Suppose -13436 = 45*w + 3574. Let k = 380 + w. Factor -3/2*h + 1/4*h**k + 9/4.
(h - 3)**2/4
Let b(x) be the first derivative of x**4 + 4*x - 4/3*x**3 + 13 - 2*x**2. Factor b(a).
4*(a - 1)**2*(a + 1)
Suppose -15 = 3*c, -5*r - 2*c = -3*c - 20. Factor 9*z - 34*z + 6*z + z - 24*z**3 + r*z**4 + 39*z**2.
3*z*(z - 6)*(z - 1)**2
Let h(w) be the second derivative of w**4/18 + 28*w**3/9 + 9*w**2 + 1497*w. Let h(d) = 0. Calculate d.
-27, -1
Let w(o) be the first derivative of 7*o**6/180 + 37*o**5/60 + 5*o**4/6 + 43*o**3/3 + 111. Let x(r) be the third derivative of w(r). Factor x(b).
2*(b + 5)*(7*b + 2)
Let n(y) = 610*y - 3048. Let s be n(5). Solve -1/7*c**3 + 0 + 1/7*c**5 + 0*c - 2/7*c**4 + 2/7*c**s = 0 for c.
-1, 0, 1, 2
Let g(k) = 2*k**3 - 7*k**2 - 14*k - 20. Let i(v) = -3*v**3 + 10*v**2 + 21*v + 32. Let r(p) = -8*g(p) - 5*i(p). Factor r(x).
-x*(x - 7)*(x + 1)
Let v(w) = -19*w**2 - 1800*w + 819035. Let f(a) = 4*a**2 - 2*a - 2. Let k(g) = -15*f(g) - 3*v(g). Solve k(p) = 0.
905
Suppose -10*r**2 + 69/2*r**3 - 6*r - 7/2*r**5 - 15*r**4 + 0 = 0. What is r?
-6, -2/7, 0, 1
Let v(r) = 5*r + 10. Let t(y) = -18*y + 13. Let b be t(1). Let a(c) = -c**2 + 6*c + 8. Let d(m) = b*a(m) + 4*v(m). Determine l so that d(l) = 0.
0, 2
Let l(g) = -2*g**4 + 20*g**3 + 14*g**2 - 8*g. Let n be 1*-4*2/4. Let j(h) = -h**3 - h**2. Let s(o) = n*l(o) - 28*j(o). What is i in s(i) = 0?
-1, 0, 2
Let i(b) be the third derivative of b**5/450 - b**4/9 - 7*b**3/15 + 787*b**2. Factor i(q).
2*(q - 21)*(q + 1)/15
Let c be (0 - (-2)/(-11)) + (-48)/(-22). Let t(w) = -w**2 + 90*w - 673. Let d(u) = -3*u**2 + 360*u - 2691. Let r(o) = c*d(o) - 9*t(o). Factor r(f).
3*(f - 15)**2
Let o(v) = -215*v**2 - 17610*v + 35090. Let c(s) = 19*s**2 + 1601*s - 3190. Let y(i) = 45*c(i) + 4*o(i). What is n in y(n) = 0?
2, 319
Let b be (-1113)/636 + (-1)/((-1)/2). Let a(r) be the second derivative of 0*r**4 + 5/2*r**3 + 0 + 5*r**2 - b*r**5 + 25*r. Factor a(j).
-5*(j - 2)*(j + 1)**2
Let k(a) be the third derivative of -1/20*a**6 + 0*a + 35/12*a**4 - 3*a**3 + 52*a**2 + 0 - 23/30*a**5. Factor k(s).
-2*(s - 1)*(s + 9)*(3*s - 1)
Let u(m) = -151*m**2 - 1511*m + 24398. Let i(f) = 34*f**2 + 378*f - 6100. Let s(g) = 9*i(g) + 2*u(g). Factor s(r).
4*(r - 14)*(r + 109)
Let y(p) be the first derivative of -p**6/15 - 168*p**5/25 - 923*p**4/5 - 2296*p**3/5 - 1681*p**2/5 + 1353. Suppose y(t) = 0. What is t?
-41, -1, 0
Let g = -222 + 271. Factor -5*n**4 + g*n**2 - 36*n**3 + 14*n**2 - 30*n + 8*n**4.
3*n*(n - 10)*(n - 1)**2
Let z(f) be the first derivative of 0*f**2 + 35*f - 25 + 1/30*f**5 + 0*f**4 - 1/9*f**3. Let d(i) be the first derivative of z(i). Suppose d(h) = 0. What is h?
-1, 0, 1
Let a(p) be the second derivative of 16*p**3 + 24*p**2 - 3/5*p**5 - 1/14*p**7 + 9*p + 4*p**4 + 4 - 1/2*p**6. Factor a(f).
-3*(f - 2)*(f + 1)*(f + 2)**3
Suppose -1/3*m**3 + 0 + 557/3*m**2 + 186*m = 0. What is m?
-1, 0, 558
Determine c so that 12*c**4 + 21*c**4 - 29*c**2 + 12*c**5 + 15*c**3 + 43*c**2 - 8*c**2 - 12*c**2 = 0.
-2, -1, 0, 1/4
Let c(g) = 3 + 5 - 4*g + 4*g**2 - 23*g. Let m(d) = 3*d**2 - 14*d + 4. Let q(v) = -19*v + 701. Let h be q(37). Let t(r) = h*c(r) + 5*m(r). Solve t(w) = 0 for w.
2/7, 2
Let f(h) be the second derivative of -h**8/1344 - h**7/56 + h**6/144 + 3*h**5/8 - 61*h**4/3 + 8*h. Let k(r) be the third derivative of f(r). Solve k(g) = 0.
-9, -1, 1
Let b be ((-24)/(-3))/((-5)/(-15)). Suppose -5*r + 49 = b. Let 5*d**2 + r*d + 146 + 5*d - 151 - 10*d**3 = 0. Calculate d.
-1, 1/2, 1
Let m(w) be the second derivative of -w**4/96 + 35*w**3/48 - 17*w**2/8 - 3251*w. Determine k so that m(k) = 0.
1, 34
Let g(p) = 6*p**3 - 21*p**2 + 48*p - 24. Let m(w) = 5*w**3 - 21*w**2 + 47*w - 25. Let a(f) = -2*g(f) + 3*m(f). Let a(o) = 0. Calculate o.
1, 3
Let m(l) = -l**3 + 4*l**2 - 8*l + 12. Let b be m(3). Let w be 0/6*(-1 - b/6). Factor w + 15/2*x**3 - 21/2*x**2 + 3*x.
3*x*(x - 1)*(5*x - 2)/2
Let c be (-73 - 1)*(0 + -1). Let z be ((-8)/10)/((-36)/90) - (-7 - -4). Suppose 2*j**3 + 73*j - 2*j**2 - j**z + 0*j**5 + 1 + j**4 - c*j = 0. Calculate j.
-1, 1
Suppose -34087*p = -34098*p. Let j(o) be the second derivative of -1/35*o**5 + 0*o**2 + 1/42*o**4 - 6*o + 1/105*o**6 + 0 + p*o**3. Factor j(r).
2*r**2*(r - 1)**2/7
Let b(q) be the second derivative of q**7/168 - 5*q**6/24 - 29*q**5/80 + 77*q**4/48 + 7*q**3/6 - 13*q**2/2 - 2*q - 2. Let b(x) = 0. Calculate x.
-2, -1, 1, 26
Let t(r) be the first derivative of r**4/102 + r**3/17 + 20*r - 97. Let v(m) be the first derivative of t(m). Factor v(x).
2*x*(x + 3)/17
Let f(j) be the second derivative of j**5/180 - 769*j**4/108 + 1535*j**3/54 - 767*j**2/18 + 4814*j - 2. Find y such that f(y) = 0.
1, 767
Let p be (-321)/9 - (-106 + 69). Factor p*h**2 + 1444/3 - 152/3*h.
4*(h - 19)**2/3
Find i, given that 227*i**4 - 16*i**2 - 14*i**2 - 25*i**3 - 232*i**4 = 0.
-3, -2, 0
Suppose -2415*k**5 + 1239*k**5 - 65*k**3 - 115*k**4 + 75*k**2 + 1201*k**5 = 0. What is k?
-1, 0, 3/5, 5
Let h(u) = 5*u**3 - 2*u**2 - 172*u + 123. Let s be h(-6). Factor 2/5*g + 0 + 9/5*g**4 + g**2 - 16/5*g**s.
g*(g - 1)**2*(9*g + 2)/5
Let l(d) be the second derivative of 99*d**5/20 + 83*d**4/2 - 193*d**3/2 - 9*d**2 + 2604*d + 2. Factor l(r).
3*(r - 1)*(r + 6)*(33*r + 1)
Determine o so that 72/13 + 2/13*o**3 - 8*o + 30/13*o**2 = 0.
-18, 1, 2
Let c(z) be the first derivative of -44/7*z**2 + 90 - 4/21*z**3 + 92/7*z. Find r such that c(r) = 0.
-23, 1
Let x(u) be the first derivative of 0*u - 2/15*u**3 - 5 + 13/5*u**2. Suppose x(f) = 0. What is f?
0, 13
Let a(l) = l**4 - 26*l**3 + 169*l**2 + l - 1. Let d(w) = -w + 1. Let j(q) = -3*a(q) - 3*d(q). Factor j(v).
-3*v**2*(v - 13)**2
Let x(z) be the third derivative of z**8/294 + 2*z**7/245 - z**6/42 - 13*z**5/105 - 3*z**4/14 - 4*z**3/21 - 9*z**2 + 13*z. Suppose x(p) = 0. Calculate p.
-1, -1/2, 2
Let k = -995 + 1024. Suppose k*u + m + 4 = 25*u, -20 = 5*u + 5*m. Factor -1/8*l + u - 3/4*l**3 - 1/8*l**5 + 1/2*l**4 + 1/2*l**2.
-l*(l - 1)**4/8
Factor -594*g + 400*g**2 + 69360 - 1780*g**3 + 10454*g + 1785*g**3.
5*(g + 12)*(g + 34)**2
Factor 468*s**2 + 2/3*s**3 + 109512*s + 8541936.
2*(s + 234)**3/3
Let x(z) be the third derivative of -z**5/30 + 71*z**4/12 - 46*z**3 + 1937*z**2. Factor x(v).
-2*(v - 69)*(v - 2)
Let p(l) be the first derivative of -2/3*l**3 - 9*l + 9/2*l**2 - 32. Find f, given that p(f) = 0.
3/2, 3
Let a be (-93)/(-434)*((-3332)/21)/(-17). Factor 1/2*v**3 + 3/2*v**a - 9/2*v - 27/2.
(v - 3)*(v + 3)**2/2
Suppose -715*p + 223*p + 3*p**2 - 3*p**2 - 30258 - 2*p**2 = 0. What is p?
-123
Let r be (-3173)/(-105) - (30 + (-18942)/630). Find f such that -r*f**2 + f**3 + 60/7*f + 0 = 0.
0, 2/7, 30
Let j(k) be the first derivative of 7*k**5/180 - 23*k**4/108 - 11*k**3/27 + 4*k**2/9 - 19*k - 63. Let i(m) be the first derivative of j(m). Factor i(d).
(d - 4)*(d + 1)*(7*d - 2)/9
Suppose 0 = 92*i - 99*i - 597*i + 604. Suppose -11/4*m**2 + 1/4*m**3 + 3/4*m**4 - 1/4*m**5 - i + 3*m = 0. What is m?
-2, 1, 2
Solve 52/3*l - 2/3*l**5 - 26/3*l**4 + 106/3*l**2 - 80/3 - 50/3*l**3 = 0.
-10, -4, -1, 1
Let c(y) be the third derivative of -y**5/210 - 17*y**4/42 - 31*y**3/7 - 28*y**2 - 32*y. Factor c(x).
-2*(x + 3)*(x + 31)/7
Suppose 1/12*x**4 - 361/4 - 10/3*x**3 + 217/6*x**2 - 152/3*x = 0. What is x?
-1, 3, 19
Factor 64*z - 4/3*z**2 - 1280/3.
-4*(z - 40)*(z - 8)/3
Let t(z) be the third derivative of -z**7/1155 + 17*z**6/33 - 14279*z**5/165 - 4845*z**4/11 - 9747*z**3/11 + 151*z**2. Solve t(g) = 0 for g.
-1, 171
Let j(f) be the first derivative of -f**3/4 + 23*f**2/2 - 56*f - 3008. Factor j(w).
-(w - 28)*(3*w - 8)/4
Let q(m) be the third derivative of -m**5/60 - 269*m**4/24 + 271*m**3/3 - 4538*m**2 - 2. Determine a, given that q(a) = 0.
-271, 2
Let x(w) be the first derivative of -w**6/1980 - w**5/60 - 2*w**4/11 - w**3/3 + 183*w + 57. Let k(t) be the third derivative of x(t). What is y in k(y) = 0?
-8, -3
Let h be 19/(-38) - (-273)/(-6). Let n = h - -49. Factor 2/5*y + 4/5 - 2/5*y**n - 4/5*y**2.
-2*(y - 1)*(y + 1)*(y + 2)/5
Suppose -2*c = 2*s - 19574, -1998 + 41116 = 4*c - 2*s. What is f in -63*f**2 - c - f**3 - 1323*f + 1490 - 969 = 0?
-21
Let x(z) be the second derivative of -z**5/4 - 175*z**4/4 + 10*z**3/3 + 1050*z**2 - 5108*z. Factor x(g).
-5*(g - 2)*(g + 2)*(g + 105)
Factor -134*n**3 + 90*n**3 + 7*n - 4 + 5 - 163*n**3 - 80*n + 279*n*