hird derivative of -1/15*i**5 + r*i + 1/3*i**4 - 2/3*i**3 - 7*i**2 + 0. Factor f(u).
-4*(u - 1)**2
Suppose -11*i + y - 223 = 0, 2*i - i + 5 = -5*y. Let l be i/6*(-57)/285. Factor 2/9*a**4 + 2/9*a - l*a**2 - 2/9*a**3 + 4/9.
2*(a - 2)*(a - 1)*(a + 1)**2/9
Let b(h) be the first derivative of 3*h**5/5 - 108*h**4 + 5183*h**3 + 216*h**2 - 15552*h + 1884. Factor b(j).
3*(j - 72)**2*(j - 1)*(j + 1)
Let s(q) be the first derivative of -q**4/10 + 28*q**3/15 + 416*q**2/5 + 768*q + 1434. Factor s(k).
-2*(k - 30)*(k + 8)**2/5
Let x(u) = u**3 - 21*u**2 + 21*u - 15. Let z be x(20). Suppose z*k - 4*y = 50, k + 1 = -4*y + 11. Find t such that -17 - 13 + 28*t + 7*t - 5*t**2 - k*t = 0.
2, 3
Let s(w) be the third derivative of -w**8/20160 - w**7/840 - w**6/90 - w**5/6 - w**2 + 58*w. Let n(k) be the third derivative of s(k). Factor n(j).
-(j + 2)*(j + 4)
Solve -2*m + 11*m + 12*m**5 - 21*m**3 + 225*m**2 - 228*m**2 + 3*m**4 = 0 for m.
-1, 0, 3/4, 1
Let o(r) = -7*r**3 + 37*r**2 - 212*r - 247. Let i(l) = 2*l**3 - l**2 - l - 1. Let c(z) = 6*i(z) + 2*o(z). Factor c(f).
-2*(f - 25)*(f - 10)*(f + 1)
Let r(z) = 7*z**4 - 48*z**3 - 61*z**2 + 31*z + 5. Let t(b) = -3*b**4 + 27*b**3 + 30*b**2 - 15*b - 3. Let n(s) = 3*r(s) + 5*t(s). Find a, given that n(a) = 0.
-2, 0, 1/2, 3
Let s(j) = 4*j**2 - 1336*j + 3908. Let n(q) = -2*q + 4. Let l(w) = -32*n(w) + s(w). Determine x, given that l(x) = 0.
3, 315
Let l be -8 + ((-2)/(-9) - (-2935)/360). Let k(a) be the first derivative of a + 8 - 1/12*a**3 - l*a**2. Factor k(b).
-(b - 1)*(b + 4)/4
Let q = -14 + 16. Let z(n) = 51*n - 5*n**3 - 7*n**2 + n**q - 46*n. Let r(g) = 4*g**3 + 5*g**2 - 4*g. Let c(w) = -6*r(w) - 5*z(w). Factor c(x).
x*(x - 1)*(x + 1)
Let n(a) = -5*a**4 - 56*a**3 - 675*a**2 + 1514*a - 782. Let d(w) = 2*w**4 + w**3 + w**2 - w - 1. Let l = 214 - 215. Let t(f) = l*n(f) - 2*d(f). Factor t(b).
(b - 1)**2*(b + 28)**2
Let m(x) = 8*x + 34. Let f be m(-4). Factor 3*s**4 + 2*s**4 - f*s**4 + 24*s - 8*s**3 + 20*s**2 - 7*s**4.
-4*s*(s - 2)*(s + 1)*(s + 3)
Let v(b) = b**2 - 11*b + 299. Let r be v(13). Let z = -623/2 + r. Factor 3/8*n**2 + z - 9/2*n.
3*(n - 6)**2/8
Let h = 13 - 9. Let c(k) = -k**3 + 5*k**2 - 4*k + 7. Let t be c(h). Factor -3*j**2 + 3*j**3 - 9*j**2 - t*j**2 + 18*j - 2*j**2.
3*j*(j - 6)*(j - 1)
Let m(x) be the second derivative of 0*x**3 + 2*x - 1/4*x**4 + 0 - 7/2*x**2 + 1/30*x**5. Let g(f) be the first derivative of m(f). Solve g(c) = 0 for c.
0, 3
Let q(n) = -45*n**4 - 65*n**3. Suppose 0 = 38*f - 22*f + 400. Let p(o) = 0 + 0 + 11*o**4 + 16*o**3. Let u(l) = f*p(l) - 6*q(l). Factor u(x).
-5*x**3*(x + 2)
Let j(u) be the second derivative of 1/120*u**6 + 1/9*u**3 - 13/2*u**2 + 3*u + 1/18*u**5 + 0 + 1/8*u**4. Let w(l) be the first derivative of j(l). Factor w(f).
(f + 1)*(f + 2)*(3*f + 1)/3
Factor 1005*h + 1735*h**3 + 1606*h + 2607*h + 2*h**4 - 5214*h**2 - h**3 - 1740.
2*(h - 1)**3*(h + 870)
Suppose -24 - 16 = -4*c - 2*m, 3*m + 39 = 5*c. Factor 27*u**2 + 4*u - 25 + u**4 - 23*u + 37 - 2*u - 10*u - c*u**3.
(u - 4)*(u - 3)*(u - 1)**2
Let g(l) = l**4 + l**3 + 1. Let o(d) = -7*d**4 + 23*d**3 - 248*d**2 + 352*d - 9. Let n(w) = -18*g(w) - 2*o(w). Let n(x) = 0. Calculate x.
-22, 0, 2, 4
Suppose -6*y = 34 - 64. Suppose 4*x - y*x = -4. Solve -4/5*b**5 - 32/5*b**3 + 0*b - 4*b**x + 0 - 16/5*b**2 = 0 for b.
-2, -1, 0
Let w(d) be the first derivative of 3*d**5/80 - 3*d**4/16 + d**3/4 - 223*d + 223. Let o(a) be the first derivative of w(a). Suppose o(p) = 0. Calculate p.
0, 1, 2
Let v(m) be the first derivative of 16/3*m**3 + 8/5*m**5 + 5*m**4 + 2*m**2 - 146 + 0*m. Determine z, given that v(z) = 0.
-1, -1/2, 0
Let i = -108650 + 108652. Suppose -8/17 + 54/17*s + 14/17*s**i = 0. What is s?
-4, 1/7
Let w(s) = 0 - 18 + 5 - 3*s. Let a be w(-6). Let 2*j**a - 20*j**5 + 15*j**4 + 10*j**3 - 7*j**5 = 0. Calculate j.
-2/5, 0, 1
Let y(w) be the second derivative of w**8/560 + 3*w**7/350 + w**6/150 - 41*w**3/3 - 2*w - 62. Let s(g) be the second derivative of y(g). Factor s(j).
3*j**2*(j + 2)*(5*j + 2)/5
Let g(o) = 8*o + 76. Let b be g(-8). Suppose -3*h - 17 = -4*v, 8 = -2*v - b*h + 8*h. Suppose 0 + 2/5*f - 1/5*f**v = 0. What is f?
0, 2
Let o(j) = 19*j - 346. Let b be o(16). Let v be 2 - (b/(-30) - 1). Factor -2/15*g**2 - v*g - 24/5.
-2*(g + 6)**2/15
Let s be (-2)/((44 + -10)/(-34)). Find y, given that 13*y + 7/2*y**s - 4 = 0.
-4, 2/7
Let r = 131/234 - 3/26. Let h = -1577/18 + 529/6. Factor -h - r*l + 1/9*l**2.
(l - 5)*(l + 1)/9
Let m = -4500 + 360001/80. Let h(o) be the second derivative of -16*o + 5/8*o**2 + 7/48*o**4 - m*o**5 + 0 - 11/24*o**3. Solve h(g) = 0 for g.
1, 5
Factor -555/2*s + 450 - 33/2*s**3 - 1/2*s**4 - 311/2*s**2.
-(s - 1)*(s + 4)*(s + 15)**2/2
Let -26*j + 1/4*j**2 - 108 = 0. What is j?
-4, 108
Let m(u) = -105*u**2 + 445*u + 2775. Let a(b) = 17*b**2 - 74*b - 463. Let s(p) = 25*a(p) + 4*m(p). Suppose s(i) = 0. Calculate i.
-5, 19
Let q = 320 - 331. Let h = q + 167/15. What is t in 2/15*t**2 + 0 - h*t = 0?
0, 1
Let l be ((105/(-25))/21*-40)/5. Determine i so that -2/5*i**4 + 0 + 8/5*i**2 + l*i - 2/5*i**3 = 0.
-2, -1, 0, 2
Let w(n) be the third derivative of -28*n - 1/315*n**7 + 0 - n**2 + 1/36*n**4 - 1/30*n**5 + 0*n**3 + 1/60*n**6. Factor w(c).
-2*c*(c - 1)**3/3
Let y(r) be the second derivative of r**4/102 + 358*r**3/51 + 32041*r**2/17 + 3922*r. Suppose y(q) = 0. Calculate q.
-179
Let p = 678755/150834 + -1/75417. What is v in p*v - 3/4*v**2 + 21/4 = 0?
-1, 7
Let j(h) be the third derivative of -2*h**8/21 + 8*h**7/105 + 13*h**6/20 + 17*h**5/30 + h**4/6 + h**2 + 744*h. Suppose j(z) = 0. Calculate z.
-1, -1/4, 0, 2
Let t(a) = 22*a - 85. Let y be t(4). Let o(v) be the first derivative of 3/4*v**4 + 4*v**y + 15 + 0*v + 9/2*v**2. Factor o(l).
3*l*(l + 1)*(l + 3)
Let m(f) be the first derivative of -25/3*f**6 - 128*f**5 - 4396/3*f**3 - 1180*f**2 - 1369/2*f**4 + 16 - 400*f. Solve m(n) = 0 for n.
-5, -2, -2/5
Let j = -1/16 - -13/16. Let o = 7/2 - j. Factor 3/2*p**3 + o*p + 3/4 - 1/4*p**4 + 7/2*p**2 - 1/4*p**5.
-(p - 3)*(p + 1)**4/4
Let a(r) be the third derivative of -r**8/5880 + r**7/588 - 74*r**3/3 - r**2 - 27*r. Let y(n) be the first derivative of a(n). Factor y(l).
-2*l**3*(l - 5)/7
Let p(i) = 2*i**3 - 3*i**2 - 45*i + 16. Let o be p(-7). Let s = o + 502. Suppose 1/4*k**4 + 0*k + 0*k**2 + 1/8*k**3 + s + 1/8*k**5 = 0. Calculate k.
-1, 0
Let v(u) = -u**3 + 2*u**2 + 15*u - 1. Let k be v(5). Let w be (12 - -2 - 4) + -3 - k. Factor -14*z**2 + 4*z - 2*z - w - 16*z**3 + 8.
-2*z*(z + 1)*(8*z - 1)
Let w be -2 + (-2 - -5) + (-589)/837. Let j = -7/54 + w. Find b such that -3/2 - j*b**2 - b = 0.
-3
Let t = -43 - -46. Let p be 6*((-2)/t - (-3 + 2)). Determine z, given that -15 + 5*z**2 + z**p - 8*z + 2*z**3 + 15 = 0.
-4, 0, 1
Let i(o) be the second derivative of 6*o**2 - 1 - 15*o - o**4 + 3/20*o**5 - 1/2*o**3. Factor i(q).
3*(q - 4)*(q - 1)*(q + 1)
Let -1/2*k**3 + 3 + 1/2*k**4 - 7/2*k**2 + 1/2*k = 0. Calculate k.
-2, -1, 1, 3
Let z be 36 + 1 + 1 + -2. Suppose -31 + z = i. Determine m so that -i*m**2 + 2 + 25*m - 12 + 4 - 14 = 0.
1, 4
Suppose 3*g = -9, 21*u - 2*g = 17*u - 1050. Let w = u + 267. Factor 1/7*h**5 - 2/7*h**4 + 2/7*h**2 + 0 - 1/7*h + 0*h**w.
h*(h - 1)**3*(h + 1)/7
Let v(z) = 20 + 5 - 15*z**2 + 454*z + 163 - 7*z**2. Let o(j) = -7*j**2 + 152*j + 63. Let g(c) = -8*o(c) + 3*v(c). Factor g(y).
-2*(y - 15)*(5*y + 2)
Suppose 0 = -4*o + 1111 + 5497. Suppose 7*s = -o + 1666. Factor -2/13 - 6/13*a**s + 2/13*a**3 + 6/13*a.
2*(a - 1)**3/13
Let i(y) = -7*y**3 + 27*y**2 + 22*y. Let w(n) = -13*n**2 + 42*n**3 - 13*n**2 - 37*n**3 + 0*n - 22*n. Let a(b) = 3*i(b) + 4*w(b). Factor a(t).
-t*(t + 1)*(t + 22)
Let t(b) be the third derivative of b**4/6 + 5*b**3/3 + 22*b**2. Let c(r) = -r**2 - 13*r - 29. Let o(x) = 2*c(x) + 7*t(x). Suppose o(n) = 0. Calculate n.
-2, 3
Let r = 2511/188 - 522/47. Factor r*m - 9/4*m**4 + 3/2*m**2 + 3/4 - 3/2*m**3 - 3/4*m**5.
-3*(m - 1)*(m + 1)**4/4
Let z(q) be the first derivative of q**5/5 - 29*q**4/2 + 997*q**3/3 - 2262*q**2 + 6084*q - 745. Factor z(l).
(l - 26)**2*(l - 3)**2
Factor 6*c**2 - 2*c**2 - 1655 - 1184*c + 467.
4*(c - 297)*(c + 1)
Let x(b) be the second derivative of 5784*b**5/5 - 2876*b**4/3 + 707*b**3/3 + 2*b**2 - 1495*b. Determine i, given that x(i) = 0.
-2/723, 1/4
Let k(n) be the third derivative of -n**8/3360 + n**7/6