. Factor z(q).
(q + 2)*(q + 8)
Let i(v) be the first derivative of -v**5/2 + 25*v**4/4 - 30*v**3 + 70*v**2 - 80*v + 111. Find s, given that i(s) = 0.
2, 4
Let b(m) be the first derivative of -m**4/36 + 11*m**3 - 7301*m**2/6 - 22201*m/9 + 820. Find d such that b(d) = 0.
-1, 149
Let d be (9 - 0)*(-2 + 1 + 2). Let v = d + -9. Solve 0*r + 0 + v*r**3 - 3/4*r**4 + 3/4*r**2 = 0.
-1, 0, 1
Let v(f) be the second derivative of -7/20*f**5 - 11/4*f**4 - 36*f + 6*f**2 - 16/3*f**3 + 0. Let v(j) = 0. What is j?
-3, -2, 2/7
Let y(m) = 20*m**2 - 38*m - 6. Let a be (3 - 1)/(-2*(-2)/(-34)). Let l(j) = -59*j**2 + 114*j + 19. Let q(z) = a*y(z) - 6*l(z). Let q(i) = 0. Calculate i.
-2/7, 3
Let i(d) = -d**3 + 3*d**2 + d - 1. Let s be i(3). Factor -24 + 86*b**2 - 82*b**s + 2*b - 6*b.
4*(b - 3)*(b + 2)
Let u = 65 + -51. Suppose 5*r - 1 - u = 0. Factor 1 - 4/3*j**2 - 2/3*j + 1/3*j**4 + 2/3*j**r.
(j - 1)**2*(j + 1)*(j + 3)/3
Factor -1/3*r**4 - 12*r**3 - 358/3*r**2 - 204*r - 289/3.
-(r + 1)**2*(r + 17)**2/3
Let s(i) be the second derivative of -2/5*i**5 + 0 - 9*i**4 - 108*i**3 - 1/135*i**6 - 8*i - 729*i**2. Factor s(q).
-2*(q + 9)**4/9
Let k(v) be the first derivative of -v**5/45 + 13*v**4/36 - 20*v**3/9 + 56*v**2/9 - 64*v/9 + 27. Factor k(u).
-(u - 4)**3*(u - 1)/9
Let i = -16 - -22. Let o(j) = -j**3 + 7*j**2 - 5*j - 4. Let f be o(i). Solve 3*y**2 - 4 + 2*y**2 - f*y - 3*y**2 = 0.
-1, 2
Let r(i) be the third derivative of -i**10/75600 - i**9/10080 + i**7/630 + 41*i**5/60 - 14*i**2. Let w(a) be the third derivative of r(a). Factor w(c).
-2*c*(c - 1)*(c + 2)**2
Let j(s) be the second derivative of s**6/10 - 3*s**5/4 + 2*s**4 - 2*s**3 + 40*s - 5. Determine y so that j(y) = 0.
0, 1, 2
Let o(z) = -5*z**3 - 436*z**2 + 351*z - 84. Let p be o(-88). Solve 2/3*u - 4*u**p + 0 - 6*u**5 + 16/3*u**3 + 4*u**2 = 0.
-1, -1/3, 0, 1
Let q(x) be the third derivative of x**8/2016 - 17*x**7/1260 + 79*x**6/720 - 47*x**5/360 - 5*x**4/9 + 16*x**3/9 + 2*x**2 + 9*x. Let q(j) = 0. Calculate j.
-1, 1, 8
Let t be -3 - (-6 + 10 - (-613)/(-87)). Let k = t - -55/696. Factor 1/8*a**5 - 1/8*a**2 + 0 + 0*a + 1/8*a**4 - k*a**3.
a**2*(a - 1)*(a + 1)**2/8
Suppose -37 = p + 50. Let f = p + 263/3. Factor 0*c**3 - 4/9*c + f*c**2 + 0 - 2/9*c**4.
-2*c*(c - 1)**2*(c + 2)/9
Let x(k) be the third derivative of 11*k**8/1176 + 5*k**7/147 - k**6/84 - 5*k**5/42 - k**4/14 - k**2 - 86*k. Suppose x(n) = 0. Calculate n.
-2, -1, -3/11, 0, 1
Let r(f) = f**2 - 6*f - 13. Let g be r(8). Determine u, given that 3*u**g - u**2 - 4*u**3 + 0*u**2 = 0.
-1, 0
Suppose -9 = -x - 4*m, 6*x + 18 = 10*x - 2*m. Let q(f) = f**2 - 7*f + 9. Let b be q(8). Factor -2*g**2 + x*g - b*g + 11 + 4*g**2 + 7.
2*(g - 3)**2
Let q(h) be the second derivative of -h**4/8 - 35*h**3/4 + 117*h**2 - 898*h. Suppose q(t) = 0. Calculate t.
-39, 4
Let q(n) be the third derivative of n**7/140 - 17*n**6/240 + 9*n**5/40 - 7*n**4/48 - n**3/2 - 144*n**2. Find c, given that q(c) = 0.
-1/3, 1, 2, 3
Suppose -3*b - 3*c + 21 = 2*b, -b - 3*c + 9 = 0. What is l in -10 + 48*l**4 + 7*l**5 - 42*l**2 - 33*l + 4 + 14*l**5 + 12*l**b = 0?
-1, -2/7, 1
Let h = 234 - 691/3. Let j = h + -41/12. Factor 0 - 1/8*z + j*z**2 - 1/8*z**3.
-z*(z - 1)**2/8
What is l in -36/7*l**2 + 36/7*l**4 + 0 - 4*l**3 + 32/7*l - 4/7*l**5 = 0?
-1, 0, 1, 8
Let q(o) = 18*o**3 - 243*o**2 - 202*o + 65. Let k(m) = -89*m**3 + 1214*m**2 + 1011*m - 325. Let v(b) = -2*k(b) - 11*q(b). What is c in v(c) = 0?
-1, 1/4, 13
Let n(v) = v**2 + 8*v + 10. Let j be n(-7). Suppose -5*b = 2*p - 14, -2*p = -0*p - j*b + 2. Factor 6/5*d - 3/5 - 3/5*d**p.
-3*(d - 1)**2/5
Factor 4*x**2 - 6/5*x**3 + 16/15 - 56/15*x.
-2*(x - 2)*(3*x - 2)**2/15
Let v be 5/((500/(-48))/(-25)). Let s be ((-4)/10)/((-1)/5). Determine u, given that 35*u - s*u**3 + u**3 - 11*u + 4*u**3 - 15*u**2 - v = 0.
1, 2
Let s(l) be the second derivative of -l**4/32 + 31*l**3/16 + 3*l - 5. Suppose s(c) = 0. What is c?
0, 31
Let k = -61 - -79. Let x be ((-2)/(-2) - 1)/(16 - k). Let 2/9*w**4 + x*w - 2/9*w**2 + 0 - 2/9*w**5 + 2/9*w**3 = 0. Calculate w.
-1, 0, 1
Solve 20/7*p**3 - 8*p**2 + 2*p**4 + 16/7*p + 0 - 6/7*p**5 = 0 for p.
-2, 0, 1/3, 2
Let p(z) be the first derivative of 0*z**2 + z + 1/80*z**5 + 3/8*z**3 - 1 + 1/8*z**4. Let c(n) be the first derivative of p(n). Solve c(d) = 0 for d.
-3, 0
Let p(s) be the first derivative of s**6/3 + 2*s**5/5 - s**4 - 4*s**3/3 + s**2 + 2*s - 200. Let p(z) = 0. What is z?
-1, 1
Let n(a) = 4*a**3 + 6*a**2 - 2*a. Let z(m) = -m**3 + 3*m + 11*m**2 - 8*m + 9*m**3. Let q(f) = -5*n(f) + 2*z(f). Determine j so that q(j) = 0.
-2, 0
Let d = 1 - -1. Suppose 3*z = -w + 4, -z + w - 2 = -3*z. Factor -i**2 - 3*i**z - 2*i - 4*i**4 + 2*i**5 + 8*i**4 + 0*i**d.
2*i*(i - 1)*(i + 1)**3
Let w(h) = -h**3 + 6*h**2 + h - 3. Let n = 21 - 15. Let k be w(n). Factor -c**4 + 3*c**3 - k*c**2 - c**4 + 5*c**4 - 3*c**5.
-3*c**2*(c - 1)**2*(c + 1)
Let l = -224575 - -56143871/250. Let t = 2/125 + l. Suppose u**3 - 1/4*u**5 - 1/2 + 0*u**4 - 3/4*u + t*u**2 = 0. Calculate u.
-1, 1, 2
Suppose -7/5*t**2 + 1/5*t**3 + 12/5 + 4/5*t = 0. Calculate t.
-1, 2, 6
Let d(u) = u**3 - 6*u**2 - 27*u + 3. Let r be d(9). Let n(j) be the first derivative of 1/6*j**4 - 1/3*j**2 - 1/9*j**r + 1/15*j**5 - 13 + 0*j. Factor n(y).
y*(y - 1)*(y + 1)*(y + 2)/3
Suppose 5*r = 115 - 0. Suppose 0 = 3*v - 5*v + 2*b + 14, r = 5*v - b. Factor -4*s**3 - 38*s**3 - 18*s + 6 + 14*s**4 - 9*s + 48*s**2 + 4*s**v - 3*s**5.
-3*(s - 2)*(s - 1)**4
Suppose 3*r = -3*i, 0*r - 5*r - 10 = 0. Let f = -29 - -29. Suppose -11/2*d**i + f + 9/2*d**3 + d = 0. Calculate d.
0, 2/9, 1
Suppose -19*u + 14 + 24 = 0. Let o(p) be the first derivative of 0*p + 2 + 1/16*p**4 + 1/6*p**3 + 1/8*p**u. Suppose o(s) = 0. What is s?
-1, 0
Find p, given that 40/3*p**2 - 2*p**3 + 374/3*p + 40 = 0.
-5, -1/3, 12
Let k be (1426/(-138))/(1/(-55)*2). Let l = k + -284. Factor l*b - 1/6*b**2 + 1/6*b**4 + 0 - 1/6*b**3.
b*(b - 1)**2*(b + 1)/6
Let v be 4*(45/12 + -3). Let q = 827/2365 - -3/215. Factor 0 - q*c**2 + 0*c - 2/11*c**v.
-2*c**2*(c + 2)/11
Let a = 31 + -23. What is w in -a + 15*w**2 + 17*w**2 - 5*w**3 - 6*w**3 - w**3 - 12*w = 0?
-1/3, 1, 2
Let k(p) be the first derivative of -p**6/360 + p**5/60 - 2*p**3 + 9. Let x(t) be the third derivative of k(t). Solve x(c) = 0.
0, 2
Solve -1/4*c - 27/4*c**2 + 1/4*c**3 + 27/4 = 0.
-1, 1, 27
Let h(w) be the first derivative of -7*w**6/5 - 22*w**5/5 + 14*w**4/5 + 64*w**3/5 - 32*w**2/5 - 32*w/5 + 20. Suppose h(t) = 0. Calculate t.
-2, -2/7, 2/3, 1
Let u(f) be the first derivative of 3*f**5/40 - 135*f**4/8 + 6075*f**3/4 - 273375*f**2/4 + 12301875*f/8 + 81. Let u(v) = 0. What is v?
45
Let h(z) = z + 23. Let p be h(-20). Factor 4*r**2 - 10*r**p - 4*r + 8*r**4 - 2*r**5 + 3*r + r.
-2*r**2*(r - 2)*(r - 1)**2
Let u(y) be the third derivative of -y**5/66 + y**4/44 + 22*y**2. Factor u(r).
-2*r*(5*r - 3)/11
Let r(f) = -3*f**3 - 19*f**2 - 13*f + 31. Let l(j) = -2*j**3 - 11*j**2 - 6*j + 15. Let t(y) = 5*l(y) - 3*r(y). Factor t(k).
-(k - 3)*(k - 2)*(k + 3)
Suppose 34 - 25 = 9*j. Let a be j/3*16/60*18. Factor 2/5*q**4 + 8/5*q**3 - a - 8/5*q + 6/5*q**2.
2*(q - 1)*(q + 1)*(q + 2)**2/5
Let g(k) be the first derivative of -k**6/480 + k**5/120 + k**4/24 - 2*k**3 + 11. Let y(w) be the third derivative of g(w). Find l such that y(l) = 0.
-2/3, 2
Suppose 25*v = -15*v + 298 + 182. Factor v*g - 3/2*g**3 + 18 - 3/2*g**2.
-3*(g - 3)*(g + 2)**2/2
Let h = 7 + -5. Solve -160*t**2 + h*t + t - 2 + 159*t**2 = 0.
1, 2
Let i(q) = q**3 + 92*q**2 - 84*q + 839. Let r be i(-93). Factor 1/2*x**r + x - 4.
(x - 2)*(x + 4)/2
Let k(o) be the first derivative of 20/9*o**3 + 4/15*o**5 + 0*o - 4/3*o**4 + 8 - 4/3*o**2. Factor k(i).
4*i*(i - 2)*(i - 1)**2/3
Let s = -19061/159 - 448/53. Let k = 133 + s. Solve -k*t + 4/3 + 10/3*t**2 = 0.
2/5, 1
Let k(v) = 136*v - v**2 - 15*v**2 + 5*v**3 - 111*v - 25 + v**2. Let q(x) = -x**3 + 4*x**2 - 6*x + 6. Let m(a) = 6*k(a) + 25*q(a). Let m(j) = 0. Calculate j.
-2, 0
Let l(b) be the third derivative of b**7/210 - b**6/15 - b**5/2 - 4*b**4/3 - 11*b**3/6 - 2*b**2 + 31. Factor l(y).
(y - 11)*(y + 1)**3
Factor -4/7*c**4 + 8/7*c + 4/7 + 0*c**2 - 8/7*c**3.
-4*(c - 1)*(c + 1)**3/7
Let w(n) = -n**3 - 34*n**2 - 62*n + 67. Let u be w(-32). Solve -8/5*v**2 + 0 - 2/5*v**u - 8/5*v = 0.
-2, 0
Let g be 9*((-3)/9 - -1). Let q be -2 - (-3 + g/(-2