z) be the second derivative of -1/10*z**w + z**4 + 0 - 10*z**2 - 43*z - z**3. Factor s(l).
-2*(l - 5)*(l - 2)*(l + 1)
Let y(m) be the second derivative of m**6/720 - 43*m**5/720 + 7*m**4/72 - 157*m**3/6 + 210*m. Let s(u) be the second derivative of y(u). Solve s(r) = 0.
1/3, 14
Let q(g) be the second derivative of g**9/19656 + g**8/10920 - g**7/5460 - g**6/2340 + 25*g**3/3 + 51*g. Let m(v) be the second derivative of q(v). Factor m(r).
2*r**2*(r - 1)*(r + 1)**2/13
Let c(v) = -19*v**2 - 157*v - 205. Let b(s) = -3*s**2 - s + 5. Let k(t) = 5*b(t) + c(t). Factor k(r).
-2*(r + 3)*(17*r + 30)
Let v = -7 - -9. Suppose 0*a - 4*a + 27 = 3*p, 5*p = v*a + 19. Solve 4 - 7*q**p - 31*q**4 - 29*q**4 - 40*q**2 - 9*q**5 - 80*q**3 = 0.
-1, 1/4
Let l(n) be the third derivative of n**6/228 - 53*n**5/570 - 2*n**4/3 - 52*n**3/57 - 949*n**2. What is q in l(q) = 0?
-2, -2/5, 13
Let t(l) be the third derivative of 7/72*l**4 - 1/360*l**6 + 0 + 1/3*l**3 + 0*l - 88*l**2 + 0*l**5. Factor t(n).
-(n - 3)*(n + 1)*(n + 2)/3
Let j(c) be the first derivative of -c**5/240 + 8*c**2 + 35. Let s(b) be the second derivative of j(b). Factor s(d).
-d**2/4
Let m(r) be the third derivative of -r**5/30 - r**4/24 - r**3/6 - 42*r**2. Let h(d) = -25*d**2 + 8*d - 3. Let z(k) = -3*h(k) + 15*m(k). Factor z(q).
3*(q - 1)*(15*q + 2)
Let o = -114438 - -457803/4. Suppose -o*m**2 + 156*m + 1/4*m**3 + 169 = 0. Calculate m.
-1, 26
Find t such that -15635*t**2 + 376*t**3 + 20*t**3 - 380*t - 28*t**4 + 18239*t**2 = 0.
-5, 0, 1/7, 19
Let x(b) = 2*b**4 - b**3 + b**2. Let s(i) = 5*i**4 + 20*i**3 - i**4 + 14*i**5 + 9*i**5 + 12*i**5 - 33*i**5 - 6*i**2. Let g(v) = s(v) + 6*x(v). Factor g(z).
2*z**3*(z + 1)*(z + 7)
Let i(o) = -10*o**2 - 150*o - 12. Let a be i(-15). Let s = a + 46/3. What is x in s + 4*x + 2/3*x**2 = 0?
-5, -1
Let h(y) be the second derivative of y**6/4 - 25*y**5/16 + 35*y**4/16 + 5*y**3 - 35*y**2/2 + 4404*y - 1. Let h(c) = 0. Calculate c.
-1, 7/6, 2
Let x be (-1 + 2)/(9 + (-245)/28). Suppose -3*c = -x*c + 2. Let 4*f**c + 2*f**2 + 6*f + 2*f**2 - 11*f**2 = 0. Calculate f.
0, 2
Let s(i) = 2*i**2 - 15*i + 7*i - 4 + 15*i. Let p be s(-4). Factor 8 + p*z**2 + 32*z + 4*z**2 + 10*z**2.
2*(z + 2)*(7*z + 2)
Determine l, given that 122*l + l**2 + 560 + 412 + 348 = 0.
-110, -12
Let g = 133054 - 133052. Suppose -1872/11*v + 3402/11*v**g - 294/11*v**3 + 24 = 0. Calculate v.
2/7, 11
Factor -5/6*z**2 + 1/6*z**4 - 1/6*z**3 + 0 - 1/2*z.
z*(z - 3)*(z + 1)**2/6
Let l(y) be the third derivative of -y**6/280 - 3*y**5/20 - 178*y**2. Let l(u) = 0. What is u?
-21, 0
Let n(j) be the third derivative of 7*j**7/120 - 2387*j**6/240 - 209*j**5/4 - 749*j**4/12 - 100*j**3/3 - 3357*j**2. Determine o so that n(o) = 0.
-2, -2/7, 100
Solve 11571*h**3 - 461*h**2 - 12263*h**3 + 4721*h**2 + 2864 - 4*h**4 - 6428*h = 0 for h.
-179, 1, 4
Let k(f) = f**4 + 2*f**3 + f - 2. Let g(h) = 18*h**4 + 93*h**3 - 261*h**2 + 402*h - 210. Let t(l) = g(l) - 21*k(l). Factor t(a).
-3*(a - 8)*(a - 7)*(a - 1)**2
Let y(r) = -r**2 + 11*r + 63. Suppose 2*f - 18 = -3*b, 2*f - 14 - 24 = 2*b. Let w be y(f). Determine i so that 8/5*i**2 + 0 - 14/5*i**w + 0*i = 0.
0, 4/7
Let u(y) be the third derivative of 1/160*y**5 + 0*y + 34*y**2 + 0 + 1/96*y**4 + 0*y**3 - 1/2688*y**8 - 1/560*y**7 - 1/960*y**6. Let u(a) = 0. Calculate a.
-2, -1, 0, 1
Solve -4/5*z**3 + 0 + 624/5*z - 4/5*z**2 = 0.
-13, 0, 12
Let z be (0 - -1)/((-2)/(-4)). Suppose 0 = -2*j - 4, -19*j = y - 18*j + z. Factor 0*a**2 - 8/5*a**3 + y*a + 0 + 4/5*a**4.
4*a**3*(a - 2)/5
Let u = -649 - -653. Suppose 4*y = w - 10, -u*w + 18 = 5*y - 10*y. Factor -2/15*a**w + 2/15*a**3 - 2/15*a + 2/15.
2*(a - 1)**2*(a + 1)/15
Suppose -11 - 12*q - 15/4*q**2 - 1/4*q**3 = 0. What is q?
-11, -2
Let u(t) be the first derivative of -75 + 4/7*t**3 + 11/7*t**2 + 1/14*t**4 + 12/7*t. Factor u(i).
2*(i + 1)*(i + 2)*(i + 3)/7
Let k = 145272 - 1016902/7. Suppose -16/7 - 40/7*t - 36/7*t**2 - k*t**4 - 2*t**3 = 0. What is t?
-2, -1
Let q(b) be the second derivative of 0*b**2 - b + 1/190*b**5 - 98 - 5/114*b**4 + 4/57*b**3. Factor q(n).
2*n*(n - 4)*(n - 1)/19
Solve 20*i**2 - 174*i**2 - 4*i**3 - 474*i**2 - 7380*i + 164*i**2 - 31752 = 0 for i.
-98, -9
Let a(x) be the first derivative of 3*x**4/4 - 24*x**3 - 165*x**2/2 + 234*x + 2255. Factor a(c).
3*(c - 26)*(c - 1)*(c + 3)
Let r = -504 + 511. What is u in -3*u**3 + 65*u + 2 - 4 - 51 - r - 2*u**3 = 0?
-4, 1, 3
Let k(l) be the second derivative of 5*l**4/48 + 5515*l**3/24 + 510*l + 3. Determine a so that k(a) = 0.
-1103, 0
Let p be (-27)/6*(-104)/156. Let u(m) be the first derivative of 35/2*m**2 + 13 + 10*m - p*m**5 - 35/4*m**4 + 5/3*m**3. Suppose u(w) = 0. What is w?
-2, -1, -1/3, 1
Let n be -4 - ((736/80)/(-1) - 1*-4). Let g(s) be the second derivative of 0 - 12*s + 2/5*s**4 + 7/50*s**5 - 5/3*s**3 + n*s**2. Factor g(i).
2*(i - 1)*(i + 3)*(7*i - 2)/5
Factor -16*n + 133*n**2 + 136*n**2 - 408*n**2 + 2484 + 135*n**2.
-4*(n - 23)*(n + 27)
Let r = 86 - -427. Suppose -5*p**2 + 0*p**2 + r - 10*p - 473 = 0. What is p?
-4, 2
Determine n so that 19344538 - 19344538 - 3*n**5 + 30*n**3 - 27*n**4 = 0.
-10, 0, 1
Factor -38 + 3*m**2 - 3920*m**4 + 55*m - 19*m**3 + 7834*m**4 - 3915*m**4.
-(m - 1)**2*(m + 2)*(m + 19)
Let y(v) = -14*v**2 + 19*v + 18. Let p be y(2). Let q(f) be the second derivative of -8*f**2 - 8/3*f**3 - 1/3*f**4 - 6*f + p. Determine i so that q(i) = 0.
-2
Let m be (848/(-28) - (-6)/21)*2. Let h be 128/m - -2 - 94/(-30). Factor -2*v**3 - 143*v**2 + 141*v**2 + 4*v**h.
2*v**2*(v - 1)
Suppose -12*g - 34*g = -56*g + 47*g. Let z(u) be the third derivative of g*u + 2*u**2 - 3/10*u**5 + 9/8*u**4 - 2*u**3 + 1/40*u**6 + 0. Factor z(a).
3*(a - 4)*(a - 1)**2
Let y = 17422574/15 + -3283273/3. Let o = 67355 - y. What is r in -588/5*r - 84/5*r**2 - o - 4/5*r**3 = 0?
-7
Let o = 1024 + -1024. Let s be (o + -1)/((-4)/20). Factor 1/5*p**s - 3/5*p**4 + 0 + 3/5*p**2 + 1/5*p**3 - 2/5*p.
p*(p - 2)*(p - 1)**2*(p + 1)/5
Let n(u) be the third derivative of -33*u**2 - 1/360*u**5 + 1/72*u**4 + 0*u**3 + 0 + 2*u - 1/360*u**6 + 1/1260*u**7. Suppose n(p) = 0. What is p?
-1, 0, 1, 2
Let p(y) be the second derivative of y**4/3 + 1028*y**3/3 + 132098*y**2 + 1145*y. What is d in p(d) = 0?
-257
Solve 69*y - 36 + 25/4*y**3 - 40*y**2 = 0.
6/5, 4
Let o(u) be the first derivative of u**6/27 + 14*u**5/45 - 19*u**4/18 - 14*u**3/27 + 2*u**2 + 242. Solve o(n) = 0 for n.
-9, -1, 0, 1, 2
Factor 0*j + 0*j - 214*j**3 - 2*j**3 + 3*j**4 - 276*j**2 + 84*j**3.
3*j**2*(j - 46)*(j + 2)
Suppose -8/11*p**3 + 0 + 314/11*p**2 - 78/11*p = 0. Calculate p.
0, 1/4, 39
Factor -24*s - 3*s**5 + 5*s**5 - 17*s**5 - 3*s**4 + 12 + 12*s**5 + 15*s**3 + 3*s**2.
-3*(s - 1)**3*(s + 2)**2
Determine n, given that -1/4*n**4 + 9/2*n + 2*n**2 + 9/4 - 1/2*n**3 = 0.
-3, -1, 3
Suppose -41*p = -29 + 193. Let k be (p/14)/(-5 + 4). Suppose -k*f**2 - 12/7 + 2*f = 0. What is f?
1, 6
Suppose -209*j**3 - 2*j - 11*j**5 + 18*j**2 + 228*j**3 - 3*j - 18*j**4 - 3*j = 0. Calculate j.
-2, -1, 0, 4/11, 1
Let w(d) be the third derivative of -1/3*d**5 + 27/8*d**3 + 3/80*d**6 - 3/16*d**4 - 1/840*d**7 + d**2 + 0*d + 11. Find j, given that w(j) = 0.
-1, 1, 9
Let v(b) = -14*b**4 - 6*b**3 + 28*b**2 + 16*b - 49. Let a(u) = 17*u**4 + 5*u**3 - 27*u**2 - 21*u + 48. Let y(z) = 5*a(z) + 6*v(z). Factor y(q).
(q - 6)*(q - 3)**2*(q + 1)
Let s = -56 - -10. Let m = 48 + s. Solve -13*q + 6*q + 12*q + m*q**2 + 3*q**2 = 0 for q.
-1, 0
Let -24/5*l**2 - 16/5*l**4 + 58/5*l**3 - 99/5*l + 0 + 1/5*l**5 = 0. What is l?
-1, 0, 3, 11
Suppose -412*v - 855*v = 286*v - 4625 - 7799. Factor 2/21*g**2 - v*g + 168.
2*(g - 42)**2/21
Let p(g) = -5*g**5 - g**4 + 3*g**3 - 7*g**2 + 6*g + 4. Let q(o) = -4*o**5 + 2*o**3 - 6*o**2 + 5*o + 3. Let c(b) = 3*p(b) - 4*q(b). Factor c(u).
u*(u - 2)*(u - 1)**2*(u + 1)
Let s be -30 - (40 - 16832/240). Factor 4/5*i + s*i**2 - 32/15.
2*(i - 2)*(i + 8)/15
Let t = 47413/20741 + -5/20741. Factor -76/7*p**2 - 64/7*p + t - 20/7*p**3.
-4*(p + 2)**2*(5*p - 1)/7
Find h, given that -6/7*h**4 + 92/7*h**3 - 156/7*h**2 - 90/7*h - 2/7*h**5 + 162/7 = 0.
-9, -1, 1, 3
Factor -68/13*k + 30/13*k**2 + 16/13.
2*(k - 2)*(15*k - 4)/13
Suppose 669*y + 78 = 673*y - 7*u, 5*y - 30 = 2*u. Solve -7/5*a**y + 4/5*a + 4/5 - 4/5*a**3 + 3/5*a**4 = 0 for a.
-1, -2/3, 1, 2
Let h(b) = -15*b - 43. Let l be h(-8). Let s = l - 7