3
Let v(d) = 109*d**3 - 92*d**2 - 29*d + 12. Let x(y) = 37*y**3 - 31*y**2 - 10*y + 4. Let w(j) = 6*v(j) - 17*x(j). Let w(t) = 0. Calculate t.
-2/5, 2/5, 1
Let f(k) be the third derivative of -k**6/1140 + k**5/57 + 19*k**2 - 2. Factor f(m).
-2*m**2*(m - 10)/19
Let q be ((-2)/1)/(22 + (-540)/20). Determine r, given that -2*r**2 + 6/5*r + q*r**3 + 18/5 = 0.
-1, 3
Find q such that -51 - 23/2*q - 1/2*q**2 = 0.
-17, -6
Let p(f) = 4*f**2 - 27*f + 28. Let t be p(1). Let -5/2*v**2 + 0 - v - 7/2*v**t + 5/2*v**4 + 9/2*v**3 = 0. What is v?
-1, -2/7, 0, 1
Suppose 13*o = 3*o + 20. Determine t, given that 7/2*t**5 + 0 + 27/2*t**3 - o*t**2 - 2*t - 13*t**4 = 0.
-2/7, 0, 1, 2
Let w = 15 - 23. Let b = 8 + w. What is f in -3/5*f**2 + b*f + 3/5 = 0?
-1, 1
Let v(o) be the third derivative of 0 - 7/240*o**6 - 1/3*o**3 + 1/224*o**8 - 7/40*o**5 - 1/3*o**4 + 1/84*o**7 + 3*o**2 + 0*o. Factor v(i).
(i - 2)*(i + 1)**3*(3*i + 2)/2
Let g be 1*((-4)/(-1) + -1). Let y be (1 + ((-102)/(-63))/(-2))*18. Factor -2/7 - y*o - 96/7*o**2 - 128/7*o**g.
-2*(4*o + 1)**3/7
Factor 10*q - 50 - 1/2*q**2.
-(q - 10)**2/2
Let k be (-9 - (-129)/15)*(5 - 200/35). Suppose -3*o = 0, 0 = -x - 3*x + 4*o + 8. Find s, given that -8/7*s - 8/7 - k*s**x = 0.
-2
Let i(x) be the second derivative of x**6/270 + x**5/36 - 2*x**4/27 - 2*x**3/9 - 251*x. Find r such that i(r) = 0.
-6, -1, 0, 2
Let q(v) be the first derivative of v**4/18 - v**2/3 - 6*v + 50. Let w(s) be the first derivative of q(s). Factor w(n).
2*(n - 1)*(n + 1)/3
Let f(s) be the third derivative of s**7/1260 + s**6/360 - s**5/90 - s**4/72 + s**3/12 + 72*s**2. Find d such that f(d) = 0.
-3, -1, 1
Suppose 4*s = -4, -6*q = -3*q + 4*s - 212. Let a be (-16)/q + (-38)/(-9). Find i such that -2*i**2 + 4*i**3 - 2*i**a - 7*i**2 + 7*i**2 = 0.
0, 1
Let k(i) = -2*i - 6. Let y be k(-5). Suppose -t - 6 = -y*t. Solve -t*f**5 + 90*f**4 + 4*f + 40*f**2 - 13*f**5 + 123*f**3 - 66*f**5 = 0.
-1/3, -2/9, 0, 2
Let a(n) = 3*n**5 + n**4 - 10*n**3 - 6*n**2 + 6*n. Let j(f) = f**5 - 2*f**3 - f**2 + f. Let d(r) = a(r) - 6*j(r). Let d(k) = 0. Calculate k.
-2/3, 0, 1
Let z(v) be the second derivative of v**5/110 + 31*v**4/66 - 100*v**3/33 + 68*v**2/11 + 447*v. Factor z(g).
2*(g - 2)*(g - 1)*(g + 34)/11
Let f(u) = -5*u**5 + 30*u**3 - 25*u**2 - 5*u + 15. Let v(g) = 3*g**5 - g**4 - 14*g**3 + 12*g**2 + 3*g - 7. Let j(k) = 2*f(k) + 5*v(k). Factor j(p).
5*(p - 1)**3*(p + 1)**2
Let d(h) = 4*h**4 + 21*h**3 - 95*h**2 + 211*h - 194. Let c(k) = -k**4 - k**3 + k**2 + k + 1. Let i(n) = -5*c(n) - d(n). Factor i(j).
(j - 7)*(j - 3)**3
Let s be (6 - 32/5) + (-17)/(-5). Solve -70*x**5 + 3*x**s - 5*x**2 + 69*x**5 + 3*x + x**4 - x = 0.
-2, 0, 1
Let z(l) be the first derivative of l**4/10 - 22*l**3/15 + 8*l**2/5 + 8*l + 41. Suppose z(a) = 0. What is a?
-1, 2, 10
Let 0 - 2/9*a**2 - 92/9*a = 0. What is a?
-46, 0
Let w(x) be the second derivative of x**7/378 - x**6/30 + x**5/6 - 23*x**4/54 + 11*x**3/18 - x**2/2 - 3*x - 33. Factor w(b).
(b - 3)**2*(b - 1)**3/9
Let q(g) be the third derivative of 9*g**5/20 + 13*g**4/2 - 6*g**3 - 3*g**2. Factor q(v).
3*(v + 6)*(9*v - 2)
Factor -8*k + 3*k**2 - 8*k + 20*k**3 - 51*k**2 + 2*k + 56 + 2*k.
4*(k - 2)*(k + 1)*(5*k - 7)
Suppose -3*a - 5*x = 25, -2*x = -a + 5 + 5. Let u(h) be the third derivative of h**2 + 0*h + 0*h**4 - 1/60*h**5 + 1/6*h**3 + a. Let u(i) = 0. What is i?
-1, 1
Suppose -2*c - 173*w = -176*w + 3, 0 = -4*c - 3*w + 21. Factor 0*y - 2*y**c - 2/3*y**5 + 0 - 2*y**4 - 2/3*y**2.
-2*y**2*(y + 1)**3/3
Let b = -1 - -10. Suppose 0 = b*n - 8*n - 6. What is y in n*y**2 + y - y**2 - 20 - y = 0?
-2, 2
Let h(l) be the second derivative of l**7/70 + l**6/20 - l**4/4 - l**3/2 - 10*l**2 + 19*l. Let b(a) be the first derivative of h(a). What is u in b(u) = 0?
-1, 1
Let z(l) = 0*l**4 - l**3 - l**2 - l + 2*l**3 - l**4 + 0*l. Let b(s) = -5*s**4 + 5*s**3 - 15*s**2 - 5*s. Let i(o) = b(o) - 10*z(o). Let i(n) = 0. What is n?
-1, 0, 1
Let d be (-6)/15 + (2 - (-14788)/70). Let q = d - 212. Factor 2/7*m + q*m**3 + 2/7 - 10/7*m**2.
2*(m - 1)**2*(3*m + 1)/7
Solve 2/11*d**5 + 4/11*d + 18/11*d**3 + 0 - 14/11*d**2 - 10/11*d**4 = 0.
0, 1, 2
Let k(p) be the first derivative of -5*p**4/16 + 39*p**3/4 + 37*p**2/4 - 12*p - 72. Find n such that k(n) = 0.
-1, 2/5, 24
Let c(j) = -11*j**2 + 15*j - 43. Let b(z) = -5*z**2 + 8*z - 21. Let x(o) = 13*b(o) - 6*c(o). Factor x(r).
(r - 1)*(r + 15)
Let h = 46 + -48. Let l(x) = -3*x**2 + 20*x - 119. Let y(v) = 4*v**2 - 19*v + 118. Let t(n) = h*y(n) - 3*l(n). What is o in t(o) = 0?
11
Let t(q) be the third derivative of 0*q**3 + 0*q**4 + 1/12*q**6 + 1/12*q**5 + 0*q + 3*q**2 - 1/14*q**7 + 0. Factor t(f).
-5*f**2*(f - 1)*(3*f + 1)
Let d(b) be the first derivative of b**7/120 + b**6/72 - 2*b**5/15 + b**4/6 - 20*b**3/3 + 16. Let q(v) be the third derivative of d(v). Factor q(s).
(s - 1)*(s + 2)*(7*s - 2)
Suppose 6 = -9*t + 8*t. Let w be ((-4)/36*t)/1. Factor 1/6*z**2 + 0*z - w.
(z - 2)*(z + 2)/6
Suppose 8*m = 5*m + 300. Let v = 3 - 0. Factor -m*z**2 + 0*z**v - 9*z**3 + 94*z**2.
-3*z**2*(3*z + 2)
Suppose 0 = -c + 22*c. Let q(k) be the third derivative of -1/70*k**5 + c - 1/21*k**3 + 0*k + 1/420*k**6 - 2*k**2 + 1/28*k**4. Determine g, given that q(g) = 0.
1
Let g be ((-1)/(-4))/((-770)/(-2240)). Let -2/11*b**2 + g + 0*b = 0. Calculate b.
-2, 2
Let p(h) = 4*h**3 + 124*h**2 + 1802*h - 2. Let m(t) = -t**3 - 2*t**2 - t + 1. Let y(l) = 2*m(l) + p(l). Factor y(u).
2*u*(u + 30)**2
Let t(g) be the first derivative of -6*g**3 - 105*g**2/2 + 18*g - 234. Solve t(s) = 0.
-6, 1/6
Solve 3/7*z**5 + 0*z + 12/7*z**2 + 0 + 24/7*z**3 + 15/7*z**4 = 0.
-2, -1, 0
Let w = 1 - 1. Let x(z) = z - 1. Let b be x(3). Factor -6*j + w*j**4 + 3*j**4 + 2*j - j**4 - 6*j**b.
2*j*(j - 2)*(j + 1)**2
Factor 2/5*f**2 + 1152/5 - 96/5*f.
2*(f - 24)**2/5
Factor 9*a**4 + 2 - 54*a**3 + 54*a**3 - 5*a**4 - 8*a**2 + 2.
4*(a - 1)**2*(a + 1)**2
Let d = 5 + 15. Let x = 23 - d. Factor 3*v**3 + 39*v - 9*v**2 + 3*v**3 - 3*v**x - 33*v.
3*v*(v - 2)*(v - 1)
Suppose 5*v - 5 = 0, -s + 6 - 1 = 4*v. Suppose 3*h - 4 = -4*x + s, -2*h + 9 = -3*x. Let -63*c**2 + 0*c - h*c**3 + 5*c + 30*c**3 - 12 + 43*c = 0. Calculate c.
2/3, 1
Let m(a) be the first derivative of 2*a**3/9 - a**2 + 4*a/3 - 70. Factor m(y).
2*(y - 2)*(y - 1)/3
Let p = 20367/4 - 5091. Let 1/4*s**5 + 0*s**3 + p*s**4 - s**2 + 0*s + 0 = 0. Calculate s.
-2, 0, 1
Factor 124/5*c - 12*c**2 - 8/5.
-4*(c - 2)*(15*c - 1)/5
Let j(a) = -2*a - 5. Let s be j(-1). Let r(k) = 2*k**2 - 2*k + 3. Let z(i) = 4*i**2 - 6*i + i**2 + 2*i + 6. Let g(t) = s*z(t) + 7*r(t). Factor g(n).
-(n - 1)*(n + 3)
Let u(h) be the first derivative of -h**6/18 - 4*h**5/5 - 5*h**4/2 - 28*h**3/9 - 3*h**2/2 + 75. Let u(q) = 0. Calculate q.
-9, -1, 0
Let f(z) = z**2 - 8*z + 15. Let v be f(9). Let a = v + -21. Factor -1/4*g**2 - 1/2*g + 1/2*g**a + 1/4.
(g - 1)*(g + 1)*(2*g - 1)/4
Let t(w) be the third derivative of 0*w + 0*w**4 + 0*w**3 + 0 + 1/180*w**5 - 19*w**2. Factor t(n).
n**2/3
Let b(l) = l**3 - 28*l**2 + 51*l + 29. Let s be b(26). Find q, given that 2/3 - 1/6*q**s - 2/3*q**2 + 1/6*q = 0.
-4, -1, 1
Let n = -22031 - -22031. Factor 7/4*i**2 + 5/4*i**3 + 1/4*i**4 + n + 3/4*i.
i*(i + 1)**2*(i + 3)/4
Let f(m) be the first derivative of -5*m - 1/54*m**4 - 4/9*m**2 + 3 - 4/27*m**3. Let r(p) be the first derivative of f(p). Determine n, given that r(n) = 0.
-2
Let f(p) be the first derivative of -p**6/30 + 5*p**4/12 - 2*p**2 - 11*p - 2. Let z(d) be the first derivative of f(d). Solve z(a) = 0 for a.
-2, -1, 1, 2
Let f(r) be the second derivative of 0 + 1/24*r**4 + 0*r**2 + 5*r + 1/240*r**5 + 1/3*r**3 - 1/720*r**6. Let v(j) be the second derivative of f(j). Factor v(d).
-(d - 2)*(d + 1)/2
Factor 1/7*v**2 + 1/7*v + 0 - 5/7*v**3 + 3/7*v**4.
v*(v - 1)**2*(3*v + 1)/7
Let y(x) = -x**3 + 14*x**2 + 10*x + 10. Let t(a) = -2*a**3 + 18*a**2 + 9*a + 11. Let s(o) = -2*t(o) + 3*y(o). Factor s(g).
(g + 2)**3
Suppose -232/3*u + 64 - 28*u**2 = 0. Calculate u.
-24/7, 2/3
Factor 5/2*n**2 + 5/2*n + 5/6*n**3 + 5/6.
5*(n + 1)**3/6
Let g be (-9 + 6)*(-3 - 14/(-6)). Solve 3/2*j**g + 0 - 3*j + 3/2*j**3 = 0 for j.
-2, 0, 1
Let r(y) = y**2 + 8*y - 44. Let l be r(4). Let u(b) be the first derivative of 3/16*b**l + 1/12*b**3 + 1/10*b**5 + 0*b + 7 + 0*b**2. Let u(m) = 0. What is m?
-1, -1/2, 0
Let v(w) = -w**4 + 73*w**3 + 57*