t o(g) be the second derivative of -g**5/4 - 25*g**4/4 - 105*g**3/2 - 245*g**2/2 - 23*g + 7. Factor o(d).
-5*(d + 1)*(d + 7)**2
Let f(v) be the first derivative of v**5/25 + 3*v**4/4 + 23*v**3/5 + 97*v**2/10 + 42*v/5 + 376. Suppose f(w) = 0. What is w?
-7, -6, -1
Let h(t) be the first derivative of 3/5*t**5 + 9/2*t**4 - 9*t**2 + 4*t**3 - 15*t + 61. Let h(b) = 0. Calculate b.
-5, -1, 1
Let p(v) be the third derivative of -34*v**2 + 0 + 1/18*v**4 + 0*v**3 + 0*v - 1/45*v**5 + 1/360*v**6. Factor p(o).
o*(o - 2)**2/3
Let b(v) be the first derivative of -20*v**2 - 51 - 5/3*v**3 - 80*v. Factor b(j).
-5*(j + 4)**2
Determine j, given that -71*j - 24*j**3 + 78*j**2 + 4*j**5 + 10*j**2 - 25*j - 12*j**4 + 24*j**2 = 0.
-3, 0, 2
Suppose 1115*n = 1126*n. Factor n + 6/7*o**2 + 0*o - 33/7*o**3.
-3*o**2*(11*o - 2)/7
Let t be (4221/(-5))/(55/(-110)). Let u = -1686 + t. What is w in -16/5 + 32/5*w - u*w**2 = 0?
2/3, 2
Let w be (0 - 114) + 3 + 1. Let z be (-11)/w - 33/(-30). Suppose -2 + z*d**2 - 28/5*d = 0. Calculate d.
-1/3, 5
Let w = -401 + 403. Determine v, given that 2 + 22*v**2 - w*v**2 - 6 - 7 - 4*v + 7 - 12*v**3 = 0.
-1/3, 1
Let y(b) be the first derivative of -18/7*b**2 + 17 + 9/7*b**4 - 10/7*b**3 + 33/7*b - 3/35*b**5. Solve y(l) = 0.
-1, 1, 11
Let y(u) be the third derivative of 0 + 0*u - 1/210*u**5 + 61*u**2 + 4/21*u**3 - 1/28*u**4. Suppose y(f) = 0. Calculate f.
-4, 1
Let x be 100/105 + (-54)/81. Let w = 40 - 278/7. Suppose -w*i + 0 - x*i**2 = 0. What is i?
-1, 0
Factor -56*p - 20*p**2 - 196/5.
-4*(5*p + 7)**2/5
Let x(b) be the first derivative of -b**4/2 + 10*b**3/3 + 46*b**2 + 80*b - 1651. Determine t so that x(t) = 0.
-4, -1, 10
Let o be (30/20)/(-3) - (-1316)/1064. Factor 4/19 + 10/19*q - o*q**2.
-2*(q - 1)*(7*q + 2)/19
Let u(a) be the second derivative of a**4/10 - 140*a**3 + 73500*a**2 - 9*a + 47. Factor u(p).
6*(p - 350)**2/5
Let r(z) be the third derivative of -1/630*z**7 + 0 - 1/60*z**6 + 0*z**3 + 0*z - 1/12*z**4 + 135*z**2 - 11/180*z**5. Factor r(d).
-d*(d + 1)*(d + 2)*(d + 3)/3
Let t(f) be the first derivative of -16*f**4 + 416*f**3 - 2322*f**2 - 14792*f - 450. Suppose t(v) = 0. Calculate v.
-2, 43/4
Factor -100 + 105*z + 15/2*z**3 + 125/2*z**2.
5*(z + 4)*(z + 5)*(3*z - 2)/2
Let n(x) = 7*x**2 - 8*x. Let v(y) = -3*y**2 + 4*y. Suppose 3*t - 12 = -3*u, -t + 3*t + 3*u = 8. Let m(q) = t*n(q) + 10*v(q). What is d in m(d) = 0?
0, 4
Solve 1050625/8 + 1/8*t**2 - 1025/4*t = 0 for t.
1025
Factor -12*i**3 + 540*i + 1/2*i**4 + 2025/2 + 27*i**2.
(i - 15)**2*(i + 3)**2/2
Let q = 8 + 40. Let i be 512/q*9/2. Factor 0*u**2 + i*u**3 - 28*u**4 + 6*u**2 + 8*u**2 + 2*u**2.
-4*u**2*(u - 2)*(7*u + 2)
Let a(p) be the first derivative of 3/11*p**4 + 0*p + 6/55*p**5 - 42/11*p**3 + 54/11*p**2 - 28. Factor a(f).
6*f*(f - 3)*(f - 1)*(f + 6)/11
Let w = 5/15458 + 30901/46374. Let v be ((-6)/(-4))/(6/8). Factor 4/3*j + w*j**3 + 2*j**v + 0.
2*j*(j + 1)*(j + 2)/3
Factor 0*f**2 - 5*f**2 + 1592644 + 385*f - 3286*f - 2147*f + 9*f**2.
4*(f - 631)**2
Let p = -1272 + 1272. Let z(s) be the first derivative of 1/6*s**6 + 0*s**5 + 2/3*s**3 + p*s + 0*s**2 + 7 - 3/4*s**4. Factor z(n).
n**2*(n - 1)**2*(n + 2)
Let 3774*h - 3058722 + 6234*h - 3201282 - 23*h**2 - 19*h**2 + 38*h**2 = 0. What is h?
1251
Let y(g) be the second derivative of g**7/84 - 97*g**6/30 + 307*g**5 - 9834*g**4 - 91476*g**3 - 287496*g**2 - 3*g + 427. Factor y(s).
(s - 66)**3*(s + 2)**2/2
Let g(n) be the first derivative of 4*n**5/25 + 7*n**4/6 + 32*n**3/15 - 3*n**2/5 - 563. Factor g(i).
2*i*(i + 3)**2*(6*i - 1)/15
Let q(u) be the third derivative of -62*u**2 + 1/160*u**6 + 37/32*u**4 + 0 - 9/4*u**3 + 0*u - 1/4*u**5. Find p such that q(p) = 0.
1, 18
Let x = -279095/3 - -93043. Factor x*f + 32/3*f**2 + 2*f**3 + 8/3.
2*(f + 1)*(f + 4)*(3*f + 1)/3
Factor 2/15*x**2 - 8/5*x - 6.
2*(x - 15)*(x + 3)/15
Suppose 5*w = -2*c - 52, -2*c = 4*w + 25 + 23. Let v be c/(-4) - 60/(-84). Factor -15/7*g**2 - v*g - 6/7.
-3*(g + 2)*(5*g + 1)/7
Let y = 62772 + -251085/4. Factor -9/4*c + 9/2*c**2 - y*c**3 - 15/2.
-3*(c - 5)*(c - 2)*(c + 1)/4
Factor -3*t**3 + 5281*t + 12264*t + 31*t**2 - 3*t**3 + 99825 + 684*t**2 + t**3.
-5*(t - 165)*(t + 11)**2
Let b(n) = 187 + 2358*n**2 + 1617*n**2 - 2375*n + 173. Let d(o) = 497*o**2 - 297*o + 45. Let t(c) = 3*b(c) - 25*d(c). Factor t(i).
-5*(10*i - 3)**2
Let q = -1583/42 - -233/6. Find i such that -2/7*i**3 + q*i + 8/7*i**2 - 32/7 = 0.
-2, 2, 4
Let r = 802 - 800. Solve -5*u**r - 36 + u**2 - 12*u - 19*u + 15*u - 24*u = 0.
-9, -1
Let m be 187/2 - (2 - (-1)/(-2)). Factor 147*k + m*k**3 + 480*k**2 + 22*k**4 - 95*k - 18*k**4 - 628*k.
4*k*(k - 1)*(k + 12)**2
Let i(r) be the second derivative of -63*r**5/10 + 50*r**4 + 77*r**3/3 - 10*r**2 + 24*r - 166. Determine p so that i(p) = 0.
-1/3, 2/21, 5
Let m(t) = 5*t + 23. Let d be m(-4). Determine p so that -20*p**2 - 4*p - 12 + 97*p**d + 0*p - 93*p**3 + 32 = 0.
-1, 1, 5
Let g = 30536 + -30532. Let j(b) be the third derivative of 0 - 2*b**2 - 49/60*b**g + 0*b**3 + 0*b + 7/75*b**5 - 1/300*b**6. Factor j(f).
-2*f*(f - 7)**2/5
Let l be (-56)/(-476) + ((-134)/(-17) - -1). Let w be (-6 + (l - 3))/(-1). Factor 4/13*m**2 + 0 - 6/13*m**3 + 2/13*m**4 + w*m.
2*m**2*(m - 2)*(m - 1)/13
Let s(m) be the first derivative of -2*m**3/33 + 76*m**2/11 + 810*m/11 - 672. Solve s(c) = 0.
-5, 81
Let u be ((-54)/(-30))/3*10. Suppose 9*k + u*k + 5*k = 0. Factor k*a - 1/7 + 1/7*a**2.
(a - 1)*(a + 1)/7
Suppose 462*n - 3154 - 6085 = -923. Let v(b) be the first derivative of -12*b + 33 - 13*b**3 - 9/2*b**4 - 3/5*b**5 - n*b**2. Find i such that v(i) = 0.
-2, -1
Let d be (9 + 1255/(-140))*(1 + 29). Let p = d - -67/42. Factor -p*z**3 + 2/3*z**5 - 4/3 + 0*z**4 + 4/3*z**2 + 2*z.
2*(z - 1)**3*(z + 1)*(z + 2)/3
Let h(u) be the third derivative of -2149*u**5/270 - u**4/54 + 5537*u**2. Find t, given that h(t) = 0.
-2/2149, 0
Let x = 5 + -5. Suppose 12*a - 9*a - 57 = x. Find f, given that 7*f**3 + 7*f - 4*f**2 - a*f**3 - 2 + 8*f**3 = 0.
-2, 1/2
Suppose 27 - 5 = 2*s + 4*d, 4*d - 19 = -s. Suppose -4*v = o - 8, 2 = -s*v + v - 2*o. Factor 15*x**v + 5*x**3 - 2*x - 18*x**3.
2*x*(x - 1)*(x + 1)
Let a be 18/24*12 + 5/(-140)*244. Factor 0 + 8/21*f**2 - 2/21*f**3 - a*f.
-2*f*(f - 3)*(f - 1)/21
Suppose -5 + 5 + 64*i**2 + 51*i**3 + 46*i + 4*i**4 + 25*i**3 - 190*i = 0. Calculate i.
-18, -2, 0, 1
Let y be (1 + -2)*(-1 - 16). Let q(a) be the second derivative of y*a + 0 - 1/90*a**6 + 1/12*a**4 - 1/18*a**3 + 1/60*a**5 - 1/3*a**2. Factor q(u).
-(u - 2)*(u - 1)*(u + 1)**2/3
Let n(y) be the first derivative of -y**7/14 - 13*y**6/40 - 9*y**5/80 + 13*y + 26. Let t(i) be the first derivative of n(i). Solve t(c) = 0 for c.
-3, -1/4, 0
Let x(m) be the first derivative of -m**4/2 + 14*m**3/3 + 10*m**2 - 32*m + 1406. Factor x(t).
-2*(t - 8)*(t - 1)*(t + 2)
Let n be (-80)/(-6)*(-111)/(-370) + (-21)/12. Solve 0 - 3/8*z**2 - n*z = 0.
-6, 0
Let g(x) = 14*x**2 - 2423*x - 3. Let o(z) = 11*z**2 - 2422*z - 2. Let u(m) = -2*g(m) + 3*o(m). Factor u(w).
5*w*(w - 484)
Let k be ((-147)/13377)/(8/(-1232)). Suppose 16/13 + k*w**2 - 2/13*w**4 + 36/13*w + 0*w**3 = 0. What is w?
-2, -1, 4
Let j be (-17271)/30 - (-12)/(540/9). Let v = j - -577. Suppose 0*l + v*l**2 + 0 - 3/2*l**3 = 0. What is l?
0, 1
Let r(u) be the first derivative of -2*u**5/55 - 3*u**4/22 + 4*u**2/11 - 1124. Factor r(h).
-2*h*(h - 1)*(h + 2)**2/11
Let u = 70580 + -70580. Determine i so that -12/7*i - 2/7*i**2 + u = 0.
-6, 0
Suppose 0 = 40*j - 38*j - 74. Factor -12*c**2 - j*c + 13*c + 2260*c**4 - 2257*c**4 + 6*c**3.
3*c*(c - 2)*(c + 2)**2
Let n = 190 - 186. Factor -35*q**2 + 20*q**3 + 1194*q**n + 16*q - 1198*q**4 + 3*q**2.
-4*q*(q - 2)**2*(q - 1)
Let s(b) = -341*b**3 - 1566*b**2 - 929*b - 144. Let c(k) = -171*k**3 - 783*k**2 - 465*k - 72. Let i(u) = 5*c(u) - 3*s(u). Factor i(a).
3*(a + 4)*(7*a + 2)*(8*a + 3)
Suppose 10*p = -8*p + 77 - 23. Let n(z) be the first derivative of -75/8*z + 26 - 15/16*z**4 + 15/8*z**2 + p*z**3 + 3/40*z**5. Factor n(x).
3*(x - 5)**2*(x - 1)*(x + 1)/8
Let v(f) be the second derivative of -f**3 + 11/12*f**4 + 14*f - 1/10*f**6 + 1/42*f**7 - 3/20*f**5 + 0*f**2 - 5. Suppose v(k) = 0. Calculate k.
-2, 0, 1, 3
Let n(u) be the second derivative of -u**7/14 + 13*u**6/5 - 81*u**5/2 + 350*u**4 - 3625*u**3/2 + 5625*u**2 - 525*u - 2. Let n(r) = 0. What is r?
5, 6
Let w(