*y.
(y - 1)*(y + 2)/3
Let k(n) be the third derivative of -n**8/672 + n**7/14 - 311*n**6/240 + 233*n**5/20 - 219*n**4/4 + 126*n**3 - 4*n**2 - n + 913. Find l such that k(l) = 0.
1, 3, 6, 14
Factor a**5 - 32*a**2 + 1914389*a**3 - 5*a**5 + 12*a - 1914365*a**3.
-4*a*(a - 1)**3*(a + 3)
Let v be (2/(-40) - 0)*127/((-10795)/340). Factor 0 + t + 1/5*t**4 - t**3 - v*t**2.
t*(t - 5)*(t - 1)*(t + 1)/5
Let f(u) = -u**4 + 2*u**2 + u + 2. Let m(z) = 2*z**5 - 52*z**4 - 12*z**3 + 344*z**2 - 458*z + 160. Let t(r) = -4*f(r) - m(r). Factor t(o).
-2*(o - 28)*(o - 1)**3*(o + 3)
Let k be 1365/(-63)*18/(-16 - -7). Determine c, given that 2*c**4 + k*c**2 + 8 + 55/3*c**3 + 100/3*c = 0.
-6, -2, -2/3, -1/2
Let p(q) be the first derivative of 5*q**4/12 - 3885*q**3 + 27167805*q**2/2 - 21109384485*q - 9122. Factor p(t).
5*(t - 2331)**3/3
Let z(d) = d**3 - 154*d**2 + 3018*d - 653. Let c be z(131). Factor -338/7 + 23/7*y**3 - 65*y - 93/7*y**c - 1/7*y**4.
-(y - 13)**2*(y + 1)*(y + 2)/7
Find g such that -9*g - 15*g**2 + 2*g**2 - 228*g - 11*g**2 + 3*g**3 + 546 = 0.
-7, 2, 13
Let t(j) be the third derivative of -2*j**7/105 - 314*j**6/15 - 33074*j**5/5 - 98282*j**4/3 - 195938*j**3/3 + 522*j**2 + j. Factor t(v).
-4*(v + 1)**2*(v + 313)**2
Factor 568/11*v - 190/11 + 184/11*v**3 - 564/11*v**2 + 2/11*v**4.
2*(v - 1)**3*(v + 95)/11
Let v = -49 - -547. Let a = v + -291. Suppose -207 - 8*d + a + 3*d**3 - 3*d**2 + 2*d = 0. Calculate d.
-1, 0, 2
Let z - z + 368*z**4 - 24*z**3 - 138*z**4 - 6*z**5 - 156*z**4 = 0. Calculate z.
0, 1/3, 12
Let f(h) = -4*h**3 + 47*h**2 + 12*h + 10. Let j be f(12). Suppose -13*u + j = -8*u. Factor v**3 + 1/2*v**2 + 0*v + 0 + u*v**5 - 7/2*v**4.
v**2*(v - 1)**2*(4*v + 1)/2
Let f = 369 + -389. Let u be -10*1*((-35)/f - 2). Solve 0 + k**2 + u*k**3 + 0*k - 3/2*k**4 = 0.
-1/3, 0, 2
Let j(y) be the second derivative of -13*y**4/4 + 34*y**3 - 45*y**2/2 - 9*y - 205. Factor j(t).
-3*(t - 5)*(13*t - 3)
Let g(f) = -38*f**2 + 1749*f - 33. Let i be g(46). Let n(h) be the first derivative of -7/2*h**4 - i - 8*h + 16*h**2 - 10/3*h**3. Let n(x) = 0. What is x?
-2, 2/7, 1
Let c = -73 - -128. Suppose 16*l = 563 - 131. Solve 2*g**3 - 30*g**5 + 6*g**4 - l*g**5 - 6*g**2 + c*g**5 = 0.
-1, 0, 1, 3
Let u = -11967 + 23937/2. Let q(z) be the second derivative of -u*z**2 + 1/120*z**5 + 0 - 1/12*z**3 + 1/18*z**4 - 51*z. Factor q(g).
(g - 2)*(g + 3)**2/6
Let r(p) be the first derivative of -14*p**3 + 141*p**2/2 - 99*p - 10796. Factor r(o).
-3*(o - 1)*(14*o - 33)
Suppose 11*y = -3*i + 15*y + 10, 4*i - 12 = 4*y. Suppose 2*s - i*n + 66 = 58, 4*s = -n + 4. Let 0*h - 2/3*h**4 + 4/3*h**3 + 2*h**2 + s = 0. Calculate h.
-1, 0, 3
Let b(c) be the third derivative of -269*c**2 + 0*c**3 + 0 + 1/15*c**5 + 0*c**4 + 0*c + 1/540*c**6. Factor b(z).
2*z**2*(z + 18)/9
Let u(f) be the first derivative of -5*f**4/12 + 30*f**3 - 810*f**2 + 201*f - 222. Let d(t) be the first derivative of u(t). Let d(b) = 0. Calculate b.
18
Suppose 0 = c + 99 - 108. Suppose c*w + 11 = 11. Factor w*j + 4/9*j**2 + 2/9*j**3 + 0.
2*j**2*(j + 2)/9
Let x(k) = -2*k**2 + 14*k + 18. Let f be x(8). Let i(j) = -j**3 + 24*j + 7. Let n be i(5). Factor -6/7 - 8/7*y**f + n*y.
-2*(y - 1)*(4*y - 3)/7
Let h be (-8)/(-5)*(-205)/(-246). Let v = -1/89 - -92/267. Solve h - 5/3*q**2 - 2/3*q**5 - 8/3*q + v*q**4 + 10/3*q**3 = 0.
-2, -1, 1/2, 1, 2
Suppose 3*w - 13 = 2*i, -53*w - 2*i = -49*w + 6. Suppose -3*a + w = x - 2*x, 0 = -2*x - 3*a + 7. Factor 0 - 1/10*g**3 + 0*g**x + 0*g.
-g**3/10
Let k(g) be the third derivative of 12*g**2 - 200/9*g**3 - 55/9*g**4 - 41/180*g**5 - 1/360*g**6 - 1 + 0*g. Suppose k(n) = 0. Calculate n.
-20, -1
Let s(h) be the first derivative of 2*h**3/3 + 14*h**2 - 28*h - 206. Let u be s(-15). What is n in 0 - 2/5*n**3 + 0*n**u + 2/5*n = 0?
-1, 0, 1
Determine z so that 115/4*z + 1/4*z**2 + 57/2 = 0.
-114, -1
Let r = -31/3036 + 3/44. Let g(a) be the second derivative of r*a**3 - 2*a + 0 + 3/23*a**2 + 1/138*a**4. Factor g(p).
2*(p + 1)*(p + 3)/23
Let f be (2*1)/(-8)*2016/(73 - 185). Solve 6*v**3 + f*v**2 - 6*v + 3/2*v**4 - 6 = 0 for v.
-2, -1, 1
Let b(q) be the second derivative of -q**6/120 - q**5/15 - q**4/6 + 137*q**2/2 - 5*q. Let x(l) be the first derivative of b(l). Factor x(y).
-y*(y + 2)**2
Suppose 5*p + 62 = -4*w, 5*w + p + 0*p + 67 = 0. Let t = w + 25. Factor 7*k - k - t*k - 3*k**2.
-3*k*(k + 2)
Let d be (-46)/(-460) + (-422417)/(-445830). Let b = d + 2/14861. Factor -32/21*p - 128/21 + 24/7*p**2 - b*p**3 + 2/21*p**4.
2*(p - 4)**3*(p + 1)/21
Let g(o) be the second derivative of 3*o**5/20 - 49*o**4/4 + 150*o**3 - 378*o**2 - 320*o - 4. Factor g(j).
3*(j - 42)*(j - 6)*(j - 1)
Suppose 312/11 - 630/11*h + 324/11*h**2 - 6/11*h**3 = 0. Calculate h.
1, 52
Factor -12/7*x**2 - 2/7*x**3 - 10/7*x + 24/7.
-2*(x - 1)*(x + 3)*(x + 4)/7
Let x(y) be the second derivative of -13*y**6/15 + 18*y**5/5 - 5*y**4 + 4*y**3/3 + 3*y**2 + 265*y. Factor x(a).
-2*(a - 1)**3*(13*a + 3)
Suppose 2*x = 2*l - 6, 0 = 5*x - 3*l + 12 - 9. Let p(b) be the second derivative of -5/3*b**2 - 34*b - 1/30*b**5 - 1/6*b**4 + b**x + 0. Factor p(k).
-2*(k - 1)**2*(k + 5)/3
Determine n, given that 1/6*n**2 - 161 + 481/6*n = 0.
-483, 2
Let x(u) be the third derivative of -97*u**5/60 + 33*u**4/8 - u**3/3 - 1487*u**2. Suppose x(w) = 0. What is w?
2/97, 1
Let l(u) be the second derivative of 3*u**2 - 1/3*u**4 + 1/60*u**5 + 8/3*u**3 + 6*u + 0. Let h(i) be the first derivative of l(i). Factor h(a).
(a - 4)**2
Let y(i) be the first derivative of 4/15*i**3 - 4/5*i**2 - 59 + 0*i. Factor y(g).
4*g*(g - 2)/5
Suppose 11*k + 15*k = -390. Let h be (-32)/48 - 16/k. Suppose -h*b**2 - 18/5 - 12/5*b = 0. Calculate b.
-3
Let q(p) = 13*p + 94. Let o be q(-7). Factor 19 + 14*t - 2*t + 0*t**3 - 3 - t**o.
-(t - 4)*(t + 2)**2
Let b(y) be the first derivative of -y**5/180 + 5*y**4/12 + 31*y**3/18 - y**2 - 73*y - 28. Let t(o) be the second derivative of b(o). Factor t(x).
-(x - 31)*(x + 1)/3
Solve 96*g - 118*g**2 + 43/2*g**3 + 0 + 1/2*g**4 = 0.
-48, 0, 1, 4
Let b be (2*(-2779)/(-7))/2. Let q = 400 - b. Factor 2/9*j**4 + 0*j + 2/3*j**2 + 0 + 8/9*j**q.
2*j**2*(j + 1)*(j + 3)/9
Let q(n) be the first derivative of -n**5/30 - 28*n**4/3 - 6272*n**3/9 - 4623. Let q(i) = 0. What is i?
-112, 0
Let u(n) be the first derivative of -3*n**4/8 + 31*n**3/2 + 321*n**2/2 + 444*n + 4627. What is v in u(v) = 0?
-4, -2, 37
Let v(j) = 5*j + 8. Let w(n) = 12*n + 15. Let r(y) = 5*v(y) - 2*w(y). Let q be r(-6). Factor 8 - 33*k**4 + 145*k**2 + 20*k**4 - 100*k + 28*k**q - 80*k**3 + 12.
5*(k - 2)**2*(k - 1)*(3*k - 1)
Suppose 173*j + 535 - 130 - 5*j**4 + 400*j**2 + 51*j + 586*j - 10*j**3 = 0. Calculate j.
-9, -1, 9
Let -338/3 - 4/3*q**4 - 111*q**2 - 64/3*q**3 - 611/3*q = 0. Calculate q.
-13/2, -2, -1
Let w(z) = z**3 - 22*z**2 - 18*z - 56. Let y be w(23). Let a = 61 - y. Factor -26*l**a - 53 + 4*l**3 - 22*l**2 - 147 + 180*l.
4*(l - 5)**2*(l - 2)
Let l(x) be the first derivative of -31 - 11*x - 20/3*x**3 + 1/6*x**4 + 100*x**2. Let z(v) be the first derivative of l(v). Find n such that z(n) = 0.
10
Suppose -91/3*u + 0 - 1/3*u**3 - 20/3*u**2 = 0. Calculate u.
-13, -7, 0
Let r be (10/(-15))/(4/(-18)). Let h = 77563/3 + -25850. What is w in 8/3*w + 4/3 + 5/3*w**5 + 7/3*w**4 - h*w**r - 11/3*w**2 = 0?
-2, -1, -2/5, 1
Factor 745 + 5/2*h**2 + 1495/2*h.
5*(h + 1)*(h + 298)/2
Let c = 80790 + -242368/3. Let a be (-12)/(-10)*(-10)/(-9). Factor a*i**3 + 1/3*i**5 - c - 2/3*i**2 - 5/3*i + 4/3*i**4.
(i - 1)*(i + 1)**3*(i + 2)/3
Let g(w) be the first derivative of -w**6/21 - 2*w**5/35 + w**4/14 + 2*w**3/21 - 411. Suppose g(j) = 0. Calculate j.
-1, 0, 1
Let d(w) be the second derivative of -w**5/240 + 3*w**4/32 - 6*w**2 - 11*w. Let q(r) be the first derivative of d(r). Factor q(i).
-i*(i - 9)/4
Determine l, given that 8*l - 8*l**3 + 4*l**2 + 225*l**4 + 225*l**4 - 679*l**4 + 0 - 6 + 231*l**4 = 0.
-1, 1, 3
Let f(n) be the second derivative of n**6/2160 + n**5/20 - 88*n**3/3 - n - 20. Let g(v) be the second derivative of f(v). Factor g(u).
u*(u + 36)/6
Let m(p) be the first derivative of 3*p**5/5 + 57*p**4/2 + 268*p**3 - 2961*p**2 - 6615*p + 889. Factor m(o).
3*(o - 5)*(o + 1)*(o + 21)**2
Factor -656/5 + 4/5*s**3 + 992/5*s - 68*s**2.
4*(s - 82)*(s - 2)*(s - 1)/5
Suppose 9 = 3*w, 4*w + 2 + 2 = 4*q. Factor -1735*z**2 + 30*z**3 + 9*z + 17*z - 2*z**q