 + 9*c**2/5 - 223. Determine f, given that n(f) = 0.
-1/4, 0, 1, 3, 6
Factor 82*t**2 - 31*t + 487 - 273*t - 2*t**3 - 191.
-2*(t - 37)*(t - 2)**2
Factor 7448*s**2 + 421*s**3 - 3467044*s - 252*s**3 - 173*s**3.
-4*s*(s - 931)**2
Suppose 0 = -5*r + 3*m + 12, -3*r + 10*m - 8*m + 8 = 0. Let -2/3*n + r + n**2 - 1/3*n**3 = 0. What is n?
0, 1, 2
Let v(k) = -k**5 + k**3 + 2*k**2 + 2. Let j(b) = 2*b**5 - b**3 - 4*b**2 - 5. Let x be 3/((1 - (4 - 2))/(-5)). Let i(p) = x*v(p) + 6*j(p). Factor i(a).
-3*a**2*(a - 2)*(a + 1)**2
Let f(r) be the third derivative of -r**8/336 - r**7/3 - 299*r**6/40 + 1014*r**5/5 - 18*r**2 - 37. Find n, given that f(n) = 0.
-39, 0, 8
Let z(y) be the third derivative of y**6/540 + y**5/90 - y**4/27 + 41*y**2 - 16*y. Find x such that z(x) = 0.
-4, 0, 1
Let o(t) be the third derivative of 3/4*t**4 + 12*t**2 + 0*t + 1/30*t**5 + 8/3*t**3 + 0. Factor o(a).
2*(a + 1)*(a + 8)
Suppose 27 = 4*i + 147. Let j = 32 + i. Factor 2*n**3 + 21*n**3 + 6*n**3 + 3*n**4 - 2*n**3 + 81*n + 81*n**j.
3*n*(n + 3)**3
Let q(w) = -1768*w - 47733. Let g be q(-27). What is h in 0 - 4*h**5 + 72/5*h**g - 112/5*h**2 + 32/5*h + 28/5*h**4 = 0?
-2, 0, 2/5, 1, 2
Let q(v) be the first derivative of -128 + 1/12*v**3 - 1/8*v**2 - 1/2*v. Determine d, given that q(d) = 0.
-1, 2
Let j be (4 - (-59)/4) + (141 - 153). Factor -1/4*c**3 - 13/2*c + j*c**2 + 0.
-c*(c - 26)*(c - 1)/4
Let b = -25/2313 + 94/771. Factor -1/3*u - 2/9 - b*u**2.
-(u + 1)*(u + 2)/9
Let i be -1*(4 - 5) - (-136)/85 - -11. Solve -2/5*x**2 + 14 + i*x = 0.
-1, 35
Let o(w) be the second derivative of -w**4/48 + 55*w**3/24 - 129*w**2/2 + 2*w - 4076. Factor o(f).
-(f - 43)*(f - 12)/4
Let x(s) = 102*s - 241. Let z be x(7). Let p = z - 470. Determine g so that 3*g**4 + 0 + 48/5*g**2 + 12/5*g + 51/5*g**p = 0.
-2, -1, -2/5, 0
Let p(j) be the first derivative of 7 + 0*j - 3/4*j**4 + 2*j**3 + 9/2*j**2. Factor p(i).
-3*i*(i - 3)*(i + 1)
Let u = -137/3 + 47. Let j(n) = 24*n - 718. Let g be j(30). Let -2/3*c**g + 2/3*c + u = 0. What is c?
-1, 2
Let y(z) be the first derivative of -z**4/6 - 14*z**3/9 + 28*z**2/3 - 40*z/3 + 2704. Factor y(c).
-2*(c - 2)*(c - 1)*(c + 10)/3
Let x(a) be the second derivative of -a**6/180 + 11*a**5/120 - 5*a**4/36 - 212*a. Factor x(z).
-z**2*(z - 10)*(z - 1)/6
Let p(q) = 8*q**2 - 196*q - 96. Let d be p(25). Suppose 1/4*r**d - 2*r**3 + r**2 + 0*r + 3/4*r**5 + 0 = 0. Calculate r.
-2, 0, 2/3, 1
Let w(x) be the third derivative of 17/105*x**7 - 13/15*x**5 + 3/10*x**6 - 7/4*x**4 + 3*x**3 + 0 + 1/56*x**8 + 0*x - 71*x**2. Suppose w(p) = 0. What is p?
-3, -1, 1/3, 1
Let x be (54/12)/(-9) - (-117)/18. Let g(m) be the second derivative of 1/6*m**x + 17/20*m**5 + 0 + 4/3*m**4 - 21*m + 0*m**2 + 2/3*m**3. Factor g(c).
c*(c + 1)*(c + 2)*(5*c + 2)
Suppose 665*k - 2470 = -570*k. Factor 0 - 5/2*t**3 - 1/2*t - 2*t**k - t**4.
-t*(t + 1)**2*(2*t + 1)/2
Let t be (5 + -15 + 7)/((-3)/2). Let k = 910/2323 + -22/101. Factor -k + 6/23*p**t + 10/23*p.
2*(p + 2)*(3*p - 1)/23
Suppose 0 = -210*x + 198*x - 1620. Let g be (-138)/x + (-40)/300. Factor 4/3*c + 0 + 22/9*c**2 + g*c**3 - 2/9*c**4.
-2*c*(c - 6)*(c + 1)**2/9
Let l(k) be the second derivative of -k**4/4 + 956*k**3 - 1370904*k**2 + 802*k + 1. Factor l(s).
-3*(s - 956)**2
Let v(z) be the third derivative of 0*z**4 + 0*z + 1/42*z**7 - 1/60*z**6 - 52 + z**2 + 0*z**3 + 0*z**5. Factor v(w).
w**3*(5*w - 2)
Factor -69*r + 36*r - 317 - 223 - 2*r**2 + 4*r**2 + r**2.
3*(r - 20)*(r + 9)
Let p = 138326 + -968276/7. Find r, given that -6/7*r**2 + p + 2/7*r**3 - 2/7*r = 0.
-1, 1, 3
Let y(n) be the first derivative of -n**9/13608 + n**7/3780 - 26*n**3/3 - 158. Let p(z) be the third derivative of y(z). Solve p(i) = 0.
-1, 0, 1
Let z(c) be the third derivative of -c**6/120 + 7*c**5/60 - c**4/4 + c**3/3 - 118*c**2. Let r be z(6). Factor 4/3*p - 2/9 - 10/9*p**r.
-2*(p - 1)*(5*p - 1)/9
Let i(o) be the second derivative of -5*o**4/24 - 1249*o**3/6 + 250*o**2 + 1670*o. Factor i(v).
-(v + 500)*(5*v - 2)/2
Let v(f) be the third derivative of -3*f**6/140 - 11*f**5/140 + 5*f**4/14 - 3*f**3/14 - 1963*f**2. What is d in v(d) = 0?
-3, 1/6, 1
Let k(w) be the first derivative of -4/3*w**3 + 0*w - 2*w**2 + 1/4*w**4 + 1 + 1/5*w**5. Factor k(i).
i*(i - 2)*(i + 1)*(i + 2)
Let -10/3*v**2 + 8/3 + 2/3*v**4 + 5/3*v**3 - 1/3*v**5 - 4/3*v = 0. Calculate v.
-2, -1, 1, 2
Let p(t) be the first derivative of -5*t**2 - 15*t + 7 + 5/12*t**4 + 5/6*t**3. Let j(w) be the first derivative of p(w). Factor j(m).
5*(m - 1)*(m + 2)
Let d(v) be the third derivative of -1/48*v**4 + 0 - v**3 - 16*v**2 + 1/120*v**5 - 4*v. What is t in d(t) = 0?
-3, 4
Let m(x) = -10*x**2 - 37*x + 13. Let c be 9*(-4 - (-50)/15). Let i(j) = -5*j**2 - 19*j + 6. Let s(q) = c*m(q) + 13*i(q). Factor s(g).
-5*g*(g + 5)
Factor 45/4 - 3/8*m**3 + 9/2*m**2 + 129/8*m.
-3*(m - 15)*(m + 1)*(m + 2)/8
Factor 61950/17*u - 706/17*u**2 + 2/17*u**3 + 62658/17.
2*(u - 177)**2*(u + 1)/17
Let y(u) = u - 27. Let p be y(22). Let i be p - -532 - (0 + 3 + -3). Let 542*r**2 - i*r**2 - 2*r**5 - 15*r**3 + 5*r**5 + 12*r - 12 - 3*r**4 = 0. Calculate r.
-2, -1, 1, 2
Let m(q) be the third derivative of q**6/840 + q**5/70 - 13*q**4/24 - 74*q**2. Suppose m(o) = 0. What is o?
-13, 0, 7
Let a be (11592/648 - 18)*(1 - 101/2). Factor -7 - a*f**3 - 33/2*f**2 - 1/2*f**4 - 37/2*f.
-(f + 1)**2*(f + 2)*(f + 7)/2
Let y = 16511 + -16507. Let v be 0 + (-2*2)/(-2). Factor -1/5*m**5 + 0*m + 3/5*m**y + 1/5*m**v - 3/5*m**3 + 0.
-m**2*(m - 1)**3/5
Let k(v) = 9*v - 187. Let g be k(21). Suppose g*l**2 + 36 + 60 + 44*l + l**2 + 3*l**2 - 8*l**2 = 0. Calculate l.
-2, 24
Suppose -4*v = -4*n + 36, 15*v = n + 17*v + 6. Let h(z) be the first derivative of -23 + 0*z**2 - 1/8*z**n + 0*z**3 + 0*z. Solve h(f) = 0.
0
Suppose 12541 = 15*m - 2909. Let q = 1030 - m. Factor q + 24/7*s**3 + 16/7*s**4 + 4/7*s + 16/7*s**2 + 4/7*s**5.
4*s*(s + 1)**4/7
Factor 137 - 2*g**2 + 90 + 271*g + 421 - 917*g.
-2*(g - 1)*(g + 324)
Let m(z) be the first derivative of -4/3*z**2 + 7/9*z**3 - 4/3*z + 5/12*z**4 + 48. Factor m(u).
(u - 1)*(u + 2)*(5*u + 2)/3
Factor -1/4*m**4 + 209*m - 605/4 + 7*m**3 - 129/2*m**2.
-(m - 11)**2*(m - 5)*(m - 1)/4
Let -2/17*h**3 - 396050/17*h + 0 + 1780/17*h**2 = 0. What is h?
0, 445
Factor -4/9*i**2 + 1/9*i**3 + 4/9 - 1/9*i.
(i - 4)*(i - 1)*(i + 1)/9
Let p(l) = -l + 9. Let d be p(1). Let s be (-4)/(-18) - -4*(-50)/(-720). Factor -4*o + d + s*o**2.
(o - 4)**2/2
Let t(k) = 2*k**2 - 5*k - 344. Let q be t(-12). Let j(u) be the first derivative of 1/5*u**5 - 5/3*u**3 - 3/4*u**q + 4*u + 5 + 3/2*u**2. Factor j(b).
(b - 4)*(b - 1)*(b + 1)**2
Let i(q) be the third derivative of q**6/300 + 67*q**5/50 + 4489*q**4/20 + 300763*q**3/15 + 1080*q**2. Factor i(y).
2*(y + 67)**3/5
Let k(c) be the third derivative of 2*c**2 + 65 + 3/16*c**4 + 7/6*c**3 + 0*c + 1/120*c**5. What is m in k(m) = 0?
-7, -2
Suppose -3097 = -7*b - 773. Let l = 335 - b. Factor -4/9*o**l + 2/9*o**2 + 0 + 2/9*o.
-2*o*(o - 1)*(2*o + 1)/9
Suppose -40*p**3 + 35*p**4 + 22*p**5 - 76*p**4 - 21*p**5 + 47*p**4 = 0. What is p?
-10, 0, 4
Suppose 144*n - 69*n + 7 = 7. Factor 1/4*p + n + 1/8*p**2.
p*(p + 2)/8
Let k(u) = -u + 3. Let o be k(0). Factor -256*z - 83 - 52*z**2 - 3*z**3 + 4*z**3 + 3*z**o - 189.
4*(z - 17)*(z + 2)**2
Let g(i) = -74*i**3 + 53*i**2 - 235*i + 181. Let q(b) = -394*b**3 + 264*b**2 - 1174*b + 904. Let f(m) = -16*g(m) + 3*q(m). Factor f(a).
2*(a - 23)*(a - 4)*(a - 1)
Suppose 246*o - 123 = -115 + 280 + 696. Determine b, given that 84 + 6*b**3 - 24*b - 3/7*b**o - 135/7*b**2 = 0.
-2, 2, 7
Let w = 152/375 - 2/375. Let g(z) be the third derivative of 0*z - 6*z**2 - w*z**5 + 19/8*z**4 - 1/8*z**6 - 3*z**3 + 0. Suppose g(k) = 0. What is k?
-3, 2/5, 1
Suppose 0 = -5*y + 47 - 7. Let c be (-5)/((-5)/y) + -5. Find z, given that 8/7*z**c - 10/7*z**2 - 2/7*z**4 + 0 + 4/7*z = 0.
0, 1, 2
Let h(n) be the third derivative of n**6/120 - n**5/60 - n**3/6 - 34*n**2. Let m(f) = -19 - 4*f**2 + 22 + 0*f**2. Let r(v) = -5*h(v) + 5*m(v). Factor r(s).
-5*(s - 1)*(s + 2)**2
Let b be 81/(-9)*4/(-18). What is a in -1547 + 5*a**2 + 6*a**2 - a**b + 1547 + 5*a**3 = 0?
-2, 0
Let s = -2/6781 + 13772/712005. Let d(r) be the third derivative of 1/3*r**4 + 0*r**3 + 0*r - s*r**7 - 1/15*r**6 + 1/15*r**5 + 23*r**2 + 0. Factor d(b).
-4*b*(b - 1)*(b + 1)*(b + 2)
Let j = -1075 + 21