33)**2/5
Determine b so that 1/2*b**2 + 50 + 101/2*b = 0.
-100, -1
Let x be 24210/66 + 2/11 - 1. Suppose -13*p + 245 = -x. Find l, given that -32 - 16*l + 22*l**3 - p*l**3 + 23*l**3 + 14*l**2 = 0.
-1, 4
Let u be (356/10)/((-165)/1725) - 4. Let q = u + 378. Factor -2/11*k**5 - 10/11*k + 2/11 + 10/11*k**4 + 20/11*k**2 - q*k**3.
-2*(k - 1)**5/11
Suppose 22/5*s - 78/5*s**3 + 2/5*s**2 - 54/5*s**4 - 4/5 = 0. What is s?
-1, 2/9, 1/3
Let o(w) be the second derivative of w**6/135 - 2*w**5/9 + 25*w**4/9 - 500*w**3/27 + 625*w**2/9 + w - 257. Determine t so that o(t) = 0.
5
Let n = 22 - 12. Let m = 15 + n. Determine b so that -10 + 33 + 15*b**2 - 20*b**4 - m*b**3 - 18 + 25*b = 0.
-1, -1/4, 1
Determine j so that 13*j**2 + 46/3*j - 80 - 1/3*j**3 = 0.
-3, 2, 40
Let w(h) be the third derivative of -h**6/30 - h**5/5 + 77*h**4/3 - 442*h**2. Suppose w(b) = 0. What is b?
-14, 0, 11
Let a = 159 + -156. Find w, given that -w**4 + w**2 + 12*w + 3*w**2 + 5*w**a + w**2 - w**5 - 320 + 316 - 16*w = 0.
-2, -1, 1, 2
Suppose -173*w + 141 = -144 - 234. Let c(t) be the third derivative of 0 + 19*t**2 + 0*t + 1/240*t**5 - 7/96*t**4 + 0*t**w. Factor c(k).
k*(k - 7)/4
Factor -58647*n**2 - 121810268*n - 5*n**3 - 130198086720 - 9969172*n + 14187*n**2.
-5*(n + 2964)**3
Let o(f) be the second derivative of f**4/6 + 33*f**3 - 100*f**2 + 2315*f. Factor o(d).
2*(d - 1)*(d + 100)
Suppose -35000/11*v**3 - 11400/11*v**2 - 4/11 - 414/11*v = 0. What is v?
-2/7, -1/50
Let f = -122 - -123. Let h be 6/2 + f + (-15 - -15). Factor 12 + h*c**2 + 2*c - 44 + 26*c.
4*(c - 1)*(c + 8)
Let l be (105/10 - 9)*2. Determine r, given that -r**2 + 14*r + 3*r**3 + 2*r**2 + l*r**2 - 5*r**3 + 8 = 0.
-1, 4
Suppose -24 = -7*f + 5*f. Factor o**4 - 12*o**2 + 14 + 32*o - 4*o**3 + 38 + f.
(o - 4)**2*(o + 2)**2
Determine s, given that -50*s**3 + 12*s + 51*s**3 + 26*s + 7*s**2 - 44*s - 72 = 0.
-6, -4, 3
Find y such that -612*y**2 - 12167000 + 158700*y - 6*y**3 + 22*y**3 - 78*y**2 + 19*y**3 - 34*y**3 = 0.
230
Let k(t) = -68*t**2 - 335*t - 96. Let o = -421 + 434. Let h(b) = -11*b**2 - 56*b - 16. Let n(p) = o*h(p) - 2*k(p). Factor n(i).
-(i + 8)*(7*i + 2)
Let o(h) = -h**3 + 43*h**2 - 41*h - 39. Let d be o(42). Find a such that -4*a**4 - 492*a**5 - 16*a + 4*a**2 + 494*a**5 + 2*a**4 - 28*a**2 - 4*a**d + 8*a**4 = 0.
-2, -1, 0, 2
Suppose 0 = -k + 2*h - 8, 7*k - 6*k - 16 = -4*h. Let t(u) be the second derivative of 0 + k*u**2 - 12*u - 1/3*u**4 + 4/3*u**3. Factor t(c).
-4*c*(c - 2)
Let j(n) be the first derivative of -3*n**4/16 - 92*n**3/3 + 125*n**2/2 + 124*n + 262. Factor j(o).
-(o - 2)*(o + 124)*(3*o + 2)/4
Let x be (8/5)/(3940/100 + -39). Let q(t) be the second derivative of 0*t**2 - 2/7*t**3 - 1/14*t**x - 23*t + 9/70*t**5 + 0. Factor q(p).
6*p*(p - 1)*(3*p + 2)/7
Let t be (31*16/(-8))/(-19 - -5). Let i = t - 141/35. Suppose i*k**2 - 16/5 + 14/5*k = 0. Calculate k.
-8, 1
Let o(d) = 2*d**3 + 19*d**2 - 8*d + 23. Let m be o(-10). Let m*l**3 - 28*l**2 + 55*l + 38*l - 45*l**2 - 23*l**2 = 0. Calculate l.
0, 1, 31
Suppose 0 = -5*y - v - 25, 3*y + 13 = -3*v + 2*v. Let x be (21/(-35))/(1 + y/5). Find j such that 4/3*j**4 + 2/3*j + 0*j**x + 0 - 4/3*j**2 - 2/3*j**5 = 0.
-1, 0, 1
Let f(h) be the first derivative of 0*h**3 - 116 + 1/2*h**5 + 0*h**2 + 0*h + 1/12*h**4. Determine i so that f(i) = 0.
-2/15, 0
Solve -2/17*r**2 - 16/17 + 12/17*r = 0.
2, 4
Let s(v) = 5*v**3 + 231*v**2 + 3520*v + 12107. Let y(z) = -15*z**3 - 695*z**2 - 10560*z - 36320. Let h(n) = -20*s(n) - 7*y(n). Factor h(t).
5*(t + 5)*(t + 22)**2
Let m(y) be the third derivative of 2*y**7/945 - 23*y**6/270 + 79*y**5/135 - 19*y**4/18 - 54*y**2 + 8*y. Let m(v) = 0. What is v?
0, 1, 3, 19
Let f(y) = y**2 + 23*y. Let x = -67 - -44. Let s be f(x). Factor 215*d**2 + s - 212*d**2 + d**3 - 4.
(d - 1)*(d + 2)**2
Let g be (21/2)/((-360)/(-480)) + -14. Let g - 22/5*q**3 + 14/5*q + 8/5*q**5 - 54/5*q**4 + 54/5*q**2 = 0. What is q?
-1, -1/4, 0, 1, 7
Suppose -24092*d = -24065*d. Factor 0 - 2/5*l**4 + 8/5*l**3 + d*l - 6/5*l**2.
-2*l**2*(l - 3)*(l - 1)/5
Let u(v) = 85*v**2 + 19503*v - 19627. Let b(d) = 52*d**2 + 11700*d - 11776. Let r(t) = 13*b(t) - 8*u(t). Factor r(q).
-4*(q - 1)*(q + 982)
Let c(a) = a**3 + 24*a**2 - 2*a - 45. Let y be c(-24). Factor -5*w**5 - 80*w - 5*w**3 + 39*w**y + 6*w**3.
-5*w*(w - 2)**2*(w + 2)**2
Suppose -2356 = 24*o - 196. Let u = -87 - o. Factor 4/9*x**u - 55/9*x**2 + 182/9*x + 49/9.
(x - 7)**2*(4*x + 1)/9
Let c(g) be the third derivative of g**7/735 - 3*g**6/35 - 5*g**5/14 - 19*g**4/42 + 350*g**2. Factor c(o).
2*o*(o - 38)*(o + 1)**2/7
Let m(k) = -k**4 + k**2. Let b = 13 + -37. Let j be 1/(-7) - b/(-28). Let n(g) = -21*g**4 + 21*g**2. Let f(l) = j*n(l) + 18*m(l). Let f(i) = 0. Calculate i.
-1, 0, 1
Let n(b) = b**3 - 8*b**2 - 20*b + 13. Let p be n(10). Factor 6 - p + 3*j**2 - 5 + 16*j.
(j + 6)*(3*j - 2)
Suppose 3*b = l + 2080, 46*l - 41*l = 3*b - 2060. Let m = 697 - b. Determine s, given that -7*s**3 + 5*s**4 + 1 + s - 27/4*s**m = 0.
-1/2, 2/5, 2
Let z(w) be the second derivative of w**8/2240 - w**6/60 + 49*w**4/12 - 2*w + 34. Let d(r) be the third derivative of z(r). Suppose d(h) = 0. Calculate h.
-2, 0, 2
Let j = -5539 + 5578. Let c(o) = o**2 - o - 3. Let b be c(3). Factor -j*p + 125 + b*p - 233 - 3*p**2.
-3*(p + 6)**2
Factor 1/3*w**2 + 5/3*w - 104/3.
(w - 8)*(w + 13)/3
Let w(m) be the third derivative of m**8/840 - 11*m**7/525 + 17*m**6/150 - 23*m**5/75 + 29*m**4/60 - 7*m**3/15 - 6669*m**2. Let w(s) = 0. Calculate s.
1, 7
Let d(s) be the second derivative of 1/120*s**5 + 0*s**2 - 15*s - 17/6*s**3 + 0 + 0*s**4 - 1/180*s**6. Let g(h) be the second derivative of d(h). Factor g(t).
-t*(2*t - 1)
Suppose -16*m + 21*m = 0. Suppose -3*i + 11*i = m. Factor 10/3*b**2 + 20/3*b**3 + 5*b**4 - 1/3 + 4/3*b**5 + i*b.
(b + 1)**4*(4*b - 1)/3
Let x(i) be the first derivative of 4*i**6/15 + i**5/10 - 2*i**4/3 - i**3/3 + 76*i + 70. Let o(v) be the first derivative of x(v). Factor o(h).
2*h*(h - 1)*(h + 1)*(4*h + 1)
Let w = 1155 + -1157. Let v be ((0/(-10))/7)/w. Let -2/5*z**4 - 2/5*z**5 + 2/5*z**3 + 0*z + 2/5*z**2 + v = 0. What is z?
-1, 0, 1
Suppose 4*o + 3*b - 112 = -b, 0 = 3*o - 4*b - 56. Suppose -x + 4*c - 20 = -2*x, 3*c - o = -3*x. Determine v, given that -18*v + v**2 - x*v**2 + 0*v = 0.
-6, 0
Suppose 5*q - 2*q = 18. Let z = -49038 + 49041. Suppose q*k**2 - 1/3*k**z - 36*k + 72 = 0. What is k?
6
Let t = 17309/34614 + -1/17307. Factor 0*v + 0 - t*v**3 + v**2.
-v**2*(v - 2)/2
Suppose 0 = -4*x - 23 + 31. Let p be -3 + x/(2/25). Factor -g**3 - 6*g**2 - g**2 + 6 - 11*g**2 + p*g**2 + 11*g.
-(g - 6)*(g + 1)**2
Let l be 366/15 + (-88)/220. Determine k, given that l*k**2 + 594*k - 2 + 10*k**2 - 626*k = 0.
-1/17, 1
Suppose -9 = 3*v, -5*v = -2*f - 3*f + 30. Let j be f + (-10)/(-1) + 0 + 1. Determine w so that 26*w**2 - 6*w + 5 - w**2 - j*w - 10*w**3 = 0.
1/2, 1
Let t(x) be the third derivative of 1/80*x**5 + 0*x**3 + 0*x**4 + 0 + 1/840*x**7 - 1/96*x**6 + 1/1344*x**8 + 0*x - 53*x**2. What is m in t(m) = 0?
-3, 0, 1
Let b(d) be the first derivative of d**4/6 + 10*d**3/9 - 14*d**2/3 + 1342. Factor b(j).
2*j*(j - 2)*(j + 7)/3
Let r(o) be the first derivative of -5*o**4/4 - 130*o**3/3 + 475*o**2/2 + 21660*o + 256. Find k, given that r(k) = 0.
-19, 12
Determine b so that -262/3*b - 7/2*b**2 + 25/6 = 0.
-25, 1/21
Let k(n) be the first derivative of -2*n**6/15 + n**5 + 13*n**4/3 + 14*n**3/3 - 68*n - 276. Let z(g) be the first derivative of k(g). Solve z(v) = 0.
-1, 0, 7
Suppose 4*r + 3*u - 43 = 0, 3*r + 3*u + 11 - 44 = 0. What is s in 3*s**5 + 16*s**5 - 20*s**2 - 15*s**3 + 20*s - 14*s**5 + r*s**4 = 0?
-2, 0, 1
Let t(k) = -3*k**2 - 9738*k - 7902384. Let j(x) = -21*x**2 - 68166*x - 55316687. Let i(u) = 3*j(u) - 22*t(u). Factor i(d).
3*(d + 1623)**2
Suppose 2*d - 17 = -3*t, 3*t = 2*d + 2*d - 7. Find u such that 8*u**3 - 4*u**2 + 239*u**4 - 118*u**d - 116*u**4 = 0.
-2, 0, 2/5
Suppose -3*h = -42*h + 156. Suppose 16 + h*d**3 + 7*d**2 - 120*d + 152*d + 13*d**2 = 0. Calculate d.
-2, -1
Let v(c) = 15*c**4 - 208*c**3 + 1386*c**2 - 1193*c + 7. Let m(f) = 52*f**4 - 728*f**3 + 4852*f**2 - 4176*f + 24. Let w(h) = -7*m(h) + 24*v(h). Factor w(q).
-4*q*(q - 15)*(q - 10)*(q - 1)
Let j = -2 - -7. Suppose -5*b = -3*s + 7*s - 34, 2*s = j*b - 28. Factor -b*w + 0 - 3/2*w**2.
-3*w*(w + 4)/2
Let c(k) be the third d