+ 4*s. Find r, given that 23*r - 3*r - s - 4*r - 16*r**3 + 12*r**2 + 4*r**4 = 0.
-1, 1, 2
Let m(a) be the second derivative of a**7/630 + a**6/6 - 31*a**5/30 + 67*a**4/12 + 10*a - 2. Let o(p) be the third derivative of m(p). Factor o(y).
4*(y - 1)*(y + 31)
Let t(m) be the third derivative of 0 + 11/420*m**7 - 1/24*m**4 + 5*m + 3/40*m**5 + 0*m**3 + m**2 - 1/16*m**6 - 1/224*m**8. Factor t(k).
-k*(k - 1)**3*(3*k - 2)/2
Let q(v) be the third derivative of 1/1260*v**6 - 6*v**2 + 27/7*v**4 + 2 + 648/7*v**3 + 0*v + 3/35*v**5. Factor q(j).
2*(j + 18)**3/21
Factor -53/2*k + 52 + 1/4*k**2.
(k - 104)*(k - 2)/4
Find n, given that -1875*n**3 + 17280*n + 2742*n**2 + 758*n**2 - 5*n**5 + 180*n**4 + 0*n**5 - 46080 = 0.
-3, 3, 4, 16
Let q(t) be the third derivative of 0 + 0*t + 1/48*t**5 - 54*t**2 - 45/4*t**3 - 5/32*t**4. Factor q(g).
5*(g - 9)*(g + 6)/4
Let c(b) be the second derivative of -b**9/30240 + b**8/2400 - b**7/560 + b**6/400 + 71*b**3/6 + 54*b. Let w(v) be the second derivative of c(v). Factor w(z).
-z**2*(z - 3)**2*(z - 1)/10
Let m(y) be the first derivative of -5*y**3/3 - 7975*y**2 - 12720125*y + 5375. Solve m(o) = 0.
-1595
Let k(a) be the first derivative of 0*a - 1/6*a**3 + 75 + 0*a**2 + 1/24*a**4. Factor k(b).
b**2*(b - 3)/6
Find q such that 158/9*q + 2/9*q**2 + 52/3 = 0.
-78, -1
Solve -1334*w - 583*w + 828100 - 1723*w + 4*w**2 = 0.
455
Let k(u) = 14*u**3 + 70*u**2 - 23*u - 19. Suppose -12*a + 0*a = 60. Let h(d) = d**3 + 2*d**2 - 1. Let r(w) = a*h(w) + k(w). Factor r(l).
(l + 7)*(3*l - 2)*(3*l + 1)
Let z(c) be the second derivative of c**4/6 - 1630*c**3 + 5978025*c**2 + 6*c - 609. Factor z(u).
2*(u - 2445)**2
Determine w, given that -869*w**2 - 27*w**3 + 273*w**2 - 18*w**4 + 301*w**2 + 283*w**2 - 3*w**5 = 0.
-4, -1, 0
Let z(w) be the second derivative of -8*w**3 - 4*w**4 + 1/5*w**6 + 48*w**2 - 1/14*w**7 - 4*w + 6/5*w**5 - 7. Factor z(m).
-3*(m - 2)**3*(m + 2)**2
Let q be (-6 + (-247)/(-38))*0. Let f(h) be the second derivative of 1/3*h**4 - 18*h**2 - 16/3*h**3 + q + 19*h. Factor f(s).
4*(s - 9)*(s + 1)
Let v = -689 + 691. Factor v*i**2 - 24*i + 243 - 479 + 236.
2*i*(i - 12)
Let l(g) = -71*g**2 + 247*g - 450. Let w(x) = 45*x**2 - 165*x + 300. Let u(j) = -5*l(j) - 8*w(j). Suppose u(a) = 0. Calculate a.
2, 15
What is i in -1583*i**3 - 545*i**2 + 419070*i - 2027*i**2 - 1091*i**2 + 52441 + 1591*i**3 = 0?
-1/8, 229
Let h = 53987/2 - 26993. Let i be 3 - (-2 + 51/12). Suppose -i*w**2 + h*w + 1/4 = 0. What is w?
-1/3, 1
Let t = -567 - -570. Factor -150 - 37*i + 3*i**2 - 3*i**t + 174 + 67*i.
-3*(i - 4)*(i + 1)*(i + 2)
Let k = 1767244 + -1767244. Factor 0*i**2 + 10/3*i**4 + 25/3*i**3 + 0 + 1/3*i**5 + k*i.
i**3*(i + 5)**2/3
Let k(d) be the first derivative of 72 + 5/3*d**2 + 8/9*d**3 + 1/6*d**4 + 4/3*d. What is x in k(x) = 0?
-2, -1
Let d(v) be the first derivative of -10*v**6/3 + 128*v**5/5 + 26*v**4 - 128*v**3/3 - 42*v**2 - 566. Suppose d(o) = 0. Calculate o.
-1, -3/5, 0, 1, 7
Factor 150*o**2 + 166*o**2 - 1079*o - 1913*o + 0*o**3 - 4*o**3.
-4*o*(o - 68)*(o - 11)
Let y(v) be the second derivative of v**4/24 + 43*v**3/6 - 44*v**2 - 4*v - 1029. Solve y(f) = 0.
-88, 2
Suppose 4*g - 3 = -4*j + 29, 2*j - 10 = g. Suppose 2*c - c = -4*h + 1, 4*h = 4*c - 4. Solve c + j*s**3 + 4*s**3 + 15*s**2 + 1 - 7 = 0.
-1, 1/2
Let r(l) be the first derivative of l**5/360 + l**4/72 - l**3/12 - 37*l**2/2 - 2*l - 69. Let p(a) be the second derivative of r(a). Factor p(i).
(i - 1)*(i + 3)/6
Suppose 12*p - 8 = 4. Let b be p*(4 - (72/(-6))/(-3)). Factor b - 1/8*k - 1/8*k**2 + 1/8*k**3 + 1/8*k**4.
k*(k - 1)*(k + 1)**2/8
Let k(g) be the second derivative of 0 - 1/28*g**4 + 4*g**3 - 168*g**2 + 56*g. Suppose k(t) = 0. What is t?
28
Let l(q) be the second derivative of -q**7/126 - 19*q**6/30 - 103*q**5/30 + 161*q**4/18 + 23*q**3/2 - 265*q**2/6 - 7244*q. Determine h so that l(h) = 0.
-53, -5, -1, 1
Let u(n) be the second derivative of -5*n + 2/7*n**3 + 3/35*n**5 + 11/42*n**4 + 0*n**2 + 1/105*n**6 + 1. Determine l, given that u(l) = 0.
-3, -2, -1, 0
Solve -4*b**4 + 208/9 - 142/9*b**3 - 148/9*b**2 + 40/3*b - 2/9*b**5 = 0 for b.
-13, -2, 1
Let s(i) be the third derivative of -i**6/60 - 8*i**5/3 + i**4/12 + 80*i**3/3 + 579*i**2. Factor s(v).
-2*(v - 1)*(v + 1)*(v + 80)
Factor 3*m**3 + 510 - 3*m - 242*m**2 + 0*m**2 - 268*m**2.
3*(m - 170)*(m - 1)*(m + 1)
Let b(i) = 4*i**2 + 6*i - 151. Let o be b(-7). Let r(y) be the first derivative of 1/30*y**o - 7/20*y**2 + y - 29. Factor r(t).
(t - 5)*(t - 2)/10
Let j(g) = -3*g**4 - 68*g**3 - 4*g**2 + 54*g + 21. Let b(v) = -3*v**4 - 66*v**3 - 3*v**2 + 54*v + 18. Let q(n) = -7*b(n) + 6*j(n). Factor q(t).
3*t*(t - 1)*(t + 1)*(t + 18)
Let g be 13/((-78)/(-261))*4*1. Factor 0*j**3 - 2*j**3 + 6*j**3 + 41*j**2 - g - 399*j - 5*j**3 - 267.
-(j - 21)**2*(j + 1)
Determine h so that 6*h**3 + 170*h - 25*h**4 + 54*h**3 + 57 - 20*h**3 - 17 + 209*h**2 - 14*h**2 = 0.
-1, -2/5, 4
Suppose -3*b + 25 = 4*i, 5*i = -0*b - 2*b + 33. Factor 5*n**2 + 5*n**3 - 23*n + i*n + 8*n - 2*n.
5*n*(n - 1)*(n + 2)
Let x = 347172 + -347169. Let 15/4*f**2 + 5/4*f**x - 30*f + 35 = 0. What is f?
-7, 2
Let a(r) be the second derivative of -r**4/54 - 565*r**3/27 + 126*r**2 - 729*r. Find q, given that a(q) = 0.
-567, 2
Let w(x) be the second derivative of -39 + 1/50*x**5 - 2/15*x**4 - 4/5*x**3 + 0*x**2 - 2*x. Factor w(q).
2*q*(q - 6)*(q + 2)/5
Suppose -3*a + 4*y - 1429 = 0, 5*a - 2*a - 3*y = -1431. Let d = a - -4315/9. Factor d + 2/9*s**2 + 2/3*s.
2*(s + 1)*(s + 2)/9
Let u = 926 + -890. Find w such that -14*w - 2 - 10 + 24*w**2 - 73*w**4 - 6*w**5 + 77*w**4 + u*w**3 = 0.
-1, 2/3, 3
Let m(a) be the second derivative of a**10/6048 - a**9/168 + 17*a**8/1344 - 33*a**4/4 - 17*a - 3. Let o(u) be the third derivative of m(u). Solve o(d) = 0.
0, 1, 17
Let v(x) = -5*x**2 - 719*x + 4. Let n(i) = -5*i**2 - 728*i + 3. Let l(g) = -4*n(g) + 3*v(g). Factor l(j).
5*j*(j + 151)
Let h(r) = -r**3 - 15*r**2 - 13*r + 27. Let p be h(-14). Let s = p - 11. Factor 10*z**2 - 16*z**3 - 118*z**4 + 0*z**2 - s*z**2 + 112*z**4 + 18*z**5.
2*z**2*(z + 1)*(3*z - 2)**2
Let s(o) = 85*o**2 - 1245*o - 8280. Let v(n) = -7*n**2 + 103*n + 690. Let x(h) = 2*s(h) + 25*v(h). Factor x(d).
-5*(d - 23)*(d + 6)
Let l(z) be the first derivative of -48*z**2 + 32*z + 14*z**3 + 93 + 49/4*z**4. Factor l(d).
(d + 2)*(7*d - 4)**2
Let j(y) be the first derivative of 2*y**6/15 + 13*y**5/20 + 5*y**4/4 + 7*y**3/6 + y**2/2 - 82*y - 29. Let u(g) be the first derivative of j(g). Factor u(o).
(o + 1)**3*(4*o + 1)
Let l(b) be the first derivative of b**6/3 + 174*b**5/5 + 924*b**4 - 3872*b**3/3 - 442. Let l(p) = 0. What is p?
-44, 0, 1
Let b = 2351 - 2351. Let g(t) be the second derivative of 1/30*t**4 + b - 3/5*t**2 + t - 2/15*t**3. Suppose g(a) = 0. Calculate a.
-1, 3
Let z(u) be the first derivative of 58*u**5/5 - 375*u**4/2 - 52*u**3/3 - 1787. Let z(c) = 0. Calculate c.
-2/29, 0, 13
What is v in -36 + 35/2*v + 1/4*v**2 = 0?
-72, 2
Let l = -73964/15 - -295901/60. Factor -l*a - 3/8*a**4 + 3/8 + 0*a**2 + 3/4*a**3.
-3*(a - 1)**3*(a + 1)/8
What is g in -64/15*g**3 + 0 - 68/15*g - 134/15*g**2 + 2/15*g**4 = 0?
-1, 0, 34
Let g(f) be the first derivative of -19 + 12*f - f**2 - 2/3*f**3. Let g(l) = 0. What is l?
-3, 2
Let x(q) be the third derivative of q**7/1050 + q**6/100 - q**5/4 + 49*q**4/30 - 26*q**3/5 + 11069*q**2. What is d in x(d) = 0?
-13, 2, 3
Factor 416/11 + 36/11*j - 2/11*j**2.
-2*(j - 26)*(j + 8)/11
Let b(x) = 340*x**3 - 3202*x**2 + 9724*x - 9778. Let y(n) = -n**4 + 338*n**3 - 3201*n**2 + 9726*n - 9780. Let u(q) = 3*b(q) - 2*y(q). What is a in u(a) = 0?
-181, 3
Factor -3*l**4 + 5*l**4 - 1418*l**2 + 1438*l**2 + 8*l**4 - 5*l**5 + 35*l**3.
-5*l**2*(l - 4)*(l + 1)**2
Solve -3375/2 + 1/4*c**3 - 675/4*c + 0*c**2 = 0 for c.
-15, 30
Let v(r) be the second derivative of -1/2*r**5 - 68/3*r**3 + 0 + 53/6*r**4 + 201*r - 36*r**2. Determine u so that v(u) = 0.
-2/5, 2, 9
Let v(k) = 3 + k**2 - 123950*k + 123950*k. Let x(l) = 2*l**3 - 16*l**2 - 2*l - 16. Let n(h) = 8*v(h) + x(h). Factor n(z).
2*(z - 4)*(z - 1)*(z + 1)
Let h(x) be the first derivative of x - 1/6*x**4 + 2*x**2 + 1/3*x**3 - 8. Let w(u) be the first derivative of h(u). Factor w(r).
-2*(r - 2)*(r + 1)
Suppose 162*t**2 - 123*t**4 + 1258*t**5 - 9*t - 39 - 1267*t**5 + 76*t - 66*t**3 + 8*t = 0. Calculate t.
-13,