 92*q**2 - 1562.
5*(q - 1)*(q + 87)
Suppose 0*d - 3*d = -9. Let w = 2033 - 2029. Factor 912 - 912 - w*n**d - 4*n**4 + 8*n**2.
-4*n**2*(n - 1)*(n + 2)
Let c(l) = -l**2 + 2*l + 35. Let p(s) = -5*s**2 - 46*s - 589. Let y(z) = 4*c(z) - p(z). Solve y(t) = 0 for t.
-27
Let a be ((-50)/(-20))/((-5)/(-4)). Factor -112*o**a + 398*o - 280*o + 6*o**3 - 4*o**3 + 1450*o.
2*o*(o - 28)**2
Let s = -55 + 58. What is z in -4900 + 76*z + 125*z - z**2 + 79*z - s*z**2 = 0?
35
Let n(a) be the third derivative of 0 + 3*a**2 - 5/2*a**4 + 0*a**3 + 0*a + 1/12*a**5. Factor n(o).
5*o*(o - 12)
Let a(m) = -m**3 + 19*m**2 - 12*m + 22. Let b be a(18). Let t be (-10)/(b/3)*8/(-6). Suppose -18/13*n - 10/13*n**2 + t = 0. What is n?
-2, 1/5
Find p such that 78/5*p - 2/5*p**2 - 648/5 = 0.
12, 27
Let p(y) be the second derivative of 2*y + 0*y**2 - 2*y**3 - 10/9*y**4 - 28 - 13/60*y**5 - 1/90*y**6. Factor p(o).
-o*(o + 2)**2*(o + 9)/3
Solve 94/7*d + 36/7 + 2/7*d**4 + 82/7*d**2 + 26/7*d**3 = 0 for d.
-9, -2, -1
Factor -21*l + 210 - 192*l - 76*l**4 + 30*l**4 + 20*l**4 + 213*l**3 + 23*l**4 - 207*l**2.
-3*(l - 70)*(l - 1)**2*(l + 1)
Suppose 907 - 482 = -15*w + 470. Let j(m) be the first derivative of 3/5*m**5 + 23 + 0*m - m**w + 3*m**2 - 3/2*m**4. What is t in j(t) = 0?
-1, 0, 1, 2
Let n(i) = 2*i**4 - 7*i**3 - 5*i**2 - 8*i. Let g(m) = 83*m - 5*m**3 + 4*m**3 - 84*m. Let v(q) = 6*g(q) - n(q). Factor v(h).
-h*(h - 2)*(h + 1)*(2*h + 1)
Suppose -2*t + 49 = 1. Let y = t + -15. Factor 253*n**3 - n**2 - y*n**2 - 248*n**3 + 5*n.
5*n*(n - 1)**2
Let u(p) be the first derivative of -2*p**3/3 - 752*p**2 - 282752*p - 1015. Suppose u(j) = 0. What is j?
-376
Let q(f) be the third derivative of -2*f + 1/2*f**4 - 11*f**2 + 0 + 0*f**3 + 11/30*f**5 + 1/10*f**6 + 1/105*f**7. Factor q(i).
2*i*(i + 1)*(i + 2)*(i + 3)
Factor 35103026*u + 5*u**5 - 3640*u**3 + 7440*u**2 + 425*u**4 - 35103026*u.
5*u**2*(u - 4)**2*(u + 93)
Let -2913*s**2 + 575*s**4 + 16240*s**3 - 8316*s**2 + 5*s**5 - 5140*s**2 - 451*s**2 = 0. What is s?
-58, 0, 1
Determine j so that -1444/3 + 1684*j + 7/3*j**2 = 0.
-722, 2/7
Let f = 1507/8 - 7247/40. Find n, given that 3/5*n**2 - f - 33/5*n = 0.
-1, 12
Let r(i) = 26*i**2 + 343*i + 54. Let q(n) = -12*n**2 - 172*n - 24. Let f(c) = 9*q(c) + 4*r(c). Determine t so that f(t) = 0.
-44, 0
Let r = 316 + -314. Suppose -g - 3 = -r*m, -4*g + 8*g - 2 = m. Factor -9/2*w - m*w**2 - 5/2.
-(w + 1)*(4*w + 5)/2
Suppose 8*y - 36 = -12. Let a(d) be the first derivative of 0*d + 0*d**2 + d**5 - 3 + 5/4*d**4 + 0*d**y. Factor a(g).
5*g**3*(g + 1)
Let g(m) = 28*m - 616. Let i be g(22). Let d(w) be the third derivative of 1/6*w**3 + 0 + 12*w**2 + i*w - 13/24*w**4 + 169/240*w**5. Factor d(a).
(13*a - 2)**2/4
Let y(n) be the second derivative of n**4/42 - 754*n**3/21 + 142129*n**2/7 - 3553*n. Factor y(h).
2*(h - 377)**2/7
Let y(b) = 2*b**2 - 14*b + 34 + 2*b**2 - 16 - 5*b**2. Let u be y(-15). Find p, given that -3*p**2 + p**2 - 2*p + 3*p - 13*p**u + 14*p**3 = 0.
0, 1
Let f(t) be the second derivative of t**6/60 - 9*t**5/10 + 121*t**4/8 - 236*t**3/3 - 336*t**2 + 2*t - 2765. Determine j, given that f(j) = 0.
-1, 8, 21
Let n(c) be the third derivative of c**8/56 - c**7/15 - 7*c**6/60 + c**5/10 + 2054*c**2. Find k such that n(k) = 0.
-1, 0, 1/3, 3
Let w(j) = j**3 - 3*j**2 + 3. Suppose 0*z + 6*z - 18 = 0. Let t be w(z). Factor -7*r**2 - 8*r**2 + 5*r**t + r + 13*r - 4*r.
5*r*(r - 2)*(r - 1)
Let r(f) = -70*f + 10013. Let a be r(143). Let l = -5/8 - -127/152. Factor -l*q**4 + 4/19 + 16/19*q**2 - 2/19*q**5 + 14/19*q + 4/19*q**a.
-2*(q - 2)*(q + 1)**4/19
Let q(y) = y**2 - 8*y - 18. Let s be q(10). Suppose -5 = r + 4*d - s*d, -2*r - 4 = 2*d. Factor -4*z**2 + 5*z**2 - 3*z + 0*z - r + 3*z**3 + 0*z**2.
(z - 1)*(z + 1)*(3*z + 1)
Let w(v) = 24*v**3 + 40*v**2 - 7*v - 7. Let t = -157 + 150. Let f(p) = 11*p**3 + 20*p**2 - 3*p - 3. Let b(x) = t*f(x) + 3*w(x). Let b(y) = 0. Calculate y.
-4, 0
Let g(r) = 7*r**3 - 3*r**2 + 19*r + 5. Let h be g(5). Let x = 902 - h. Factor -18*v**x + 2/3*v**3 + 162*v - 486.
2*(v - 9)**3/3
Let f(p) be the first derivative of -1/20*p**5 - 31 - 2*p**2 - 4/3*p**3 - 5/12*p**4 - 29*p. Let y(v) be the first derivative of f(v). Factor y(j).
-(j + 1)*(j + 2)**2
Let -2000*p**3 + 14*p**2 - 48*p + 662*p**3 + 671*p**3 + 666*p**3 = 0. Calculate p.
0, 6, 8
Let m(f) be the first derivative of 15/2*f**5 + 0*f**2 + 0*f - 134 + 8*f**3 + 3/4*f**6 + 21*f**4. Factor m(i).
3*i**2*(i + 4)**2*(3*i + 1)/2
Let y(g) be the second derivative of -g**4/126 - 94*g**3/21 + 285*g**2/7 + 9755*g. Find h such that y(h) = 0.
-285, 3
Let i(d) be the first derivative of 0*d + 5/3*d**3 + 15*d**2 - 78. Factor i(u).
5*u*(u + 6)
Let n(c) be the second derivative of c**7/70 + 23*c**6/50 + 18*c**5/5 - 36*c**4/5 - 1844*c. Factor n(b).
3*b**2*(b - 1)*(b + 12)**2/5
Let h(b) = 2*b**2 + 10684*b - 1890392. Let z(a) = -a**2 - 3562*a + 630131. Let w(j) = -6*h(j) - 17*z(j). Factor w(u).
5*(u - 355)**2
Determine m so that 0 + 184/5*m**2 - 1/5*m**4 + 59/5*m**3 + 124/5*m = 0.
-2, -1, 0, 62
Let u(b) be the first derivative of 7/12*b**4 + 1/15*b**5 + 0*b - 2*b**2 + 4/9*b**3 - 9. Factor u(l).
l*(l - 1)*(l + 2)*(l + 6)/3
Let a be 256086/11451 - 1*22. Solve 86/11*v**3 - 30/11*v**4 + a*v**5 + 72/11*v - 16/11 - 116/11*v**2 = 0 for v.
1/2, 1, 2
Let v = 68 - 63. Suppose 0*n - v*d - 304 = -3*n, -d + 292 = 3*n. Factor 9*a**2 + 3*a**5 - 7*a**4 - n*a - 2*a**4 + 92*a + 3*a**3.
3*a*(a - 2)*(a - 1)**2*(a + 1)
Let x = -308 - -322. Suppose -2*t = -r - 1, 17*t + x = 18*t + 4*r. Factor 64/7*b**t + 4/7*b**4 + 0*b - 32/7*b**3 + 0.
4*b**2*(b - 4)**2/7
Let s = 261/13 + -5159/312. Let q(p) be the third derivative of 1/6*p**5 + 5/3*p**4 + 0 - s*p**6 + 2*p**2 - 3*p + 0*p**3 + 1/2*p**7. What is t in q(t) = 0?
-2/7, 0, 1/3, 4
Let h(z) = -z**3 + 4*z**2 - 4*z + 2. Let p be h(2). Let u = -897/511 - -970/511. Factor 1/7*a + u + 1/7*a**4 + 1/7*a**5 - 2/7*a**p - 2/7*a**3.
(a - 1)**2*(a + 1)**3/7
Find c such that -123821*c - 652 + 61807*c + 5*c**3 + 30*c**2 - 1558 + 60949*c = 0.
-17, -2, 13
Let l be ((-6)/(-5))/(4/(-1 + 21)). Let a be (-2)/((-8)/l) - (-6)/12. Factor -15*u - 20 + 0*u**2 - 5*u**a - 10*u.
-5*(u + 1)*(u + 4)
Let i(m) be the third derivative of 5*m**2 - 1/105*m**7 - 1/336*m**8 - m - 1/3*m**3 + 1/60*m**6 - 1/24*m**4 + 1/15*m**5 + 0. Factor i(r).
-(r - 1)**2*(r + 1)**2*(r + 2)
Let v(o) be the second derivative of o**6/6 + 45*o**5/2 - 2405*o**4/12 - 475*o**3 - 4*o + 1164. Factor v(h).
5*h*(h - 6)*(h + 1)*(h + 95)
Let g(v) be the third derivative of -v**6/60 + 32*v**5/5 - 735*v**4 - 38416*v**3/3 - 24*v**2 - 21*v. Factor g(y).
-2*(y - 98)**2*(y + 4)
Let d be 1 + (3 + 0)*(0 - -1). Suppose -4*w - 7 = -0*o + 3*o, d*o = -4*w - 12. Let -8*r**3 - 14*r**2 + 29*r**w + 9 + 5*r**3 - 21*r = 0. What is r?
1, 3
Let b be 49*14/196*(1 - 177/(-63)). Factor 400/3 - b*o + 1/3*o**2.
(o - 20)**2/3
Let g be 18248/(-6)*(-109)/436. Let q = g - 757. Find y, given that -2/3*y + 8/3*y**5 - 2*y**3 - q*y**4 + 0 + 10/3*y**2 = 0.
-1, 0, 1/4, 1
Let x = 124 - 116. Let o(p) = -6*p + 53. Let g be o(x). Let 3*v**g - v**5 + 54*v**3 - 22*v**4 + 16*v**3 - 50*v**2 = 0. What is v?
0, 1, 5
Factor -118/7*s + 6 - 26/7*s**2 + 6/7*s**3.
2*(s - 7)*(s + 3)*(3*s - 1)/7
What is y in 1129*y**3 + 4765*y**2 + 158*y**5 + 315 + 2274*y**4 - 238*y**5 - 7354*y**4 + 2525*y - 3574*y**3 = 0?
-63, -1, -1/4, 1
Let v(o) be the second derivative of 13 - 3*o + o**2 - 7/36*o**3 + 1/72*o**4. Factor v(d).
(d - 4)*(d - 3)/6
Let u(a) be the second derivative of -a**5/10 - a**4/6 + a**3/3 + a**2 + 382*a. Factor u(m).
-2*(m - 1)*(m + 1)**2
Suppose 187*f - 1298 = -363. Determine d, given that 9/5*d**3 - 23*d**2 - 1/5*d**f + 7/5*d**4 + 0 + 20*d = 0.
-4, 0, 1, 5
Let k be (72/21)/(-3)*63/(-54). Let o = -2/825 + 4406/2475. Factor 4/9*h**2 + k + o*h.
4*(h + 1)*(h + 3)/9
Suppose 76 = -2*p - 26. Let n = p - -56. Determine z, given that -n*z + 8*z - 4*z**3 + z**3 = 0.
-1, 0, 1
Let a = -604934/5 - -120994. Determine r so that -2*r**3 - 54/5*r + 27/5 + 1/5*r**4 + a*r**2 = 0.
1, 3
Let p(v) = -v - 7. Let f be p(-11). Suppose -l + 4*h = -10, f*l - h - 4*h = 18. Solve -46*q**l + 50*q**2 + 0*q**3 + q**3 - 4*q - q**4 + 0*q**4 = 0 for q.
-2, 0, 1, 2
Let i(y) be the first derivative of -y**6/5 - 296*y**5/25 + 737*y**4/10 - 2044*y**3/15 + 44*y**2 + 432*y/5 + 7324. Suppose i(h) = 0. Calc