1
Factor -15*z**2 + 10*z - 3*z**3 + 40 + 8*z**3 + 2*z**2 + 0*z - 12*z**2.
5*(z - 4)*(z - 2)*(z + 1)
Let p be ((-20)/(-8))/(15/50). Let q(w) be the second derivative of 10*w**4 + 0*w**2 + 5*w - 8/3*w**3 + p*w**6 + 0 - 15*w**5. Factor q(z).
2*z*(5*z - 2)**3
Let z(h) = -h**3 + 5*h**2 + 150*h - 596. Let w be z(13). Factor 2/9*a**w + 50/9 + 20/9*a.
2*(a + 5)**2/9
Let w = -22618/11 + 233723/33. Let i = w - 4973. Let -28/3*l**3 - 68*l - i*l**2 + 24 = 0. Calculate l.
-3, 2/7
Let n(r) be the third derivative of -1369*r**6/24 - 1517*r**5/12 - 95*r**4/3 - 10*r**3/3 + 61*r**2. Let n(s) = 0. What is s?
-1, -2/37
Let d(u) be the third derivative of -6*u**2 - 3/40*u**6 + 5/8*u**4 + u**3 + 0 + 0*u - 1/5*u**5. Factor d(s).
-3*(s - 1)*(s + 2)*(3*s + 1)
Let i be 27/(-81)*5/9. Let r = i - -251/189. Solve 2/7*n**2 + 0*n - r = 0.
-2, 2
Let b(o) be the first derivative of 3*o**5/5 - 18*o**4 + 45*o**3 - 33*o**2 + 341. Suppose b(z) = 0. Calculate z.
0, 1, 22
Factor -25/2*u + 1/2*u**2 - 13.
(u - 26)*(u + 1)/2
Let w = -796 + 798. Let l(a) be the first derivative of -1/2*a**w + 1/2*a**3 + 5/16*a**4 - 2*a + 1/20*a**5 - 7. Suppose l(k) = 0. What is k?
-2, 1
Let v(d) be the first derivative of 40*d**5 - 435*d**4/4 + 109*d**3 - 52*d**2 + 12*d - 105. Factor v(s).
(s - 1)*(5*s - 2)**2*(8*s - 3)
Let j(o) be the first derivative of o**5/5 + 5*o**4/3 + 16*o**3/3 + 8*o**2 - 3*o - 9. Let t(l) be the first derivative of j(l). What is p in t(p) = 0?
-2, -1
Let i(v) = 3*v**2 - 45*v + 105. Let r(b) = 3*b**2 - 45*b + 104. Let x(o) = 4*i(o) - 3*r(o). Suppose x(q) = 0. Calculate q.
3, 12
Let r be ((-4)/(-26))/((-211)/(120692/(-264))). Factor 2*c + r*c**2 + 3.
(c + 3)**2/3
Let k = 40389 - 40387. Factor -3 + 5/3*q**k + 1/3*q**3 + q.
(q - 1)*(q + 3)**2/3
Let z be 70/(-8) + (-3)/12. Let i be 1/(3/8)*z/(-6). Find w such that 0*w + 3/2*w**2 + 0*w**3 - 3/2*w**i + 0 = 0.
-1, 0, 1
Let n(l) be the third derivative of l**6/200 + 3*l**5/100 - 2*l**4/5 + 6*l**3/5 - 123*l**2. Factor n(i).
3*(i - 2)*(i - 1)*(i + 6)/5
Let b(p) be the second derivative of -2*p**4 + 0 - 12*p**2 - 1/5*p**5 - 22/3*p**3 + 20*p. Factor b(z).
-4*(z + 1)*(z + 2)*(z + 3)
Let g = 144 + 16. Let r be 22/12*g/60. Let 2/9*v**5 + 2*v + 16/3*v**2 + 16/9*v**4 + r*v**3 + 0 = 0. What is v?
-3, -1, 0
Suppose 0 = 3*a + 15, a + 355 = 5*w - a. Let l be (-184)/w*(-6)/4. Factor 0 - 3/5*k**l + 3/5*k**2 + 3/5*k**3 - 3/5*k**5 + 0*k.
-3*k**2*(k - 1)*(k + 1)**2/5
Solve 0 - 44/3*t**3 + t**4 - 26/3*t + 67/3*t**2 = 0.
0, 2/3, 1, 13
Let z(k) be the second derivative of 0 + 3*k**2 + 1/4*k**4 + 16*k - 3/2*k**3. Factor z(i).
3*(i - 2)*(i - 1)
Let n(m) = m**5 + m**4 + m**2 - 2. Let u(j) = 3*j**5 + 14*j**4 + 21*j**3 + 12*j**2 - 4. Let t(x) = -6*n(x) + 3*u(x). Factor t(y).
3*y**2*(y + 1)**2*(y + 10)
Let w(i) be the first derivative of -i**7/168 - i**6/12 - i**5/2 - 5*i**4/3 + 3*i**3 + 9. Let j(d) be the third derivative of w(d). Factor j(q).
-5*(q + 2)**3
Let s = 37 - 22. Factor 6*p**3 - 25*p + 17*p + 2*p - s*p**4 + 15*p**2.
-3*p*(p - 1)*(p + 1)*(5*p - 2)
Let v(t) be the first derivative of 2/3*t**2 - 1/18*t**3 - 8/3*t - 6. Factor v(r).
-(r - 4)**2/6
Let h(v) = -3*v**2 + 2*v**2 - 6*v + 2*v**2 + 8*v. Let o(b) = -3*b. Let x(y) = -3*h(y) - 4*o(y). Factor x(w).
-3*w*(w - 2)
Let m(q) be the second derivative of q**9/151200 - q**7/25200 - q**4/6 - 7*q. Let o(s) be the third derivative of m(s). Factor o(t).
t**2*(t - 1)*(t + 1)/10
Suppose 3*y - 16*s - 4 = -18*s, 0 = -5*y - 5*s + 10. Suppose -24/7*j**3 + 0 + y*j - 8/7*j**2 - 10/7*j**4 = 0. Calculate j.
-2, -2/5, 0
Suppose 2*n - 3 = -5*j, 3*j + 4*n + 49 = 34. Factor 0 + 2/19*u**j - 14/19*u**2 + 12/19*u.
2*u*(u - 6)*(u - 1)/19
Factor 0 + 3/5*i**4 + 0*i - 3/5*i**5 + 0*i**3 + 0*i**2.
-3*i**4*(i - 1)/5
Let g be -7 - 212/(-20) - (-3)/(-5). Factor 1/6*m**4 + m**2 + 2/3*m - 5/6*m**g - 4/3.
(m - 2)**3*(m + 1)/6
Suppose 2*q - 4 - 8 = 3*n, -5*n - 13 = -q. Let k be n/3*(0 + -2 - -1). Factor k*s**2 - 4/9 + 10/9*s.
2*(s + 2)*(3*s - 1)/9
Suppose 0 = 2*o - 3*c + 54, 3*c - 102 = 4*o - 0*c. Let l be -1 - -2*(-15)/o. Factor -5/4*z**2 - 1 - l*z**3 - 2*z.
-(z + 1)*(z + 2)**2/4
Factor -3473*v**2 + 3469*v**2 + 4*v**3 + 0*v + 0*v.
4*v**2*(v - 1)
What is w in -31*w**2 - 202*w - 2 + 113*w + 45*w**4 + 104*w - 2*w**3 - w**3 = 0?
-1, 1/3, 2/5
Let 81 - 316*g - 5*g + 468*g**2 + 465*g**2 - 945*g**2 = 0. What is g?
-27, 1/4
Let n(x) be the first derivative of -x**4/3 + 28*x**3/9 + 28*x**2/3 - 64*x + 494. Solve n(r) = 0 for r.
-3, 2, 8
What is u in 9/8*u + 0 - 3/2*u**2 = 0?
0, 3/4
Let i be ((-1)/(-6))/(85/51 + 5). Let h(t) be the third derivative of 4*t**2 + 0*t**3 + 1/8*t**4 + i*t**6 + 0*t + 0 - 1/10*t**5. Let h(f) = 0. What is f?
0, 1
Let y(z) be the first derivative of 0*z**2 + 5/3*z**3 + 15 - 20*z. What is u in y(u) = 0?
-2, 2
Determine u, given that -114*u**3 + 54 - 3*u**5 + 204*u**2 + 44*u**4 - 66*u**4 + 52*u**4 - 171*u = 0.
1, 2, 3
Factor 0 - 1/3*u**3 + u**2 - 2/3*u.
-u*(u - 2)*(u - 1)/3
Suppose 21 - 21 + 4*n**5 - 5*n**5 - n + 2*n**3 = 0. What is n?
-1, 0, 1
Let o(b) be the second derivative of 4*b**3/3 - 14*b**2 - 16*b - 1. Let u be o(4). Factor 0*p + 0 + 1/4*p**2 + 3/4*p**3 - p**u.
-p**2*(p - 1)*(4*p + 1)/4
Let q(c) be the first derivative of c**6/90 - c**5/30 + c**3/9 - c**2/6 - 21*c - 6. Let y(w) be the first derivative of q(w). Factor y(n).
(n - 1)**3*(n + 1)/3
Let l be (-10)/(-35) - ((-330)/14)/5. Let r(u) be the third derivative of -1/70*u**7 + 0 - 5/8*u**4 - 10*u**2 + 1/40*u**6 + 0*u + u**3 + 3/20*u**l. Factor r(f).
-3*(f - 1)**3*(f + 2)
Let i(v) be the third derivative of v**8/1512 - 2*v**7/315 + v**6/60 - 4*v**2 - 5. Solve i(t) = 0 for t.
0, 3
Let w(a) be the second derivative of a**4/30 + 6*a**3 - 506*a. Let w(p) = 0. Calculate p.
-90, 0
Let i(n) be the third derivative of n**8/10080 + n**7/1260 + n**6/540 + 13*n**4/24 + 12*n**2. Let y(f) be the second derivative of i(f). Solve y(s) = 0.
-2, -1, 0
Let l(s) be the third derivative of s**7/315 - s**6/36 + s**5/15 + s**4/9 - 8*s**3/9 - s**2 - 65. Find d, given that l(d) = 0.
-1, 2
Suppose -32 = 4*n - 44. Suppose 2*h - 3 = 6*h - m, 4*m - 12 = -n*h. Factor -3/2*q**4 + h*q**2 + 0*q + 0 + 0*q**3.
-3*q**4/2
Let f = 8686247/1062 + -53963900509/6600330. Let m = f + -2/3729. Factor -m*u**2 - 28/5*u + 8/5.
-4*(u + 2)*(4*u - 1)/5
Let h be 19/(-2 + 21) - 1*8/(-6). Factor -h*p**2 - 4/3 + 16/3*p.
-(p - 2)*(7*p - 2)/3
Let -138/5*y - 1/5*y**2 - 4761/5 = 0. Calculate y.
-69
Let j(p) = p**2 + 13*p - 30. Let z be j(-15). Let o = 3 + z. Let -24/11*l**o - 2/11*l**2 + 18/11*l - 4/11 = 0. Calculate l.
-1, 1/4, 2/3
Let f(k) be the second derivative of 14*k + 0 + 2/21*k**3 + 0*k**2 + 1/21*k**4. Solve f(x) = 0.
-1, 0
Let a(v) be the first derivative of -v**5/40 - v**4/16 + v**3/2 - 6*v**2 - 15. Let f(d) be the second derivative of a(d). Factor f(c).
-3*(c - 1)*(c + 2)/2
Let f(a) = 7*a**2 - 23*a + 22. Let l(p) = p**2 + 2. Let i(t) = f(t) - 4*l(t). Determine w so that i(w) = 0.
2/3, 7
Determine y, given that -14*y**4 + 8227*y**2 - 8210*y**2 - 67*y**3 + 12*y - y - y = 0.
-5, -2/7, 0, 1/2
Let q = 27059/13 + -2079. Determine w, given that -8/13*w**5 - 76/13*w**3 + 50/13*w**4 - 18/13 - q*w**2 + 84/13*w = 0.
-1, 1/4, 1, 3
Let y(x) be the first derivative of -5*x**6/6 + 4*x**5 + 115*x**4/4 - 190*x**3/3 - 550*x**2 - 1000*x + 338. Factor y(z).
-5*(z - 5)**2*(z + 2)**3
Let g = -46 + 74. What is h in 15*h + 19*h - g*h + 9*h**2 + 3*h**3 = 0?
-2, -1, 0
Suppose 10*m**4 - 22*m**4 - 4*m**2 + 14*m**4 - 2*m**3 = 0. What is m?
-1, 0, 2
Let z = -8058 + 8058. Let p = -169/3 - -57. Factor 2*k**3 + 2*k**2 + p*k + z + 2/3*k**4.
2*k*(k + 1)**3/3
Let a be (5/(-10))/(3/(-12)). Factor 9*d - 2*d**a - 3 - 6*d**2 + 103*d**3 - d**2 - 100*d**3.
3*(d - 1)**3
Factor 11 - 41 - 148*o - 2 - 130*o**2 - 14*o**3.
-2*(o + 1)*(o + 8)*(7*o + 2)
Let p(z) be the first derivative of 0*z**2 - 15 + 0*z + 4/55*z**5 - 1/22*z**4 + 0*z**3 - 1/33*z**6. Let p(u) = 0. Calculate u.
0, 1
Suppose 0 = 2*b - 40 + 4. Suppose -3*z + b*y - 19*y = -6, -2*z - 5*y = -4. Find m, given that 0 + 3/2*m**z - 3/2*m**4 + 1/2*m**5 - m + 1/2*m**3 = 0.
-1, 0, 1, 2
Let x(m) be the second derivative of -m**5/60 + m**4/9 - 5*m**3/18 + m**2/3 + 26*m - 4. Factor x(d).
-(d - 2)*(d - 1)**2/3
Let v = -27/62 - -205/186. Factor -2/9*z**2 - 4/9 - v*z.
-2*(z + 1)*(z + 2)/9
Let j = 18984 - 11389