 h(m) be the first derivative of m**2 + 11*m**4 + u*m**6 + 0*m + 14 + 48/5*m**5 + 16/3*m**3. What is z in h(z) = 0?
-1, -1/3, 0
Let q(r) be the second derivative of r**4/12 - 5*r**3/6 - 3*r**2 + r - 114. Solve q(y) = 0.
-1, 6
Let k = 13 + -11. Let x be (-5)/(-3)*12/10. Solve -x*j - 127 - k*j**2 + 123 + 8*j = 0 for j.
1, 2
Let n(m) be the first derivative of m**6/50 - 3*m**4/10 - 4*m**3/5 - 9*m**2/10 - 28*m + 48. Let q(v) be the first derivative of n(v). Factor q(c).
3*(c - 3)*(c + 1)**3/5
Let p be 24/(-7) + 40/(-70)*-7. Suppose 11*g - 3*z - 14 = 7*g, 2*g = -5*z - 6. Suppose 4/7*w**3 + p - 4/7*w - 4/7*w**g = 0. What is w?
-1, 1
Let f be 15 + ((-3184)/264 - 40/(-660)). Factor 15/7*l + f*l**2 + 3/7 + 9/7*l**3.
3*(l + 1)**2*(3*l + 1)/7
Let q = 957461/9 + -106381. Solve 16/3*y**2 + 2/9*y**4 - 2*y**3 - q*y + 0 = 0.
0, 1, 4
Let s(r) = -3*r**3 - 6*r**2 + 3*r - 6. Let b be 14 - (0 + 15)/(-5). Let t(f) = 21 + f + 13 - 50 + b. Let i(y) = -s(y) - 6*t(y). Suppose i(p) = 0. Calculate p.
-3, 0, 1
Let j = 2/261477 + 3253934/261477. Solve -2/9*f**2 - 1568/9 - j*f = 0.
-28
Let p(n) be the second derivative of -1/5*n**5 - 2/15*n**6 + 1/3*n**4 + 2/21*n**7 + 0*n**2 + 37 + 0*n**3 + 4*n. Find b such that p(b) = 0.
-1, 0, 1
Let n(a) = 2*a**3 + 54*a**2 + 73*a + 546. Let w be n(-26). Let 0*h + w - 1/2*h**3 + 8*h**2 = 0. What is h?
0, 16
Let k(w) = -200*w**3 + 88240*w**2 + 70679*w + 14162. Let j(z) = -50*z**3 + 22060*z**2 + 17670*z + 3540. Let c(o) = -9*j(o) + 2*k(o). Factor c(b).
2*(b - 442)*(5*b + 2)**2
Let u(g) = 2*g**2 - 2*g - 8. Let y(o) = 11*o**2 + 46*o + 19. Let s(v) = -4*u(v) + y(v). Factor s(n).
3*(n + 1)*(n + 17)
Let b(u) be the first derivative of -13*u**4/2 + 94*u**3 + 178*u**2 + 48*u + 1825. Suppose b(q) = 0. What is q?
-1, -2/13, 12
Let h(d) be the second derivative of -18*d**5/25 + 8*d**4 + 83*d**3/15 + 7*d**2/5 + 246*d + 4. Solve h(v) = 0.
-1/6, 7
Let r(h) be the second derivative of 110/3*h**3 - 47/4*h**5 - 13/3*h**6 - 100*h**2 + 5/14*h**7 - 59 + 55/2*h**4 + h. Find d such that r(d) = 0.
-2, -1, 2/3, 1, 10
Let c be -6 + (-40)/(-5) + 1089. Let c - 5*j**3 - 4429 - 2940*j - 210*j**2 - 10382 = 0. What is j?
-14
Let z(v) = v**2 - v - 2. Let i(q) = 4*q**3 - 2*q**2 - 82*q + 68. Let m(w) = i(w) - 6*z(w). Find h, given that m(h) = 0.
-4, 1, 5
Let d be (1 - 11/14)/(-25 - 151086/(-6006)). Let 1/8*t**3 + 4*t - 7/2 - d*t**2 = 0. What is t?
2, 7
Let w be (1 - 528/52) + 13. Factor -w - 2/13*j**2 + 20/13*j.
-2*(j - 5)**2/13
Factor -180 + 3*b**2 + 61347*b - 5*b**2 - 61413*b.
-2*(b + 3)*(b + 30)
Let g(z) = 8*z + 8*z + 19 - 3*z - 6*z + 8*z. Let i be g(-1). Suppose -6/5*q**4 - 12/5*q - 24/5*q**2 - 2/5 - i*q**3 = 0. What is q?
-1, -1/3
Let r = -1/62137 - -186415/248548. Factor -6*u - 45/4 - r*u**2.
-3*(u + 3)*(u + 5)/4
Let y(x) be the second derivative of -x**4/12 - 35*x**3/2 - 533*x. Solve y(n) = 0.
-105, 0
Let b = 95 - 93. Let f(x) = -38*x**b + 3*x + 29*x**2 + 4 - 9*x. Let j(u) = -8*u**2 - 7*u + 3. Let t(c) = 3*f(c) - 4*j(c). Factor t(o).
5*o*(o + 2)
Let r(t) be the first derivative of 0*t + 1/9*t**3 - 1/15*t**5 + t**2 + 84 - 1/2*t**4. Factor r(b).
-b*(b - 1)*(b + 1)*(b + 6)/3
Let n(r) be the third derivative of -r**5/30 + r**4 - 19*r**3/3 + 2*r**2. Let t(j) = 4*j**2 - 49*j + 77. Let v(p) = 5*n(p) + 2*t(p). Factor v(o).
-2*(o - 9)*(o - 2)
Suppose y - 28 = -5*v, -y - 2*y + 30 = -3*v. Determine i so that -54*i**3 + 24*i**3 + y - 14*i**2 + 12*i + 18*i**3 + i**4 = 0.
-1, 1, 13
Let q(g) be the third derivative of -g**8/7 - 1532*g**7/105 + 243*g**6/8 + 157*g**5/30 - 239*g**4/8 - 65*g**3/3 - 2434*g**2. Suppose q(k) = 0. Calculate k.
-65, -1/4, 2/3, 1
Let x(d) = 45*d**3 + 3373*d**2 + 6102*d - 876. Let t(w) = 45*w**3 + 3375*w**2 + 6093*w - 876. Let f(h) = 2*t(h) - 3*x(h). Factor f(j).
-3*(j + 2)*(j + 73)*(15*j - 2)
Let r(n) be the third derivative of n**5/15 - 3*n**4/2 - 60*n**3 - 3417*n**2. Factor r(b).
4*(b - 15)*(b + 6)
Let i(n) = 34*n - 6. Let u be i(0). Let x be (-16)/(-32) + (-9)/u + 0. Factor -4/9*r + 4/9*r**4 + 4/9*r**3 + 0 - 4/9*r**x.
4*r*(r - 1)*(r + 1)**2/9
Factor 18*n**2 - 534*n - 1889*n + 548*n + 530 + 30*n**2 + 22*n**2.
5*(2*n - 53)*(7*n - 2)
Let q(j) be the first derivative of j**4/24 - 7*j**3/18 - 23*j**2/3 - 14*j - 2673. Determine p so that q(p) = 0.
-6, -1, 14
Suppose 0 = 12*w + 135 - 264 + 105. Let q(h) be the second derivative of 4*h**w - 1/12*h**4 + 0 - 7/6*h**3 - 16*h. Let q(v) = 0. Calculate v.
-8, 1
Let g(h) = -8*h**3 + 13*h**2 + 35*h + 29. Let q be 360/324*(-18)/(-4). Let a(f) = 7*f**3 - 11*f**2 - 34*f - 28. Let n(d) = q*a(d) + 4*g(d). Factor n(v).
3*(v - 4)*(v + 1)*(v + 2)
Find z, given that 10804*z**2 - 39 - 10805*z**2 + 28*z - 93 = 0.
6, 22
Let b(w) be the first derivative of 25/2*w**2 - 22 + 10*w + 20/3*w**3 + 5/4*w**4. Factor b(g).
5*(g + 1)**2*(g + 2)
Let u(o) be the first derivative of 0*o + 1/60*o**5 + 3*o**2 - 1/8*o**4 - 2/3*o**3 - 1. Let f(g) be the second derivative of u(g). Factor f(r).
(r - 4)*(r + 1)
Suppose p - 2*i - 3*i + 4 = 0, 0 = -3*i. Let m be p/(24/15)*-4. Let -4*j**2 - 38 + m*j**2 + 38 - 3*j**3 - 3*j = 0. What is j?
0, 1
Let a = -57368/55 + 5218/5. Factor 0 - a*h**4 + 12/11*h**3 + 0*h - 6/11*h**2.
-6*h**2*(h - 1)**2/11
Suppose -2*t + 2*o + 2 = -4*t, 4*t = o + 21. Suppose 5*x + 9 = -26*d + 23*d, 3*d + 6 = -t*x. Solve 12/17*v + 10/17 + 2/17*v**d = 0 for v.
-5, -1
Factor -2/7*s**2 + 0 - 226/7*s.
-2*s*(s + 113)/7
Let d(r) be the second derivative of -r**4/78 + 2227*r**3/39 + 2228*r**2/13 - 6510*r. Suppose d(s) = 0. What is s?
-1, 2228
Let l(h) be the third derivative of -h**7/420 + 29*h**6/240 - 37*h**5/20 + 40*h**4/3 - 152*h**3/3 + 2*h**2 + 5549*h. Solve l(k) = 0.
2, 4, 19
Let n(b) be the second derivative of -b**7/441 + 26*b**6/315 - 113*b**5/210 + 86*b**4/63 - 4*b**3/3 - 3*b + 44. Determine g so that n(g) = 0.
0, 1, 2, 21
Suppose -3*z + 6*z - 2*h - 7 = 0, -4*z - h + 13 = 0. Factor -3*u - 93*u**2 + 12*u**3 - 18*u - z*u.
3*u*(u - 8)*(4*u + 1)
Let x(m) be the second derivative of m**5/10 + 8*m**4/3 + 5*m**3 + 4174*m. Factor x(y).
2*y*(y + 1)*(y + 15)
Let d = -1102 - -1077. Let u be (15/d)/(6/(-20)). Let 2/15*r**4 - 2/15*r**u - 4/15*r**3 + 4/15*r + 0 = 0. Calculate r.
-1, 0, 1, 2
Let d(i) be the third derivative of -i**10/126000 - i**9/21600 - i**8/25200 - i**5/5 + 72*i**2. Let x(c) be the third derivative of d(c). Solve x(y) = 0.
-2, -1/3, 0
Factor 35 + 47*h - 3*h**2 - 192 + 6*h + 52*h - 131.
-3*(h - 32)*(h - 3)
Let c(b) be the third derivative of 1/15*b**4 + 0*b**3 - 1/300*b**6 + 2/75*b**5 - 1/525*b**7 + 15*b**2 + 0*b + 0. Solve c(s) = 0.
-2, -1, 0, 2
Let o = 578 + -914. Let t = o + 3698/11. Suppose -16/11*a + 10/11*a**4 - 2/11*a**2 + t*a**5 + 14/11*a**3 - 8/11 = 0. What is a?
-2, -1, 1
What is x in 20*x**3 + 232 + 74*x**2 - 401*x**2 - 213*x**2 + 85*x**2 - 352 - 595*x = 0?
-1, -1/4, 24
Suppose 18*o + 38*o = -8*o + 9*o. Let h(i) be the second derivative of 1/14*i**4 + 0*i**3 + 22*i - 9/140*i**5 + 0*i**2 + 0 + o*i**6 + 1/98*i**7. Factor h(f).
3*f**2*(f - 1)**2*(f + 2)/7
Let d = 4045 + -4042. Let s(f) be the third derivative of -1/6*f**4 + 0 + 10*f**2 - 1/30*f**5 + 0*f + 0*f**d. Factor s(t).
-2*t*(t + 2)
Let l(f) = -f. Let v(c) = -11 + 18 + 15*c**2 - 12 - 25 + 75*c. Let r(w) = 10*l(w) - v(w). Factor r(g).
-5*(g + 6)*(3*g - 1)
Find b, given that -375948/5 + 129564/5*b + 4/5*b**3 - 1428/5*b**2 = 0.
3, 177
Factor 260000/3*s + 1250/9*s**3 + 391873/9*s**2 + 43264 + 1/9*s**4.
(s + 1)**2*(s + 624)**2/9
Let n be ((-10)/(-6))/((-265)/(-30) - 8). Let k(t) = t**3 - t**2. Let m(c) = 6*c**3 - 11*c**2 - 5*c - 2. Let l(u) = n*m(u) - 14*k(u). Factor l(a).
-2*(a + 1)**2*(a + 2)
Determine n, given that 163722*n**4 + 864*n**2 - 163518*n**4 + 3*n**5 + 354*n**3 - 891*n**3 - 315*n**3 = 0.
-72, 0, 2
What is s in -176/7 + 2/7*s**2 - 174/7*s = 0?
-1, 88
Suppose 4*l + 6 = -6, -5*l - 25 = -5*g. Factor -189 + 397 + 3*t**g + 12*t - 199.
3*(t + 1)*(t + 3)
Let t = 380677 + -2664639/7. Factor t - 90/7*o + 24/7*o**2 - 2/7*o**3.
-2*(o - 5)**2*(o - 2)/7
Let w(o) be the third derivative of 4*o**2 + 0*o**3 + 0*o - 1/480*o**6 - 1/20*o**5 - 11/96*o**4 + 22. What is q in w(q) = 0?
-11, -1, 0
Let d = -419289/4 + 104823. Factor 3*t**2 - 9/2 + d*t + 3/4*t**3.
3*(t - 1)*(t + 2)*(t + 3)/4
Let o(w) be the second derivative of -w**4/9 - 62*w**3/9 + 68*w**2 - 203*w. Let o(v) = 0. Wh