d**5/270 + d**4/6 + 3*d**3 - 77*d**2/2 - 2*d + 32. Let a(o) be the first derivative of i(o). Factor a(j).
2*(j + 9)**2/9
Let o = -8424 - -25273/3. Let p(z) be the first derivative of -3/5*z**5 + 0*z**2 - o*z**3 + 1/6*z**6 + 3/4*z**4 + 0*z - 27. Factor p(q).
q**2*(q - 1)**3
Suppose -797 = -k + 5*u - 854, -u = 3*k - 21. Factor 1/6*v**4 - 24 + 4*v**k + 143/6*v**2 - 4*v.
(v - 1)*(v + 1)*(v + 12)**2/6
Let c(q) be the third derivative of -17/6*q**4 + 34*q**2 + 0*q - 1/30*q**5 - 289/3*q**3 + 0. Solve c(v) = 0.
-17
Let u(m) be the second derivative of -m**6/15 + 143*m**5/10 - 1631*m**4/2 - 15695*m**3/3 - 10658*m**2 + 1170*m. Find a such that u(a) = 0.
-2, -1, 73
Let c(v) be the third derivative of v**8/168 + 4*v**7/105 - 17*v**6/20 + 47*v**5/15 + 7*v**4/3 - 40*v**3 - 2*v**2 - 391. Suppose c(l) = 0. What is l?
-10, -1, 2, 3
Let h(k) be the first derivative of 5*k**7/252 - k**5/24 - 53*k - 22. Let x(u) be the first derivative of h(u). Factor x(n).
5*n**3*(n - 1)*(n + 1)/6
Suppose -20 - 22 = 2*q. Let b(o) = -o**3 - 20*o**2 + 18*o - 51. Let w be b(q). Factor -3*p + 0*p**2 - 2*p**2 - 5*p - w - 6*p.
-2*(p + 1)*(p + 6)
Let w(g) = -7*g**2 + 869*g - 121. Let b be w(124). Let v(h) be the first derivative of 14 + 0*h**b + 2/3*h**2 + 0*h - 1/12*h**4. Suppose v(u) = 0. What is u?
-2, 0, 2
Let f(o) = -2*o**3 + 18*o**2 + 68*o + 50. Let j be f(12). Factor 8 + 42/5*d + 2/5*d**j.
2*(d + 1)*(d + 20)/5
Suppose 0 = -3*h + 98 - 32. Let b(v) = v**2 + 4*v + 2. Let t be b(-4). Solve 6 - 20*u**2 - 13*u - 20*u + h*u**t + 34*u**2 = 0 for u.
1/4, 2/3
Let p(s) = 11*s + 118. Let t(c) = -11*c - 117. Let q(a) = -4*p(a) - 5*t(a). Let r be q(-10). Factor -5/3*o + 0 + 35/3*o**r + 10/3*o**2 + 20/3*o**4.
5*o*(o + 1)**2*(4*o - 1)/3
Let m(x) be the second derivative of -133*x + 1/30*x**4 + 3/5*x**2 + 4/15*x**3 + 0. Suppose m(y) = 0. What is y?
-3, -1
Find l, given that 43/10*l - 71/10*l**2 + 66/5 + 17/10*l**3 - 1/10*l**4 = 0.
-1, 3, 4, 11
Let s = -17132 - -17135. Let z(v) be the third derivative of 0 + 0*v + 1/90*v**5 + 13*v**2 + 8/9*v**s - 1/4*v**4. Suppose z(t) = 0. What is t?
1, 8
Factor -2678*v - 1139*v + 3018 + 3287 - 7395 - 5*v**2 - 2*v**2.
-(v + 545)*(7*v + 2)
Let v(i) be the third derivative of -i**5/120 + 143*i**4/24 - 95*i**3/4 + 12*i**2 - 40. Determine q, given that v(q) = 0.
1, 285
Let w(r) be the third derivative of r**5/30 + 17*r**4/4 - 52*r**3/3 + 3286*r**2. Factor w(k).
2*(k - 1)*(k + 52)
Suppose 14*l - 18*l = -12. Let k = 86 - 81. Solve -161*r + 173*r - k - 3 - 4*r**l = 0 for r.
-2, 1
Let j(n) be the first derivative of -n**5/110 + 5*n**4/66 - 2*n**3/33 - 8*n**2/11 - 158*n - 264. Let x(h) be the first derivative of j(h). Factor x(k).
-2*(k - 4)*(k - 2)*(k + 1)/11
Let v(w) = 858*w - 47. Let u be v(2). Let i = u - 1667. Factor -106/9*q**i + 8 + 100/3*q + q**3.
(q - 6)**2*(9*q + 2)/9
Let b(q) be the third derivative of -q**6/420 - 11*q**5/105 - 89*q**4/84 - 68*q**3/21 - 1834*q**2. Factor b(d).
-2*(d + 1)*(d + 4)*(d + 17)/7
Suppose -4 - 38 = -21*u. Let x(q) be the first derivative of 1/9*q**5 + 1/9*q**u - 8 + 0*q + 7/27*q**3 + 1/4*q**4 + 1/54*q**6. Factor x(g).
g*(g + 1)**3*(g + 2)/9
Let l be (-94)/141 - 16/(-6). What is y in 4*y**4 - 94*y - 34*y**2 - 50*y**l - 1136*y**3 - 28 + 1122*y**3 = 0?
-2, -1, -1/2, 7
Suppose -229*t + 221*t + 40 = 0. Suppose t*k - 6 = -4*p - 7, -4 = p. Find g, given that 0*g**2 + 0 - 2/5*g**k + 2/5*g = 0.
-1, 0, 1
Find u such that -2/7*u**2 + 18/7*u - 4 = 0.
2, 7
Suppose 0 = 1020*m - 1959 - 301 + 220. Factor 2*p**m - 7/3*p + 1/3.
(p - 1)*(6*p - 1)/3
Let y(h) = 3*h + 64. Let o be y(-20). Determine u so that 435*u - 387*u + 36*u**2 - o*u**3 - 11 - 69 = 0.
-2, 1, 10
Let -1595*b + 1259*b + 100*b**3 - 4*b**5 - 320*b**2 - 342*b**4 + 422*b**4 = 0. What is b?
-2, -1, 0, 2, 21
Let i(z) be the first derivative of 4*z**5/5 - 114*z**4 + 5484*z**3 - 98496*z**2 + 746496*z + 10219. Factor i(n).
4*(n - 48)**2*(n - 9)**2
Let u(i) be the third derivative of i**5/90 - 203*i**4/36 - 490*i**3/3 + 3*i**2 + i + 61. Let u(p) = 0. What is p?
-7, 210
Suppose -5*t - r = -160, 32 = -0*t + t + 3*r. Suppose -24*q = -8*q - t. Determine a, given that -4/11*a**q + 6/11*a**3 + 2/11*a**4 - 24/11*a - 16/11 = 0.
-2, -1, 2
Let h(v) be the second derivative of -306*v + 0 + 1/15*v**6 + 4*v**2 + 13/6*v**4 - 3/5*v**5 - 4*v**3. Factor h(q).
2*(q - 2)**2*(q - 1)**2
Let v(w) be the second derivative of w**5/5 + 28*w**4/3 + 106*w**3/3 + 52*w**2 - 997*w. Let v(j) = 0. Calculate j.
-26, -1
Let j(g) be the third derivative of -g**8/84 - 18*g**7/35 + 37*g**6/2 - 605*g**5/3 + 875*g**4 + 2467*g**2. Factor j(r).
-4*r*(r - 5)**3*(r + 42)
Let l(y) be the first derivative of -2*y**6/15 - 3*y**5/5 + 4*y**4/3 - y - 77. Let d(g) be the first derivative of l(g). Factor d(i).
-4*i**2*(i - 1)*(i + 4)
Let g be (-30)/(-35)*(4 - 3/6). Let d be 52/195*80/g. Factor d*f - 28/9*f**2 - 16/3 + 4/9*f**3.
4*(f - 3)*(f - 2)**2/9
Suppose -16*f**5 - 2*f**4 + 0*f**5 - 104*f**3 + 2*f**4 - 60*f**4 + 12*f**5 = 0. What is f?
-13, -2, 0
Let u be (-3)/9 - 4503/9. Let v = u - -502. Determine k so that -v*k**3 + 16/3*k + 2*k**2 - 2/3*k**4 + 8/3 = 0.
-2, -1, 2
Let o be 760/160 + (-8 - -1) + (-6191)/(-2460). Let t be (-2 - -1)*6/(-5). Factor -o*f**2 + t*f - 8/15.
-2*(f - 4)*(2*f - 1)/15
Let k(n) = 26*n**3 + 86*n**2 - 2154*n - 2295. Let y(l) = -3*l**3 + l**2 - 6*l - 1. Let a(d) = 4*k(d) + 36*y(d). Suppose a(m) = 0. What is m?
-1, 48
Factor 25/2 + 12*c**2 - 1/2*c**4 - 25*c + c**3.
-(c - 5)*(c - 1)**2*(c + 5)/2
Let q(t) be the second derivative of 3*t**5/40 - 163*t**4/8 + 6723*t**3/4 - 19683*t**2/4 + 237*t. Factor q(d).
3*(d - 81)**2*(d - 1)/2
Let j be 2*-2*406/(-116). Suppose 6*t - 2*t = 5*n - 12, 3*n - j = -t. Let 8*v - 81/4*v**3 - 45/4*v**t - 1 = 0. What is v?
-1, 2/9
Let y(r) be the first derivative of r**6/8 - 3*r**5/10 - 9*r**4/8 + 2*r**3 + 15*r**2/8 - 9*r/2 + 5036. Suppose y(g) = 0. What is g?
-2, -1, 1, 3
Let f(q) = -277*q**2 - 519*q - 3447. Let j(i) = 62*i**2 + 130*i + 862. Let a(h) = 2*f(h) + 9*j(h). Factor a(y).
4*(y + 9)*(y + 24)
Let c(g) = -31*g**3 + 864*g**2 + 37845*g + 12. Let v(q) = 25*q**3 - 865*q**2 - 37845*q - 10. Let k(t) = 5*c(t) + 6*v(t). Factor k(l).
-5*l*(l + 87)**2
Let t(i) be the second derivative of -i**6/210 + 197*i**5/140 + 1197*i. Let t(f) = 0. Calculate f.
0, 197
Suppose 0 = 544*c - 1849 + 1849. Factor -8/11*z**3 + 0*z - 10/11*z**2 + 2/11*z**4 + c.
2*z**2*(z - 5)*(z + 1)/11
Let v(r) be the second derivative of -5*r**4/12 + 105*r**3/2 + 325*r**2 - 4*r + 471. Factor v(g).
-5*(g - 65)*(g + 2)
Let 0 + 63/2*u - 3/4*u**4 - 15*u**3 + 69/4*u**2 = 0. What is u?
-21, -1, 0, 2
Let w(z) be the first derivative of -8/3*z**3 + 3*z**4 + 0*z**2 + 36 + 0*z - 4/5*z**5. Factor w(f).
-4*f**2*(f - 2)*(f - 1)
Suppose 28*h - 32*h = -4*u - 60, u = 3*h - 51. Let l(o) be the third derivative of 0 + 3/20*o**5 + 0*o + h*o**2 + 1/40*o**6 + 3/8*o**4 + 1/2*o**3. Factor l(p).
3*(p + 1)**3
Suppose -21*d = -9280 + 3001. Solve 287*q**2 + 4*q - 2 - d*q**2 + 2 - 16*q**3 = 0.
-1, 0, 1/4
Let i(u) = -u**2 + 8*u - 9. Let k(g) = 3*g - 15. Let x be k(7). Let t be i(x). Find v such that -v + 6*v**2 + 4*v - 177*v**t - 6 + 174*v**3 = 0.
-1, 1, 2
Let z(l) be the third derivative of l**7/315 + 211*l**6/30 - 11025*l**2. Find b, given that z(b) = 0.
-1266, 0
Suppose 2*v = 2*b - 12, 6 = -76*v + 73*v + b. Let g(l) be the first derivative of l**3 - 3/5*l**5 + 0*l + 0*l**2 + 16 + v*l**4. Solve g(x) = 0 for x.
-1, 0, 1
Let n(k) be the third derivative of -k**6/108 + 2*k**5/45 + 59*k**4/108 + 10*k**3/9 + 78*k**2 + k. Factor n(b).
-2*(b - 5)*(b + 2)*(5*b + 3)/9
Let m be 2/7 - (96/56)/(-3). Let u be -9*(660/(-54) - -12). Factor -2*k + 10/7*k**u + m - 2/7*k**3.
-2*(k - 3)*(k - 1)**2/7
Let j = 28254 + -310792/11. Solve j*x**3 + 14/11*x**2 - 34/11*x + 18/11 = 0.
-9, 1
Let x(d) be the second derivative of -d**7/21 - d**6/15 + 2*d**5/5 + 2*d**4/3 + 314*d + 1. Let x(g) = 0. Calculate g.
-2, -1, 0, 2
Let t = -41371/2 - -22097. Let k = 1413 - t. Determine j, given that -1/2*j**3 - 6*j + 1/2*j**5 - k*j**4 + 11/2*j**2 + 2 = 0.
-2, 1, 2
Let d(m) = -4*m**2 - 22*m + 27. Let q(r) = -5*r**2 - 23*r + 26. Let k(w) = -6*d(w) + 5*q(w). Let v be k(14). Factor 3*z**3 - 15*z**5 - v*z**5 + 22*z**5.
-3*z**3*(z - 1)*(z + 1)
Solve 1/4*u**2 + 255025 + 505*u = 0.
-1010
Let x(z) be the third 