*2 - 1/30*i**5 + k + 0*i - 1/4*i**4 - 2/3*i**3. Suppose y(b) = 0. Calculate b.
-2, -1
Solve 3*y**3 + 312*y**2 + 9867*y - 4415*y - 4252*y = 0 for y.
-100, -4, 0
Let d(v) be the third derivative of 0 - 278*v**2 + 0*v + 1/420*v**6 + 0*v**3 - 4/105*v**5 + 4/21*v**4. Factor d(z).
2*z*(z - 4)**2/7
Let y(k) be the third derivative of 1/9*k**4 + 1/180*k**6 + 1/18*k**5 + 0 + 46*k**2 + 0*k + 0*k**3. Determine j, given that y(j) = 0.
-4, -1, 0
Factor -4*v**4 - 26543*v**2 - 128*v**3 + 39375 + 150825*v - 118*v**3 + 873*v**3.
-(v - 75)**2*(v - 7)*(4*v + 1)
Suppose 301*f + 53 + 122 = 415*f - 167. Find d such that -1/6*d**5 + 11/6*d**2 + 2/3 + 2*d - 1/2*d**4 + 1/6*d**f = 0.
-2, -1, 2
Let f(q) = -q**2 - 1. Let d = 10 - 9. Let k(w) = -7*w**2 - 76*w + 77. Let s(v) = d*k(v) - 3*f(v). Factor s(x).
-4*(x - 1)*(x + 20)
Let i(m) = -21*m - 123. Let r be i(-6). Factor -4*p**4 + p**4 + 2*p**r - p**4 + 2*p**3.
-4*p**3*(p - 1)
Let x be -7 + 10 + 1 + -29. Let u = x - -28. Let 11 + 12*o - u*o**2 + 1 + 6*o**2 = 0. Calculate o.
-2
Factor 116*u**2 + 1424 + 1764*u + 129*u**3 + 125*u**3 - 258*u**3 + 220*u**2.
-4*(u - 89)*(u + 1)*(u + 4)
Let o(x) be the third derivative of 4/3*x**3 + 5/12*x**4 + 1/30*x**5 + 0 + 0*x + 83*x**2. Factor o(m).
2*(m + 1)*(m + 4)
Factor h**4 + 2*h**4 - 20*h**3 + 29*h**2 + 30*h**2 + 20*h - 57*h**2 - 5*h**4.
-2*h*(h - 1)*(h + 1)*(h + 10)
Let l(r) be the third derivative of -9375*r**5/32 + 125*r**4/16 - r**3/12 - 4*r**2 + r + 1. Factor l(b).
-(375*b - 2)**2/8
Let j = 28 + -22. Suppose -j*v = -v - 95. Factor 3*d**2 - v*d + 11*d + 75 - 9*d - 13*d.
3*(d - 5)**2
Let i(x) be the first derivative of 5*x**6/12 + x**5/8 - 2*x**4/3 + x**3/3 + 157*x + 130. Let t(s) be the first derivative of i(s). Find f such that t(f) = 0.
-1, 0, 2/5
Factor 2/3*k**3 + 5202*k + 88434 + 102*k**2.
2*(k + 51)**3/3
Find y, given that -351/5*y - 3/5*y**2 - 1026/5 = 0.
-114, -3
Let v(h) be the first derivative of 7*h**6/18 + 20*h**5/3 + 63*h**4/4 - 52*h**3/9 - 98*h**2/3 - 16*h + 3525. Suppose v(k) = 0. Calculate k.
-12, -2, -1, -2/7, 1
Suppose -3*w + 2*f = -18, 0 = -3*w - 3*f + 3. Factor -128 - x - 15*x - 11*x**2 + w*x**2 + 11*x**2.
4*(x - 8)*(x + 4)
Let z(o) be the first derivative of o**4/24 + 5*o**3/18 - 26*o**2 - 456*o + 4004. Factor z(v).
(v - 19)*(v + 12)**2/6
Let b(n) be the second derivative of -n**4/96 + 161*n**3/24 - 5244*n + 2. Factor b(k).
-k*(k - 322)/8
Let m(h) = -h**4 - 18*h**3 - h + 1. Let d(n) = 120*n**4 + 885*n**3 - 5580*n**2 + 8315*n - 3835. Let s(j) = -d(j) + 5*m(j). Find v such that s(v) = 0.
-12, 1, 8/5
Determine n, given that -63/4 - 3/4*n + 2*n**2 = 0.
-21/8, 3
Let b(r) be the first derivative of 0*r**3 - 3/7*r**2 + 1/14*r**4 - 8 + 4/7*r. Let b(z) = 0. Calculate z.
-2, 1
Let q(p) = -p**2 - 137*p - 1270. Let r be q(-10). Let o(b) be the first derivative of r*b - 22 + 0*b**2 - 2/9*b**3. Factor o(h).
-2*h**2/3
Let x be 8/6*(-12)/(-40). Suppose -81*v + 201 + 66 = -57. Factor -6/5*m**3 + x*m**5 + 0*m**v + 0*m + 0 + 4/5*m**2.
2*m**2*(m - 1)**2*(m + 2)/5
Let s(q) be the second derivative of 1/84*q**7 + 3*q + 3 - 1/12*q**4 + 1/12*q**3 + 1/4*q**2 + 1/60*q**6 - 1/20*q**5. Factor s(h).
(h - 1)**2*(h + 1)**3/2
Find o such that -3599*o + 188*o**3 + 98*o**2 + 13 - 3*o**4 + 3507*o - 12*o**4 = 0.
-1, 1/5, 1/3, 13
Let u = -98 + 102. Suppose -2*x = h - 0*x + u, 4*x = -4*h. Factor 9*s**3 - 33*s**4 - 27*s**3 + 37*s**h + 20*s**2 - 6*s**3.
4*s**2*(s - 5)*(s - 1)
Let s = 3355 - 73885/22. Let t = 54/11 + s. Determine u so that t*u**2 + 3 - 9/2*u = 0.
1, 2
Let a = 388847/5 + -77763. Determine h so that a*h**2 + 28/5*h**3 + 2/5*h**5 + 18/5*h + 4/5 + 12/5*h**4 = 0.
-2, -1
Let f(g) be the second derivative of -g**7/42 + g**6/15 + g**5/4 + g**4/2 + g**3 + 111*g. Let c(x) = -x**3 - x**2 - x. Let j(y) = 6*c(y) + f(y). Factor j(o).
-o**3*(o - 1)**2
Let b(i) be the second derivative of 1/24*i**4 - 23/12*i**3 - 10 + 21/2*i**2 - 5*i. Let b(j) = 0. What is j?
2, 21
Let i(u) be the third derivative of u**5/140 + 5*u**4/8 - 18*u**3/7 + 510*u**2 - u. Solve i(h) = 0.
-36, 1
Let d(a) be the second derivative of -4*a**6/75 - 111*a**5/25 - 371*a**4/15 - 244*a**3/5 - 208*a**2/5 + 4*a - 769. Find w, given that d(w) = 0.
-52, -2, -1, -1/2
Let r(y) = 11*y**3 + 10*y**2 + y - 2. Let w be r(-1). Let i be w/18 + (-4600)/(-2475). Find o such that 12/11*o**2 + 0*o - 30/11*o**4 + 0 + i*o**3 = 0.
-2/5, 0, 1
Let c = -5/412 - -27/103. Let x(a) be the first derivative of 6 + 0*a - 1/6*a**3 - c*a**2. Factor x(v).
-v*(v + 1)/2
Let q(d) be the first derivative of -d**5/5 + 15*d**4/4 - 9*d**3 - 103*d**2/2 - 60*d - 347. Find x, given that q(x) = 0.
-1, 5, 12
Let z(k) = 18*k**3 - 4239*k**2 - 82176*k + 86772. Let b(g) = g**3 - 223*g**2 - 4325*g + 4567. Let f(t) = -75*b(t) + 4*z(t). Suppose f(s) = 0. Calculate s.
-39, 1
Let k be 230/(-69) - (2/3 + 0). Let y = -2 - k. Solve 12*n**4 - 20*n**y + 2*n - 32*n**4 + 5*n**5 + 40*n**3 - 10*n**3 + 3*n = 0 for n.
0, 1
Let m(l) = -2*l**3 + 12*l**2 + 2*l + 3. Let o be m(6). Let -15 + o - 4*i**2 - 49*i - 123*i + 4*i = 0. Calculate i.
-42, 0
Let r(s) = -5*s - 6. Let g be r(-2). Suppose -3*w + 54 = g*t - 3, 33 = t - 3*w. Solve t*d**4 + 5*d**5 - 15*d**2 - d**4 - 5*d**3 - 2*d**4 = 0.
-3, -1, 0, 1
Let t be (-71467)/(-146146) - 7/(-637). Solve 1/8*c**2 + 1/2 - t*c = 0.
2
Let y(l) = 123*l + 1002. Let b be y(-8). Let z(x) be the third derivative of b*x**2 + 0*x - 1/3*x**3 + 1/40*x**5 + 1/12*x**4 + 0. Factor z(w).
(w + 2)*(3*w - 2)/2
Determine x, given that -407 - 19*x**2 - 716 + 3587*x - 33*x**3 - 23*x**2 - 1469 + 3*x**4 - 2435*x = 0.
-6, 4, 9
Suppose 26 = -5*f + 66. Suppose j - f = 8. Factor j*n**4 - 19*n**4 + 4*n**2 - n**2.
-3*n**2*(n - 1)*(n + 1)
Let r(c) be the first derivative of 177 + 1/6*c**3 - 18*c + 5/4*c**2. Factor r(h).
(h - 4)*(h + 9)/2
Let k(o) be the third derivative of -1/2*o**4 + 51*o**2 + 14/15*o**5 + 0*o**3 + 0 + 1/6*o**6 + 0*o. Let k(f) = 0. Calculate f.
-3, 0, 1/5
Let w be 2/(8/(-12))*(-44 - 3). Let m = w - 138. Solve 18/7*z**2 - 3/7*z**m - 15/7*z + 0 = 0 for z.
0, 1, 5
Let f(o) be the third derivative of 11/120*o**5 - 22*o**2 + 1/96*o**6 + 0 - o + 7/24*o**4 + 1/3*o**3. Determine q so that f(q) = 0.
-2, -2/5
Let z be 53/318 + -34*5/(-60). Determine r, given that 0 - 15/2*r - 15/4*r**5 - 21/4*r**2 + 117/4*r**z - 51/4*r**4 = 0.
-5, -2/5, 0, 1
Let j(u) be the first derivative of 2*u**3/15 - 329*u**2/5 + 273. What is v in j(v) = 0?
0, 329
Factor 1/5*i**4 - 71/5*i**3 - 73/5*i - 29*i**2 + 0.
i*(i - 73)*(i + 1)**2/5
Let b(p) = -124*p**2 - 158*p + 316. Let h(k) = k**2 + k - 6. Let q(l) = -2*b(l) - 68*h(l). Factor q(g).
4*(g + 2)*(45*g - 28)
Let v(m) = 8*m**5 - 29*m**4 + 55*m**3 - 48*m**2 + 24*m - 3. Let b(f) = 2*f**5 + 3*f**2 + f + 1. Let y(z) = -2*b(z) + 2*v(z). Let y(r) = 0. What is r?
1/2, 1, 4/3
Let c(j) = -2*j**3 + 65*j**2 - 513*j + 828. Let f(p) = -4*p**3 + 64*p**2 - 512*p + 828. Let z(y) = 4*c(y) - 3*f(y). Solve z(l) = 0.
-23, 3
Let g(j) be the first derivative of 4*j**2 - 1/50*j**5 + 6 - 3/40*j**4 + 1/5*j**3 + 0*j. Let r(d) be the second derivative of g(d). Factor r(l).
-3*(l + 2)*(2*l - 1)/5
Let r(v) = 2*v**2 + 5*v - 72. Let o be r(-6). Let p be o/(-54)*64/80. Find a, given that 0 + 0*a**2 - 1/9*a**4 - 1/3*a**3 + p*a = 0.
-2, 0, 1
Let w(i) be the first derivative of 3*i**4/16 + 29*i**3/4 - 93*i**2/4 + 5502. Let w(f) = 0. What is f?
-31, 0, 2
Let n(b) be the third derivative of -2/9*b**3 - 41*b**2 + 0 + 1/72*b**4 - 1/360*b**6 + 1/45*b**5 + 0*b. Let n(q) = 0. Calculate q.
-1, 1, 4
Let s be (-4)/((-20)/95) - -6. Factor -311*z**2 + 11*z**4 + 324*z**2 - z**5 + 0*z**5 + s*z**3.
-z**2*(z - 13)*(z + 1)**2
Suppose 7/6*g + 55/6*g**2 - 71/6*g**3 + 0 + 3/2*g**4 = 0. Calculate g.
-1/9, 0, 1, 7
Let i(s) be the first derivative of 14 - 1/54*s**3 - 1/9*s**2 + 16*s + 1/108*s**4. Let k(d) be the first derivative of i(d). Factor k(p).
(p - 2)*(p + 1)/9
Suppose 4*u + 3*b - 63 = 0, 4*u - 3*b - 7 = 50. Let j be (10/u)/(2/9). Factor -x**3 - j*x**3 - 16*x**4 - 11*x**2 + 19*x**2 + 12*x**5.
4*x**2*(x - 1)**2*(3*x + 2)
Let i = -4756/55 - -19079/220. Find a such that 0*a**2 + 3/8*a - 1/8*a**3 + i = 0.
-1, 2
Let k(m) be the second derivative of 3*m**5/20 - 45*m**4/4 + 133*m**3 + 78*m + 2. Determine t, given that k(t) = 0.
0, 7, 38
Let g(q) be the third derivative of 208/7*q**3 + 11/70*q**6 - 75*q**2 + 230