be the second derivative of 0*f**2 - 2/9*f**3 + 0 + 31*f - 1/36*f**4. Suppose b(l) = 0. Calculate l.
-4, 0
Factor -113*i - 5*i**4 - 120*i + 233*i + 55*i**2 - 50*i**3.
-5*i**2*(i - 1)*(i + 11)
Find j, given that -10*j**2 - 7*j - 5*j**4 - 31*j**3 + 7*j + 16*j**3 = 0.
-2, -1, 0
Let k = -8619 - -25867/3. Factor 3*c - 1/3*c**2 + k.
-(c - 10)*(c + 1)/3
Let p(b) be the third derivative of 0 - b**2 + 0*b + 1/60*b**5 + 1/420*b**7 + 0*b**4 - 1/80*b**6 + 0*b**3. Find l such that p(l) = 0.
0, 1, 2
Let n(q) be the second derivative of -5/42*q**4 - 2/35*q**5 - 2/21*q**3 + 0*q**2 - 1/105*q**6 - 15*q + 0. Factor n(t).
-2*t*(t + 1)**2*(t + 2)/7
Let q(y) be the second derivative of y**9/756 - y**8/210 + y**7/630 + y**6/90 + y**4/2 + 10*y. Let z(c) be the third derivative of q(c). Factor z(h).
4*h*(h - 1)**2*(5*h + 2)
Let k(m) = 8*m**4 + 7*m**3 - 2*m**2 - 3*m + 5. Let y(s) = -s**4 - s**3 - s**2 + s - 1. Let c(i) = k(i) + 5*y(i). Suppose c(t) = 0. What is t?
-2, 0, 1/3, 1
Let o(f) = f**2 + 2*f - 1. Let s be o(-5). Factor -2*h + 6*h + s*h**3 + 2*h - 18*h**2 - 2*h.
2*h*(h - 1)*(7*h - 2)
Let i = 22931 + -22927. Let f be 0 + -1 - (-6)/2. Determine u, given that -i - 8/3*u + 4/3*u**f = 0.
-1, 3
Let j = -3/20258 - -39705689/60774. Let 4/3*k**4 - j*k - 88/3*k**3 + 224*k**2 + 1372/3 = 0. Calculate k.
1, 7
Let k(d) be the second derivative of 2/27*d**3 + 0 + 1/54*d**4 + 1/9*d**2 - 8*d. Determine n so that k(n) = 0.
-1
Let t(l) be the first derivative of l**5/20 + l**4/12 - 9*l + 18. Let n(o) be the first derivative of t(o). Determine x, given that n(x) = 0.
-1, 0
Let f(q) be the second derivative of -27*q**6/40 + 9*q**5/20 + 77*q**4/48 - 3*q**3/2 + q**2/2 + 6*q - 1. Determine o, given that f(o) = 0.
-1, 2/9, 1
Let y(v) be the second derivative of -2*v**7/105 - 14*v**6/25 - 19*v**5/25 + 7*v**4/5 + 8*v**3/3 + 200*v. Solve y(g) = 0.
-20, -1, 0, 1
Let s = -417660 + 142839553/342. Let c = 2/171 - s. Find q such that -3/2*q**3 - q**2 + 0*q + 0 + c*q**5 + 0*q**4 = 0.
-1, 0, 2
Let q be ((-20)/125)/((-140)/50). Let c(z) be the first derivative of 4/7*z**2 - 16/7*z + 3 - 5/14*z**4 + q*z**5 + 4/7*z**3. Solve c(m) = 0.
-1, 2
Let d(a) = -41*a**2 + 242*a + 261. Let u(h) = 15*h**2 - 80*h - 87. Let m(j) = 4*d(j) + 11*u(j). Factor m(r).
(r + 1)*(r + 87)
Solve 310*j**2 - 147*j**2 + 33*j - 157*j**2 + 137*j + 56 = 0 for j.
-28, -1/3
Suppose 6*t - 2*t = 3*n + 22, t + 5*n = -6. Suppose 0 = 2*j - j - t. Solve 3*c**j - c**4 - c**3 - c**3 = 0.
0, 1
Let z be 20 - 1*(-7 - -2). Factor z*p + 52*p - 126 - 5*p**2 + 33*p - 479.
-5*(p - 11)**2
Let t be ((-6)/4)/((-18)/(-36)). Let a be -4*(-4 - t)*2/20. Factor 4/5*z + 2/5*z**2 + a.
2*(z + 1)**2/5
Let l be 7 - 1 - (-1 - 209/(-33)). Factor -l - 1/6*q**2 + 5/6*q.
-(q - 4)*(q - 1)/6
Let s be 27/2*(-20)/15. Let v = s + 20. What is g in -2/5*g - 2/5*g**3 + 0 - 4/5*g**v = 0?
-1, 0
Let n(m) = -320*m**3 + 354*m**2 - 36*m + 20. Let l(x) = x**3 - 2*x**2 + x + 1. Let p(i) = 36*l(i) - 2*n(i). Factor p(f).
4*(f - 1)*(13*f - 1)**2
Suppose 7*i - 1838 = -1824. Factor -3/7*f - 3/7*f**i + 0.
-3*f*(f + 1)/7
Factor -3/2 + 1/4*y**2 - 5/4*y.
(y - 6)*(y + 1)/4
Suppose -8 - 13 = 3*h. Let r = h + 9. Factor 2*c**2 + 2*c**r - 7*c**2.
-3*c**2
Let h(t) be the third derivative of -t**7/630 - t**6/120 + t**5/18 + t**4/3 + 64*t**2. Factor h(a).
-a*(a - 3)*(a + 2)*(a + 4)/3
Let p be 2042/12 - (-1)/6. Let c = 171 - p. Factor -c*r**3 + 0*r + 0*r**2 + 0 + 4/3*r**4 - 2/3*r**5.
-2*r**3*(r - 1)**2/3
Let t be 378/175 + -1 + (-2)/10. Let x(v) be the first derivative of -2/15*v**6 + 8/5*v + 64/15*v**3 - 7 - 14/5*v**4 + t*v**5 - 18/5*v**2. Factor x(d).
-4*(d - 2)*(d - 1)**4/5
Let q(d) be the first derivative of 2*d**6/15 + 4*d**5/5 - 23*d - 21. Let f(g) be the first derivative of q(g). Factor f(j).
4*j**3*(j + 4)
What is t in -7*t**4 + 27*t + 12*t**5 - 15*t + 4 - 8*t**2 - 24*t**3 + 11*t**4 = 0?
-1, -1/3, 1
Let g(c) be the second derivative of c**5/180 - c**4/72 - c**3/9 + 3*c**2 + 19*c. Let l(r) be the first derivative of g(r). Solve l(o) = 0.
-1, 2
Suppose 4*r = 66 - 58. Determine k, given that 0 - 2/19*k**3 - 4/19*k**r - 2/19*k = 0.
-1, 0
Let n(k) be the first derivative of -2*k**3/3 - 9*k**2 + 4*k + 53. Let j be n(-9). Factor -1/5*x**5 - 3/5*x + 0*x**j + 2/5*x**2 - 2/5 + 4/5*x**3.
-(x - 2)*(x - 1)*(x + 1)**3/5
Let p(y) = y**2 - 16*y - 54. Let u be p(19). Suppose 2*x = -5*i + 18, u*i + x = -x + 14. Factor 0 + 1/3*j + j**3 + j**i + 1/3*j**4.
j*(j + 1)**3/3
Suppose -112/5*n + 8/5*n**4 - 24/5 - 54/5*n**2 + 42/5*n**3 = 0. Calculate n.
-6, -1, -1/4, 2
Let q(x) = -21*x**3 - 16*x**2 - 7*x + 4. Let j(g) = -3*g**3 - g**2 + g + 1. Let b(f) = -40*j(f) + 5*q(f). Factor b(k).
5*(k - 4)*(k + 1)*(3*k + 1)
Let m(d) = 13*d**5 + 20*d**4 + 16*d**3 + 14*d**2 - 5*d + 5. Let z(b) = 6*b**5 + 10*b**4 + 8*b**3 + 6*b**2 - 2*b + 2. Let i(s) = 4*m(s) - 10*z(s). Factor i(t).
-4*t**2*(t + 1)**2*(2*t + 1)
Let z(a) = -2*a**2 + 2*a + 3. Let k be z(0). Let -21/4*i**4 - 9*i**k + 0*i + 3*i**2 + 0 = 0. What is i?
-2, 0, 2/7
Let w(p) = -p**2 + p + 1. Let c(o) = -8*o**2 + 2*o + 4. Let g(n) = -n - 1. Let m be g(4). Let l = m + 4. Let h(t) = l*c(t) + 6*w(t). Factor h(x).
2*(x + 1)**2
Suppose 85*v**2 - 162*v + 7*v**3 - 21*v**3 + 3*v**3 + 315 + 6*v**3 - 233*v = 0. What is v?
1, 7, 9
Let c(q) = 4*q**2 + 60*q - 56. Let i(a) = 13*a**2 + 181*a - 166. Let j(r) = 14*c(r) - 4*i(r). Factor j(t).
4*(t - 1)*(t + 30)
Let o(u) be the third derivative of 13*u**7/210 + 7*u**6/30 + u**5/15 + u**2 - 128. What is d in o(d) = 0?
-2, -2/13, 0
Let l(h) = -h**5 - h**3 - h**2 + h. Let p(v) = -6*v + 6*v**3 - 15*v**4 - v + 0*v + 26*v**2 + 11*v**5 + v. Let a(d) = 6*l(d) + p(d). Factor a(k).
5*k**2*(k - 2)**2*(k + 1)
Let g(f) be the second derivative of 1/8*f**3 + 0 + 0*f**2 + 3*f + 1/16*f**4. Factor g(k).
3*k*(k + 1)/4
Factor -17/3*s - 7/6*s**2 + 20/3 + 1/6*s**3.
(s - 10)*(s - 1)*(s + 4)/6
Factor 2717 + v**3 + 1728*v + 218*v**2 - 290*v**2 - 16541.
(v - 24)**3
Let x(t) be the first derivative of -t**4/34 - 2*t**3/17 - 2*t**2/17 - 68. Factor x(u).
-2*u*(u + 1)*(u + 2)/17
Let g(t) be the third derivative of -t**8/110880 + t**7/9240 - t**6/1980 + t**5/4 + 12*t**2. Let o(k) be the third derivative of g(k). Factor o(r).
-2*(r - 2)*(r - 1)/11
Let m(y) be the first derivative of -2*y**3/33 - 21*y**2/11 - 40*y/11 + 37. Let m(d) = 0. Calculate d.
-20, -1
Let p(y) be the second derivative of 1/168*y**7 + 0 + 8*y + 0*y**3 + 0*y**4 + 0*y**2 - 1/80*y**5 + 0*y**6. Factor p(j).
j**3*(j - 1)*(j + 1)/4
Let x be ((-10)/(-36))/((-380)/(-114)). Let w(t) be the second derivative of 1/18*t**3 + 0*t**2 + 1/90*t**6 + 7*t + 0 + 1/20*t**5 + x*t**4. Factor w(c).
c*(c + 1)**3/3
Let b(u) be the first derivative of u**4/10 + 34*u**3/15 + 71*u**2/5 + 22*u - 270. Suppose b(y) = 0. What is y?
-11, -5, -1
Let a(v) be the third derivative of -v**5/210 - v**4/14 - 8*v**3/21 - 37*v**2 - 2. Suppose a(r) = 0. Calculate r.
-4, -2
Let 360/7 + 78/7*w + 3/7*w**2 = 0. What is w?
-20, -6
Suppose -7*o = 2 - 16. Factor 3*s**2 - 7*s**4 + 3*s**o - 3*s**2 + 4*s**4.
-3*s**2*(s - 1)*(s + 1)
Let r(m) be the second derivative of -m**5/20 + m**4/8 + m**3 + 15*m**2 + 11*m - 1. Let n(j) be the first derivative of r(j). Factor n(p).
-3*(p - 2)*(p + 1)
Suppose -5*c + 5 = -30. Let k = c + -2. Factor 9*t**2 + k - 3 + 4*t - 6*t**2 - 1.
(t + 1)*(3*t + 1)
Factor -4/5*p**3 + 4/5*p + 2/5*p**2 - 2/5*p**4 + 0.
-2*p*(p - 1)*(p + 1)*(p + 2)/5
Let r(q) = q**2 - 142*q - 286. Let p be r(-2). Factor 6/5*c**p + 0*c + 0.
6*c**2/5
Let n(c) be the second derivative of -c**7/14 - 11*c**6/10 - 6*c**5 - 12*c**4 - 12*c + 6. Let n(p) = 0. Calculate p.
-4, -3, 0
Let k(o) be the third derivative of 12*o**2 + 0*o - 2/3*o**3 + 1/6*o**5 - 1/4*o**4 + 0. Factor k(l).
2*(l - 1)*(5*l + 2)
Let p = -590 + 37171/63. Let a(d) be the second derivative of 1/9*d**3 + 0*d**2 - 4/45*d**6 - 2/9*d**4 + p*d**7 + d + 0 + 1/5*d**5. Find x, given that a(x) = 0.
0, 1
Let k(t) = -7*t**2 - 67*t + 437. Let c(n) = 2*n**2 - n - 1. Let i(s) = 5*c(s) + k(s). Find d such that i(d) = 0.
12
Let l(r) = -3*r**2 + 63*r + 12. Let j(q) = -q**2 + 25*q + 5. Let w = 0 - -12. Let f(n) = w*j(n) - 5*l(n). Factor f(h).
3*h*(h - 5)
Let j(q) = -8*q**5 + 4*q**3 + 4*q**2 - 20*q - 4. Let v(z) = z**5 - z**4 + z**3 + z**2 + 4*z. Let g(l) = -j(l) - 4*v(l). Factor g(h).
4*(h - 1)**2*(h + 1)**3
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