 51). Let z be g/17 - 56/476. Factor 435/4*k + 75/2 + 39*k**2 + 15/4*k**z.
3*(k + 5)**2*(5*k + 2)/4
Suppose o - 3 = -a, -a + 33 = 2*o + 23. Let z(n) be the second derivative of 4 - 5/12*n**4 - 1125/2*n**2 + 25*n**3 + o*n. Suppose z(h) = 0. Calculate h.
15
Suppose 26 = -4*z - 14. Let d be 2/((-5)/(75/z)). Factor 5*g**4 - g**4 + 173*g**3 - 5*g**4 - 174*g**d.
-g**3*(g + 1)
Let f(m) = -m**3 + 2*m**2 - 1208*m + 4867. Let u be f(4). Factor 2/13*c**4 + 6/13*c**u - 2/13*c**2 - 6/13*c + 0.
2*c*(c - 1)*(c + 1)*(c + 3)/13
Let b(m) be the first derivative of 2/5*m**5 - 2*m**2 + m**4 + 0*m**3 - 2*m + 60. Factor b(g).
2*(g - 1)*(g + 1)**3
Suppose 5 + 42 - 47 = -86*i. Factor 12*a - 11/2*a**2 + i + 1/2*a**3.
a*(a - 8)*(a - 3)/2
Let o(f) be the second derivative of -5*f**4/12 + 95*f**3/2 - 275*f**2 + f - 19. Factor o(g).
-5*(g - 55)*(g - 2)
Let t(s) be the second derivative of s**7/21 + 4*s**6/15 - 13*s**5/10 - 14*s**4/3 + 20*s**3 - 7886*s. Factor t(m).
2*m*(m - 2)**2*(m + 3)*(m + 5)
Suppose 6*o - 10936 = 2*o + 2*g, 4*o - 4*g - 10932 = 0. Factor -o*u - 1010*u + 2916 + 1080*u**2 - 112*u**3 - 888*u + 745*u + 4*u**4.
4*(u - 9)**3*(u - 1)
Suppose 0 = -3*v + 4*n - 21, 15 = 5*n - 0. Let k(w) = -23*w**2 + 68*w + 67. Let i(y) = -8*y**2 + 23*y + 22. Let d(a) = v*k(a) + 8*i(a). Let d(z) = 0. What is z?
-1, 5
Let s = 27/1246 + 2357/6230. Factor -s*w**2 + 2/5*w + 0.
-2*w*(w - 1)/5
Let g(k) be the first derivative of k**6/36 - 11*k**5/90 - 13*k**4/36 + k**3/3 + 109*k**2/2 - 22. Let c(s) be the second derivative of g(s). Solve c(q) = 0.
-1, 1/5, 3
Let n be (-30)/12*(288/60)/(-6). Let o(p) be the first derivative of 0*p - 2/5*p**5 + 0*p**3 + 0*p**n + 4 - p**4. Determine c so that o(c) = 0.
-2, 0
Let g(y) be the second derivative of 1 - 35*y - 1/16*y**4 + 15/8*y**2 + 1/2*y**3. Determine j, given that g(j) = 0.
-1, 5
Suppose 367*n - 1/2*n**2 - 134689/2 = 0. What is n?
367
Let m(d) be the first derivative of 6/7*d**3 + 16/7*d + 38/7*d**2 - 37. Let m(h) = 0. What is h?
-4, -2/9
Let j(z) be the first derivative of 7*z**6/60 + z**5/6 - z**4/6 + 3*z**2/2 + 17*z - 42. Let q(p) be the second derivative of j(p). Suppose q(r) = 0. What is r?
-1, 0, 2/7
Let o(r) = 2*r**4 + r**3 + r**2 - 3*r + 1. Let v(q) = 17*q**4 + 51*q**3 + 141*q**2 + 107*q + 54. Let n(i) = -18*o(i) + 2*v(i). Suppose n(h) = 0. What is h?
-1, 45
Let r = 198 - 196. Let -45*w**2 + 11*w**2 + 5*w**4 + 14*w**r = 0. What is w?
-2, 0, 2
Suppose -4*i + 3*n = -16, -2*i = -5*n + 14 - 36. Factor 6*l + 0*l - 5*l**3 + 4 - 5*l**2 - l + i.
-5*(l - 1)*(l + 1)**2
Let r(w) be the third derivative of w**5/30 - 103*w**4/4 + 668*w**2. Factor r(a).
2*a*(a - 309)
Let r(h) be the third derivative of 3*h**4 + 0 - 2*h**2 - 1/30*h**5 + 37/3*h**3 + 0*h. Factor r(x).
-2*(x - 37)*(x + 1)
Let r(a) = 9*a**3 - 4*a**2 - 4*a + 14. Let j be 42/(-10) - (220/(-25))/(-11). Let f(l) = 7*l**3 - 5*l**2 - 4*l + 13. Let c(s) = j*r(s) + 6*f(s). Factor c(h).
-(h + 2)**2*(3*h - 2)
Let f = -1/702 - -53/9828. Let m(k) be the second derivative of -1/36*k**3 - f*k**7 + 1/180*k**6 - 13*k + 0 + 1/12*k**2 + 1/60*k**5 - 1/36*k**4. Factor m(s).
-(s - 1)**3*(s + 1)**2/6
Let b(q) be the first derivative of -q**6/72 - 5*q**5/24 + 3*q**3 + q**2 + 26. Let p(a) be the third derivative of b(a). Factor p(l).
-5*l*(l + 5)
Let i(j) be the second derivative of -8/21*j**3 - 2*j - 1/14*j**4 + 64 + 9/70*j**5 + 4/7*j**2. Factor i(m).
2*(m + 1)*(3*m - 2)**2/7
Let m(b) be the third derivative of 5*b**2 - 1/30*b**5 - 47/6*b**4 + 3 + 0*b - 2209/3*b**3. Factor m(x).
-2*(x + 47)**2
Let g = 347330 + -1389287/4. Solve 57/4*l - g*l**2 - 27/4 + 3/4*l**3 = 0 for l.
1, 9
Let w(n) be the first derivative of 5*n**5/4 + 255*n**4/4 + 2701*n**3/3 + 1020*n**2 + 400*n - 3048. What is o in w(o) = 0?
-20, -2/5
Factor 171/4 - 3/4*b + 3/4*b**3 - 171/4*b**2.
3*(b - 57)*(b - 1)*(b + 1)/4
Let n be (-9)/5 + 1908/(-140) + 16. Solve -4/7 + n*y**2 - 4/7*y + 4/7*y**3 = 0.
-1, 1
Let a(i) be the first derivative of -4*i**3/3 + 2708*i**2 + 5420*i - 10676. Let a(q) = 0. Calculate q.
-1, 1355
Solve -202/7*f**3 - 97/7*f**4 + 0 - 11/7*f**5 + 24/7*f - 92/7*f**2 = 0.
-6, -2, -1, 0, 2/11
Let s be 19 - (81328/(-102))/(-52). Factor 1/6*p**2 - 23/6*p + s.
(p - 22)*(p - 1)/6
Let t(a) be the second derivative of 49*a + 7/36*a**4 + 19/18*a**3 + 0 - a**2. Factor t(b).
(b + 3)*(7*b - 2)/3
Let k(s) = -s**3 - s**2 + 3. Let z(g) = -21*g**3 - 1875*g**2 + 54. Let o(a) = -18*k(a) + z(a). Solve o(f) = 0.
-619, 0
Let g(r) be the first derivative of 5*r**3/3 + 875*r**2/2 + 1730*r + 3180. Factor g(f).
5*(f + 2)*(f + 173)
Let w = -2875 - -2881. Let h(u) be the first derivative of -27/4*u - 1/4*u**3 - 9/4*u**2 + w. Find a, given that h(a) = 0.
-3
Factor -347*h**2 - 34*h**3 + 311*h**2 - 34*h + 34*h + 2*h**4.
2*h**2*(h - 18)*(h + 1)
Let l be (-2682)/(-810) + (-88)/(-3960). Let -2/3*v**3 + 16/3*v + l*v**2 - 8 = 0. Calculate v.
-2, 1, 6
Let k(m) be the second derivative of -2*m**6/15 - 286*m**5/5 - 20449*m**4/3 + 4871*m. Let k(t) = 0. Calculate t.
-143, 0
Let k = 394/53 - 17359/2385. Let v(y) be the first derivative of -37 - k*y**5 - 1/6*y**4 + 10/27*y**3 - 1/3*y + 5/54*y**6 + 1/18*y**2. Factor v(t).
(t - 1)**3*(t + 1)*(5*t + 3)/9
Factor -71/2*o**3 - 23/2*o**2 + 0 + 45*o + 2*o**4.
o*(o - 18)*(o - 1)*(4*o + 5)/2
Let n(j) be the first derivative of j**3/6 + 11*j**2 + 170*j + 1543. Factor n(f).
(f + 10)*(f + 34)/2
Let q be -7*(24/(-28))/1. Let o be (-1)/6 + 91/q. Factor 7*w**2 - 32*w**3 + 16*w + o*w**2 + 22*w**3 + 14*w**2.
-2*w*(w - 4)*(5*w + 2)
Let h = -394053 + 394056. Factor -7/2 + 1/2*t - 1/2*t**h + 7/2*t**2.
-(t - 7)*(t - 1)*(t + 1)/2
Let i(w) = -3*w**5 - w**4 + w**2 + 2*w. Let x(g) = -28*g**5 + 26*g**4 - 38*g**3 + 10*g**2 + 20*g. Let v(a) = 10*i(a) - x(a). What is q in v(q) = 0?
-19, 0, 1
Solve 2*k + 54*k + 198085911 + 12*k**2 - 198085931 = 0 for k.
-5, 1/3
What is f in 244*f - 247/4*f**2 + 1/4*f**3 - 243 = 0?
2, 243
Let r(q) be the first derivative of -q**4/10 - 106*q**3/3 - 1563*q**2/5 - 4662*q/5 - 11222. Factor r(g).
-2*(g + 3)**2*(g + 259)/5
Let b(n) be the third derivative of -n**6/160 - n**5/40 - n**4/32 + 649*n**2. Factor b(y).
-3*y*(y + 1)**2/4
Let 6444239*b - b**5 - 24*b**3 - 14*b**4 - 6444239*b = 0. What is b?
-12, -2, 0
Let x be (90/(-42))/(3/(-21)). Suppose 0 = 3*k - 8*k + x. Suppose 2*h**3 - 4*h**4 + 6*h**k + 6*h**5 - 10*h**5 = 0. What is h?
-2, 0, 1
Let b(i) be the second derivative of -i**5/20 - 17*i**4/6 + 37*i**3/2 + 4499*i. Factor b(g).
-g*(g - 3)*(g + 37)
Let k = -9/1256 - -119/5652. Let y(a) be the second derivative of 0 + 0*a**2 + 1/9*a**3 - 15*a - k*a**4. Factor y(m).
-m*(m - 4)/6
Suppose -8 = t + 3*u, 0 = 205*t - 203*t + u - 9. Let o(h) be the second derivative of -18*h**2 + 0 - 1/12*h**4 - 2*h**3 + t*h. Factor o(b).
-(b + 6)**2
Let x(i) = -293*i**2 + 573*i - 172. Let c(w) = -1904*w**2 + 3724*w - 1112. Let n(q) = -5*c(q) + 32*x(q). Factor n(j).
4*(4*j - 7)*(9*j - 2)
Let y(l) = -2*l**3 - 338*l**2 - 885*l + 18426. Let c be y(-166). Factor 63/5*n**2 + c + 12/5*n.
3*n*(21*n + 4)/5
Let s = 464404 - 2321972/5. Determine w so that -2/5*w**2 + 10*w - s = 0.
1, 24
Suppose -3*h + 0*p + 438 = -p, 2*h - 306 = -4*p. Let m be 1/((-2)/4)*(-42)/h. Factor -10/7*o**3 + 10/7*o - 4/7*o**2 + m.
-2*(o - 1)*(o + 1)*(5*o + 2)/7
Let v(w) be the first derivative of -5*w**3/3 - 6775*w**2 - 9180125*w - 2969. Factor v(i).
-5*(i + 1355)**2
Let q(m) = 33*m**2 + 1225*m + 150. Let h be q(-37). Factor 3/2*d**3 + 0*d - 9/4*d**h + 0 + 3/4*d**4.
3*d**2*(d - 1)*(d + 3)/4
Let m be (-72)/24*(-8)/6. Let o be m*4/1280*8. Determine d so that 0 + o*d**2 + 1/5*d - 3/10*d**3 = 0.
-2/3, 0, 1
Let z(f) be the second derivative of 11*f**4/30 - 647*f**3/15 - 118*f**2/5 - 893*f. Factor z(s).
2*(s - 59)*(11*s + 2)/5
Let 243*h + h**2 - 260*h**3 - 243*h - 5*h**2 - 616*h**3 = 0. What is h?
-1/219, 0
Let g be (1512/(-70))/((-1)/(-5)). Let c be (-48)/g*(-3)/(-4). Determine w so that 1/3*w**2 + c*w + 0 = 0.
-1, 0
Let k(j) = -506*j + 27834. Let c be k(55). Solve -3/4*t - 3*t**2 + 3/2 + 3/2*t**c - 3/4*t**5 + 3/2*t**3 = 0 for t.
-1, 1, 2
Let x be -1 - 6/198*1011/2. Let d = x + 196/11. Factor 1/4*h**2 + 5/4*h + d.
(h + 2)*(h + 3)/4
Factor -52*d + 2/5*d**2 - 1918/5.
2*(d - 137)*(d + 7)/5
Let r(y) = y**2. Suppose -10*f = 3*f + 468. Let i(o) = 22*o**2 + 15*o + 2. Let t(b) = f*r(b) + 4*i