uppose 3*a - 4*c = c + 14, a = -c + 2. Solve 3*t**4 + 5*t**2 + 3*t - 3 + 3*t - 6*t**a - 5*t**2 = 0.
-1, 1
Let r(x) be the second derivative of -5*x**4/12 + 25*x**3/3 - 40*x**2 - 2*x + 6. Find w, given that r(w) = 0.
2, 8
Let j(z) be the second derivative of z**6/60 - 3*z**5/20 + 11*z**4/24 - z**3/2 - 22*z. What is f in j(f) = 0?
0, 1, 2, 3
Let b be (-2)/(-20)*62 - 3/15. Let d = -133 - -535/4. Determine i so that -3 - 15/4*i**2 - d*i**3 - b*i = 0.
-2, -1
Let x = 111 - 76. Factor x*o**3 - 31*o**5 - 2*o**2 + 12*o**2 + 46*o**5 + 40*o**4.
5*o**2*(o + 1)**2*(3*o + 2)
Let o(q) = -q**3 - 7*q**2 - 8*q - 7. Let u be 2/5*(-7 + -8). Let g be o(u). What is d in 4*d**2 + 6*d**g + 0*d**5 - 3*d**2 - 2*d**3 + 3*d**2 - 8*d**4 = 0?
-2/3, 0, 1
Find v, given that -60*v**5 - 4*v + 25*v**3 - 76*v**4 + v**2 - 25*v**2 + 72*v**2 + 95*v**3 - 28*v = 0.
-2, -2/3, 0, 2/5, 1
Let b(m) be the first derivative of -m**7/1470 - m**6/126 - m**5/70 + 3*m**4/14 - 8*m**3 - 5. Let n(u) be the third derivative of b(u). Factor n(a).
-4*(a - 1)*(a + 3)**2/7
Let o be ((-7)/(-111 + 6))/(7/42). Factor -o - 2/5*d**2 + 4/5*d.
-2*(d - 1)**2/5
Let l(o) = -2*o**3 - 9*o**2 + 16*o - 8. Let d be l(-6). Let 0 + 2/17*v**d + 0*v + 2/17*v**2 + 4/17*v**3 = 0. What is v?
-1, 0
Suppose -1 = 4*m - 9. Factor m - 4 - 8 + r**2 + 8 - r.
(r - 2)*(r + 1)
Let s(q) be the first derivative of -6*q**5/35 - q**4/2 + 2*q**3/21 + q**2 + 4*q/7 + 440. Find o, given that s(o) = 0.
-2, -1, -1/3, 1
Solve -8/3*s - 8 + 14/3*s**2 - 2/3*s**3 = 0.
-1, 2, 6
Let i = 169 + -43. Let m be 7/(i/(-4))*-9. Factor 2/11*g + 0*g**4 + 0*g**m - 4/11*g**3 + 0 + 2/11*g**5.
2*g*(g - 1)**2*(g + 1)**2/11
Factor 9*s - 2*s**3 + 2*s**2 + s + 1 - 9*s - 9 + 7*s.
-2*(s - 2)*(s - 1)*(s + 2)
Suppose 0 = -h + 4. Solve -5*g**2 - 19*g + g**3 - h - 18*g + 45*g + 0*g**2 = 0 for g.
1, 2
Let q(o) be the first derivative of -o**6/6 - 16*o**5/5 + 71*o**4/4 + 1730*o**3/3 - 350*o**2 - 49000*o - 53. Factor q(w).
-(w - 7)**2*(w + 10)**3
Let b(f) be the first derivative of -12*f + 13*f**2 + 7 + 10/3*f**3. Find o such that b(o) = 0.
-3, 2/5
Solve 23 + 22 + 111 + 3*z**2 - 159*z = 0 for z.
1, 52
Suppose 0 = -4*o + 5*w + 35, -2*w - 20 = -3*o + 1. Factor 5*b + 1 - 1 + o*b**3 + 9*b**2 - 19*b**2.
5*b*(b - 1)**2
Let h be -11 + 23 + (-132)/11. Let f(a) be the first derivative of -7 + 12/5*a - 3/5*a**3 - 3/20*a**4 + h*a**2. Suppose f(v) = 0. Calculate v.
-2, 1
Suppose 0 = 4*l - 26 + 26. Let a(i) be the third derivative of 0*i - 3/10*i**5 - 1/5*i**6 + 5*i**2 + 1/2*i**3 + l - 3/70*i**7 + 0*i**4. Solve a(p) = 0.
-1, 1/3
Let m(h) = -h**3 + h**2 + h - 1. Let q(l) = 15*l**3 - 209*l**2 + 1075*l - 395. Let j(r) = 5*m(r) + q(r). Suppose j(i) = 0. Calculate i.
2/5, 10
Determine c so that 0 + 15*c**2 + 18*c + 7/2*c**3 + 1/4*c**4 = 0.
-6, -2, 0
Let p(c) = 6*c**3 - 17*c**2 - 17*c - 8. Let x(g) = -5*g**3 + 16*g**2 + 17*g + 8. Let w(r) = -6*p(r) - 7*x(r). Factor w(t).
-(t + 1)**2*(t + 8)
Let u(b) be the first derivative of -b**6/24 + 3*b**5/10 + 3*b**4 + 37*b**3/6 + 33*b**2/8 - 213. Suppose u(y) = 0. What is y?
-3, -1, 0, 11
Let n = 1558630/146121 - 2/48707. Factor -n*h**4 - 6*h**5 + 4/3*h**2 + 0*h + 0 - 10/3*h**3.
-2*h**2*(h + 1)**2*(9*h - 2)/3
Let y be (60/(-75))/(4/(-10)). Factor -4*r**4 - 6*r**4 + 3*r + 0*r - 15*r**3 + 5*r**5 + 20*r**y + 17*r.
5*r*(r - 2)**2*(r + 1)**2
Let v be (12/(-5))/((-10)/25). Let y be 305/5 - 2*1. Factor -62 + 3*j**4 + v*j - j**3 - 5*j**3 + y.
3*(j - 1)**3*(j + 1)
Let u(g) be the third derivative of -g**8/2352 - g**7/245 - g**6/840 + 2*g**5/35 - 2*g**4/21 + 2*g**2 - 262*g. Factor u(j).
-j*(j - 1)**2*(j + 4)**2/7
Let k(h) be the second derivative of 9*h**4/4 + 17*h**3/2 + 11*h**2 + 61*h + 2. What is z in k(z) = 0?
-11/9, -2/3
Let y = 1893 - 1891. Factor 1/2*i**y + 1/4*i**3 + 0 + 1/4*i.
i*(i + 1)**2/4
Let r(j) be the third derivative of j**8/1848 - 8*j**7/1155 + 13*j**6/660 + 13*j**5/165 - 16*j**4/33 + 32*j**3/33 + 76*j**2. Suppose r(b) = 0. Calculate b.
-2, 1, 4
Determine h, given that 3*h**3 + 9*h**3 - 7*h**3 - h**2 - 29*h**2 = 0.
0, 6
Let a(k) = 15*k**4 + 9*k**3 - 13*k**2 - 17*k + 2. Let y(q) = 46*q**4 + 26*q**3 - 40*q**2 - 52*q + 7. Let f(i) = 13*a(i) - 4*y(i). Factor f(s).
(s - 1)*(s + 1)**2*(11*s + 2)
Let a(l) be the third derivative of l**7/210 + l**6/30 - 2*l**4/3 - 8*l**3 - 9*l**2 - 3*l. Let p(d) be the first derivative of a(d). Solve p(t) = 0.
-2, 1
Let p = 4/9 + 1/18. Let n = 641 + -641. Factor 0 - 3/2*u**4 - 3/2*u**3 - 1/2*u**5 - p*u**2 + n*u.
-u**2*(u + 1)**3/2
Let a(w) = w**3 + 10*w**2 - 15*w + 28. Let d be a(-12). Let f be (74/(-185))/(6/d). Factor 16*z + 6 + f*z**3 + 2/3*z**4 + 44/3*z**2.
2*(z + 1)**2*(z + 3)**2/3
Let a(r) be the third derivative of r**7/350 + r**6/100 - 7*r**5/100 - r**4/5 + 6*r**3/5 + 12*r**2 + 3*r. Determine h so that a(h) = 0.
-3, -2, 1, 2
Let x(n) = -n**3 - n**2 + n + 3. Let o be x(0). Suppose o = -3*i + 12. Factor 1 - d**2 + 6*d**i - 5*d**3 + 4*d**2 + 3*d + 0.
(d + 1)**3
Let s be 16/(-10) - (0 + -2). Let i = -1893 + 1895. Factor s*y**i + 0 + 2/5*y.
2*y*(y + 1)/5
Let g(c) be the second derivative of -c**5/110 + 4*c**4/33 + 20*c**3/33 + 66*c. Factor g(q).
-2*q*(q - 10)*(q + 2)/11
Let -2*n**3 + 2/3*n**5 - 2*n**4 + 22/3*n**2 + 0 - 4*n = 0. Calculate n.
-2, 0, 1, 3
Suppose 4*s - 42 = 18. Factor -7*h**2 - 5*h**5 + 0*h**2 - 15*h**4 + 0*h**5 - s*h**3 + 2*h**2.
-5*h**2*(h + 1)**3
Let j(n) be the third derivative of n**8/3360 - 3*n**4/4 - 22*n**2. Let a(i) be the second derivative of j(i). Factor a(h).
2*h**3
Suppose -13*r + 7*r - 1086 = 0. Let t = -1625/9 - r. Factor 2*h**5 - 8/9*h**2 + 8/3*h**4 + 0 - t*h**3 + 2/9*h.
2*h*(h + 1)**2*(3*h - 1)**2/9
Let b(x) = 6*x - 9. Let a(z) = -z + 1. Let l(r) = 3*a(r) + b(r). Let s be l(5). Let -3*v**2 - 3*v**5 - 9*v**3 + 10*v - s*v**4 + 0*v**2 - 10*v = 0. What is v?
-1, 0
Let o(x) be the third derivative of 1/120*x**5 - 24*x**2 + 5/24*x**4 + 0 + 25/12*x**3 + 0*x. Factor o(y).
(y + 5)**2/2
Let l = 18 + -16. Let w be (-4)/(-7)*35/10. Suppose 4*f**2 - 4*f - f**l - 2*f**2 - 3*f**w = 0. Calculate f.
-2, 0
Let z(c) = c - 9. Suppose 3*t = 2*t + 11. Let v be z(t). Factor 0 + 0*b**v - 2/11*b**3 + 0*b - 2/11*b**4.
-2*b**3*(b + 1)/11
Let n be ((-33)/242)/((-48)/22 + 2). Determine y, given that -3/2*y**2 + 0 + 0*y - n*y**3 = 0.
-2, 0
Let i(r) be the second derivative of 2*r**6/15 - 12*r**5/5 + 15*r**4 - 100*r**3/3 - 49*r. Factor i(n).
4*n*(n - 5)**2*(n - 2)
Let a(v) = v**2 + 2*v - 1. Let s(i) = -i**3 + 34*i**2 - 33*i + 16. Let d(f) = -24*a(f) + 3*s(f). Factor d(x).
-3*(x - 24)*(x - 1)**2
Let i(y) be the third derivative of -3*y**7/56 + y**6/36 + 3*y**5/8 - 5*y**4/12 - 3*y**3 - 4*y**2. Let p(g) be the first derivative of i(g). Factor p(u).
-5*(u - 1)*(u + 1)*(9*u - 2)
Factor 27*k**2 + 4*k - 13*k**3 - 2*k**3 + 2*k + 0*k.
-3*k*(k - 2)*(5*k + 1)
Let n(y) = -5*y**3 + 27*y**2 - 26*y + 2. Let g(i) = -23*i**3 + 134*i**2 - 131*i + 9. Let c(v) = 2*g(v) - 11*n(v). Let c(t) = 0. Calculate t.
2/9, 1, 2
Let t(g) = 3*g**2 + 3*g**3 + 0*g**4 - 3*g**2 + 32*g**4 + 5*g. Let d(q) = -16*q**4 - 2*q**3 - 2*q. Let i(n) = 5*d(n) + 2*t(n). Find l, given that i(l) = 0.
-1/4, 0
Suppose 21 = 2*p + 3*x, 5*p - 4*x = -0*p - 5. Let w(d) = -d + 9. Let n be w(p). Factor z + 6*z**3 - 2*z**2 + 5*z**3 + n*z**3 - 16*z**3.
z*(z - 1)**2
Let g be 5/(600/(-782)) - (-5 - 0). Let v = 34/15 + g. Solve -1/4*n**2 - v*n - 1/2 = 0.
-2, -1
Let h(p) be the third derivative of 11*p**6/72 + 19*p**5/90 - 31*p**4/18 + 20*p**3/9 - 367*p**2. Suppose h(x) = 0. What is x?
-2, 2/5, 10/11
Let f = 9078 - 27233/3. Factor 5/3*p + 2/3 + 4/3*p**2 + f*p**3.
(p + 1)**2*(p + 2)/3
Let x(q) be the first derivative of q**7/105 - q**6/60 - q**5/30 + q**4/12 - q**2 - 4. Let s(j) be the second derivative of x(j). Let s(u) = 0. Calculate u.
-1, 0, 1
Factor -6/13*k**3 - 2/13*k**4 + 0 - 4/13*k**2 + 0*k.
-2*k**2*(k + 1)*(k + 2)/13
Let u(y) be the third derivative of 0*y - 39*y**2 + 1/4*y**4 - 1/120*y**5 + 0*y**3 + 0. Factor u(k).
-k*(k - 12)/2
Let v(q) be the first derivative of 3*q**4/8 - 3*q**3/2 - 27*q**2/2 - 234. Suppose v(u) = 0. Calculate u.
-3, 0, 6
Suppose 5*u = -3*u + 16. Determine m so that -28*m + 8*m**u + 12*m**2 - 22*m - 40 - 5*m**2 = 0.
-2/3, 4
Let g(l) be the second derivative of -4/45*l**5 + 2/27*l**3 - 1/18*l**4 - 3*l + 0 + 0*l**2 - 1/45*l**6. What is t in g(t) = 0?
-2, 