546)/(135/3). Let t(k) be the third derivative of -7*k**2 - 1/60*k**5 + 0*k**6 + b*k**7 + 0 + 0*k**4 + 0*k**3 + 0*k. Factor t(g).
g**2*(g - 1)*(g + 1)
Let z(n) be the second derivative of 0*n**2 - 19*n - 2/45*n**6 + 0*n**4 + 0 + 2/45*n**5 + 0*n**3 + 2/189*n**7. What is y in z(y) = 0?
0, 1, 2
Let s be 6*3/(-6)*-1. Let r(l) be the first derivative of 0*l + 1 + 1/10*l**4 + 0*l**s - 1/5*l**2. Determine h so that r(h) = 0.
-1, 0, 1
Let m(c) be the third derivative of 0 + 1/210*c**7 + 0*c - 1/60*c**6 - 3*c**2 - 1/15*c**5 + 1/2*c**3 + 1/12*c**4. Factor m(n).
(n - 3)*(n - 1)*(n + 1)**2
Suppose 0 = -q + 5*q + 88. Let m = -20 - q. Factor -3 + 0*j**3 + 0*j + m*j + 2 - 2*j**3 + j**4.
(j - 1)**3*(j + 1)
Solve 4*u - 17*u**2 - 16*u**2 - 24*u**2 + 61*u**2 + 0*u = 0 for u.
-1, 0
Let u be 1654/9030 - 4/30. Let g = u - -4/43. Let -4/7 - 4/7*d - g*d**2 = 0. What is d?
-2
Let r be 48/(-22) - 6/(-33). Let z be 3 + (0/r)/(-3). Factor 0*u**2 + 51*u + 2*u**4 - u**2 - 2*u**z - 49*u - u**2.
2*u*(u - 1)**2*(u + 1)
Let g = 51 + 1. Let p be 1/4 - (-195)/g. Determine x so that -8/3 - 1/3*x**3 - 2*x**2 - p*x = 0.
-2
Let b(n) be the third derivative of -n**6/30 - 22*n**5/15 - 70*n**4/3 - 400*n**3/3 - 2*n**2 + 5. Find k such that b(k) = 0.
-10, -2
Let y(d) be the first derivative of -2*d**5/115 + 9*d**4/46 - 14*d**3/23 + 19*d**2/23 - 12*d/23 - 71. Find m such that y(m) = 0.
1, 6
Let o(l) be the first derivative of 4*l**3/21 - 8*l**2/7 - 80*l + 665. Suppose o(d) = 0. Calculate d.
-10, 14
Suppose 0 = -2*i - 8, f - 21*i + 22*i = -2. Let 1/3*v**f + 1/3 + 2/3*v = 0. What is v?
-1
Let r = 1153 + -1153. Let c(f) be the second derivative of 2/25*f**6 + 2*f + 0*f**2 + 0 - 2/105*f**7 - 9/100*f**5 + 1/30*f**4 + r*f**3. Solve c(l) = 0.
0, 1/2, 2
Let k(v) be the first derivative of -v**6/4 + 3*v**5/10 + 9*v**4/8 - 5*v**3/2 + 3*v**2/2 - 338. Factor k(w).
-3*w*(w - 1)**3*(w + 2)/2
Factor -2/9*u**3 + 0 + 4/9*u**2 + 0*u.
-2*u**2*(u - 2)/9
Let l be (-1)/(-1)*6/2. Suppose -409 = -22*m - 0*m - 321. Factor 2/9*t**2 - 2/3*t**l - 2/9*t**5 + 0 + 2/3*t**m + 0*t.
-2*t**2*(t - 1)**3/9
Let b(t) be the second derivative of t**10/7560 - t**9/1890 + t**7/315 - t**6/180 - 11*t**4/4 - 27*t. Let k(s) be the third derivative of b(s). Factor k(n).
4*n*(n - 1)**3*(n + 1)
Let c = 11377/1572 + 5/393. Factor 9/4*h**3 - 39/4*h**2 - c*h - 5/4.
(h - 5)*(3*h + 1)**2/4
Let d be 2/3 - 85/15. Let q = d - -8. Suppose -2*b**3 + 5*b**q - b**3 = 0. What is b?
0
Suppose -8*i + 12*i - 4*u = 0, 0 = i + 5*u - 12. Determine v, given that -i*v - 34/9*v**2 + 4/9 + 116/9*v**3 + 64/9*v**5 + 64/3*v**4 = 0.
-2, -1, -1/2, 1/4
Let j be (144/(-882))/(3/(-42)). Factor -j - 40/7*d + 90/7*d**3 + 20/7*d**2 + 0*d**4 - 54/7*d**5.
-2*(d - 1)**2*(3*d + 2)**3/7
Let r(t) be the third derivative of t**6/6 - t**5/4 - 35*t**4/24 + 3*t**2 - 22. Determine g, given that r(g) = 0.
-1, 0, 7/4
Find c, given that 2/25*c**3 + 2/25*c**5 + 6/25*c**4 - 6/25*c**2 - 4/25*c + 0 = 0.
-2, -1, 0, 1
Let t = 3/3550 + 50341/81650. Let v = t + -5/23. Factor -v + 0*c + 2/5*c**2.
2*(c - 1)*(c + 1)/5
Let a be 9/(-12) - 54/(-8). Let o(c) be the third derivative of -1/40*c**5 - 1/240*c**a + 2*c**2 - 1/16*c**4 - 1/12*c**3 + 0*c + 0. Solve o(z) = 0.
-1
Determine j, given that 1419/2*j**2 + 2*j**4 - 1331/2 + 4961/2*j + 131/2*j**3 = 0.
-11, 1/4
Let r(q) = 13*q**2 + 5*q. Let u = 14 - 21. Let h(k) be the first derivative of 7*k**3/3 + k**2 + 32. Let v(z) = u*h(z) + 4*r(z). Factor v(b).
3*b*(b + 2)
Let y(s) be the first derivative of 3*s**3 + 102*s**2 + 132*s - 254. Factor y(d).
3*(d + 22)*(3*d + 2)
Let f(n) = -15*n - 45. Let j be f(-8). Let w = 78 - j. Factor 15/2*s**w + 0*s + 3*s**4 + 0 + 3*s**2.
3*s**2*(s + 2)*(2*s + 1)/2
Let w(n) = n**3 + n**2 + 1. Let c = 11 + -13. Let d be 2 + c + (-3)/(-1). Let y(a) = -2*a**3 + 2*a - 3. Let t(q) = d*w(q) + y(q). Factor t(g).
g*(g + 1)*(g + 2)
Factor -24/11 + 24/11*n**2 - 6/11*n**3 + 6/11*n.
-6*(n - 4)*(n - 1)*(n + 1)/11
Let m be (42/(-12))/((-2)/(-56)). Let l be (-28)/m + 128/238. Determine v, given that 0 - l*v**2 - 4/17*v - 10/17*v**3 = 0.
-1, -2/5, 0
Factor -144*u + 265*u**3 - 42*u**2 - 160*u**2 - 38*u**2 - 365*u**3.
-4*u*(5*u + 6)**2
Let m be (0/(-11))/(-1 + -1). Let n(i) be the third derivative of -1/2*i**3 - 12*i**2 + 0 + m*i - 1/20*i**5 - 1/4*i**4. Factor n(w).
-3*(w + 1)**2
Find r such that -4/3*r**4 + 0 + 2*r**3 - 2/3*r**5 + 8/3*r**2 - 8/3*r = 0.
-2, 0, 1
Let j(g) = 42*g - 6885. Let t be j(164). Factor i**t + 1/5*i**5 + 4/5*i**4 + 2/5*i**2 + 0*i + 0.
i**2*(i + 1)**2*(i + 2)/5
Let j be (4/(-45))/((-111)/1110). Factor -j + 2/3*i + 2/9*i**2.
2*(i - 1)*(i + 4)/9
Suppose -15*o = -73 + 13. Let n(x) be the second derivative of 0*x**3 + 0*x**2 - 5*x - 1/30*x**5 - 1/18*x**o + 0. Factor n(c).
-2*c**2*(c + 1)/3
Let k(t) = -t**3 + t. Let y(v) = 18*v**3 + 15*v**2 - 33*v. Let f(r) = 15*k(r) + y(r). Factor f(q).
3*q*(q - 1)*(q + 6)
Let h(s) = s**2 - 9*s - 18. Let b be h(11). What is x in -x**3 + 2*x**2 - 8*x**2 - 3*x + 3*x**5 + x**3 + 6*x**b = 0?
-1, 0, 1
Let k = -8 + 12. Determine w so that -24*w + 8 - 4*w**2 - 16*w**k + 30*w**2 + 18*w**4 - 12*w**3 = 0.
1, 2
Let q be (-3535)/(-4340) + 4/(-62). Let 3/4*g - 3/2*g**2 - q*g**3 + 3/2 = 0. Calculate g.
-2, -1, 1
Factor 20 + 21/2*q + 1/4*q**2.
(q + 2)*(q + 40)/4
Let k(c) be the third derivative of c**7/70 - 37*c**6/120 + 13*c**5/5 - 10*c**4 + 32*c**3/3 - c**2 - 13. Factor k(y).
(y - 4)**3*(3*y - 1)
Let u be (1/(-2))/(117/30 + -4). Let d(w) = -w**2 + 4*w + 8. Let h be d(u). Factor 1/4*n**h + n - n**2 + 0.
n*(n - 2)**2/4
Let o(k) be the third derivative of -2*k**7/105 + k**6/30 + k**5/15 - k**4/6 + 8*k**2 + 4. What is g in o(g) = 0?
-1, 0, 1
Let t(m) be the second derivative of -m**4/8 + m**3/3 - m**2/4 - 344*m. Factor t(i).
-(i - 1)*(3*i - 1)/2
Let f(a) = -33*a**2 - 330*a + 3. Let q be f(-10). Let 12/7*y**q - 6/7*y**2 + 3/7*y**4 - 36/7*y + 27/7 = 0. Calculate y.
-3, 1
Factor -334/5 + 2/5*i**2 + 332/5*i.
2*(i - 1)*(i + 167)/5
Suppose -14 = -5*a - 4. Factor 9*i + 125 - 3*i**3 + 0*i**a - 119 + 0*i**2.
-3*(i - 2)*(i + 1)**2
Let g = -84 - -88. Let x(y) be the second derivative of -3*y + 0*y**2 - 2/21*y**3 + 0 - 1/42*y**g. Find z, given that x(z) = 0.
-2, 0
Let b(s) be the third derivative of -s**6/2700 - s**5/150 - s**4/20 - 2*s**3 + 10*s**2. Let j(r) be the first derivative of b(r). Find f, given that j(f) = 0.
-3
Let y(b) be the third derivative of 0*b**4 + 0*b + 0*b**3 + 0 - 1/70*b**5 - 1/490*b**7 - 36*b**2 + 3/280*b**6. Find p such that y(p) = 0.
0, 1, 2
Suppose 4*g = 4*s + 16, 3*g - g - 10 = 0. Suppose 2*z = -0*d - 5*d - s, 3*d = 3*z + 12. Solve 2 + 1 + t**2 - 3 + 2*t + d = 0.
-1
Let r(q) be the third derivative of q**7/42 - 7*q**6/120 + q**5/30 - 9*q**2. Let d(a) = -24*a**4 + 34*a**3 - 10*a**2. Let n(u) = 2*d(u) + 11*r(u). Factor n(y).
y**2*(y - 1)*(7*y - 2)
What is v in 7*v**2 - 19*v**3 + 4*v + 23*v**3 + v**2 = 0?
-1, 0
Solve -3/2*w**3 - 84*w**2 - 2175/2*w + 2523 = 0.
-29, 2
Let s = 133 - 75. Let m = s - 56. Factor 2/3*g**4 + 0 + 4/3*g + 0*g**3 - m*g**2.
2*g*(g - 1)**2*(g + 2)/3
Let j(v) = v**2 - 16*v - 57. Let k be j(19). Let a be (k - 1) + (-416)/(-352). Factor 0 - a*x - 6/11*x**3 - 6/11*x**2 - 2/11*x**4.
-2*x*(x + 1)**3/11
Let w = 6063 - 6063. Let w*u**2 + 0 + 0*u + 1/4*u**5 + 0*u**3 + 1/4*u**4 = 0. What is u?
-1, 0
Let i be 1 - 4*(-10)/(-40). Factor i + 1/4*h - 1/4*h**3 - 7/8*h**4 + 7/8*h**2.
-h*(h - 1)*(h + 1)*(7*h + 2)/8
Let s be (0 - 2)/(5/(-5)). Factor 4*n + 6*n**3 - 5*n - s*n**3 - 3*n.
4*n*(n - 1)*(n + 1)
Let y(j) = -7*j**5 - 14*j**2 + 9*j + 6. Let k(u) = -20*u**5 + u**3 - 41*u**2 + 26*u + 17. Let t(n) = -6*k(n) + 17*y(n). Let t(l) = 0. Calculate l.
-3, 0, 1
Suppose 3*w + 34 = 88. Let k = 21 - w. Factor -2*v**5 - 2*v**4 - 3*v**5 + 10*v**3 - k*v**4.
-5*v**3*(v - 1)*(v + 2)
Let p(o) = -3*o**3 - 48*o**2 + 567*o + 588. Let t(f) = -f**3 - 19*f**2 + 227*f + 235. Let w(j) = -5*p(j) + 12*t(j). Let w(v) = 0. Calculate v.
-8, -1, 5
Let -30*p**2 + 51*p**3 - 14*p**4 - 27*p**3 + 52*p**3 = 0. Calculate p.
0, 3/7, 5
Let v(c) be the third derivative of 1/24*c**6 + 0 + 25/24*c**4 + 0*c - 18*c**2 - 5/3*c**3 - 1/3*c**5. What is n in v(n) = 0?
1, 2
Let n(s) = -4*s**2 + 219*s - 2934. Let x(v) = 4*v**2 - 218*v + 2928. Let u(j) = -2*n(j) - 3*x(j). Suppose u(k) = 0. Calculate k.
27
Factor 573*h - 109443/2 - 3/2*h**2