. Factor 2/9*n**3 - m - 8/3*n**2 + 10*n.
2*(n - 5)**2*(n - 2)/9
Let g(z) be the first derivative of 2/27*z**3 - 136/9*z**2 + 74 + 9248/9*z. Factor g(s).
2*(s - 68)**2/9
Let i = 121 - 119. Factor -38*g**3 - 3*g**i + 33*g**3 + 6*g**3.
g**2*(g - 3)
Let b(a) be the third derivative of -5*a**6/72 - 13*a**5/12 - 25*a**4/24 + 67*a**3/6 + 73*a**2. Let s(z) be the first derivative of b(z). Factor s(r).
-5*(r + 5)*(5*r + 1)
Find i such that 4/21*i**4 - 6/7 - 2/7*i + 46/21*i**2 - 26/21*i**3 = 0.
-1/2, 1, 3
Let r(b) be the third derivative of b**2 + 0*b**3 - 5/4*b**4 + 0*b + 1/105*b**7 - 9 - 13/60*b**6 - 29/30*b**5. Factor r(g).
2*g*(g - 15)*(g + 1)**2
Let l be (-4)/98*(-1253)/358. Factor 0 + 5/7*w - l*w**2.
-w*(w - 5)/7
Let y(w) be the second derivative of -w**4/21 + 40*w**3/21 + 264*w**2 - 15*w + 79. Factor y(c).
-4*(c - 42)*(c + 22)/7
Let x(k) be the first derivative of 5/2*k**2 + 0*k**3 + 0*k + 0*k**5 - 5/2*k**4 + 10 + 5/6*k**6. Let x(a) = 0. Calculate a.
-1, 0, 1
Let v(n) be the first derivative of 2*n**3/3 - 16*n**2 - 264*n + 5612. Solve v(f) = 0.
-6, 22
Let z(q) be the first derivative of -q**6/180 + 17*q**5/45 - 289*q**4/36 + 71*q**2/2 - 112. Let b(t) be the second derivative of z(t). Factor b(s).
-2*s*(s - 17)**2/3
Let b(s) be the second derivative of -s**4/6 + 775*s**3/3 - 774*s**2 + 1246*s - 2. What is d in b(d) = 0?
1, 774
Suppose 0 = 4*f - 0 + 4, -r + f + 1564 = 0. Find t, given that -2 + 4*t**2 + 8 + r*t**5 + 22*t - 28*t**3 - 10*t**4 - 1557*t**5 = 0.
-1, -1/3, 1, 3
Suppose 0 = -7*s + 23 + 68. Suppose 4 = s*h - 12*h. Factor 2*z**h - 4*z**3 + z**3 + 2*z**2 + 0*z**4 - z**3.
2*z**2*(z - 1)**2
Let w(q) be the second derivative of -q**7/840 - q**6/10 - 18*q**5/5 - 40*q**4/3 + 159*q. Let t(a) be the third derivative of w(a). Find r such that t(r) = 0.
-12
Let r(g) be the first derivative of 0*g**2 - 25/12*g**4 + 125/12*g**3 + 1/8*g**5 + 17 - 13*g. Let s(z) be the first derivative of r(z). Solve s(a) = 0 for a.
0, 5
Factor -28*h**2 + 82*h**2 - 31*h**2 + 720 - 50*h - 28*h**2.
-5*(h - 8)*(h + 18)
Let j(z) be the first derivative of z**4/16 + z**3 - 315*z**2/8 - 2025*z/2 - 3113. Factor j(w).
(w - 18)*(w + 15)**2/4
Suppose -1228 = -433*y - 362. Factor -8/3*g**y - 6 + 74/3*g.
-2*(g - 9)*(4*g - 1)/3
Factor -82*g**3 + 102*g**2 + 902*g + 96*g**3 - 968 - 52*g**3 + 2*g**4.
2*(g - 11)**2*(g - 1)*(g + 4)
Suppose -4*i - 1799*p + 29 = -1804*p, 3*i - 21 = 4*p. Suppose -5/2*u**5 + 5*u**2 - i*u**4 + 0*u + 17/2*u**3 + 0 = 0. What is u?
-5, -2/5, 0, 1
Factor -396 + 74*n**4 - 628 + 48*n**2 + 52*n**3 - 143*n**4 + 73*n**4 - 1024*n.
4*(n - 4)*(n + 1)*(n + 8)**2
Let o(t) be the first derivative of 103*t**4 + 8*t**3/3 - 206*t**2 - 8*t + 1245. Factor o(d).
4*(d - 1)*(d + 1)*(103*d + 2)
Let b(h) = h**3 + 3*h**2 - h - 1. Let m(u) = -35*u**2 - 1350*u - 1325. Let z(p) = -5*b(p) - m(p). Factor z(n).
-5*(n - 19)*(n + 1)*(n + 14)
Suppose s - 7*s + 18 = 0. Factor -60*i**2 - 9*i**s - 9*i**3 - 20*i - 7*i**3.
-5*i*(i + 2)*(5*i + 2)
Let q(f) be the first derivative of -64 + 75/7*f**3 - 15/28*f**4 - 3/5*f**5 + 0*f + 1/14*f**6 + 0*f**2. Let q(x) = 0. Calculate x.
-3, 0, 5
Let w be 54/216 - (-62)/8 - 1. Suppose w*i + 4*i = i. Factor 0 + 2/13*q**3 + 0*q + i*q**2 - 2/13*q**4.
-2*q**3*(q - 1)/13
Let t(d) be the third derivative of d**5/12 - 55*d**4/2 - 2800*d**3/3 - 32*d**2 - 170*d. Factor t(s).
5*(s - 140)*(s + 8)
Find i such that -2*i**4 + 34*i**2 - 307*i - 72 + 156*i + 8*i**3 + 103*i = 0.
-3, -1, 2, 6
Let o = -2/15881 + 21010567/31762. Factor o + 63*u + 3/2*u**2.
3*(u + 21)**2/2
Let y(s) be the third derivative of -s**7/315 + 4*s**6/45 - 53*s**5/90 + 31*s**4/18 - 8*s**3/3 - 562*s**2. Determine h so that y(h) = 0.
1, 2, 12
Suppose -6*y - 3*j + 24 = 0, -y - 651*j + 652*j - 8 = 0. Factor -7/3*p**2 + y - 5/3*p**4 - 2/3*p - 1/3*p**5 - 3*p**3.
-p*(p + 1)**3*(p + 2)/3
Determine l so that 193*l**2 + 15*l**3 - 121*l**2 + 8199*l**4 - 8202*l**4 = 0.
-3, 0, 8
Let i = -139075/2 + 69539. Factor i*b + 3/4*b**2 - 9/4.
3*(b - 1)*(b + 3)/4
Let b(p) be the first derivative of -p**6/15 - 4*p**5/5 - 27*p**4/10 + 4*p**3/3 + 124*p**2/5 + 48*p + 433. Find m, given that b(m) = 0.
-5, -3, -2, 2
Factor -1063/3*y - 1/6*y**2 - 1129969/6.
-(y + 1063)**2/6
Let q be 1 + -405 + (-53 - -52). Let k = q + 408. Find w such that 6/5*w**5 - 16/5*w**4 + 0*w**2 - 2/5*w + 12/5*w**k + 0 = 0.
-1/3, 0, 1
Let z = -98599 + 98602. Factor 160*t - 78/5*t**z + 144*t**2 + 0 + 2/5*t**4.
2*t*(t - 20)**2*(t + 1)/5
Let v(g) be the second derivative of 7*g**4/66 + 4699*g**3/33 + 122*g**2 + 2*g - 820. Factor v(q).
2*(q + 671)*(7*q + 2)/11
Let s(l) = -l**3 + 10*l**2 + 28*l - 33. Let u be s(12). Let z be -6*(508/102 + -20 + u). Determine m, given that z*m + 2/17*m**2 - 12/17 = 0.
-3, 2
Let s(d) be the second derivative of -d**6/75 - 12*d**5/5 - 1239*d**4/10 - 6962*d**3/15 + 44*d + 7. Find c, given that s(c) = 0.
-59, -2, 0
Let y(t) = -1757*t**3 + 5*t**2 + 3*t - 2. Let l be y(-1). Let d = 12329/7 - l. Let 18/7*a**2 + 6*a + 12/7 - d*a**4 - 6*a**3 = 0. What is a?
-1, -2/5, 1
Find d, given that -6137*d**5 - 18 - 36*d + 6135*d**5 + 20*d**3 + 180*d - 104*d**2 - 46 + 6*d**4 = 0.
-4, 1, 2
Suppose -v + 36 = -5*i, -39*v - 221*i + 204 = -216*i. Let 0*x + v*x**4 + 2/3*x**5 + 0 + 32/3*x**2 + 16*x**3 = 0. Calculate x.
-4, -1, 0
Let u(g) be the third derivative of g**6/180 - 32*g**5/45 - 199*g**4/36 - 134*g**3/9 + 2698*g**2. Solve u(s) = 0 for s.
-2, -1, 67
Let z(j) be the second derivative of j**7/315 + 4*j**6/225 - 19*j**5/75 + 2*j**4/3 - 3*j**3/5 + 97*j - 6. Suppose z(b) = 0. What is b?
-9, 0, 1, 3
Let b(r) = 12*r**2 - 5096*r + 1643528. Let c(o) = -10*o**2 + 5104*o - 1643527. Let s(y) = 3*b(y) + 4*c(y). Factor s(w).
-4*(w - 641)**2
Let o(t) be the third derivative of t**6/30 - 23*t**5/15 + 11*t**4/3 - 12*t**2 + 4. What is r in o(r) = 0?
0, 1, 22
Let v(u) = u**3 + 129*u**2 + 131*u + 387. Let f be v(-128). Factor 4/3*g + 0 - 5/3*g**2 + 1/3*g**f.
g*(g - 4)*(g - 1)/3
Let n(r) be the third derivative of 17*r**2 + 0 + 25/24*r**4 - 1/6*r**6 + 1/6*r**5 - 5/336*r**8 - 2/21*r**7 + 5/3*r**3 + 0*r. Find s, given that n(s) = 0.
-2, -1, 1
Let h(f) = -15*f**2 - f + 1. Let v(p) = -32*p**2 + 1600*p - 1598. Let i(g) = -2*h(g) + v(g). Factor i(d).
-2*(d - 800)*(d - 1)
Let z = -18311/28 + 4583/7. Suppose z*u + 0 + 1/4*u**2 = 0. Calculate u.
-3, 0
Let y be ((-4)/7)/((-4)/14). Suppose 5*n - 22 = -y. Factor 48 - 72*z**2 + 11*z**3 - 4*z**n - 18*z**3 - 41*z**3 - 5*z**4.
-3*(z + 2)**3*(3*z - 2)
Let r(t) = -5*t + 7*t**2 - 4*t - 10 - 11. Let s(n) = 3*n**2 - 4*n - 10. Suppose -17*p - 28 = 142. Let a(i) = p*s(i) + 4*r(i). Factor a(u).
-2*(u - 4)*(u + 2)
Factor -119*u + 703 + 414*u + 105 - 51 - 5*u**2 + 503.
-5*(u - 63)*(u + 4)
Let v(p) = p**3 + 36*p**2 - 40*p - 106. Let o be v(-37). Suppose 0 = 3*q + o*d - 37, q + 3*d - 2 = 17. Find l, given that -6*l - 9/4 - q*l**2 = 0.
-3/4
Let h(j) be the third derivative of -3*j**8/280 + j**7/35 + 31*j**6/300 - 37*j**5/90 + 5*j**4/18 + j**2 + 99*j. Solve h(k) = 0 for k.
-2, 0, 1/3, 5/3
Let u be 8/((-6 + 3)/6). Let h be (4/u + -5)*(-6)/14. Determine o so that -21/4*o - h - 3/4*o**3 - 15/4*o**2 = 0.
-3, -1
Let i be 6/15 + (2 - 1179/(-15)). Let c be (-4)/(-1) - ((-6120)/i)/20. Determine v, given that 58/3*v**2 - 32/9*v**4 + 8/9 + 80/9*v**3 + c*v = 0.
-1, -1/4, 4
Let p = -7213/3 + 2406. Let q(u) be the third derivative of 0 + 20*u**2 + 0*u + 1/36*u**5 + 25/72*u**4 - p*u**3. Factor q(d).
5*(d - 1)*(d + 6)/3
Let c = 8283 + -8281. Let v(i) be the third derivative of 2*i**3 - 27*i**c + 1/36*i**6 + 0*i + 0 + 37/180*i**5 + 5/6*i**4 + 1/630*i**7. Factor v(r).
(r + 2)**2*(r + 3)**2/3
Determine o so that -18*o**3 + 300 - 8*o**4 - 1/3*o**5 - 635*o + 1084/3*o**2 = 0.
-15, 1, 4
Let k(b) be the second derivative of -3*b**5/8 + 275*b**4/48 - 155*b**3/8 + 35*b**2/4 - 7843*b. Factor k(l).
-5*(l - 7)*(l - 2)*(6*l - 1)/4
Find u such that -82*u**4 + 90*u**5 + 16*u - 230*u**3 + 24*u**5 + 328*u**2 - 28*u**5 - 118*u**3 = 0.
-2, -2/43, 0, 1, 2
Let a = -81 + 138. Suppose -a = 2*p - 5*p. Suppose y**2 - 4 - 19*y + p*y = 0. What is y?
-2, 2
Let r(o) be the third derivative of -o**7/14 - 13*o**6/40 - o**5/20 + 13*o**4/8 + 3*o**3 - 12*o**2 + 47. Let r(q) = 0. What is q?
-2, -1, -3/5, 1
Factor 0*q + 4563*q**2 + 0 + 1/12*q**5 + 469/12*q**4 + 4602*q**3.
q**2*(q + 1)*(q + 234)**2/12
