et w(s) be the first derivative of s**4 + 104 + 8*s**2 + 28/3*s**3 - 48*s. Factor w(c).
4*(c - 1)*(c + 2)*(c + 6)
Let h(q) be the second derivative of q**7/17640 + q**6/720 + 67*q**4/12 + 182*q. Let x(c) be the third derivative of h(c). Factor x(l).
l*(l + 7)/7
Let z = -2771981236/903645 - 4/903645. Let v = z + 3081. What is q in -v*q**2 + 44/9*q - 4/9 = 0?
2/11
Let r = -32 - -295. Suppose -5*b + 8 = -b. Factor -10*h - 11*h + r*h**2 + 10 + 6*h - 258*h**b.
5*(h - 2)*(h - 1)
Let s(o) = -405*o - 260. Let k be s(-3). Let r be (-2)/(-16) - (k/120 - 10). Let -r*g**3 + 2*g**2 - 2/3*g + g**4 - 1/6*g**5 + 0 = 0. Calculate g.
0, 1, 2
Let i be (520/(-39) + (3 - -9))/(-3). Factor -i*b**2 + 0 - 2/3*b + 2/9*b**3.
2*b*(b - 3)*(b + 1)/9
Let w(i) = 272*i**2 - 1352*i + 228483. Let v(f) = -870*f**2 + 4056*f - 685448. Let u(m) = 5*v(m) + 16*w(m). Factor u(j).
2*(j - 338)**2
Suppose -w - 231 = 3*o + 447, 3*w - 4*o + 2021 = 0. Let q = w + 6083/9. Factor 0 - 4/9*h**2 + q*h.
-4*h*(h - 2)/9
Determine w so that -20*w - 1/2*w**4 + 24 - 4*w**2 + 6*w**3 - 1/4*w**5 = 0.
-6, -2, 2
Factor -4*l - 64/9 - 2/9*l**2.
-2*(l + 2)*(l + 16)/9
Let v(f) be the second derivative of -1/3*f**4 + 0*f**2 + 0 + 38*f + 16/3*f**3. Find l, given that v(l) = 0.
0, 8
Let i(c) be the third derivative of c**6/120 + 7*c**5/15 + 121*c**4/24 + 23*c**3 + c**2 + 499*c. Suppose i(z) = 0. Calculate z.
-23, -3, -2
Let u(a) be the third derivative of 1/780*a**6 + 11/78*a**5 + 2*a + 243/13*a**3 + 0 + 261/52*a**4 + 92*a**2. Find f, given that u(f) = 0.
-27, -1
Let l(b) be the second derivative of 245/2*b**2 + b + 5/12*b**4 - 35/3*b**3 - 6. Factor l(p).
5*(p - 7)**2
Let t(z) be the first derivative of z**5/20 + 31*z**4/16 + 5*z**3/2 - 955. Let t(k) = 0. Calculate k.
-30, -1, 0
Let r be (-9)/(-6)*(-40)/(-15). Find z such that -360*z + 81*z**2 - 130*z**3 + 339*z**2 + 93*z**5 - r*z**4 - z**4 - 88*z**5 = 0.
-6, 0, 2, 3
Let a be (-24)/(-348)*(-2813)/(-388). Suppose 18*l + a*l**2 + 162 = 0. What is l?
-18
Let m(y) be the first derivative of -90*y**5 + 55*y**4/2 + 476*y**3 - 540*y**2 + 208*y + 9950. Suppose m(d) = 0. Calculate d.
-2, 2/5, 13/9
Let o(i) be the second derivative of i**7/14 - 33*i**6/10 + 87*i**5/5 + i - 12. Factor o(y).
3*y**3*(y - 29)*(y - 4)
Let r(b) be the third derivative of b**8/1344 + 19*b**7/120 + 87*b**6/80 + 389*b**5/120 + 517*b**4/96 + 43*b**3/8 - 7*b**2. Factor r(c).
(c + 1)**4*(c + 129)/4
Solve -73529*v + 613*v**2 + 73529*v - 86*v**3 - 509*v**3 - 123*v**2 + 110*v**4 - 5*v**5 = 0.
0, 1, 7, 14
Factor -43*x**2 + 1260 + 96*x**2 + 42*x - 51*x**2 + 12 + 88*x.
2*(x + 12)*(x + 53)
Let r(z) be the second derivative of z**4/3 - 136*z**3/3 + 213*z - 3. Factor r(s).
4*s*(s - 68)
Let f = 19337 + -19335. Let n(w) be the second derivative of 0*w**3 + 0 - 1/60*w**5 - 26*w + 2/3*w**f - 1/12*w**4. Determine j, given that n(j) = 0.
-2, 1
Factor 245*d**2 - 113*d**2 - 127*d**2 - 1235 - 30*d.
5*(d - 19)*(d + 13)
Let w(m) be the third derivative of -155/4*m**4 + 0 - 75/2*m**3 - 1/30*m**6 - 121/60*m**5 + 45*m**2 + 0*m. Let w(x) = 0. What is x?
-15, -1/4
Let s(r) = 5*r**3 - 11*r + 11. Let v(j) = 2*j**3 - 6*j + 6. Let u(y) = 6*s(y) - 11*v(y). Let z be u(1). Factor 6*q**2 - 3*q**2 + z + 2*q**2 - 7*q**2.
-2*(q - 2)*(q + 2)
Let k be 60/(-2520)*(-5 - 22/4). Factor -12*m**2 + 16 + m - k*m**4 - 19/4*m**3.
-(m - 1)*(m + 2)**2*(m + 16)/4
Suppose -5*c = -x + 20, 6*c + 12 = -3*x + 3*c. Suppose x = -4*r + 3*r + 110. Factor 6*s**3 + 57 + 0*s**4 + 103 - r*s**2 - 5*s**4 + 39*s**3.
-5*(s - 4)**2*(s - 2)*(s + 1)
Let m(v) be the second derivative of 7/4*v**4 + 1/2*v**6 + 0 + 1/14*v**7 + 27/20*v**5 + 0*v**2 + v**3 - 40*v. Factor m(i).
3*i*(i + 1)**3*(i + 2)
Let k(m) be the third derivative of m**6/420 - 33*m**5/70 + 36*m**4 - 1260*m**3 - 12*m**2 + 82. Factor k(q).
2*(q - 42)**2*(q - 15)/7
Let m be -2 + 6 + 4/2 + -21. Let c = m + 46. Determine j so that 16 + 138*j**4 - 41*j - c*j - 333*j**3 - 268*j**2 + 1287*j**3 + 996*j**4 = 0.
-1, -2/7, 2/9
Let r = 32 + -69. Let p = -32 - r. Find x, given that -p + 36*x**2 - 3 - 6*x - 22*x = 0.
-2/9, 1
Let q be (-15)/(-9) + 59290/(-39930). Suppose -8/11*y - q*y**2 - 8/11 = 0. Calculate y.
-2
Let m(f) be the first derivative of -f**3/9 - 14*f**2 - 83*f/3 - 429. Factor m(p).
-(p + 1)*(p + 83)/3
Let q be 48/96*(10 - 2)*25/125. Find w such that 0*w - 1/5*w**3 + 0 - q*w**2 + 1/10*w**4 = 0.
-2, 0, 4
Suppose 2136*c + 628 = 2375*c + 150. Suppose -22/5*x + 2/5*x**c + 22/5*x**3 - 2/5*x**4 + 0 = 0. Calculate x.
-1, 0, 1, 11
Find r, given that -2/23*r**3 - 1854/23 - 1254/23*r - 218/23*r**2 = 0.
-103, -3
Let w(x) be the third derivative of x**5/12 - 8035*x**4/4 + 38736735*x**3/2 + 2*x**2 + 1620*x. Factor w(r).
5*(r - 4821)**2
Let f be (-1)/(0 + -2)*0. Let w be ((-16)/120 - 46/(-120))*(8 + -6). Factor f*s - w*s**4 + s**2 - 1/2 + 0*s**3.
-(s - 1)**2*(s + 1)**2/2
Let d(l) = 43*l - 215. Let h be d(12). Suppose 53*t + 36 = h. What is w in 0*w**2 - 2/7*w**t - 1/7*w**3 + 0*w - 3/7*w**4 + 0 = 0?
-1, -1/2, 0
Let i(g) be the first derivative of 25*g**4/4 + 340*g**3/3 + 685*g**2/2 - 330*g - 1647. Factor i(l).
5*(l + 3)*(l + 11)*(5*l - 2)
Let j = 9870 + -187514/19. Let l(u) be the first derivative of -12/19*u**3 + 28/19*u**2 + 2/19*u**5 + 38 - j*u - 7/38*u**4. Suppose l(r) = 0. What is r?
-2, 2/5, 1, 2
Let o(b) = b**2 - b + 1. Let a be ((-10)/25)/((-3)/15 - 0). Let z(h) = -51*h + 40*h + 16*h**a - 7*h**3 + 6*h**2 - 1. Let f(u) = -3*o(u) + z(u). Factor f(x).
-(x - 2)*(x - 1)*(7*x + 2)
Suppose 10718450/9 + 2/9*l**2 - 9260/9*l = 0. What is l?
2315
Suppose 5*r = -3*t + 265, 4*t - 305 = -5*r + 9*t. Let f be (-4)/14 + r/49. Factor -f + 15/7*u**2 + 9/7*u.
3*(u + 1)*(5*u - 2)/7
Let g(p) = -21*p**3 + 486*p**2 + 13122*p + 118089. Let j(w) = 9*w**3 - 243*w**2 - 6561*w - 59045. Let d(a) = 4*g(a) + 9*j(a). Factor d(h).
-3*(h + 27)**3
Suppose -1601*b = -1613*b. Let j(h) be the first derivative of 1/2*h**4 + 0*h**5 + 0*h - 18 - 1/2*h**2 - 1/6*h**6 + b*h**3. Solve j(m) = 0.
-1, 0, 1
Let d(k) be the third derivative of -k**5/150 + 49*k**4/60 - 38*k**3 - 2*k**2 - 5*k + 81. Factor d(z).
-2*(z - 30)*(z - 19)/5
Factor -25809*x**2 + 342*x**3 + 25809*x**2 + 1728*x**3 - 2*x**4.
-2*x**3*(x - 1035)
Let q = -2775/332 + 1429/166. Factor 0 + q*a**3 + 3/4*a + a**2.
a*(a + 1)*(a + 3)/4
Let j = 100823 + -302461/3. Factor -j*x - 4/3*x**2 - 4/3.
-4*(x + 1)**2/3
Let u = 5732 - 5729. Let m(y) be the first derivative of -6 + 64/9*y**u - 8/3*y + 5*y**4 + 16/15*y**5 + 2*y**2. What is h in m(h) = 0?
-2, -1, 1/4
Let z(n) be the second derivative of -7*n**5/10 - 2*n**4 - n**3 + 2*n**2 - 23*n + 2. Factor z(j).
-2*(j + 1)**2*(7*j - 2)
Let o(z) be the third derivative of z**6/420 - 13*z**5/210 - 95*z**4/28 + 1275*z**3/7 + 3868*z**2. Factor o(a).
2*(a - 15)**2*(a + 17)/7
Let s(j) be the third derivative of -j**6/1020 + j**5/51 - 23*j**4/204 + 14*j**3/51 + 109*j**2 + 2*j. Solve s(f) = 0 for f.
1, 2, 7
Let p be -4 + (5*10/25 - -5). Factor 2*w**p - 108*w + 101*w + 16*w**2 + 32 + 47*w.
2*(w + 2)**2*(w + 4)
Suppose 4*n = -4*d + 28, 10 = n + n. Solve 0*m**4 - 2*m**4 + 6*m**4 - 17*m + 3*m**4 + d*m - 8 + 15*m**3 + m**2 = 0 for m.
-8/7, -1, 1
Let y(w) be the first derivative of w**3/12 + 215*w**2/8 + 211*w - 1376. Factor y(a).
(a + 4)*(a + 211)/4
Let x(l) = -2*l**3 - 96*l**2 - 196*l - 3. Let q(g) = -2*g**3 - 94*g**2 - 196*g - 4. Let h(m) = 3*q(m) - 4*x(m). What is n in h(n) = 0?
-49, -2, 0
Let u = -9184 - -9186. Let h(f) be the third derivative of 0*f + 0*f**6 + 1/112*f**8 - 1/10*f**5 + 0*f**3 + 0 - 17*f**u - 1/8*f**4 + 1/35*f**7. Factor h(l).
3*l*(l - 1)*(l + 1)**3
Let z(w) = 3*w**2 + 227*w - 225. Let t(a) = 2*a**2 + 114*a - 114. Let q(k) = 5*t(k) - 2*z(k). Determine v, given that q(v) = 0.
-30, 1
Let g(k) be the first derivative of k**4/21 - 10*k**3/7 + 52*k**2/7 - 186*k + 91. Let t(d) be the first derivative of g(d). Factor t(o).
4*(o - 13)*(o - 2)/7
Let b(i) be the second derivative of -25*i**4/36 - 199*i**3/6 + 12*i**2 - 2442*i. Suppose b(f) = 0. What is f?
-24, 3/25
Let p(t) = 2*t + 6. Let d be p(-2). Determine o, given that 0*o - 34*o**4 - o**2 - 5*o**d + 36*o**4 + 4*o = 0.
-2, 0, 1
Suppose 2*d + 5*z = -5 + 38, 4*z - 16 = d. Let g(s) be the first derivative of 2/9*s**2 + d + 1/18*s**4 - 2/9*s**3 + 0*s. Factor g(q).
2*q*(q - 2)*(q - 1)/9
Let c be -41 + (-106760)/(-258