**2
Let s(h) be the first derivative of 5*h**3/3 + 100*h**2 + 1680*h + 5177. Factor s(y).
5*(y + 12)*(y + 28)
Suppose -3*t = -r - 6, -4*r - 3*t + 31 - 10 = 0. Solve r*j**2 - 226 - 3*j + 226 + 3*j**3 - 3*j**4 = 0.
-1, 0, 1
Let y be (-8786)/(-2898) - (7 - 5707/819). Determine x, given that -2662*x**4 - 108/7 - 8514/7*x**2 + 1566/7*x + 20570/7*x**y = 0.
3/11, 2/7
Factor 1/2*t**2 - 8*t + 15/2.
(t - 15)*(t - 1)/2
Let l(b) be the third derivative of b**7/1260 - 2*b**6/9 + 20*b**5 + 67*b**3/3 - 201*b**2 - 2*b. Let n(w) be the first derivative of l(w). Factor n(r).
2*r*(r - 60)**2/3
Factor 226*a**2 + 5916 - 2400*a - 397*a**2 - 110 - 269*a**2 - 5*a**4 - 46 + 110*a**3.
-5*(a - 12)**2*(a - 2)*(a + 4)
Let n(x) be the second derivative of x**4/114 + 32*x**3/57 - 105*x**2/19 - 361*x. Factor n(h).
2*(h - 3)*(h + 35)/19
Let h be 60*8/(-500)*-1*(-1175)/(-940). Factor -16/15*j - 2/15*j**2 + h.
-2*(j - 1)*(j + 9)/15
Let a(s) = 7*s**2 + 2*s - s**3 + 4 + s**2 - 9*s. Let u be a(7). Find j, given that 4*j**u + 4*j**5 - 266 + 266 = 0.
-1, 0
Suppose 3 = 3*r - 3. Suppose 4*c + 4 - 2 = r*b, b - 9 = -2*c. Factor 66*g**2 - 30*g + 80*g + 15 + 30*g**3 + 10*g**4 - 6*g**2 - b*g**4.
5*(g + 1)**3*(g + 3)
Suppose -4/3*f**4 - 20*f**2 - 68/3*f**3 + 64/3 + 68/3*f = 0. What is f?
-16, -1, 1
Let g = 2659 - 2656. Let q(p) be the second derivative of 0 - 1/36*p**g + 12*p + 0*p**2 - 1/144*p**4. Factor q(w).
-w*(w + 2)/12
Let y(k) be the second derivative of 38/3*k**3 + 156*k - 1/5*k**5 + 0 + 40*k**2 - 2/3*k**4. Factor y(s).
-4*(s - 4)*(s + 1)*(s + 5)
Let a(k) be the third derivative of k**7/1470 - 11*k**6/120 + 227*k**5/70 + 580*k**4/21 + 1600*k**3/21 + 592*k**2. Factor a(n).
(n - 40)**2*(n + 1)*(n + 2)/7
Let y be (-58)/3 - 20/(-15). Let a(q) = q**2 + 18*q + 2. Let d be a(y). Factor d*f**2 + f**2 - 3*f**2 - 50 - 10*f**2 + 105*f.
-5*(f - 10)*(2*f - 1)
Let b(m) be the third derivative of m**5/510 - 109*m**4/204 - 74*m**3/17 + 11*m**2 - 22. Suppose b(k) = 0. Calculate k.
-2, 111
Let m be (-2 - -2) + (-12 - -17). Find a such that 6*a**2 + 10*a**2 - 2*a**4 + 12*a**3 - 4*a**4 + 13*a**m - 15*a**5 = 0.
-4, -1, 0, 2
Let 27*h**4 - 104*h**2 + 38*h**4 + 16*h**3 + 3*h**3 - 61*h**4 + 25*h**3 = 0. What is h?
-13, 0, 2
Let t(r) = -24*r + 108. Let d be t(7). Let k be -3 + 0 - d/10. Factor -12/7*u**2 - 2/7 - 2/7*u**4 + 8/7*u**k + 8/7*u.
-2*(u - 1)**4/7
Let g(d) be the first derivative of 3*d**5/10 - 177*d**4/4 + 3481*d**3/2 - 1673. Factor g(v).
3*v**2*(v - 59)**2/2
Let a(p) be the second derivative of -4/9*p**3 - 61*p + 1/9*p**6 - 17/30*p**5 + 0*p**2 + 0 + 8/9*p**4. Solve a(y) = 0.
0, 2/5, 1, 2
Let g(p) be the third derivative of -p**8/1512 - p**7/35 - 73*p**6/180 - 101*p**5/54 - 38*p**4/9 - 16*p**3/3 - 3*p**2 + 97. Solve g(o) = 0.
-12, -1
Let b(t) be the second derivative of t**6/10 - 12*t**5/5 + 39*t**4/2 - 56*t**3 + 147*t**2/2 + 744*t. Factor b(o).
3*(o - 7)**2*(o - 1)**2
Let d(r) = r**2 + 3*r - 2. Let a be d(-4). Let x be (-3720)/(-6240) - 6/(-39). Factor 3/2*s**a + 0 - 3/4*s**3 - x*s.
-3*s*(s - 1)**2/4
Let o be -5*(0 - (-6)/(-2))/9. Factor -5/3*f**3 + o*f - 35/3*f**2 + 35/3.
-5*(f - 1)*(f + 1)*(f + 7)/3
Let c(h) be the second derivative of -h**5/150 - 187*h**4/90 - 8648*h**3/45 + 8836*h**2/15 - 40*h + 1. Solve c(a) = 0.
-94, 1
Let l(r) be the second derivative of 0 - 114*r - 3/14*r**2 - 1/28*r**4 - 1/7*r**3. Factor l(d).
-3*(d + 1)**2/7
Factor 1131 - 1183*d**3 + 57 + 1180*d**3 + 114*d**2 + 765*d.
-3*(d - 44)*(d + 3)**2
Let y = 27865 + -27865. Let s(n) be the third derivative of 1/6*n**5 - 10*n + 0 + 1/6*n**4 + y*n**3 + 2*n**2. Determine o so that s(o) = 0.
-2/5, 0
Suppose -16*r - 2529 = -6929. Suppose -68*a = -63*a - r. Determine q, given that -2*q**2 + 25*q**3 + a*q**4 + 8*q**2 - 16*q**2 + 20*q**5 = 0.
-2, -1, 0, 1/4
Let l(q) be the first derivative of -q**6/6 - 16*q**5/5 + 171*q**4/2 + 5848*q**3/3 + 5491*q**2/2 - 11181. Solve l(j) = 0.
-17, -1, 0, 19
Suppose -121 = -124*j + 201 + 50. Let a(t) be the third derivative of -1/480*t**6 + 0 + 0*t**5 + 1/96*t**4 - 19*t**2 + 0*t**j + 0*t. What is d in a(d) = 0?
-1, 0, 1
Let a be -56*8*46/(-10304). What is n in 0 - 12/7*n**a - 6*n**3 + 0*n - 30/7*n**4 = 0?
-1, -2/5, 0
Let d(y) be the second derivative of -y**4/32 - 97*y**3/16 - 423*y**2/8 - 10*y - 14. Factor d(l).
-3*(l + 3)*(l + 94)/8
Let d(z) = -11 + 14 - 58*z**2 + 5*z**4 + 30*z**2 - 17*z**3. Let m(a) = -15*a**4 + 52*a**3 + 83*a**2 - 8. Let i(k) = -8*d(k) - 3*m(k). Factor i(b).
5*b**2*(b - 5)*(b + 1)
Let m(k) be the second derivative of -56*k**3 - 3528*k**2 + 0 - 1/3*k**4 + 36*k. Factor m(l).
-4*(l + 42)**2
Let d(s) be the second derivative of s**6/3 + 119*s**5/5 - 186*s**4 + 1448*s**3/3 - 416*s**2 - 2099*s. Let d(r) = 0. What is r?
-52, 2/5, 2
Let d = -659 - -659. Let p be (-76)/(-36) + -2 + d. Determine k, given that 0*k + p*k**2 - 4/9 = 0.
-2, 2
Let s be (-1 + 825/780)/(9/24). Let -2/13*k**4 - 2/13*k**5 + 0 + 0*k + s*k**2 + 2/13*k**3 = 0. What is k?
-1, 0, 1
Let v(c) be the first derivative of 2*c**6/3 + 12*c**5/5 - 6*c**4 - 40*c**3/3 + 42*c**2 - 36*c - 170. Determine n, given that v(n) = 0.
-3, 1
Let x(u) = -u**3 + 6*u**2 + 15*u + 12. Let z be x(8). Factor 17*b**3 - 4*b**5 - 39*b**4 - 44*b**z - 65*b**3 + 31*b**4.
-4*b**3*(b + 1)*(b + 12)
Suppose 0 = -4*c - 3*m - 0*m + 18, -16 = -2*c - 5*m. Let b = 209/1062 + 3/118. Factor 0 + 2/9*v**c + b*v**2 - 4/9*v.
2*v*(v - 1)*(v + 2)/9
Let p(m) = -m**2 - 40*m - 1. Let a(c) = -9*c**2 - 930*c - 1524. Let o(d) = a(d) - 4*p(d). Determine h so that o(h) = 0.
-152, -2
Let p(x) be the second derivative of -x**4/12 - 73*x**3/6 + 114*x**2 - 1093*x. Factor p(l).
-(l - 3)*(l + 76)
Let r(h) be the first derivative of -h**3/7 - 1041*h**2/14 - 1038*h/7 - 412. Factor r(f).
-3*(f + 1)*(f + 346)/7
Factor 212/7*n + 580/7 - 8/7*n**2.
-4*(n - 29)*(2*n + 5)/7
Let t be (3*(-8)/18)/(2/(-3)). Factor -2*i**3 + 0*i**3 + 21*i**2 - 14*i**2 - 15*i**t.
-2*i**2*(i + 4)
Let j(t) be the second derivative of t**6/35 - 13*t**5/14 - 415*t**4/42 - 65*t**3/3 - 108*t**2/7 + 3649*t. Suppose j(p) = 0. Calculate p.
-4, -1, -1/3, 27
Let y(n) = -2*n**2 - 72*n - 150. Let m be y(-33). Let b be (21/(-10))/(m/(-80)). Factor 0 - b*f**4 + 0*f - 2*f**2 + 8*f**3.
-f**2*(f - 2)*(7*f - 2)/2
Let c be 21 + 8277/(-403) - (-58)/(-182). Determine g so that -8/7*g**3 - 6/7*g**2 + 40/7*g - 25/7 - c*g**4 = 0.
-5, 1
Let u(f) be the second derivative of -f**7/27 - 17*f**6/45 + 49*f**5/90 + 67*f**4/54 - 14*f**3/9 - 16*f**2/9 + 721*f. Solve u(h) = 0 for h.
-8, -1, -2/7, 1
Solve 16/7*a**4 - 356/7*a**3 + 80/7 - 484/7*a + 744/7*a**2 = 0 for a.
1/4, 1, 20
Solve 40/3*q**3 + 22/9*q**4 + 70/9*q**2 - 8 - 4/9*q**5 - 136/9*q = 0 for q.
-2, -1/2, 1, 9
Let l(r) = -r**3 + 2*r**2 - 10*r + 12. Let t be l(6). Let y be (1/4)/((-4)/t*3). Factor -1/3*a - 1/9*a**5 + 4/9*a**3 - 2/9*a**2 + 0*a**y + 2/9.
-(a - 1)**3*(a + 1)*(a + 2)/9
Let p(g) be the third derivative of 2*g**7/105 - 47*g**6/3 + 1403*g**5/15 - 467*g**4/3 + 12*g**2 - 38*g + 2. Find b, given that p(b) = 0.
0, 1, 2, 467
Suppose -5*m = -3*k - 171, -5*m + 160 + 5 = -5*k. Suppose -4*c + m = -c. Factor 3*h + h - 10*h**2 - c + 22*h**2 - 4*h**3.
-4*(h - 3)*(h - 1)*(h + 1)
Solve -1/4*y**5 - 47/4*y**3 - 13/4*y**4 + 0 - 35/4*y**2 + 0*y = 0.
-7, -5, -1, 0
Let x(f) be the second derivative of -18*f + 1 + 0*f**2 + 13/12*f**4 + 7/6*f**3 + 1/4*f**5 - 1/30*f**6. Factor x(g).
-g*(g - 7)*(g + 1)**2
Let k = -69 - -70. Let b be ((-5)/(10/(-4)))/k. Determine r, given that -17 - 7 + 9 - 5*r**b - 20*r = 0.
-3, -1
Let n be (-20)/(-160)*((-6)/27 - 28/72*-16). Solve 39/4*k**3 + n*k**4 - 9 + 33/4*k**2 - 39/4*k = 0 for k.
-12, -1, 1
Let o(n) = 5*n**2 + 98*n + 464. Let y be o(-12). Factor 60*c + 225/2 + y*c**2.
(4*c + 15)**2/2
Let c(l) be the first derivative of l**9/756 - 2*l**7/105 + 7*l**3/3 - 2*l**2 + 80. Let s(k) be the third derivative of c(k). Factor s(n).
4*n**3*(n - 2)*(n + 2)
Let s be -70 - 1875/(-25) - 0. Let -48/13*y**3 + 96/13*y + 6/13*y**s - 16/13*y**2 + 2/13*y**4 + 32/13 = 0. Calculate y.
-2, -1/3, 2
Let m be (-1840)/(-30)*12/2. Let j = m + -366. Find v such that 2/3 + 1/6*v**j + 2/3*v = 0.
-2
Let g(v) = 21*v**3 - 315*v**2 + 1119*v - 15. Let i(c) = 3*c**3 - 45*c**2 + 160*c - 2. Let u(s) = -2*g(s) + 15*i(s). Find t, given that u(t) = 0.
0, 6, 9
Suppose -5*j + 70 + 3 = -3*b, 4*j + 97 = -5*b. Let f