Let m(w) = 54*w**2 + 60*w - 12. Let g(i) = 1. Let y(x) = 4. Let t(r) = -2*g(r) + y(r). Let z(n) = -2*m(n) + 4*t(n). Factor z(l).
-4*(3*l + 4)*(9*l - 2)
Factor 525/8 + 3/8*m**2 + 66*m.
3*(m + 1)*(m + 175)/8
Let x be (-5700)/(-125) - (5 + -1)*-3. Find r, given that -48/5*r + x*r**2 + 2/5 = 0.
1/12
Factor 3*t**3 - 414333 + 2697*t - 552*t**2 + 205844 + 206341.
3*(t - 179)*(t - 4)*(t - 1)
Let t(l) be the third derivative of 23/48*l**4 - 4/15*l**5 - l + 7/6*l**3 + 0 - 1/48*l**6 + 34*l**2. Factor t(b).
-(b - 1)*(b + 7)*(5*b + 2)/2
Let u = 7724400407675/17001 + -454349769. Let y = 2/1889 - u. Find v such that 26/3*v**3 + 8/9*v**2 - 70/9*v**5 - 8/9*v**4 - y*v + 0 = 0.
-1, -2/5, 0, 2/7, 1
Let m be -31 - (27 + -26 - 179). Factor -1/3*j**2 - m - 14*j.
-(j + 21)**2/3
Suppose 696/5*d - 693/5 - 3/5*d**2 = 0. What is d?
1, 231
Let k(l) be the second derivative of 0 + 14/15*l**6 + 88*l + 0*l**2 - 2/3*l**4 + l**5 + 0*l**3. Solve k(w) = 0 for w.
-1, 0, 2/7
Let c(o) be the second derivative of 10/3*o**4 + 1/72*o**6 + 19*o + 25/6*o**3 + 1/3*o**5 + 0 + 0*o**2. Let n(z) be the second derivative of c(z). Factor n(k).
5*(k + 4)**2
Let r be (-15921)/(-36) - ((-13)/(-4) + -3). Let i = r - 439. Factor -10*d**2 + 5/2*d**i + 0 + 15/2*d.
5*d*(d - 3)*(d - 1)/2
Let f(z) be the first derivative of -4/5*z**2 + 60 - 2*z + 2/15*z**3. Determine g, given that f(g) = 0.
-1, 5
Let g = -214 - -129. Let z = -85 - g. Factor 3/4*c**4 + 0*c**3 - 9/4*c**2 - 3/2*c + z.
3*c*(c - 2)*(c + 1)**2/4
Let l(n) = 6*n**4 - 40*n**3 + 22*n**2 - 8*n + 4. Let b(a) = 13*a**4 - 81*a**3 + 41*a**2 - 18*a + 9. Let k(q) = -4*b(q) + 9*l(q). Let k(r) = 0. What is r?
0, 1, 17
What is y in 9/2*y**3 - 36 - 197*y - 313/2*y**2 = 0?
-1, -2/9, 36
Let s(h) = -7*h**2 - h + 6. Let u(g) = g**2. Let f be (-50)/(-30)*36/(-10). Let d = 20 - 21. Let c(b) = d*s(b) + f*u(b). Suppose c(z) = 0. Calculate z.
-3, 2
Let w(q) be the first derivative of -7/12*q**2 - 88 - 7/18*q**3 - 1/3*q - 1/12*q**4. Let w(t) = 0. Calculate t.
-2, -1, -1/2
Let g(i) = -44*i**3 + 1084*i**2 - 2161*i + 1086. Let o(h) = -105*h**3 + 2709*h**2 - 5403*h + 2715. Let r(y) = 12*g(y) - 5*o(y). Factor r(v).
-3*(v - 1)**2*(v + 181)
Let 16 + 4/5*n**2 - 321/5*n = 0. What is n?
1/4, 80
Let n = 3038 - 3033. Let f(d) be the first derivative of 0*d**3 + 0*d**2 - 47 - 3/5*d**4 + 0*d + 4/25*d**n. Solve f(t) = 0 for t.
0, 3
Let -63/2*d - 39/2*d**2 + 15/2*d**4 + 39/2*d**3 + 0 = 0. What is d?
-3, -1, 0, 7/5
Let v(s) be the first derivative of 2/55*s**5 + 12/11*s - 50 + 14/11*s**3 + 9/22*s**4 + 19/11*s**2. Determine j so that v(j) = 0.
-6, -1
Let p be 1/(1/3)*1. Let a = -1631146/3 - -543718. Factor a*s**p - 2*s**2 + 2/3*s**4 - 12*s + 0.
2*s*(s - 2)*(s + 3)**2/3
Let r(z) = -3*z + 54. Let f be r(35). Let h = 51 + f. Solve 2/11*o - 2/11*o**2 + h = 0.
0, 1
Let t = -2049 - -26657/13. Let n = -90/143 + t. Suppose -n*p + 28/11 - 2/11*p**2 = 0. Calculate p.
-7, 2
Suppose -16*u + 23*u - 21 = 0. Factor 34*g**3 - u*g - 2*g - 29*g**3.
5*g*(g - 1)*(g + 1)
Find t, given that 0 - 1/2*t**4 + 9/2*t + 1/2*t**2 - 9/2*t**3 = 0.
-9, -1, 0, 1
Find n, given that 2*n**5 + 3*n**4 + 333*n - 216*n**2 + n**5 + 213*n**2 - 63*n - 273*n**3 = 0.
-10, -1, 0, 1, 9
Suppose -98 = -5*f + 4*b, -3*b + 13 - 19 = 0. Suppose -420*y - f - 173*y**2 - 1079*y**2 - 596*y**2 - 602*y**2 = 0. What is y?
-3/35
Let l be (-6)/24 - (-33)/(-44)*-7. Suppose -271 = -5*f - 31. Factor -10*b**4 - 62*b**4 - 118*b**2 + f*b**l + 115*b**2 + 27*b**3.
3*b**2*(b - 1)*(4*b - 1)**2
Let z(h) be the first derivative of -8/13*h + 8/39*h**3 + 22 + 1/26*h**4 - 1/13*h**2. Factor z(v).
2*(v - 1)*(v + 1)*(v + 4)/13
Let p(i) = -17*i**3 - 94*i**2 + 180*i - 116. Let j(r) = -17*r**3 + r**2 - 2. Let k(t) = -2*j(t) + p(t). Let k(u) = 0. Calculate u.
28/17, 2
Let l(s) = -15*s**2 - 136*s + 61. Let u(f) = -5*f**2 - 45*f + 20. Suppose 0 = j + 10*j + 44. Let d(g) = j*l(g) + 14*u(g). Solve d(t) = 0.
-9, 2/5
Suppose 0 = -5*m + 2*m. Suppose -778 = -g - 771, -4*i = g - 15. Determine s so that m*s - 2 + 1/2*s**i = 0.
-2, 2
Suppose 1350*l - 1456*l = -4452. Suppose -2*s + 22/7*s**2 - l - 2/7*s**3 = 0. What is s?
-3, 7
Let s(h) = -54*h**3 + 100*h**2 + 53*h - 101. Suppose 0 = -22*a + 21*a + 5. Let x(g) = 27*g**3 - 49*g**2 - 26*g + 50. Let q(b) = a*x(b) + 2*s(b). Factor q(k).
3*(k + 1)*(3*k - 4)**2
Let c(z) = -z**3 - 242*z - 1332. Let n be c(-5). Factor y**5 + 1/2*y**n + 1/4 + 2*y**2 - 3/2*y - 9/4*y**4.
(y - 1)**3*(y + 1)*(4*y - 1)/4
Suppose -n + 79 = 2*i, 29*n - 26*n = 2*i - 67. Let j(u) = 19*u**2 + u. Let l be j(1). Let l - 3*s**2 + 20*s - 5*s - i = 0. What is s?
2, 3
Let i(c) be the third derivative of -2209*c**7/3360 - 47*c**6/80 - 9*c**5/40 - 29*c**4/12 + 104*c**2. Let a(r) be the second derivative of i(r). Factor a(j).
-3*(47*j + 6)**2/4
Let p(k) = -2*k**4 - 87*k**3 + 98*k**2 + 143*k + 5. Let b(c) = 2*c**4 + 86*c**3 - 96*c**2 - 148*c - 4. Let q(u) = -5*b(u) - 4*p(u). Factor q(g).
-2*g*(g - 2)*(g + 1)*(g + 42)
Let o be (24 - 1 - (4 + -2)) + -5. Let c(s) be the first derivative of -11/15*s**3 + 0*s + o - 21/20*s**4 - 1/5*s**2 - 1/6*s**6 - 17/25*s**5. Solve c(a) = 0.
-1, -2/5, 0
Let i be (-34)/(-153)*(3 + (-18)/8). Let n(k) be the first derivative of -3/4*k**2 - 30 + 0*k + i*k**3. Solve n(l) = 0.
0, 3
Let w(j) be the first derivative of 1/5*j**5 + 2*j - 5/4*j**4 - 7/2*j**2 - 74 + 3*j**3. Determine x so that w(x) = 0.
1, 2
Suppose 56*b = 84 + 196. Let z(r) be the third derivative of -1/30*r**b + 0 + 2/3*r**3 + 0*r + 7*r**2 + 1/12*r**4. Factor z(g).
-2*(g - 2)*(g + 1)
Let l(c) be the second derivative of -c**5/160 - 3*c**4/32 - 23*c**3/48 - 15*c**2/16 + 2*c + 252. Factor l(b).
-(b + 1)*(b + 3)*(b + 5)/8
Let f(d) be the third derivative of 3*d**5/10 + d**4/6 - 40*d**3/3 - 5*d**2 + 59. What is k in f(k) = 0?
-20/9, 2
Suppose -17 = -4*z + 3*p, 3*z = 2*p + 15 - 1. Suppose -21*a = -23*a + z. Find m such that a*m**4 - 3*m**2 + 19*m**2 - 16*m**3 + 0*m**3 = 0.
0, 2
Let j(m) be the first derivative of 6*m**6/5 + 816*m**5/25 + 133*m**4/5 + 88*m**3/15 + 10162. Factor j(o).
4*o**2*(o + 22)*(3*o + 1)**2/5
Let v(x) be the second derivative of -x**7/2520 + x**5/360 - x**3/2 + 22*x**2 + x. Let p(w) be the second derivative of v(w). Solve p(y) = 0 for y.
-1, 0, 1
Let f(o) = o**2 + 3*o - 2. Let k(d) = 6*d**2 + 19*d - 12. Let y be 88/2 - (6 + -1). Suppose 8*g = 12 - 60. Let i(n) = g*k(n) + y*f(n). Solve i(s) = 0.
-2, 1
Let g = 491/2 - 245. Let x = -390 + 392. Factor g*p**x + 1/2 + p.
(p + 1)**2/2
Let b(g) = -5*g**2 - 14 + 0*g - 2 + g. Let o(c) = -8*c**2 + 8*c**2 - 6*c**2 - 3 + 5*c**2. Let q(i) = -2*b(i) + 11*o(i). Factor q(s).
-(s + 1)**2
Let u(m) = -m + 12. Let i be u(9). Let -k**3 - 4*k**3 - 10*k + 12*k**2 + 2*k**i + 10*k = 0. What is k?
0, 4
Suppose -4*r = 3*c - 29, 2*c + 0*r = -r + 11. Factor -2*f - 4*f - 39*f - c*f**2.
-3*f*(f + 15)
Let t(g) = 40*g**3 - 1688*g**2 + 176372*g + 359552. Let d(x) = 86*x**3 - 3376*x**2 + 352742*x + 719104. Let u(i) = 6*d(i) - 13*t(i). Factor u(n).
-4*(n - 212)**2*(n + 2)
Let y(k) = -4*k + 1. Let r be y(0). Let n be (-2924)/(-1020) - r/(-3). Factor 7/5*b**5 + 11/5*b**3 + n*b**4 + 0*b + 0 + 2/5*b**2.
b**2*(b + 1)**2*(7*b + 2)/5
Let m(t) be the second derivative of -t**5/4 + 105*t**4/4 - 1485*t**3/2 - 16335*t**2/2 - 1160*t. Let m(i) = 0. Calculate i.
-3, 33
Let x = 129/11 + -365/33. Let o = 49/51 + -5/17. Suppose -o*t**2 - 1/3*t + 1/3*t**3 + x = 0. Calculate t.
-1, 1, 2
Let s(d) be the first derivative of 50*d**5 + 105*d**4 - 10768*d**3/15 + 1632*d**2/5 - 256*d/5 - 468. Let s(n) = 0. Calculate n.
-4, 4/25, 2
Suppose -131*u + 128*u + 24 = 0. Factor 4*b - 6*b**3 - 28*b**2 + 2*b**5 + b + 8*b**4 - 13*b - u*b.
2*b*(b - 2)*(b + 1)**2*(b + 4)
Factor 12*a**2 + 75*a - 693 + 441 - 9*a**2.
3*(a - 3)*(a + 28)
Let d(x) = 8*x - 6. Let n be d(1). Find u such that 5*u**5 - 65*u**3 + 25*u**n - 75*u**2 + 4*u**4 - 8*u**4 - 6*u**4 = 0.
-2, -1, 0, 5
Let z(u) be the second derivative of u**8/7560 - u**7/315 + u**6/45 - 3*u**3 - 5*u + 5. Let n(o) be the second derivative of z(o). Find j such that n(j) = 0.
0, 6
Let p be (-2)/(-2) - (2 - 0). Let h be (-21)/(-14) - -1*p/(-2). Suppose -8*a + 234*a**2 - 254*a**2 + h*a**3 + 10*a**3 = 0. Calculate a.
-1/3, 0, 2
Suppose -4*y = -4*a - 12, 5*y - 13 = -4*a - 7. Determine n so that -29*n**2 - 26*n**y - 27*n**2 + 80*n**2 - 2*n = 0.
-1, 0
S