vative of w(z). Factor l(i).
-i*(i - 3)*(i + 1)*(i + 2)
Solve 1215/4*y + 5/4*y**2 + 1195 = 0.
-239, -4
Let h(n) = 2*n**3 + 402*n**2 + 794*n + 392. Let c(m) = 3*m**3 + 805*m**2 + 1591*m + 784. Let k(u) = -2*c(u) + 5*h(u). Factor k(d).
4*(d + 1)**2*(d + 98)
Let f(q) = 2*q - 15. Let i be f(-8). Let c = i - -60. Factor 22 + 10 + 31*g**2 - c*g**2 - 16*g.
2*(g - 4)**2
Let k(m) = -m**2 + 1026*m - 269373. Let f(i) = -i**2 + 1024*i - 269375. Let r(h) = -6*f(h) + 7*k(h). Factor r(d).
-(d - 519)**2
Let g(a) = -5*a**4 + 18*a**3 - 12*a**2 + 6*a - 3. Let l(o) = -26*o**4 + 94*o**3 - 60*o**2 + 30*o - 16. Let h(x) = 11*g(x) - 2*l(x). Factor h(u).
-(u - 1)**3*(3*u - 1)
Let n(d) be the second derivative of 33*d + 1/30*d**6 + 0*d**2 - 1/3*d**4 + 2/3*d**3 + 0 - 1/20*d**5. Solve n(g) = 0 for g.
-2, 0, 1, 2
Suppose 3*p + 5*k = 107, -3*p = -5*p + k + 67. Let -30*y**2 + 17*y**3 + 4 + 5*y**4 - 9*y**3 - 3*y**4 + p*y - 2*y**3 - 16 = 0. Calculate y.
-6, 1
Let p(j) be the second derivative of -j**5/90 + 7*j**4/54 - 2*j**3/9 - 269*j + 1. What is d in p(d) = 0?
0, 1, 6
Let k = -95 - 36. Let s = 136 + k. Factor 0 + 0*w + 5/2*w**4 + s*w**3 + 5/2*w**2.
5*w**2*(w + 1)**2/2
Suppose 5*d - 4*g = 16, 174*g - 2 = 172*g. Let w(t) = t**2 - 16*t - 33. Let v be w(18). Factor -4/11*a**v + 0 + 2/11*a**d + 2/11*a**2 + 0*a.
2*a**2*(a - 1)**2/11
What is o in -135*o**5 + 17443*o**2 + 6512*o**3 - 23939*o**2 - 1640*o**4 + 139*o**5 = 0?
0, 2, 406
Suppose 4*l = -5*h - 225, 2*l - 4*h = 1 - 107. Let i be (l/165)/(2/(-8)). Factor -1/3*m**3 + 0 + m**2 + i*m.
-m*(m - 4)*(m + 1)/3
Let u(z) be the third derivative of z**6/1620 - z**5/540 - z**4/54 + 7*z**3 + 5*z**2 + z. Let o(v) be the first derivative of u(v). Let o(n) = 0. Calculate n.
-1, 2
Let l(r) be the first derivative of 0*r + 1/36*r**5 + 1/72*r**6 - 5/36*r**4 - 3/2*r**2 - 27 + 0*r**3. Let f(a) be the second derivative of l(a). Solve f(v) = 0.
-2, 0, 1
Determine r, given that -99/4*r**2 - 1725/4 + 3/4*r**3 + 765/4*r = 0.
5, 23
Factor 2/3*p**3 + 0 - p**2 + 1/3*p**4 + 0*p.
p**2*(p - 1)*(p + 3)/3
Let n = -45463 + 45466. Factor 0 - 4/3*p**n + 0*p**2 + 4/3*p.
-4*p*(p - 1)*(p + 1)/3
Let i(m) be the third derivative of m**7/840 + m**6/240 - 7*m**5/240 - 5*m**4/24 - m**3/2 - 273*m**2. Factor i(s).
(s - 3)*(s + 1)*(s + 2)**2/4
Let l = 10342 - 10340. Let q(b) be the first derivative of -5/12*b**3 - 180*b + 3 - 15*b**l. Factor q(u).
-5*(u + 12)**2/4
Let l = 1303/510 - -19/170. Let v(u) be the first derivative of -1/5*u**5 - 5/4*u**4 + 12 + 0*u - l*u**3 - 2*u**2. Factor v(f).
-f*(f + 1)*(f + 2)**2
Suppose 0 = -3*u - 5*s + 9, -u = 193*s - 190*s - 3. Suppose 15*d - u*w - 163 = 11*d, -4*d + w = -161. Find r, given that -d*r + 5/4*r**2 + 320 = 0.
16
Let d be (1484/(-120) + (4 - -8))*(-22 - -18). Factor -64/15*m - d*m**2 - 56/15 - 2/15*m**3.
-2*(m + 2)**2*(m + 7)/15
Let s = -100 + 103. Let g = -4 + 6. Factor 8*a**s + 21*a**2 - 8*a - 15*a**2 + 0*a - 8 + g*a**4.
2*(a - 1)*(a + 1)*(a + 2)**2
Let w(n) = 3*n**3 + 75*n**2 - n + 27. Let y be w(-25). Factor 9 + 9 - 1565*s**3 + 1573*s**3 - 78*s**2 + y*s.
2*(s - 9)*(s - 1)*(4*s + 1)
Let z(m) = -9*m - 18. Let g(o) = 8*o + 17. Let l(u) = 7*g(u) + 6*z(u). Let f be l(-4). Suppose -f + 3*d**3 - 2*d + 4 - 5 - d**3 + 4*d**2 = 0. What is d?
-2, -1, 1
Let u = 11044/3 + -3681. Let l(f) be the first derivative of -u*f**3 + 1/8*f**4 - 18 + 0*f**2 + 0*f. Factor l(g).
g**2*(g - 2)/2
Let o(r) be the third derivative of -r**5/150 + 49*r**4/30 - 376*r**3/15 + 1229*r**2. Find s such that o(s) = 0.
4, 94
Let t(z) be the second derivative of z**4/78 - 10*z**3/3 - 675*z**2/13 - 1720*z. Factor t(r).
2*(r - 135)*(r + 5)/13
Factor 450 + 8*j**3 + 16881*j - 70*j**2 - 16986*j - 3*j**3.
5*(j - 15)*(j - 2)*(j + 3)
Suppose 3*s = -2*s - f + 15, 5*s + 2*f = 20. Let u be -1 - s*21/(-18). Factor 2/3*d**3 + 0*d - u*d**2 + 0 + 2/3*d**4.
2*d**2*(d - 1)*(d + 2)/3
Suppose -23*z = -6*z + 1683. Let t = z + 110. Factor 13*r**2 - t - 9*r**2 - 13 + 20*r.
4*(r - 1)*(r + 6)
Let y(b) be the third derivative of 4/15*b**5 - 4/105*b**7 - 1/10*b**6 + 2/3*b**4 + 0*b - 2*b**2 + 3 + 1/84*b**8 + 0*b**3. Factor y(g).
4*g*(g - 2)**2*(g + 1)**2
Let j(k) be the first derivative of 8*k**5/5 + 45*k**4 + 976*k**3/3 + 582*k**2 + 360*k - 2119. Determine o, given that j(o) = 0.
-15, -6, -1, -1/2
Let 6507/4*g**2 - 2592*g - 1821/4*g**3 + 201/4*g**4 - 3/4*g**5 + 1539 = 0. What is g?
2, 3, 57
Let d = -319765 + 319790. Factor 5/4*k**2 + d - 105/4*k.
5*(k - 20)*(k - 1)/4
Let h(c) be the first derivative of c**6/660 + 7*c**5/165 + 19*c**4/44 + 24*c**3/11 + 22*c**2 - 29. Let g(i) be the second derivative of h(i). Factor g(m).
2*(m + 3)**2*(m + 8)/11
Let c = 29273 + -29269. Let j(s) be the third derivative of 2/105*s**7 + 1/6*s**6 + 0 + 0*s + 0*s**3 + 0*s**5 + 30*s**2 + 0*s**c. Suppose j(i) = 0. Calculate i.
-5, 0
Let m be (-1937309)/1590 + -1 + (-5)/(-6). Let l = 1219 + m. Factor -l*i**2 + 24/5*i - 72/5.
-2*(i - 6)**2/5
Suppose 3*g + 0*g - 18 = 0. Let o be (-2)/(-1 + 8/10) + 5. Factor 3*n**2 + 2*n**2 + 0*n**2 + 7*n**2 - 3*n**3 + g - o*n.
-3*(n - 2)*(n - 1)**2
Let y = -74 + 45. Let k = y + 31. Determine t so that 2*t**k - 11*t + 138 - 152 - t = 0.
-1, 7
Suppose 0 = -z - 2*z + 12, -4*n = -5*z. Let h(k) be the second derivative of 1/28*k**4 + 33*k - 3/14*k**2 + 3/140*k**n + 0 - 1/14*k**3. Factor h(v).
3*(v - 1)*(v + 1)**2/7
Let w(p) be the first derivative of p**4/16 - 205*p**3/6 + 817*p**2/8 - 102*p - 4933. Factor w(r).
(r - 408)*(r - 1)**2/4
Factor -5*t**2 + 222862 + 3020*t - 1362912 + 7*t**2 - 4*t**2.
-2*(t - 755)**2
Let q be 40105/(-9255)*((-77)/(-39) - 2). Find a, given that 0 + 11/9*a - q*a**2 = 0.
0, 11
Let s = -32 + 34. Let t be 5/s*(-3)/(30/(-8)). Determine j, given that -t*j**3 + 4*j + 5*j**4 - 6*j**2 - 2*j**5 + j**4 + 0*j**3 = 0.
-1, 0, 1, 2
Let t be (-473)/55 - -1 - -3*72/27. Factor 14/5 - t*h**2 + 12/5*h.
-2*(h - 7)*(h + 1)/5
Let s(b) be the third derivative of -b**6/108 + b**5/45 + b**4/36 - 19*b**3/6 + 41*b**2. Let w(u) be the first derivative of s(u). Factor w(n).
-2*(n - 1)*(5*n + 1)/3
Let k(y) be the second derivative of 0*y**2 + 5/24*y**4 + 38*y + 0*y**3 + 0 + 0*y**5 - 1/12*y**6. Determine x so that k(x) = 0.
-1, 0, 1
Let s = -126977/130 - -25645/26. Factor s + 0*p**3 - 24/5*p**2 + 0*p + 3/5*p**4.
3*(p - 2)**2*(p + 2)**2/5
Let i(w) be the first derivative of 3*w**4/4 - 52*w**3 + 552*w**2 - 2112*w + 135. Factor i(t).
3*(t - 44)*(t - 4)**2
Let r(s) be the third derivative of -8 + 1/1344*s**8 + 1/160*s**6 - 1/210*s**7 + 0*s + 17*s**2 + 1/60*s**5 + 0*s**3 - 1/24*s**4. Factor r(m).
m*(m - 2)**2*(m - 1)*(m + 1)/4
Solve 4*c**3 + 12/7 + 178/7*c + 142/7*c**2 = 0.
-3, -2, -1/14
Let b = -9902/5 + 29713/15. Let v(s) be the first derivative of -1/18*s**4 - 11 + 0*s**2 - b*s**5 + 0*s + 1/9*s**3. What is d in v(d) = 0?
-3/7, 0, 1/3
Let w(h) = h**3 + 2*h**2 - h + 62. Let r be w(0). Let l = 69 - r. Solve 2*o + 2*o**2 - 15 + o + 3*o**2 + l*o = 0 for o.
-3, 1
Let j(w) = -2*w - 42. Let p be j(-21). Suppose -3*d = -p*l - l - 10, 4*d + 5*l + 12 = 0. Let -2*i + 4 - 16*i**d - 4*i + 5*i + 13*i = 0. Calculate i.
-1/4, 1
Let q = 2/67403 + 103463599/202209. Let t = q + -7603/15. What is z in -4/5*z**4 + 32/5*z**2 + t*z**3 - 28/5 - 24/5*z = 0?
-1, 1, 7
Determine b so that -111*b + 0 - 1187/8*b**2 - 1/8*b**4 - 75/2*b**3 = 0.
-296, -3, -1, 0
Let m(y) be the third derivative of -17*y**8/224 - y**7/2 + 251*y**6/40 + 44*y**5 - 1925*y**4/16 - 125*y**3/2 - 15*y**2 - 47. Find u such that m(u) = 0.
-5, -2/17, 1, 5
Factor -507 - 26*d**3 + 1/3*d**4 + 1520/3*d**2 + 26*d.
(d - 39)**2*(d - 1)*(d + 1)/3
Let v(n) be the first derivative of 3*n**4/4 + 25*n**3 + 369*n**2/2 + 513*n + 1945. Factor v(i).
3*(i + 3)**2*(i + 19)
Let c(o) be the first derivative of 24*o**2 + 7*o**4 - 64/3*o**3 - 4/5*o**5 + 0*o - 41. Factor c(a).
-4*a*(a - 3)*(a - 2)**2
Suppose 0 = -3*m + 3*d - 132, 2*m + 188 = -2*m - 2*d. Let f = 50 + m. What is z in 16*z**2 + 48*z**3 + 4*z**5 + 4*z**5 - 33*z**f + 69*z**4 = 0?
-2, -1/2, 0
Let m = 315849/5 - 63402. Let y = 233 + m. Solve 28/5*x**3 + 8*x**4 + y*x**2 + 0 + 0*x = 0.
-1/2, -1/5, 0
Let d(s) be the first derivative of s**4/72 + 11*s**3/36 + 5*s**2/6 - 98*s + 41. Let y(a) be the first derivative of d(a). What is b in y(b) = 0?
-10, -1
Let k = 332 + -327. Solve -2*t**4 - 9*t - 16*t**2 - 44 - 14*t**3 - 