the third derivative of 0*s**3 - 9/40*s**6 + 1/4*s**4 + 6*s**2 + 0*s + z + 3/20*s**5 - 1/7*s**7. Let y(t) = 0. Calculate t.
-1, -2/5, 0, 1/2
Let -451*x + 722*x - 399*x - 2*x**2 - 1470 = 0. What is x?
-49, -15
Let x(g) be the second derivative of 1953*g**5/20 - 521*g**4/4 - 73*g**3 + 24*g**2 + 46*g + 13. Solve x(n) = 0 for n.
-2/7, 8/93, 1
Let s(f) = 2*f**2 + f - 19. Let y = -756 - -759. Let g be s(y). Solve -n**2 + 0*n + 1/2*n**5 - g*n**4 + 5/2*n**3 + 0 = 0.
0, 1, 2
Let g be ((152/28 - -4) + -1)/6. Let o = g + 2/21. Factor 3/2*c**2 + 0*c - o.
3*(c - 1)*(c + 1)/2
Let r(l) = -3*l**3 - 207*l**2 - 198*l - 8. Let g(u) = -5*u**3 - 415*u**2 - 395*u - 20. Let x(i) = -2*g(i) + 5*r(i). Factor x(s).
-5*s*(s + 1)*(s + 40)
Let v(x) = -3*x**2 - 67*x - 19. Let w be v(-22). What is k in -406*k + 268*k + 490 + 243*k - 60*k**2 + 5*k**w = 0?
-2, 7
Let b(t) = -66*t**2 - 2625*t - 45111. Let j = -218 - -191. Let q(m) = 5*m**2 + 202*m + 3470. Let d(v) = j*q(v) - 2*b(v). Factor d(u).
-3*(u + 34)**2
Let z = -4610/7 + 9325/14. Let -5*p + 0 + z*p**2 - 5/2*p**3 = 0. Calculate p.
0, 1, 2
Let l(u) = 49*u**2 + u - 6. Let t(y) = 41 - 9*y**2 + 71 - 111. Let q(z) = -2*l(z) - 11*t(z). Factor q(x).
(x - 1)**2
Let d(p) = 3*p - 58. Let g be d(20). What is b in 8*b**g + 0*b**4 + 4*b**3 - 17*b - 2*b**5 - 2*b**4 + 8*b**3 + b = 0?
-2, 0, 1, 2
Let i(m) be the third derivative of 5/2*m**3 - 1/12*m**5 - 7/24*m**6 + 44*m**2 + 0*m + 35/24*m**4 + 0 - 1/21*m**7. Solve i(u) = 0 for u.
-3, -1, -1/2, 1
Let j(q) be the second derivative of -85*q**4/12 + 1015*q**3/6 + 30*q**2 - 62*q. Let j(s) = 0. What is s?
-1/17, 12
Let d(j) = -15*j**2 - 1580*j - 1505. Let f(i) = -5*i**2 - 527*i - 501. Let q(t) = -7*d(t) + 20*f(t). Suppose q(n) = 0. What is n?
-103, -1
Let f(d) be the first derivative of -d**7/3360 + 13*d**6/1440 + 7*d**5/240 + 44*d**3 - 133. Let c(b) be the third derivative of f(b). Find r such that c(r) = 0.
-1, 0, 14
Let j(g) be the second derivative of g**5/30 - 223*g**4/9 + 3905*g. Solve j(u) = 0.
0, 446
Suppose -b + 553 = -2*b + 2*c, 0 = 3*b - c + 1664. Let r = 1231 + b. Find o such that 324*o**4 - 240*o - r*o**3 - 56*o**5 + 24 + 680*o**2 - 64*o**2 + 8 = 0.
2/7, 1/2, 1, 2
Let z = -4920/23 - -14783/69. Let q(n) be the second derivative of -13*n - 2/15*n**6 + 0*n**5 + 0*n**2 + 0 - z*n**3 + 1/21*n**7 + 1/3*n**4. Factor q(a).
2*a*(a - 1)**3*(a + 1)
Let k be 8/1 + 15*(420/(-50) - -8). Determine s so that -1/4*s**3 + 0 - 1/2*s**k + 0*s = 0.
-2, 0
Let s(o) = 3*o**3 + 2*o - 2. Let z be s(1). Let l be -1 + ((-4)/4 + z - -3). Factor -5*t**4 + 4*t**2 - 4 + 11*t**l - 10*t**3 + 4.
2*t**2*(t - 1)*(3*t - 2)
Suppose 9*n + 14*n - 69 = 0. Suppose 4*l - 7*l = n*r - 12, 3*l + 4 = r. Let -10*o**2 + l - 12/5*o + 14/5*o**4 - 24/5*o**3 = 0. Calculate o.
-1, -2/7, 0, 3
Let k = 7173 - 7173. Let r(f) be the second derivative of -1/21*f**7 + 0 + k*f**3 + 0*f**2 + 0*f**4 + 1/10*f**5 + 0*f**6 - 19*f. Factor r(q).
-2*q**3*(q - 1)*(q + 1)
Let o(v) be the second derivative of -v**4/24 + 58*v**3/3 - 3364*v**2 + v + 905. Suppose o(y) = 0. Calculate y.
116
Let w(o) be the third derivative of -o**6/360 - 131*o**5/180 - 64*o**4/9 - 254*o**3/9 + 6308*o**2. Find r such that w(r) = 0.
-127, -2
Let b(m) be the second derivative of 2*m**4 - 1 + 0*m**2 + 1/10*m**5 + 12*m**3 + m. Factor b(u).
2*u*(u + 6)**2
Let r(d) be the third derivative of -d**7/420 + 3*d**6/80 + d**5/10 - 5*d**4/12 + 6*d**2 - 12. Factor r(i).
-i*(i - 10)*(i - 1)*(i + 2)/2
Let v(g) = -3*g**2 + 2*g. Let c(o) = -4*o**2 + 80*o + 722. Let r(u) = c(u) - 2*v(u). Suppose r(z) = 0. What is z?
-19
Let t(k) be the first derivative of 3*k**5/20 + k**4/2 - 7*k**3/2 + 6*k**2 - 40*k + 34. Let q(j) be the first derivative of t(j). Let q(r) = 0. Calculate r.
-4, 1
Let v(d) be the third derivative of 3*d + 2/15*d**5 - 1/105*d**7 + 0 + 1/40*d**6 + 0*d**3 - 1/336*d**8 + 1/6*d**4 + 3*d**2. Factor v(i).
-i*(i - 2)*(i + 1)**2*(i + 2)
Determine n so that 43/4*n**4 + 17/2 + 167/4*n**3 + 155/4*n + 247/4*n**2 + 1/2*n**5 = 0.
-17, -2, -1, -1/2
Let j(x) be the third derivative of -x**7/525 - x**6/50 - 4*x**5/75 - 4773*x**2. Factor j(t).
-2*t**2*(t + 2)*(t + 4)/5
Let z(a) = -2*a**2 - 32*a - 50. Let s(x) = -2*x - 5. Let h(i) = 6*i + 16. Let q(w) = 5*h(w) + 16*s(w). Let o(k) = 6*q(k) - z(k). Factor o(b).
2*(b + 5)**2
Let q(f) be the third derivative of -f**5/150 + 21*f**4 - 1259*f**3/15 - 793*f**2 - f. Let q(v) = 0. Calculate v.
1, 1259
Factor 0 - 1/5*s**3 - 4*s**2 + 44/5*s.
-s*(s - 2)*(s + 22)/5
Let b(s) be the third derivative of -217 - 1/350*s**7 + 0*s**4 - s**2 - 1/1680*s**8 + 0*s**3 - 1/300*s**5 - 1/200*s**6 + 0*s. Factor b(y).
-y**2*(y + 1)**3/5
Suppose -2*w = 2*m - 12, -5*m - w + 4*w = -22. Factor 4*l**3 - 9*l**5 + 19*l**5 - 6*l - 7*l**m + 7*l**3 - 13*l**4 + 5*l**2.
l*(l - 3)*(l - 1)**2*(3*l + 2)
Let k(g) be the second derivative of -g**6/55 - 9*g**5/55 - g**4/2 - 6*g**3/11 - 1592*g. Find t, given that k(t) = 0.
-3, -2, -1, 0
Let q = 8318 + -8272. Let m(d) be the second derivative of 0*d**2 - 5/18*d**3 - 1/24*d**5 + 0 - 5/24*d**4 - q*d. Factor m(h).
-5*h*(h + 1)*(h + 2)/6
Let y(g) be the first derivative of -g**3/2 - 1185*g**2/2 - 468075*g/2 + 2556. Factor y(w).
-3*(w + 395)**2/2
Let s be 1*18187/3510 - (6 + -1). Let l(u) be the third derivative of -s*u**6 + 14/135*u**5 + 0*u - 1/54*u**4 - 22*u**2 + 0 + 0*u**3. Factor l(a).
-4*a*(7*a - 1)**2/9
Let x(t) be the second derivative of -1/30*t**5 - 1/3*t**3 - 302*t + 5/18*t**4 + 0*t**2 + 0 - 1/45*t**6. Factor x(i).
-2*i*(i - 1)**2*(i + 3)/3
Let u(o) be the second derivative of -1/4*o**5 + 0*o**2 + 0*o**3 - 18*o + 2 + 5*o**4. Suppose u(k) = 0. What is k?
0, 12
Factor 211 - 241 + 4*k**5 - 1122 + 480*k**3 - 72*k**4 - 1472*k**2 + 2112*k.
4*(k - 6)**2*(k - 2)**3
Let c(p) be the second derivative of 0 + 17/12*p**3 + 4*p**2 - 5/8*p**4 - 1/60*p**6 - 114*p - 17/40*p**5. Find k such that c(k) = 0.
-16, -1, 1
Let q(x) = x - 23. Let m be q(14). Let o(g) = 8*g - 8. Let y(k) = -k**3 - 15*k + 16. Let l(b) = m*o(b) - 4*y(b). Factor l(i).
4*(i - 1)**2*(i + 2)
Determine p, given that 12/13 + 22/13*p - 48/13*p**2 + 20/13*p**4 + 6/13*p**5 - 12/13*p**3 = 0.
-3, -2, -1/3, 1
Let w(c) be the third derivative of c**8/21 + 274*c**7/105 - 83*c**6/10 + 36*c**5/5 - 22*c**2 + 86. Suppose w(m) = 0. Calculate m.
-36, 0, 3/4, 1
Factor 169*a**2 - 14*a + 14*a**3 - 3*a**4 + 12 + a**4 - 179*a**2.
-2*(a - 6)*(a - 1)**2*(a + 1)
Let f be (-322)/27 - 8/108. Let i be 120/800 - (-3)/f*-3. Factor -3/5*y**2 - 1/10*y**3 + 0 - i*y.
-y*(y + 3)**2/10
Let h(r) be the third derivative of r**7/525 - 17*r**6/300 + 28*r**5/75 - 13*r**4/15 + 58*r**2. Find f such that h(f) = 0.
0, 2, 13
Determine w so that 180*w**2 + 432 + 136/7*w**3 - 4/7*w**4 + 3456/7*w = 0.
-3, -2, 42
Factor -33*t + 112*t - 4*t + 2*t**2 - 13*t - 132.
2*(t - 2)*(t + 33)
Factor 63*v + 69*v + 71*v - 243*v + 11*v**2 + 48 - v**3.
-(v - 4)**2*(v - 3)
Find y such that 4/9*y + 28/9*y**4 + 4/9*y**5 - 56/9*y**2 + 28/9 - 8/9*y**3 = 0.
-7, -1, 1
Let x(q) = 2*q**3 - 1922*q**2 + 74784*q + 242024. Let r(g) = -g**3 + 641*g**2 - 24928*g - 80676. Let w(k) = 10*r(k) + 3*x(k). Factor w(l).
-4*(l - 82)**2*(l + 3)
Solve -51/4*k**3 - 47/4*k**2 + k + 0 = 0 for k.
-1, 0, 4/51
Let t(s) be the third derivative of s**5/45 + 589*s**4/18 - 1180*s**3/9 - 4009*s**2. Factor t(y).
4*(y - 1)*(y + 590)/3
Let u(f) be the third derivative of f**5/20 + 311*f**4/4 + 96721*f**3/2 - 129*f**2. Suppose u(y) = 0. What is y?
-311
Let h(s) be the first derivative of -1/24*s**3 + 15*s + 18 + 1/48*s**4 - 1/4*s**2. Let t(m) be the first derivative of h(m). What is r in t(r) = 0?
-1, 2
Suppose -131*q + 130*q = 0. Let 4/7*b**2 + q - 12/7*b = 0. Calculate b.
0, 3
Let n = -1636 - -2373. Let t = n + -737. What is a in 1/3*a**3 + 0*a + t - 1/3*a**2 = 0?
0, 1
Let x(d) be the first derivative of d**3/6 - 117*d**2/2 - 1195*d/2 - 3147. Factor x(j).
(j - 239)*(j + 5)/2
Let s(v) be the first derivative of v**6/600 - 3*v**5/100 + v**4/8 + 5*v**3/6 + v**2/2 - 33*v - 6. Let f(b) be the second derivative of s(b). Solve f(n) = 0.
-1, 5
Let t(a) = 760*a + 50162. Let h be t(-66). Let 2/3*w + 46/3*w**h + 0 = 0. What is w?
-1/23, 0
Let m(i) be the third derivative of -i**6/20 - 17*i**5/15 - 67*i**4/12 - 12*i**3 + 1027*i**2. Factor m(z).
-2*(z + 1)*(z + 9)*(3*z + 4)
Let i(d) = -23*d**2 + 56*d 