 61. Let l be (-72)/v*((-8)/(-6) + -2). Suppose 4/5*m**4 + 52/5*m**2 + l*m**3 + 16/5 + 48/5*m = 0. What is m?
-2, -1
Factor -1265 - 1052 + 3933 - 806*h - h**2.
-(h - 2)*(h + 808)
Let s(o) = 65*o**2 + 1452*o + 276. Let x(t) = -2465*t**2 - 55175*t - 10490. Let y(g) = 115*s(g) + 3*x(g). Factor y(p).
5*(p + 18)*(16*p + 3)
Let l(i) = -i**2 + 79. Let t be l(16). Let k = -1235/7 - t. Factor -8/7*a**4 + 0*a - 2*a**3 + k*a**2 + 0.
-2*a**2*(a + 2)*(4*a - 1)/7
Let f(z) = -9*z**4 - 6*z**3 + 12*z**2 + 24*z - 21. Let a(o) = 42 - 23*o**2 + 19 + 11*o**3 - 18 + 19*o**4 - 50*o. Let y(r) = 6*a(r) + 13*f(r). Factor y(c).
-3*(c - 1)**2*(c + 1)*(c + 5)
Let s(l) be the third derivative of 0*l**3 - 2/315*l**5 - 1/735*l**7 + 0 + 1/105*l**6 + 0*l**4 + 47*l**2 + 0*l - 5/3528*l**8. Let s(f) = 0. What is f?
-2, 0, 2/5, 1
Factor -11 - 24*x**4 - 15*x**3 - 3 + 24*x**4 + x**4 + 13*x**2 + 15*x.
(x - 14)*(x - 1)**2*(x + 1)
Let t be (1/(-18))/((-70)/41685) + (-2)/(-8). What is v in 40*v - t - 7*v**2 + 1/3*v**3 = 0?
1, 10
Let y(s) be the second derivative of -1/44*s**4 + 2/33*s**3 - 155*s - 1/220*s**5 + 0 + 0*s**2. Factor y(x).
-x*(x - 1)*(x + 4)/11
Let o be 10/4 + (-18)/12. Suppose o = w, -2*r = r - 2*w - 10. Let r*z**3 - 13*z**2 + 13*z + 7*z - 5*z**2 - 6 = 0. What is z?
1/2, 1, 3
Let w(b) be the third derivative of b**6/380 + 2*b**5/285 - 13*b**4/228 + 2*b**3/19 + 1099*b**2. Factor w(g).
2*(g - 1)*(g + 3)*(3*g - 2)/19
Let j = 80391 + -79716. Factor 1/4*d**3 + j*d + 6750 + 45/2*d**2.
(d + 30)**3/4
Let t(c) = 17*c**2 + 16*c**2 - 280*c - 13*c**2 - 19*c**3 + 294*c. Let a(l) = 205*l**3 - 220*l**2 - 155*l. Let i(m) = -6*a(m) - 65*t(m). Factor i(y).
5*y*(y + 2)**2
Let a(u) be the second derivative of -u**4/18 - 38*u**3/9 + 56*u**2 - 1152*u. Factor a(y).
-2*(y - 4)*(y + 42)/3
Let r be (-6)/(-12)*(1 + 3 + -2). Let h(w) = 2*w**3 - w**2 + 1. Let v be h(r). Factor -s**v - s - 2 + 14*s**2 - 10*s**2.
(s - 1)*(3*s + 2)
Let z = 3019 + -21130/7. Find o such that 6/7 - 9/7*o**2 + z*o**4 + 3/7*o - 3/7*o**3 = 0.
-1, 1, 2
Let s(f) = f**3 + 174*f**2 + 413*f + 41523. Let g be s(-173). Suppose -2/3*v**g + 0 - 4/3*v**2 + 8/3*v + 1/3*v**4 = 0. Calculate v.
-2, 0, 2
Let o = -1568187/2 + 784094. Solve 2/3*d + 0 + 1/6*d**5 - 1/3*d**4 + 2/3*d**2 - o*d**3 = 0 for d.
-1, 0, 2
Let z = -306922/3 - -2149078/21. Factor z*s + 5408/7 + 2/7*s**2.
2*(s + 52)**2/7
Suppose 157*t + 20 = 156*t. Let n be (-2)/(-6) + t/(-300). Factor -2/5*b**2 - 8/5*b + 0 + 8/5*b**3 + n*b**4.
2*b*(b - 1)*(b + 1)*(b + 4)/5
Let t(p) be the third derivative of p**6/480 + p**5/240 - p**4/48 - 885*p**2. Factor t(y).
y*(y - 1)*(y + 2)/4
Factor -2*f**2 + 126/5 + 4/5*f**3 - 248/5*f.
2*(f - 9)*(f + 7)*(2*f - 1)/5
Determine l so that -12/5*l**4 + 0 + 0*l - 628/5*l**3 - 616/5*l**2 = 0.
-154/3, -1, 0
Let u(i) be the first derivative of 4/3*i**3 - 3 - i + 3/2*i**2. Factor u(c).
(c + 1)*(4*c - 1)
Let d(k) be the second derivative of -29*k**3/6 + 3*k**2 - 5*k. Let b be d(-3). Solve -44*w + b*w**2 + 3 - 16*w**3 + 5 - 41*w**2 = 0 for w.
1/4, 1, 2
Let g(d) = d**3 + 14*d**2 - 124*d - 1519. Let x be g(-9). Factor -9/5*q - 1/5*q**x - 14/5.
-(q + 2)*(q + 7)/5
Let d(o) be the first derivative of -10 - 4/7*o - 5/14*o**4 - 6/7*o**3 - 2/35*o**5 - o**2. Factor d(p).
-2*(p + 1)**3*(p + 2)/7
Let k(j) be the third derivative of 0*j - 1/12*j**6 + 0 + 5/24*j**4 + 1/6*j**5 + 5/336*j**8 - 5/6*j**3 - 1/42*j**7 + 97*j**2. Let k(z) = 0. Calculate z.
-1, 1
Let h(k) be the third derivative of -k**8/560 + k**7/350 + 9*k**6/40 + 83*k**5/100 + k**4 + 3*k**2 + 34. Determine q, given that h(q) = 0.
-5, -1, 0, 8
Let o(w) = -w**3 - 15*w**2 - 20*w - 14. Let l be o(-14). Let d = 72 - l. Find r, given that -d*r**2 + 143*r**4 - 141*r**4 + 4*r**2 - 4*r**2 = 0.
-1, 0, 1
Suppose -917 + 929 = 3*a. Let t(c) be the third derivative of -24*c**2 - 1/90*c**5 + 4/9*c**3 + 0*c + 0 + 1/12*c**a. Suppose t(d) = 0. Calculate d.
-1, 4
What is p in 444*p - 3/4*p**2 - 65712 = 0?
296
Let c be (119/28)/((-1)/(-4)). Factor -c*w**3 - 55 - 18*w**2 + 14*w**3 - 24*w + 55.
-3*w*(w + 2)*(w + 4)
Let 0 + 82/3*h**3 - 854*h**2 + 7442/9*h - 2/9*h**4 = 0. Calculate h.
0, 1, 61
Let -77/3 + 1/3*i - 2/3*i**3 + 1/3*i**5 + 154/3*i**2 - 77/3*i**4 = 0. What is i?
-1, 1, 77
Let z(b) = -b**2 - 9*b - 9 - 6*b - b**3 + 7*b - 2*b**2. Let v be z(-2). Determine f, given that 5*f**v + 5/2*f**4 - 5/2*f**5 - 5*f**2 + 5/2 - 5/2*f = 0.
-1, 1
Factor -840 - 3085*y**2 - 5*y**5 + 450091*y**3 - 175*y**4 - 448696*y**3 - 1648*y + 4358*y.
-5*(y - 4)*(y - 1)**3*(y + 42)
Suppose 18073*a + k = 18069*a + 86, -5*a - 5*k = -160. Suppose 0 + 0*n - a*n**3 - 30/7*n**4 - 14*n**2 - 2/7*n**5 = 0. What is n?
-7, -1, 0
Let v(r) be the second derivative of -r**7/504 + 7*r**6/36 - 49*r**5/6 + 9*r**4 - 41*r. Let w(q) be the third derivative of v(q). Determine z so that w(z) = 0.
14
Let k be 1016*2/(1 + -13). Let w = k + 170. Factor 2/9*o + w*o**3 + 2/3*o**2 + 2/9*o**4 + 0.
2*o*(o + 1)**3/9
Let p(o) be the first derivative of -9 - 1/20*o**5 + 0*o - 7/72*o**4 + 3*o**2 + 1/9*o**3. Let n(c) be the second derivative of p(c). Factor n(h).
-(h + 1)*(9*h - 2)/3
Let m(k) = k**2 + 25*k + 118. Let b be m(-19). Determine d so that -42 - 128*d - 15*d**4 - 15*d**b - 48*d**3 - 17*d**4 - 132*d**2 + 45*d**4 = 0.
-21, -1
Let g(x) = -7*x**2 - 301*x + 512. Let a(u) = u**2 + u - 36. Let i(f) = 30*a(f) + 5*g(f). Suppose i(j) = 0. What is j?
-296, 1
Let r(l) = -6395*l - 95922. Let f be r(-15). Suppose -5/2*k**2 + 0 - 3/4*k + k**4 + 9/4*k**f = 0. Calculate k.
-3, -1/4, 0, 1
Let v = 399035462/771922335 + 55/502881. Let q = 5/307 + v. Factor 0 + 2/3*r**3 + 2/15*r**2 + 0*r + q*r**4.
2*r**2*(r + 1)*(4*r + 1)/15
Let m = -624 - -625. Let g(o) = -o**3 + o - 1. Let p(x) = -3*x**3 - 102*x**2 - 39*x + 6. Let d(r) = m*p(r) + 6*g(r). Factor d(f).
-3*f*(f + 11)*(3*f + 1)
Let z(b) be the second derivative of 13/2*b**3 + 9/20*b**5 - 1 - 60*b - 7/2*b**4 + 9*b**2. Solve z(k) = 0.
-1/3, 2, 3
Suppose m = 5*s - 11, -s - m = 23 - 30. Find b, given that -b - 29*b - 359*b**2 + 324*b**2 + 15*b**s = 0.
-2/3, 0, 3
Let b be 9/((-324)/(-320))*(-434)/(-1085). Factor -b - 32/9*j + 2/9*j**2 + 2/9*j**3.
2*(j - 4)*(j + 1)*(j + 4)/9
Let h = 485/12 - 2953/12. Let b = h + 206. Let 1/6*s + 1/6*s**2 - b = 0. Calculate s.
-2, 1
Let a = 23522 - 33848156/1439. Let r = a + 1435/2878. Solve 5/4*y + 3/4*y**2 + r = 0 for y.
-1, -2/3
Suppose -3*p = 3*a - 3, 0 = p - 3*p - 10. Let y be 2*a/(-24)*(1 + -7). Solve -5*m**2 - 24*m**3 + 2*m**4 + 0*m**4 - 2*m - y*m**4 + 20*m**3 = 0 for m.
-2, -1, 0
Let l(f) be the second derivative of -5*f**7/42 - 19*f**6/6 - 11*f**5 + 80*f**4/3 + 652*f - 2. Find d such that l(d) = 0.
-16, -4, 0, 1
Let a = -616949/30 + 20565. Let f(k) be the third derivative of 0 + 0*k**3 - 1/180*k**6 - 1/18*k**4 + 0*k + a*k**5 + 27*k**2. Factor f(p).
-2*p*(p - 2)*(p - 1)/3
Let l(z) be the first derivative of -z**6/285 - 3*z**5/190 - z**4/57 - 77*z + 5. Let b(v) be the first derivative of l(v). Factor b(y).
-2*y**2*(y + 1)*(y + 2)/19
Let d(a) = -a**2 + 36. Let f be d(4). Factor 66*w**2 - 3*w**3 - 595*w + 2*w**3 - f*w**2 + 642*w.
-w*(w - 47)*(w + 1)
Suppose 0 = -3910*w + 3904*w - 24. Let s(f) = f**3 - 21*f - 18. Let a be s(w). Factor 0 + 5/4*q**a + 0*q + 1/4*q**3.
q**2*(q + 5)/4
Let g(j) be the second derivative of -5*j**4/6 - 109*j**3 - 130*j**2 + 4123*j. Factor g(q).
-2*(q + 65)*(5*q + 2)
Determine p, given that -560/3*p - 4/3*p**3 + 368/3 + 196/3*p**2 = 0.
1, 2, 46
Let d(u) be the second derivative of -u**6/30 + 321*u**5/10 - 11395*u**4 + 4761175*u**3/3 + 29815125*u**2/2 + 1423*u. Factor d(l).
-(l - 215)**3*(l + 3)
Let r = -14285/7 - -2042. Let d = -77/2 + 555/14. Determine z, given that 20/7*z - r*z**3 + d + 6/7*z**2 = 0.
-2/3, 2
Factor 183 - 37*h - 27*h + 4*h**2 + 29 + 44.
4*(h - 8)**2
Let y = -431 + 436. Let p be 40/80*6/y. Factor p*n**4 - 3/5*n**5 - 3/5*n + 3/5 - 6/5*n**2 + 6/5*n**3.
-3*(n - 1)**3*(n + 1)**2/5
Suppose -11 - 7 = 5*p - 2*c, -2*p = c. Let m be p/(-5) + (-6992)/(-345). Factor 32/3*i**2 - m*i + 4 + 6*i**3.
2*(i - 1)*(i + 3)*(9*i - 2)/3
Let o = -84198 + 84202. What is i in 4/9 - 2/3*i**3 + 1/9*i**o + 13/9*i**2 - 4/3*i = 0?
1, 2
Suppose -11*t**2 + 2*t**4 - 114*t**5 + 13*t**3 + 113*t**5 - 11*t**4 + 8*t**3 = 0. What is t?
-11, 0, 1
Let b be 72/45 + 220/550. Find u, given that -2/9*u**4 - 10/9*u - 2/3*u**b +