**3 - n**2.
2*(n - 1)*(n + 1)**2
Let p be -5 - 26*2/(-4) - 1. Find n, given that 79 + 14 + p + 4*n**2 + 44 + 48*n = 0.
-6
Let g(w) be the first derivative of 0*w - 1/45*w**6 - 95 - 1/15*w**2 - 1/5*w**4 + 8/75*w**5 + 8/45*w**3. Let g(r) = 0. Calculate r.
0, 1
Factor -z**3 - 2*z**2 - 64*z**4 + 4*z**2 + 63*z**4 + 10*z**2.
-z**2*(z - 3)*(z + 4)
Let o(m) = 5*m**3 + m**2 - m - 2. Let f be 266/(-28) - -11 - (-2)/(-4). Let u be o(f). Factor 0 - 3*z**u + 3/2*z**4 - 3/2*z**2 + 3*z.
3*z*(z - 2)*(z - 1)*(z + 1)/2
Let w be (-119)/(-11) - (5 + (-456)/88). Solve 11*g**2 + 11*g**2 - w*g - g**3 - 10*g**2 = 0.
0, 1, 11
Suppose a + 3*t + 5 = 3*a, -2*a - 2*t = -10. Suppose 5*v + 6 = -5*i + i, -a = 4*i + 4*v. Find j such that j**3 - 3 - 3*j + 0 + 3*j**3 + i + 2*j**2 - j**5 = 0.
-1, 1, 2
Let y = 123409 - 123406. Solve 0 + 30*h**y + 2/7*h**4 + 1050*h**2 + 12250*h = 0 for h.
-35, 0
Let f(y) be the second derivative of 2*y**6/15 + 72*y**5/5 - 74*y**4/3 - 48*y**3 + 146*y**2 - 684*y - 4. Factor f(d).
4*(d - 1)**2*(d + 1)*(d + 73)
Let n(h) be the third derivative of 2/5*h**6 + 0 + 0*h**3 + 0*h**4 - 54*h**2 + 8/15*h**5 + 1/84*h**8 + 0*h + 4/35*h**7. Solve n(q) = 0.
-2, 0
Factor -1333*t + 233130 - 28826 - 5*t**2 - 475*t - 21*t**2 + 30*t**2.
4*(t - 226)**2
Let z(y) = y**2 + 7*y + 8. Let q be z(8). Suppose 4*k - q = -116. Determine i, given that -2/17 + 2/17*i**2 + 4/17*i - 4/17*i**k = 0.
-1, 1/2, 1
Let c(j) be the third derivative of -j**5/60 - 13*j**4/6 + 18*j**3 - 722*j**2 + 2. Factor c(k).
-(k - 2)*(k + 54)
Let q = -3280 + 22961/7. Let v(j) be the second derivative of -1/4*j**4 - 13*j - q*j**7 + 0*j**3 + 0*j**5 + 0 + 0*j**2 + 3/10*j**6. Factor v(n).
-3*n**2*(n - 1)**2*(2*n + 1)
Let z(t) = t**4 - 5*t**3 - 8*t**2 + 9*t. Let d(i) = 4*i**4 - 26*i**3 - 38*i**2 + 46*i. Let x(k) = -3*d(k) + 14*z(k). Factor x(y).
2*y*(y - 1)*(y + 2)*(y + 3)
Factor 4*v**5 - 2708*v**2 + 64*v**3 + 2708*v**2 + v + 32*v**4 - v.
4*v**3*(v + 4)**2
Let w = -271255 - -2441296/9. Factor -2 + a - w*a**2.
-(a - 6)*(a - 3)/9
Let j(u) = 100*u**2 - 11815*u + 629830. Let r(t) = -9*t**2 + 1074*t - 57257. Let p(f) = -4*j(f) - 45*r(f). Solve p(l) = 0.
107
Let j(g) be the third derivative of 19/96*g**4 - 44*g**2 + 3/8*g**3 + 1/480*g**6 + 0 + 0*g + 11/240*g**5. Find t such that j(t) = 0.
-9, -1
Let y(n) be the first derivative of -3/5*n - 1/15*n**3 - 2/5*n**2 - 3. Let y(w) = 0. Calculate w.
-3, -1
Let q(i) be the first derivative of -1/14*i**4 - 5 + 6050/7*i - 218/21*i**3 - 2915/7*i**2. Suppose q(h) = 0. What is h?
-55, 1
Factor -4/5*b**2 - 780 - 64*b.
-4*(b + 15)*(b + 65)/5
Let h be 15/10 - (1 + -2)/2. Factor 184*y**3 + 63*y**4 - 81*y**4 - 14*y - 490*y**h + 36*y + 78*y.
-2*y*(y - 5)**2*(9*y - 2)
Factor -4134*h - 4225*h - 4228*h + 12103*h + 4*h**2 - 5808.
4*(h - 132)*(h + 11)
Let h be (-6)/10 + (-196)/(-35). Suppose 10*w = h*w + 10. Factor 2*i**5 + 19*i**w - 20*i**3 - 7*i**5 + i**5 - 11*i**2 + 16*i**4.
-4*i**2*(i - 2)*(i - 1)**2
Let x be (4816/210 + -23)*-9. Solve 972/5 + 108/5*c + x*c**2 = 0.
-18
Let j(k) be the first derivative of -k**5/100 - 19*k**4/40 + 21*k**3/5 + 5*k**2/2 + 2*k - 43. Let g(l) be the second derivative of j(l). Factor g(c).
-3*(c - 2)*(c + 21)/5
Let z(s) be the second derivative of -1/36*s**4 + 37/18*s**3 + 0 + 109*s + 19/3*s**2. Factor z(l).
-(l - 38)*(l + 1)/3
Let c = 39511/180 + -439/2. Let y(v) be the third derivative of -c*v**6 + v**2 - 1/90*v**5 + 0*v + 0 + 5/36*v**4 - 1/3*v**3. What is m in y(m) = 0?
-3, 1
Suppose n = -2, 4*y - 4*n - 1380 = -0*y. Let -3*t**3 - y*t**2 + 340*t**2 + t**4 + 3*t + 2*t**4 = 0. What is t?
-1, 0, 1
Let w(l) be the first derivative of 1800/17*l - 960/17*l**2 - 124 + 122/51*l**3 - 1/34*l**4. Factor w(d).
-2*(d - 30)**2*(d - 1)/17
Let b(q) = -1 - 16 + 5*q + 29. Let d be b(-2). Find m such that -14 + 14 + 8*m + 25*m**2 + 3*m**d = 0.
-2/7, 0
Suppose -28 = -5*z + j, -j - 5 = 4*z - 22. Factor 91*s**2 + z*s**3 + 24*s + 6*s - 66*s**2.
5*s*(s + 2)*(s + 3)
Let q(k) be the third derivative of k**6/420 + 2*k**5/21 - k**4/84 - 20*k**3/21 - k**2 + 33. Suppose q(i) = 0. What is i?
-20, -1, 1
Let m be (-2880)/150*495/(-88). Determine f so that -m*f**2 + 324*f - 324 + 15*f**3 - 3/4*f**4 = 0.
2, 6
Let w(t) be the first derivative of 5*t**4/4 + 50*t**3/3 - 1250*t**2 + 15000*t + 2218. Determine n so that w(n) = 0.
-30, 10
Suppose 11*y + 562 - 1717 = 0. Let c be (-645)/y - 2*-1 - -5. Factor 2/7*t**2 - c + 4/7*t.
2*(t - 1)*(t + 3)/7
Let h(u) be the first derivative of -u**5 + 295*u**4/4 + 5*u**3/3 - 295*u**2/2 - 12558. Factor h(m).
-5*m*(m - 59)*(m - 1)*(m + 1)
Let n(t) be the third derivative of -1/24*t**5 + 4*t**2 + 0*t**3 + 2*t + 0 - 1/240*t**6 + 0*t**4. Factor n(g).
-g**2*(g + 5)/2
Let r(u) = 16*u - 234. Let q be r(15). Determine t so that -3*t**2 - 10*t**4 + q*t**3 + t**2 - 13*t**5 + 4*t**4 + 15*t**5 = 0.
0, 1
Let b be (297/(-55) + 6)*770/231. Factor -33/2*g - 3/2*g**b - 36.
-3*(g + 3)*(g + 8)/2
Suppose 12*z - h = 17*z - 15, 0 = -2*z - 2*h + 14. Determine q, given that -2*q**5 + 4*q**3 - z*q**5 - 1489*q**2 + 1489*q**2 = 0.
-1, 0, 1
Let z(i) be the second derivative of i**4/6 - 2698*i**3 + 16378209*i**2 - 13*i - 81. Determine j, given that z(j) = 0.
4047
Let s(o) be the first derivative of -5/3*o**3 + 5*o**2 + 0*o - 5/4*o**4 + 73. Factor s(x).
-5*x*(x - 1)*(x + 2)
Suppose 8*b = 13*b + 140. Let g = b + 30. Factor -2*n**2 + 61 + 60 - n - 21*n + 3*n**g.
(n - 11)**2
Let f(c) = 4*c - 108. Let r be f(32). Let m be 47/r + (-201)/268. Solve 0 + 4/5*g + 4/5*g**3 + m*g**2 = 0 for g.
-1, 0
What is f in 4*f**4 + 2*f**3 + 6 - 8*f**2 - 2 + 0 - f**5 + 1124*f - 1125*f = 0?
-1, 1, 4
Factor -r**5 - 968 - 1083 - 6*r**4 + 81*r + 54*r**2 + 2051.
-r*(r - 3)*(r + 3)**3
Let k = -70964 - -70966. Factor -2/3*d**3 - 70/3*d + 38/3*d**k + 34/3.
-2*(d - 17)*(d - 1)**2/3
Let v(c) be the second derivative of -65*c**3/6 + 195*c**2 + 37*c - 2. Let n be v(6). Factor n - 3/5*k - 1/5*k**2.
-k*(k + 3)/5
Factor -855 + 4168*o + 12503 + 5*o**3 - 353*o + 220*o**2 - 10*o**3 + 2562.
-5*(o - 58)*(o + 7)**2
Let k(l) be the second derivative of l**7/504 + l**6/24 + 45*l**4/4 - l**3/3 - 85*l. Let y(h) be the third derivative of k(h). Solve y(g) = 0 for g.
-6, 0
Let r be (7 - -7) + -15 + (-540)/(-140). Factor -64/7 - r*f**4 - 160/7*f**2 + 2/7*f**5 + 80/7*f**3 + 160/7*f.
2*(f - 2)**5/7
Let g(w) = -w**3 - 2*w**2 + 2*w + 4. Let i be g(0). Factor -4*q**4 - 45*q**3 - 10*q + 20*q**4 + 35*q**2 - 3*q**i - 5*q**5 + 12*q**4.
-5*q*(q - 2)*(q - 1)**3
Let k = -164217/5 - -32844. Determine o so that 7/10*o + 1/10*o**2 + k = 0.
-6, -1
Let s(x) be the second derivative of -x**6/225 - 19*x**5/150 - 13*x**4/90 + 29*x**3/15 - 18*x**2/5 - 5031*x. Let s(c) = 0. What is c?
-18, -3, 1
Let r(x) = -12*x - 35. Let f be r(-26). Factor -3*z**3 + 175 - f*z - 63*z**2 + 188 + 20*z - 40*z.
-3*(z - 1)*(z + 11)**2
Let j(t) be the first derivative of -t**6/36 - 4*t**5/15 + 5*t**4/8 + 25*t**3/9 - 11*t**2/3 - 12*t + 3354. Suppose j(s) = 0. Calculate s.
-9, -2, -1, 2
Let t = 33 + -88. Let n(s) = -4*s**2 - 81*s + 6. Let l(k) = 35*k**2 + 730*k - 55. Let i(g) = t*n(g) - 6*l(g). Factor i(u).
5*u*(2*u + 15)
Let y(g) be the third derivative of -g**5/90 + 355*g**4/6 - 126025*g**3 - 2*g**2 - 3*g + 176. Factor y(v).
-2*(v - 1065)**2/3
Let p(r) be the third derivative of -14*r**2 - 1/20*r**5 + 2 + 0*r - 2*r**3 - 5/8*r**4. Find t such that p(t) = 0.
-4, -1
Let h(j) = 15*j**3 + 4*j**2 - 53*j + 289. Let s be h(5). Let z = 45985/23 - s. Solve 10/23 - 2/23*r**2 - z*r = 0 for r.
-5, 1
Let i(j) be the third derivative of -j**8/1344 - 5*j**7/1008 - j**6/72 + 2*j**5/3 + 55*j**2. Let m(l) be the third derivative of i(l). Factor m(w).
-5*(w + 1)*(3*w + 2)
Let o = 141951 + -993653/7. Solve -8/7*v**4 + 0 + 2/7*v**5 - o*v**3 + 18/7*v + 24/7*v**2 = 0.
-1, 0, 3
Let h(l) be the first derivative of -86*l**2 + 25 - 3698*l - 2/3*l**3. Factor h(t).
-2*(t + 43)**2
Let m(o) = 5*o**2 - 4. Let w(s) = -s**2 - 2*s - 2. Let i be w(0). Let a be m(i). Factor -3*r**4 - r - a*r**2 + 22*r + 15*r**3 - 11*r**2 - 6.
-3*(r - 2)*(r - 1)**3
Let g(o) be the second derivative of o**7/5040 - 5*o**5/48 + o**4/6 - 67*o**3/6 + 16*o. Let v(r) be the third derivative of g(r). Factor v(f).
(f - 5)*(f + 5)/2
Let y = -731 - -736. Factor -f**4 + 0*f**y - 3*f**5 + 0*f**5 + 0*f**4 - 2*f**4.
-3*f**4*(f + 1)
Solve 76*b**4 + 1