27 + 20*o**2/9 - 200*o/9 - 62. Factor h(v).
-2*(v - 10)**2/9
Let b(k) be the first derivative of -k**6/600 - k**5/100 - k**4/40 + 14*k**3/3 + 4. Let u(g) be the third derivative of b(g). Factor u(m).
-3*(m + 1)**2/5
Let u(s) be the third derivative of s**8/112 + 6*s**7/35 + 9*s**6/8 + 27*s**5/10 + 7*s**2 + 6. Solve u(g) = 0 for g.
-6, -3, 0
Let u(p) = -p**3 - 2. Let f(w) = 24*w**2 + 63*w + 48. Let n(o) = f(o) - 3*u(o). Factor n(j).
3*(j + 2)*(j + 3)**2
Let n(r) be the first derivative of 196/3*r**6 + 16*r**2 + 0*r - 756/5*r**5 + 48*r**3 - 4 - 34*r**4. Solve n(j) = 0.
-2/7, 0, 1/2, 2
Let l(w) be the first derivative of 1 + 15*w**2 + 6*w**3 + 13*w - 7 - 4*w + 0. Let z(r) = r**2 - r - 1. Let j(o) = -l(o) - 3*z(o). Find v such that j(v) = 0.
-1, -2/7
Suppose -151*d = 671 - 973. Factor 2/3*c**3 + 14/3*c - 10/3*c**d - 2.
2*(c - 3)*(c - 1)**2/3
Let l be 21/(-14)*40/(-645). Let d = 35/86 + l. Solve -n + 1/2 + d*n**2 = 0 for n.
1
Suppose -14*a = 4*n - 17*a + 7, -n + 3*a = 13. Let s(c) be the first derivative of -1/15*c**3 - 4/5*c**n - 16/5*c + 1. Factor s(d).
-(d + 4)**2/5
Let q be (4/(-56))/(5 - 1161/231). Factor q*i**2 - 3/4*i + i**3 + 0.
i*(i + 3)*(4*i - 1)/4
Suppose -28*p = -23*p - 60. Factor -7*s**2 - 5*s**4 + 4*s**3 - p*s**3 + 3*s**4 + s**2.
-2*s**2*(s + 1)*(s + 3)
Suppose 40 = 2*g - i, -i + 100 = 7*g - 2*g. Suppose 5*f - 19*n + g*n - 5 = 0, 0 = -n - 5. Factor 1/4*x**3 - x - 2 + 1/2*x**f.
(x - 2)*(x + 2)**2/4
Let l = -24/587 - -1390/5283. Factor 0 + 2/9*a**3 + l*a**4 - 2/9*a**5 + 0*a - 2/9*a**2.
-2*a**2*(a - 1)**2*(a + 1)/9
Let n(r) be the third derivative of -r**7/1155 - 2*r**6/55 - 92*r**5/165 - 40*r**4/11 - 400*r**3/33 - 28*r**2. Determine l, given that n(l) = 0.
-10, -2
Let s(k) = -6*k**4 + 44*k**3 - 580*k**2 - 625*k + 5. Let r(y) = y**4 + y**3 + y**2 - 1. Let p(i) = -5*r(i) - s(i). What is c in p(c) = 0?
-1, 0, 25
Let p(d) be the first derivative of 2*d**5/45 - 5*d**4/18 - 2*d**3/9 + 13*d**2/9 + 20*d/9 - 43. Solve p(c) = 0.
-1, 2, 5
Suppose -5*v + 3*y + 25 = 0, 2*v - v - 5*y = 27. Factor 2*z + 3/2 - 1/2*z**4 - z**2 - v*z**3.
-(z - 1)*(z + 1)**2*(z + 3)/2
Let z = 29 + -27. Factor 10*c**3 - 5*c**4 + 43*c - 53*c + 5*c**z + 0*c**4.
-5*c*(c - 2)*(c - 1)*(c + 1)
Let z(h) be the first derivative of -8*h**5/25 + 17*h**4/10 - 44*h**3/15 + 9*h**2/5 + 355. Solve z(u) = 0 for u.
0, 1, 9/4
Suppose -10 - 5/6*t**3 + 20/3*t + 25/6*t**2 = 0. What is t?
-2, 1, 6
Suppose -3/4*t**3 - 15/2*t**2 + 3*t**4 + 0 + 21/4*t = 0. Calculate t.
-7/4, 0, 1
Let w(t) be the second derivative of 0*t**2 + 1/70*t**6 + 1/98*t**7 + 0*t**3 - 3/140*t**5 - 17*t - 1/28*t**4 + 0. Factor w(a).
3*a**2*(a - 1)*(a + 1)**2/7
Let y = 15344/28545 + -8/1903. Let 0 - 2/15*r**2 - y*r**3 + 0*r = 0. What is r?
-1/4, 0
Let o(g) be the first derivative of g**4/2 - 2*g**3 + 8*g + 113. Let o(k) = 0. Calculate k.
-1, 2
Suppose -5*b - 12 = 4*h, 15 = b - 2*b - 5*h. Let c(u) be the second derivative of -5*u - 1/12*u**3 - 1/24*u**4 + 1/4*u**2 + b + 1/40*u**5. Factor c(o).
(o - 1)**2*(o + 1)/2
Let d = -17 + 18. Let -7 - o**2 + 3*o + d + 4 = 0. What is o?
1, 2
Let r(d) = 5*d**3 - 5*d**2 + 2*d + 5. Let a be r(3). Solve 100*o**3 - a*o**3 + 1 - o**4 - 1 + o**2 + o**5 = 0.
-1, 0, 1
Let m(w) = 26*w**2 - 79*w + 5. Let u be m(3). Solve -2/13*p**3 + 4/13*p**4 + 14/13*p - 12/13*p**u - 4/13 = 0.
-2, 1/2, 1
Let f(c) = -8*c**3 + 5*c**2 + 8*c - 15. Let j(h) be the second derivative of -h**4/12 - h**2/2 - h. Let i(g) = -f(g) + 5*j(g). Factor i(d).
2*(d - 1)*(d + 1)*(4*d - 5)
Let w = 4 - 2. Let h(v) = -2*v**4 + 6*v**3 + 2*v**2 - 6*v. Let l(y) = 6*y**4 - 18*y**3 - 7*y**2 + 17*y. Let u(m) = w*l(m) + 7*h(m). Factor u(f).
-2*f*(f - 2)**2*(f + 1)
Suppose -g + 5*g = g. Suppose 0*y - 5*y + 3*i + 10 = g, -i = -4*y + 8. Determine z so that 3/7*z**y + 12/7 - 12/7*z = 0.
2
Let p be (-8 + 3 + 7)*-190. Let a be -3 + (p/(-57) - 3*1). Factor 1/3*l - 1/3*l**3 + 2/3 - a*l**2.
-(l - 1)*(l + 1)*(l + 2)/3
Let u(j) be the second derivative of 0*j**4 - 1/50*j**5 + 26*j + 0*j**2 + 0*j**3 + 0. Factor u(l).
-2*l**3/5
Let q(n) = 15*n**2 + 56*n + 54. Let h(i) = 7*i**2 + 27*i + 26. Let z(c) = 13*h(c) - 6*q(c). Factor z(y).
(y + 1)*(y + 14)
Let m = -2905 + 11621/4. Factor m*p**5 + 0 - 1/4*p**3 + 1/4*p**2 - 1/4*p**4 + 0*p.
p**2*(p - 1)**2*(p + 1)/4
Let f(k) = 1 + 0 + 12*k**2 - k - 13*k**2. Let r(o) = -2*o**3 + 24*o**2 + 6*o - 14. Let i(p) = 28*f(p) + 2*r(p). Let i(q) = 0. What is q?
0, 1, 4
Let p(n) = n + 18. Let w be p(-15). Suppose c + 2 = w. Factor -14*l**2 + c - 16*l**2 - 18*l + 3 + 8*l**2.
-2*(l + 1)*(11*l - 2)
Factor -328 - 9*r**2 + 10*r**2 + 303.
(r - 5)*(r + 5)
Let j(w) be the second derivative of w**6/1440 - w**5/480 - w**4/16 + 3*w**3/2 + 16*w. Let x(c) be the second derivative of j(c). Factor x(m).
(m - 3)*(m + 2)/4
Let i(p) = 649*p**2 + 1974*p + 51. Let r(u) = -325*u**2 - 987*u - 24. Let x(w) = -2*i(w) - 5*r(w). Find k, given that x(k) = 0.
-3, -2/109
Let r(m) = -11*m**4 + 30*m**3 - 40*m**2 - 30*m - 17. Let d(u) = 4*u**4 - 10*u**3 + 14*u**2 + 10*u + 6. Let j(a) = 17*d(a) + 6*r(a). Factor j(o).
2*o*(o - 1)*(o + 1)*(o + 5)
Let u = 6/7517 + 90162/52619. Factor 16/7*p**2 + 2/7*p**4 + 12/7*p - u*p**3 - 18/7.
2*(p - 3)**2*(p - 1)*(p + 1)/7
Suppose 3 - 18 = -5*s. Suppose s*i + 46 = 4*k, -2*k + i + 30 = -4*i. Factor -10 - 2*h**2 - 6*h - h**2 + k.
-3*h*(h + 2)
Let a(g) be the first derivative of -2*g**3/45 - 4*g**2/15 - 2*g/5 - 78. Factor a(u).
-2*(u + 1)*(u + 3)/15
Let k(m) be the third derivative of m**9/15120 + m**8/3360 + m**4/12 - 10*m**2. Let s(c) be the second derivative of k(c). Factor s(z).
z**3*(z + 2)
Let j(n) be the first derivative of 2/9*n**2 - 1/9*n**4 - 4/27*n**3 - 28 + 4/45*n**5 + 0*n. Factor j(y).
4*y*(y - 1)**2*(y + 1)/9
Suppose -209*y - 23*y**2 + 15*y**2 - 255*y + 144*y + 12*y**2 = 0. Calculate y.
0, 80
Suppose 2 = 2*b - 2. Let -5*c**3 + 5 + 10*c**b + 0 - 5 - 5*c**4 = 0. Calculate c.
-2, 0, 1
Let v(k) = 178*k**2 - 2290*k - 188. Let l(p) = -36*p**2 + 458*p + 38. Let t(i) = -16*l(i) - 3*v(i). Factor t(u).
2*(u - 11)*(21*u + 2)
Let z be 17252/(-1362)*12/(-38). Suppose 0 - r**3 - 1/10*r**z + 0*r - 5/2*r**2 = 0. What is r?
-5, 0
Let y(z) be the second derivative of z**4/54 - 5*z**3/27 + 4*z**2/9 - 113*z + 2. Factor y(t).
2*(t - 4)*(t - 1)/9
Let n = 30259/3 - 10083. Find x, given that 16/3*x**4 - 16/3*x**2 - 6*x**3 + 0 + n*x**5 + 8/3*x = 0.
-2, -1, 0, 2/5, 1
Let j(u) be the first derivative of -19*u**5/60 - 7*u**4/8 - u**3/3 - 13*u**2/2 + 1. Let w(r) be the second derivative of j(r). Factor w(c).
-(c + 1)*(19*c + 2)
Let s(b) = 14*b**2 - 6*b + 5. Let c be s(4). Factor c*u**3 - 205*u**3 + 3*u**5 - u**5.
2*u**5
Let t = -56 - -90. Let i = t + -32. Suppose -1/5 + 2/5*k + 3/5*k**i = 0. What is k?
-1, 1/3
Factor 10*f**4 + 8*f**3 + 159816*f - 16*f**2 - 159812*f - 6*f**2.
2*f*(f - 1)*(f + 2)*(5*f - 1)
Let c(l) be the third derivative of -l**5/30 + 5*l**4/12 - 2*l**3 - 5*l**2 + l. Factor c(z).
-2*(z - 3)*(z - 2)
Let f(d) be the first derivative of 3*d**4/4 - 17*d**3 + 120*d**2 - 192*d + 88. What is n in f(n) = 0?
1, 8
Solve -4*q**2 + 3*q**3 - 7*q**2 - 24 + 5*q**2 + 19*q - 51*q - q**3 = 0.
-2, -1, 6
Let d(i) = -5 + 8 + 13*i**2 + i**3 + 1 - 1. Let b be d(-13). Factor -w**3 + b*w - 5*w**3 + 15*w**2 - 15*w**2 + 3*w**5.
3*w*(w - 1)**2*(w + 1)**2
Determine l so that 10*l**2 + 5*l**5 + 165*l**3 - 140*l**3 + 26*l**4 - 6*l**4 = 0.
-2, -1, 0
Let t be (1 - (5 + -1))*(-3 - 7). Let o = t - 119/4. Let -1/4*f**3 + 0 + 0*f**2 + o*f = 0. Calculate f.
-1, 0, 1
Suppose 4*z = 4*m + 84, -4*z - z - 4*m = -105. Suppose -11*r**2 - 7*r**2 + z*r**2 + 9*r = 0. What is r?
-3, 0
Let q(g) = -16*g**3 + 45*g**2 + 70*g + 13. Let i(v) = 66*v**3 - 180*v**2 - 279*v - 51. Let m(o) = -2*i(o) - 9*q(o). Find n, given that m(n) = 0.
-1, -1/4, 5
Let b(o) = -11*o**3 + 4*o**2 + 11*o - 4. Let p(s) = 22*s**3 - 9*s**2 - 22*s + 9. Let z(g) = 13*b(g) + 6*p(g). Determine l, given that z(l) = 0.
-1, -2/11, 1
Factor 4/15*j**2 + 0 + 0*j + 0*j**4 + 2/5*j**3 - 2/15*j**5.
-2*j**2*(j - 2)*(j + 1)**2/15
Let w(l) be the second derivative of -l**6/21 - 11*l**5/35 - l**4/14 + 22*l**3/21 + 8*l**2/7 - 2*l + 27. Determine y so that w(y) = 0.
-4, -1, -2/5, 1
Let h = 2877 - 2813. Let i(w) be the first derivative of -112*w**2 + 32/3*w**3 + 12 - 52*w**5 + 92*w**4 + 25/3*w**6 - h*w. Determine x so that i(x) 