213. Let s(x) be the first derivative of 0*x - 8/45*x**5 + 28/27*x**p + 25 + 1/3*x**2 + 7/18*x**4. Determine n so that s(n) = 0.
-1, -1/4, 0, 3
Let m(u) = -u**2 - 23*u + 127. Let q be m(-27). Let j(f) be the first derivative of -f**5 + 10/3*f**3 - 5*f + 0*f**2 + q + 0*f**4. Factor j(k).
-5*(k - 1)**2*(k + 1)**2
Let b = -4304511/7 + 613891. Let u = -1038 - b. Suppose 4/7*g**2 - 32/7 + u*g = 0. Calculate g.
-4, 2
Let b(n) be the second derivative of n**6/150 + 1437*n**5/50 + 2070709*n**4/60 + 274946*n**3 + 823690*n**2 + 8824*n. Factor b(o).
(o + 2)**2*(o + 1435)**2/5
Let j = -40959 + 40964. Let h(u) be the second derivative of -22/21*u**4 - 2/7*u**2 - 11*u + 25/21*u**3 + 3/10*u**j + 0. Solve h(i) = 0 for i.
2/21, 1
Let g(s) be the third derivative of -s**8/7 - 622*s**7/105 - 457*s**6/6 - 1144*s**5/5 - 120*s**4 - 40*s**2 - 16*s. Determine w so that g(w) = 0.
-12, -5/3, -1/4, 0
Let w(l) be the first derivative of -l**3/15 + 77*l**2/5 + 312*l/5 - 2408. Find u such that w(u) = 0.
-2, 156
Factor 5/4*j - 1/4*j**4 + 0 + 9/4*j**2 + 3/4*j**3.
-j*(j - 5)*(j + 1)**2/4
Solve -4*i**2 - 57*i + 633*i - 1986*i + 297*i - 1727*i = 0 for i.
-710, 0
Let i(p) be the third derivative of p**5/72 + 1975*p**4/72 + 780125*p**3/36 + 23*p**2 + 18*p. Factor i(s).
5*(s + 395)**2/6
Solve 6515 + 98*g**4 + 21100*g + 2061 + 2218*g**3 - 1932*g - 1060*g**2 + 13770*g**2 - 2*g**5 = 0 for g.
-8, -1, 67
Let l(i) = -52*i**3 - 6009*i**2 - 5926*i - 31. Let z(c) = 5*c**3 + 601*c**2 + 593*c + 3. Let q(b) = -6*l(b) - 62*z(b). Factor q(k).
2*k*(k - 605)*(k + 1)
Let x be 2 + (14/7)/((-3)/(-12)). Suppose -x*f + 110 = 70. Suppose -f*d**2 + 4*d + 4/3*d**3 - 4/3 = 0. What is d?
1
Let t(r) be the first derivative of -22*r**3/3 - 79*r**2/4 + 9*r + 7256. Factor t(i).
-(i + 2)*(44*i - 9)/2
Determine t, given that -3590 + 5/2*t**3 - 3605/2*t**2 + 5390*t = 0.
1, 2, 718
Suppose 18*h = 28*h. Suppose -2*d - 3*n = h, 4 + 11 = 3*d - 3*n. Factor d - 3*a + 3/4*a**2.
3*(a - 2)**2/4
Let w be 15/(-30) + 15/2. Suppose -3*h + 40 = 5*p + 2*h, -p - w = -4*h. Find b such that -3*b**3 + 14*b**2 - 5 + 5 - 3*b**p - 12*b**4 + 4*b**2 = 0.
-3, -2, 0, 1
Let n be (32 + (-21541)/(-78))*12/9. What is s in -172/9*s - n - 2/9*s**2 = 0?
-43
Let y(w) be the first derivative of -w**6/6 + w**5/5 + 17*w**4/4 - 7*w**3 - 36*w**2 + 108*w - 341. Suppose y(v) = 0. What is v?
-3, 2, 3
Let c = -4/1209 + 21782/6045. Let 8/5 + 26/5*r + c*r**2 = 0. Calculate r.
-1, -4/9
Let l(j) be the first derivative of j**3/9 - 29*j**2/6 + 28*j/3 - 1459. What is k in l(k) = 0?
1, 28
Factor 2/5*y**3 + 30246/5*y + 426/5*y**2 + 715822/5.
2*(y + 71)**3/5
Let u(b) be the first derivative of b**6/18 - 2*b**5/5 - b**4/12 + 2*b**3/3 - 980. Factor u(f).
f**2*(f - 6)*(f - 1)*(f + 1)/3
Let j(s) = -7*s**3 - 22*s**2 + 188*s + 60. Let g(i) = -14*i**3 - 45*i**2 + 380*i + 122. Let l(m) = 6*g(m) - 13*j(m). Find t, given that l(t) = 0.
-6, -2/7, 4
Let q(w) = 4*w**3 + w**2 - w + 1. Let j(z) = 54*z**3 - 20*z**2 + 146*z - 154. Let x(u) = -j(u) + 14*q(u). Factor x(m).
2*(m - 2)**2*(m + 21)
Let a(s) be the third derivative of 1/40*s**5 + 0 + 1/24*s**4 + 0*s - 1/672*s**8 - 11*s**2 - 1/240*s**6 + 0*s**3 - 1/140*s**7. What is z in a(z) = 0?
-2, -1, 0, 1
Let m = 627139/8 - 78392. Let m*b**2 + 0 + 0*b - 3/8*b**3 = 0. What is b?
0, 1
Let s(a) be the first derivative of 0*a - 15 + 10*a**6 - 2*a**2 - 128/5*a**5 + 18*a**4 + 0*a**3. Find j, given that s(j) = 0.
-1/5, 0, 1/3, 1
Let a be ((-22)/(-7) + -4)*(-840)/270. Let j(d) be the first derivative of a*d**3 + 1/2*d**4 + 0*d - 13 - 4*d**2 - 2/5*d**5. Suppose j(k) = 0. What is k?
-2, 0, 1, 2
Let f(b) be the second derivative of -18*b**6/35 - 93*b**5/35 - 115*b**4/21 - 118*b**3/21 - 20*b**2/7 + 1050*b + 4. Solve f(u) = 0 for u.
-10/9, -1, -1/3
Let w(l) be the third derivative of -3*l**5/80 - l**4 + 6*l**3 - 686*l**2. Factor w(x).
-3*(x + 12)*(3*x - 4)/4
Let b(k) be the second derivative of k**4/3 - 182*k**3 - 548*k**2 - 300*k. Suppose b(q) = 0. What is q?
-1, 274
Suppose -5*a = 3*z - 31315 + 4909, -4*a - 44010 = -5*z. Suppose 2*p**4 - 1782*p**2 - 448*p**3 - 6*p**4 - 777924 - 148176*p + 112*p**3 - z*p**2 = 0. What is p?
-21
Let o(w) be the first derivative of -3*w**5/20 - 621*w**4/8 - 42849*w**3/4 + 3077. Factor o(t).
-3*t**2*(t + 207)**2/4
Let r(f) be the second derivative of -f**4/10 + 117*f**3/5 + 216*f**2 + f - 11271. Suppose r(a) = 0. What is a?
-3, 120
Let u = -7/141 + 242/141. Let n(t) be the first derivative of 4/3*t + 19 + 1/6*t**4 - 2/15*t**5 + 2/3*t**3 - u*t**2. Factor n(r).
-2*(r - 1)**3*(r + 2)/3
Let i = -21642/209 + 1146/11. Let w = -617 + 11727/19. What is h in -10/19*h + 2/19*h**3 - i + w*h**2 = 0?
-3, -1, 2
Let n = -914 + 1169. Suppose -257 = -v - n. Factor 6/19*d - 2/19*d**3 + 4/19*d**v + 0.
-2*d*(d - 3)*(d + 1)/19
Factor -2/3*t**4 - 4*t**3 + 0 + 0*t + 2/9*t**5 + 0*t**2.
2*t**3*(t - 6)*(t + 3)/9
Let y(x) be the first derivative of 2*x**6/3 + 16*x**5/5 - 6*x**4 - 64*x**3/3 + 58*x**2 - 48*x + 1933. Factor y(f).
4*(f - 1)**3*(f + 3)*(f + 4)
Let v(y) be the third derivative of -y**5/50 - 753*y**4/40 + 377*y**3/10 + 23*y**2 - 14. Solve v(l) = 0.
-377, 1/2
Let x(k) be the second derivative of -11*k**5/130 - 67*k**4/39 - 140*k**3/13 - 72*k**2/13 - 32*k + 16. What is t in x(t) = 0?
-6, -2/11
Let p(c) = 5*c**3 + 1133*c**2 - 1152*c - 2276. Let s(b) = -35*b**3 - 7930*b**2 + 8065*b + 15930. Let l(v) = 15*p(v) + 2*s(v). Factor l(q).
5*(q - 2)*(q + 1)*(q + 228)
Determine j, given that 172 - 50*j + 365 + 1239 - 222*j - 4*j**2 = 0.
-74, 6
Let v(l) be the second derivative of 5/42*l**4 - 1/21*l**6 + 1/147*l**7 - 9*l + 3/70*l**5 - 2 - 4/21*l**3 + 0*l**2. Let v(u) = 0. What is u?
-1, 0, 1, 4
Let 2/9*b**3 + 4480/3*b + 3136 - 332/9*b**2 = 0. What is b?
-2, 84
Let v = -5679 + 5694. Let r(k) be the first derivative of -14/3*k**3 - 1/2*k**4 - v*k**2 - 19 - 18*k. Factor r(a).
-2*(a + 1)*(a + 3)**2
Let q(p) be the second derivative of 5*p**7/42 - 19*p**6/6 - 22*p**5 - 115*p**4/3 + 9*p + 45. Find i, given that q(i) = 0.
-2, 0, 23
Let c(x) be the third derivative of -x**5/12 - 5*x**4/2 - 45*x**3/2 + 796*x**2. Solve c(a) = 0 for a.
-9, -3
Let u(d) be the third derivative of 7*d**6/120 - 13*d**5/30 + 877*d**2 + 2*d. Determine p so that u(p) = 0.
0, 26/7
Let k(j) be the second derivative of -81*j + 0*j**2 + 3/2*j**3 - 5/2*j**4 + 0. Let k(q) = 0. What is q?
0, 3/10
Let s(f) be the first derivative of f**5/30 + 23*f**4/24 - 119*f**3/6 - 2793*f**2/4 + 2147. Factor s(g).
g*(g - 19)*(g + 21)**2/6
Let y be -5*(4 + (-25)/1). Suppose -y*q - 4 = -106*q. What is b in -11*b**q + 3*b**4 + 15*b**2 + 3*b**4 - 10*b = 0?
-2, 0, 1
Let k(j) be the second derivative of j**5/90 - j**4/2 + 17*j**3/9 - 25*j**2/9 + 223*j + 3. Find w, given that k(w) = 0.
1, 25
Let k = 585 + -589. Let r be k - 18/(-351)*81. Solve 10/13*n**2 - r*n**5 - 2/13*n**4 - 24/13 - 32/13*n + 18/13*n**3 = 0.
-3, -1, 2
Let p = -2/19653 - -393086/255489. Let -14/13*z**2 + 0 - 2/13*z**3 - p*z = 0. What is z?
-5, -2, 0
Let p(b) = b**3 + 2*b**2 + b - 2. Let q(w) = w**5 - 63*w**4 + 1385*w**3 - 12749*w**2 + 45258*w - 33844. Let l(j) = -6*p(j) - q(j). Let l(g) = 0. Calculate g.
1, 8, 23
Suppose -102 = -5*b - 92. Solve -6*i**2 + 0*i**2 + 45*i - 2*i**2 + 3*i**b = 0 for i.
0, 9
Suppose -1120 = -2*o + 3*d, 2*d + 325 + 797 = 2*o. Factor 332 + 2*i**2 - 111 + 112*i + o + 2*i**2.
4*(i + 14)**2
Let r be ((-23)/(-2))/((-7)/140*2). Let k = r - -119. Determine o, given that -27/4*o**3 + 15/4*o**5 + 6*o**k - 6*o**2 + 0 + 3*o = 0.
-2, -1, 0, 2/5, 1
Factor 2938*t**3 + 2667*t**3 - 5785*t**3 - 177*t**2 + 3*t.
-3*t*(t + 1)*(60*t - 1)
Let p(w) be the third derivative of -w**6/80 - 7*w**5/40 + 55*w**4/2 - 675*w**3 - 27*w**2 + 7*w. Find y such that p(y) = 0.
-27, 10
Suppose 968256/7 + 4/7*m**2 + 3936/7*m = 0. Calculate m.
-492
Factor 48 + 16*g**2 + 214 + 606 - 224 + 662*g - 2*g**3.
-2*(g - 23)*(g + 1)*(g + 14)
Factor -128/9*m - 2/9*m**2 + 550/3.
-2*(m - 11)*(m + 75)/9
Suppose -l + 5*l - 8 = 0. Let s = -543398 + 2173619/4. Solve -3/2 + s*h - 15/4*h**3 + 9/2*h**l = 0 for h.
-1, 1/5, 2
Suppose 0 = -510*n + 490*n + 13420. Let u be 15/12 - n/(-244). Find a, given that -8/7 + 12/7*a**3 - 2/7*a**u + 24/7*a - 26/7*a**2 = 0.
1, 2
Suppose 4*f + l = 11, -2*f - l + 5 = -0*f. Suppose -15*s + 5*x + 13 = -14*s, 2*x = 2*s - 26. Factor -f - 50*n + 