4. Let c(a) = -30*a**4 - 170*a**3 - 24*a**2 + 72*a + 72. Let b(u) = 2*c(u) - 36*x(u). Solve b(k) = 0.
-6, -3/5, 0, 1/3
Suppose t = -4*u + 48, 39*t - 36*t = -3*u + 36. Factor u*j**3 - 2073*j**4 + 6*j**5 + 36*j**2 - 2*j**5 + 2053*j**4.
4*j**2*(j - 3)**2*(j + 1)
Let j(r) be the second derivative of r**5/20 + 17*r**4/48 - 59*r**3/6 - 15*r**2/2 + 4*r + 21. Let j(s) = 0. What is s?
-10, -1/4, 6
Let u be ((-21)/(-21))/((-1)/(-85)). Suppose -143 + 5*r + 0*r + 228 - u*r**2 - 5*r**3 + 0*r = 0. What is r?
-17, -1, 1
Let h be 1/(-3)*2 - 132/(-36). What is v in -446 + v**h + 14 - 75*v**2 - 504*v - 4*v**3 = 0?
-12, -1
Let s(r) be the second derivative of r**4/3 + 440*r**3/3 - 1338*r**2 + 6420*r. Determine k, given that s(k) = 0.
-223, 3
Let a be -2 - ((-20)/(-160) + 11619/(-4472)). Let n = -1/86 + a. Suppose -2/13 + n*g**2 + 4/13*g**3 + 0*g = 0. Calculate g.
-1, 1/2
Let t(z) be the third derivative of -z**6/540 - 23*z**5/54 + 13*z**4/6 - 12*z**2 + 14*z - 4. Factor t(i).
-2*i*(i - 2)*(i + 117)/9
Let v be (6/635)/(40/(-100)). Let w = 1309/1651 + v. Factor 0 - w*j - 2/13*j**2.
-2*j*(j + 5)/13
Suppose -6696 = -213*d - 185*d - 1276*d. Factor -9/7*w**3 + 3/7*w**d + 0*w + 0 + 6/7*w**2.
3*w**2*(w - 2)*(w - 1)/7
Let h(d) = d**2 + 17*d - 20. Let y(q) = 7*q**2 + 69*q - 73. Let l(p) = 6*p**2 + 69*p - 75. Let v(w) = 4*l(w) - 3*y(w). Let s(r) = -9*h(r) + 2*v(r). Factor s(m).
-3*(m - 1)*(m + 6)
Let d(n) = n**2 - 2*n - 2. Let a(w) = -w**5 - 104*w**4 - 600*w**3 - 1192*w**2 - 768*w + 16. Let x(i) = -3*a(i) - 24*d(i). Let x(u) = 0. What is u?
-98, -2, 0
Let k be 1/36*8 - 508/18. Let z be (k/252)/((-1)/2). Factor -7/9*a**3 - 11/9*a + 16/9*a**2 + z.
-(a - 1)**2*(7*a - 2)/9
Let o be 0/((-60)/(-27) - 12/54). Let k be o - (1/(-4))/((-25)/(-320)). Let 3/5*r**5 + 24/5*r**3 - k*r - 16/5*r**4 + 0 + 0*r**2 = 0. Calculate r.
-2/3, 0, 2
Let 2/3*r**2 - 77/9 - 71/9*r = 0. What is r?
-1, 77/6
Let q be (43/(-172))/(2/(-16)). Find y, given that y + 28 + 8*y - 9*y**q + 15*y + 5*y**2 = 0.
-1, 7
Let t(g) be the first derivative of -9/4*g**4 + 12*g - 12 - 5*g**3 + 3/5*g**5 + 9/2*g**2. Factor t(l).
3*(l - 4)*(l - 1)*(l + 1)**2
Let u(a) be the first derivative of -2*a**5/35 + 85*a**4/7 - 338*a**3/21 + 14163. Factor u(c).
-2*c**2*(c - 169)*(c - 1)/7
Let w(c) be the third derivative of -105*c**2 - 5/132*c**4 - 1/330*c**5 + 0 + 0*c + 2/11*c**3. Factor w(a).
-2*(a - 1)*(a + 6)/11
Factor -2/11*k**3 + 28/11*k**2 + 1160/11*k + 6800/11.
-2*(k - 34)*(k + 10)**2/11
Let q(w) be the third derivative of 16*w**4 - w**2 - 28*w + 1/60*w**6 + 4/5*w**5 + 512/3*w**3 + 0. Determine t so that q(t) = 0.
-8
Let t(x) be the second derivative of -x**7/1260 - 11*x**6/180 + 17*x**5/90 - 205*x**3/6 + 68*x. Let m(b) be the second derivative of t(b). Factor m(q).
-2*q*(q - 1)*(q + 34)/3
Factor -1/4*o**3 + 1/4*o**2 + 0 + 325/2*o.
-o*(o - 26)*(o + 25)/4
Let v be (-1974)/15 - (-30)/(-75). Let p = 400/3 + v. Let -2/3*x**2 + p*x - 2/3 = 0. What is x?
1
Suppose -1170 = -829*l + 699*l. Factor 9/2 - l*b**2 - 51/2*b.
-3*(b + 3)*(6*b - 1)/2
Let k = -138 + 168. Let j(v) be the first derivative of -22 + 9*v**3 - k*v + 12*v**2 - 18*v - 10*v**3. Factor j(x).
-3*(x - 4)**2
Let x = 239 + -244. Let j be (24 - 19) + (x - 1) + 4. Solve 12/5*p + 0 + 2/5*p**2 - 2/5*p**j = 0.
-2, 0, 3
Let l(q) be the first derivative of q**3 - 84*q**2 + 2352*q + 1391. Find b such that l(b) = 0.
28
Let n = -1744 + 1724. Let g = n - -99/4. Factor 1/2*q**4 + g*q - 1/4*q**5 + 3/2*q**3 - 5*q**2 - 3/2.
-(q - 2)*(q - 1)**3*(q + 3)/4
Let s be 644/105 + (-6)/(-45)*-1. Let u(o) be the first derivative of 0*o - 1/39*o**s + 2/13*o**5 - 14 + 8/39*o**3 - 4/13*o**4 + 0*o**2. Factor u(y).
-2*y**2*(y - 2)**2*(y - 1)/13
Let v(o) be the second derivative of -o**7/210 + 2*o**6/45 + o**5/6 + 17*o**3/3 + 96*o. Let x(i) be the second derivative of v(i). Factor x(c).
-4*c*(c - 5)*(c + 1)
Let o be (-2)/6 + 16/48. Suppose o = f + 4*f - 2*j - 14, -5*j - 2 = 4*f. Find a, given that 3 + a**f + 94*a + 5*a**2 - 102*a - a**4 = 0.
-3, 1
Let i(z) be the second derivative of z**4/48 + 7*z**3/24 - 9*z**2/4 - 2*z + 168. Factor i(c).
(c - 2)*(c + 9)/4
Let f(x) be the third derivative of -3*x**7/14 + 547*x**6/24 - 209*x**5/6 - 25*x**4 + 1270*x**2 - 2. Find s such that f(s) = 0.
-2/9, 0, 1, 60
Factor -216 + 3/5*p**3 - 33/5*p**2 - 486/5*p.
3*(p - 20)*(p + 3)*(p + 6)/5
Let y = 476 - 287. Suppose -y*g = -187*g. Factor 3/5*k**3 + 0 + 0*k + g*k**2.
3*k**3/5
Let k be 8/5*-3*-45. Find q, given that -576*q - 37 + k*q**2 - 21*q**3 - 27*q**3 + 469 + 48*q**2 + 3*q**4 = 0.
2, 6
Let m(r) be the first derivative of -r**5/30 + 13*r**4/24 - 53*r**3/18 + 83*r**2/12 - 7*r - 5435. Determine q so that m(q) = 0.
1, 2, 3, 7
Let q(f) be the second derivative of f**7/70 - f**6/10 - 15*f**2 + 77*f. Let i(j) be the first derivative of q(j). Factor i(w).
3*w**3*(w - 4)
Let t be (-27)/12*(-32)/(-3). Let b = 26 + t. Factor 2*x + 4*x**4 + 7*x**2 - b*x**5 - 11*x**2 + 0*x**2.
-2*x*(x - 1)**3*(x + 1)
Let f = -1373/17 - -4136/51. Find w such that -1/3*w + 2/3*w**2 + 0 - f*w**3 = 0.
0, 1
Let u(i) be the second derivative of 0 - 25/12*i**4 - 1/4*i**5 + 5*i**3 + 0*i**2 - 51*i. Suppose u(d) = 0. Calculate d.
-6, 0, 1
Factor -7*w**3 - 2025/4 - 315*w - 1/4*w**4 - 143/2*w**2.
-(w + 5)**2*(w + 9)**2/4
Let u(r) be the second derivative of -r**4/20 + 98*r**3/5 - 14406*r**2/5 + 3*r - 144. Factor u(g).
-3*(g - 98)**2/5
Let y(q) be the first derivative of 3*q**4/4 + 22*q**3 - 393*q**2/2 + 324*q + 464. Factor y(w).
3*(w - 4)*(w - 1)*(w + 27)
Let g(v) = 154*v + 2005. Let f be g(-13). Suppose 3*b + 10 = 2*m, 2*b = m + b - 4. Factor -2/7*c**f + 0 + 2/7*c**m + 0*c.
-2*c**2*(c - 1)/7
Let r be ((-4)/10)/((-4)/(((-220)/(-33))/2)). Suppose 4*i - i - 6 = 0. Factor r*l**3 - i - 11/3*l - 4/3*l**2.
(l - 6)*(l + 1)**2/3
Let j = -41907 - -41910. Let i(o) be the first derivative of -4/5*o**5 - 2*o**4 + 4/3*o**j + 23 + 4*o**2 + 0*o. Find b, given that i(b) = 0.
-2, -1, 0, 1
Let w(t) be the third derivative of 2/9*t**6 + 0*t**3 + t**2 + 1/15*t**5 + 0*t**4 + 48*t + 0. Suppose w(q) = 0. Calculate q.
-3/20, 0
Let i(p) be the third derivative of 0 + 126*p**2 - 1/180*p**5 + 0*p - 13/36*p**4 + 3/2*p**3. Factor i(k).
-(k - 1)*(k + 27)/3
Let t(r) be the third derivative of 0 + 9/7*r**3 + 83*r**2 + 0*r + 75/56*r**4 + 1/40*r**6 + 11/35*r**5. What is x in t(x) = 0?
-3, -2/7
Let g(a) be the first derivative of -a**4/96 - 7*a**3/48 - 3*a**2/8 - 135*a - 47. Let p(o) be the first derivative of g(o). Factor p(f).
-(f + 1)*(f + 6)/8
Let g be (-7)/21 - (102/(-36) - (-2 - (-20 + 11))). Factor g*z + 19/6*z**2 - 5/3 - z**3.
-(z - 5)*(z + 2)*(6*z - 1)/6
Let j = 154450 - 154448. What is h in -4/5*h**j + 8/5*h + 0 = 0?
0, 2
Find a such that -96 - 14*a**2 + 162*a**4 + a**3 - 7*a**2 - 24*a - 165*a**4 + 57*a**2 + 5*a**3 = 0.
-2, 2, 4
Let k(t) be the first derivative of 5*t**3/3 - 1575*t**2/2 - 1580*t + 6741. Find s such that k(s) = 0.
-1, 316
Let q(v) = -33*v**3 - v**2 - 2*v - 1. Let u be q(-1). Suppose -16 - u = -7*g. Suppose 4*x**3 - 1299*x - g*x**5 + 14*x**4 + 1299*x - x**5 = 0. Calculate x.
-1/4, 0, 2
Factor -101614/9 + 142/9*o**2 - 2/9*o**3 - 94/9*o.
-2*(o - 47)**2*(o + 23)/9
Let b = 8 - 5. Let r(y) = 5151*y + 20606. Let i be r(-4). Determine n so that 0 - 1/2*n**b - 3/2*n**i + 0*n = 0.
-3, 0
Factor -104/5*n - 10*n**2 + 53/5*n**3 + 0 - 1/5*n**4.
-n*(n - 52)*(n - 2)*(n + 1)/5
Let x(i) be the second derivative of -i**4/48 - 1339*i**3/12 - 1792921*i**2/8 + 2687*i. Factor x(b).
-(b + 1339)**2/4
Let h = 24483 - 1591431/65. Let j = -151/390 - h. Factor j*p**2 + 3/2 - p.
(p - 3)**2/6
Suppose -82*h + 163 = n, 420*h - 7 = 418*h + 3*n. What is x in -1/4*x**h - 9/2 - 9/4*x = 0?
-6, -3
Let s(g) = -3*g**3 - g**2 + 3*g + 2. Let u(t) = 16*t**3 + 116*t**2 - 72*t - 68. Let d(a) = 8*s(a) + u(a). Factor d(z).
-4*(z - 13)*(z - 1)*(2*z + 1)
Let w(o) = -o**3 + 190*o**2 + 407*o + 204. Let x(z) = z**3 + 3*z + 1. Suppose -8 = -2*h, 0 = -4*n - 2*h + h. Let j(b) = n*w(b) + 4*x(b). Factor j(k).
5*(k - 40)*(k + 1)**2
Let j(r) = 90*r**3 - 2*r**2 + 3*r + 4. Let v be j(-1). Let z be (-16)/4 - 468/v. Factor -2/7*b**4 - 18/7*b**2 + z*b + 0 + 12/7*b**3.
-2*b*(b - 4)*(b - 1)**2/7
Let r(t) = -9*t**2 - 3316*t - 2214. Let j(c) = 90*c**2 + 33159*c + 22143. Let m(n) = -2*j(n) - 21*r(n). Suppose m(s) = 0. What is s?
-368, -2/3