*u**4. What is g in l(g) = 0?
0, 5
Let k(o) be the second derivative of -o**5/10 - 77*o**4/6 + 107*o**3 - 243*o**2 + 65*o - 9. Solve k(d) = 0 for d.
-81, 1, 3
Let r(f) be the first derivative of 4/5*f**3 + 6/25*f**5 - 2/5*f**2 + 0*f - 13/20*f**4 - 1/30*f**6 + 8. Factor r(t).
-t*(t - 2)**2*(t - 1)**2/5
Let v = 97091/226545 + -2/1585815. Solve 51/7*d**2 + v*d**3 + 297/7 + 225/7*d = 0 for d.
-11, -3
Let i(p) be the first derivative of 2*p**3/27 - 7*p**2/3 + 20*p - 1049. Let i(g) = 0. Calculate g.
6, 15
Let r(y) be the second derivative of -y**5/20 - 3*y**4/4 + 5*y**3/3 + 208*y + 2. Factor r(w).
-w*(w - 1)*(w + 10)
Let h(m) = -34*m**2 - 24*m + 1550. Let z(r) = -3*r**2 + 2*r - 1. Let x(q) = h(q) - 10*z(q). Factor x(p).
-4*(p - 15)*(p + 26)
Let h be 5304/680 - (-76)/(-20). Factor 16/9*a + 10/9*a**h - 4/3*a**3 - 8/9*a**2 + 0 - 2/9*a**5.
-2*a*(a - 2)**3*(a + 1)/9
Let i(r) be the first derivative of r**3/12 - 1715*r**2/8 + 857*r/2 - 936. Determine p so that i(p) = 0.
1, 1714
Let n(r) = -5*r**3 + 159*r**2 - 283*r + 10082. Let t be n(32). Suppose -2*i**3 + 26/3*i**t + 56/3*i + 8 = 0. Calculate i.
-1, -2/3, 6
Let b be 1/(-4) - (-4009420)/2456*(-1)/100*-2. Factor -2/5*w**2 + 36/5*w - b.
-2*(w - 9)**2/5
Let z(y) = 