et b(j) be the first derivative of -j**6/45 + 254*j**5/25 - 5952*j**4/5 - 221176*j**3/45 - 512*j**2/5 + 98304*j/5 - 3839. What is c in b(c) = 0?
-2, 1, 192
Let n(o) be the third derivative of -o**7/105 + o**6/5 + 22*o**5/15 - 40*o**4 - 1600*o**3/3 + 1522*o**2. Determine z, given that n(z) = 0.
-4, 10
Let y(b) be the second derivative of -b**5/40 - 29*b**4/12 - 713*b**3/12 + 961*b**2 + 7*b + 106. Determine p, given that y(p) = 0.
-31, 4
Factor 5431808/9 + 2/9*k**2 + 6592/9*k.
2*(k + 1648)**2/9
Let m(b) = -4*b - 1. Let f(u) = 6*u**3 + 92*u**2 + 148*u - 101. Let z(n) = 2*f(n) + 22*m(n). Factor z(y).
4*(y + 2)*(y + 14)*(3*y - 2)
Let o be (5/2 - 0)/(195/156)*1. Let y(f) be the first derivative of 5/2*f**o - 28 + 5/2*f**3 + 5/8*f**4 + 0*f. Find c such that y(c) = 0.
-2, -1, 0
Let b = 26442029/34644 + 1/8661. Let i = b - 758. Determine u so that 9/2 + i*u + 3/4*u**2 = 0.
-6, -1
Let o(v) be the second derivative of 2*v**6/5 + 52*v**5/5 - 370*v**4/3 + 328*v**3 + 414*v**2 - 4*v + 595. Find j, given that o(j) = 0.
-23, -1/3, 3
Solve -74*q**4 - 6*q**3 + 84*q + 96*q**2 + 77*q**4 + 45*q**3 - 6*q**3 = 0.
-7, -2, 0
Let m = 429368 + -3005552/7. Factor 3/7*q**2 + 0 + m*q.
3*q*(q + 8)/7
Let n be 18/27*(-4 + 35/10)*-1. Let f(l) be the third derivative of 0*l**3 - 5/8*l**4 + 0*l + 16*l**2 + 0 - 1/24*l**6 + n*l**5. Factor f(m).
-5*m*(m - 3)*(m - 1)
Factor -46 - 136/3*q + 2/3*q**2.
2*(q - 69)*(q + 1)/3
Let g(w) be the third derivative of 0 + 3*w + 1/240*w**5 - 2*w**2 + 19/24*w**4 + 361/6*w**3. Find v, given that g(v) = 0.
-38
Factor 72 + 17*y - 4967*y**3 - 112*y**2 + 4987*y**3 - 77*y.
4*(y - 6)*(y + 1)*(5*y - 3)
Let w(g) be the third derivative of g**6/120 - 2*g**5/3 - 707*g**4/24 - 441*g**3 + g**2 - 15*g + 8. Factor w(p).
(p - 54)*(p + 7)**2
Let w(l) be the third derivative of -7*l**5/150 - 3*l**4/8 - 3*l**3/10 - l**2 - 52*l - 58. Suppose w(y) = 0. What is y?
-3, -3/14
Suppose 0 = -2*o - y - 5, -3*y = y + 20. Suppose o = 17*a - 37*a + 40. Solve 2/9*x**a - 2/3*x + 4/9 = 0 for x.
1, 2
Suppose 412051*a**4 - 812*a**2 - 593*a**2 + 695*a**3 - 412046*a**4 + 705*a = 0. Calculate a.
-141, 0, 1
Let k(p) be the second derivative of -p**9/40320 + 13*p**8/53760 + p**7/2016 + 19*p**4/4 + 59*p. Let i(c) be the third derivative of k(c). Factor i(n).
-n**2*(n - 5)*(3*n + 2)/8
Let a be 120/((-120)/(-32) - 6/2). Factor 12032*y + a*y**4 - 176*y**5 - 4096 + 3340*y**3 - 11524*y**2 - 174*y**5 + 354*y**5 + 84*y**4.
4*(y - 1)**3*(y + 32)**2
Let i = -7/2669 + -20265682/13345. Let f = -1512 - i. Factor 18/5*h**2 + 18/5 + 3/5*h**3 + f*h.
3*(h + 1)*(h + 2)*(h + 3)/5
Let y = 288 + -286. Let w(j) = j + 8. Let m be w(-6). Factor 3*c**2 - 5*c**3 + 4*c**2 - 5*c + c**m + y*c**2.
-5*c*(c - 1)**2
Determine j so that 8/11*j**3 - 54/11 + 6/11*j**2 - 72/11*j = 0.
-3, -3/4, 3
Let x(v) = -18*v - 177. Let f be x(-10). Solve 4*u**3 + 7*u**3 + 4 - 12*u**2 - 4*u**3 + u**f = 0.
-1/2, 1
Suppose -45160*y - 612 + 14699*y + 14409*y + 15140*y - 297*y**2 + 3*y**3 = 0. What is y?
-2, -1, 102
Let f(a) = 246*a**4 - 5455*a**3 - 17*a**2 - 17*a. Let p(g) = 87*g**4 - 1818*g**3 - 6*g**2 - 6*g. Let w(r) = -6*f(r) + 17*p(r). Suppose w(s) = 0. What is s?
-608, 0
Determine n, given that 5043/5 - 246/5*n + 3/5*n**2 = 0.
41
Let r be -2596 + 2593 - (-7 + 1)/(13 - 12). Solve 0 + 3/2*k**2 - 3/2*k**5 - 3/2*k**4 + 0*k + 3/2*k**r = 0.
-1, 0, 1
Let g(o) = -o**2 - 5186*o + 2239486. Let l(x) = 5*x**2 + 15559*x - 6718457. Let n(r) = 7*g(r) + 2*l(r). Find k such that n(k) = 0.
864
Let z(l) be the second derivative of 2*l**7/21 - 4*l**6/3 - 527*l**5/5 + 2312*l**4 + 3050*l. Factor z(r).
4*r**2*(r - 17)**2*(r + 24)
Factor -457*a**2 + 225*a**2 + 235*a**2 + 32282679 - 20016*a + 16388489 - 15284480.
3*(a - 3336)**2
Suppose 12*n = 16*n - 4724. Factor 8*d**2 - n*d + 8*d**2 - 4*d**3 + 1169*d.
-4*d*(d - 3)*(d - 1)
Let v = 4066/15 - 1342/5. Let a(i) be the second derivative of -4/9*i**3 + 11*i + v*i**2 + 1/36*i**4 + 0. Let a(m) = 0. What is m?
4
Let s(v) be the third derivative of -v**7/42 - 35*v**6/24 - 107*v**5/4 - 1105*v**4/24 + 1445*v**3/3 - 745*v**2. Factor s(c).
-5*(c - 1)*(c + 2)*(c + 17)**2
Let d(g) be the first derivative of -5*g**3/3 + 330*g**2 + 1340*g - 104. Factor d(a).
-5*(a - 134)*(a + 2)
Let s(m) = 4*m**2 + 633*m - 632. Let j be s(1). Factor 3/7*x**3 + 0 - 1/7*x**2 + 0*x + 1/7*x**j - 3/7*x**4.
x**2*(x - 1)**3/7
Let i(l) be the first derivative of -4/3*l**3 - 179 + 0*l**2 - l**4 - 1/5*l**5 + 0*l. Factor i(q).
-q**2*(q + 2)**2
Let p be 18/(-261) - (-2756)/7163. Let w be (5 + (-2)/1)/(627/44). Factor p*d**2 - w - 2/19*d.
2*(d - 1)*(3*d + 2)/19
Suppose -11*k = 28*k + 2*k. Factor 1/11*l**3 + 6/11*l + k - 7/11*l**2.
l*(l - 6)*(l - 1)/11
Let s(u) = 4*u**5 + 12*u**4 - 14*u**3 - 6*u**2 + 12*u. Let n(o) = 13*o**5 + 37*o**4 - 42*o**3 - 16*o**2 + 36*o. Let d(c) = -2*n(c) + 7*s(c). Factor d(x).
2*x*(x - 1)**2*(x + 1)*(x + 6)
Let d be 183 - (-1 - -4)/((-6)/8). Let r = d - 373/2. Factor 1/2*i**2 + r*i**3 - i + 0.
i*(i - 1)*(i + 2)/2
Suppose -5*d**3 - 9535*d + 660 - 5425 - 68*d**2 - 3349*d**2 - 1358*d**2 = 0. Calculate d.
-953, -1
Let x be ((-675)/60 + 12)/((-1)/(-4)). Let n be 0 - (-2 + 0/(-2)). Suppose 39*h**n + x*h**3 + 3*h**4 - 36*h**2 + 3*h**3 = 0. Calculate h.
-1, 0
Factor -1/3*g**2 - 680/3 + 114*g.
-(g - 340)*(g - 2)/3
Let d(y) = -519*y**2 + 6009*y + 11949. Let f(b) = -94*b**2 + 1202*b + 2390. Let c(s) = -2*d(s) + 11*f(s). What is a in c(a) = 0?
-299, -2
Let f(a) be the second derivative of 1/50*a**5 - 2 - 45*a + 1/150*a**6 + 40*a**2 - 4/3*a**3 - 13/20*a**4. Determine q, given that f(q) = 0.
-5, 4
Suppose 13 = 4*m - 4*s - 19, -4*m - 3*s = 3. Let y(i) be the third derivative of -2/3*i**m + 0*i + 5*i**2 + 0 - 4/15*i**5 + 5/6*i**4. Factor y(f).
-4*(f - 1)*(4*f - 1)
Suppose -14*y + 18*y = -10*y. Let p be (0 - y) + (-2)/(-5). Find a, given that -2/5 + 4/5*a**2 + 0*a**3 - p*a**4 + 0*a = 0.
-1, 1
Let v(l) = -l + 8. Let x be v(-15). Suppose 3*d - 52 = 2*m, -5*m - x = -2*d + 30. Factor -1 + 13 + 3*b**2 + d*b - 4.
(b + 4)*(3*b + 2)
Let g = -2053/3210 + 72/107. Let t(z) be the third derivative of -7*z**2 - g*z**6 - 8/3*z**3 + 4/15*z**5 + 1/6*z**4 + 0*z + 0. Factor t(h).
-4*(h - 4)*(h - 1)*(h + 1)
Let i(c) be the third derivative of -5/2*c**3 + 1/20*c**5 + 0*c + 1/2*c**4 + 0 + 130*c**2. Let i(p) = 0. Calculate p.
-5, 1
Let w(i) be the third derivative of -6*i**2 - 1/120*i**4 - 1/50*i**6 + 0 + 0*i + 1/50*i**5 + 19/6*i**3. Let q(f) be the first derivative of w(f). Factor q(y).
-(6*y - 1)**2/5
Let v(g) = 11*g**3 + 71*g**2 - 154*g. Let r(h) = -h**3 - h**2 + 2*h. Let z(b) = 8*r(b) + v(b). Factor z(s).
3*s*(s - 2)*(s + 23)
Let g = 56 + -54. Suppose 3*z - g*n - 11 = 0, 4*z - 7*z - 3*n + 6 = 0. Factor -4/5*d**2 + 21/10*d + 1/10*d**z - 9/5.
(d - 3)**2*(d - 2)/10
Let n(u) = -u**4 - 2322*u**3 - 9010*u**2 - 9006*u + 7. Let t(k) = -k**4 - 1158*k**3 - 4506*k**2 - 4502*k + 3. Let f(o) = 3*n(o) - 7*t(o). Factor f(r).
4*r*(r + 2)**2*(r + 281)
What is v in -42*v**3 + 24*v**2 - 551*v + 298*v + 3*v**4 - 30 + 3*v**4 + 292*v + 3*v**5 = 0?
-5, -1, 1, 2
Let -128/7*h**4 - 446/7 - 5354/7*h - 21432/7*h**2 - 28640/7*h**3 = 0. Calculate h.
-223, -1/4
Let x be 3608/138 + (-3084)/(-5911). Find q such that -x*q**2 - 4*q**3 + 12*q + 56/3 = 0.
-7, -2/3, 1
Let t(d) = 8*d**2 - 453*d - 3766. Let g be t(64). Factor 55/6*a**2 - g*a**3 + 5/6*a**4 + 0 + 0*a.
5*a**2*(a - 11)*(a - 1)/6
Factor 2/7*g**2 - 30/7*g - 32/7.
2*(g - 16)*(g + 1)/7
Let p = -302 - -200. Let k be (-3)/(p/4) - 806/(-663). Factor 2*a**4 + 2/3*a**5 + k*a**3 - 4/3*a**2 - 2*a - 2/3.
2*(a - 1)*(a + 1)**4/3
Let g(l) = l**3 - 5*l**2 - 6*l. Let j be g(6). Let f = 109546 + -219087/2. Factor -10 + j*x + f*x**2.
5*(x - 2)*(x + 2)/2
Suppose 4*a = -13453 + 13453. Let r(i) be the second derivative of 1/6*i**4 + 7*i + 1/20*i**5 + 0*i**2 + a - 4/3*i**3. Suppose r(f) = 0. What is f?
-4, 0, 2
Let m = 449/39 + -744/65. Let y(w) be the first derivative of 0*w**2 + 0*w**4 + 4/9*w**3 + 0*w - m*w**5 - 45. Factor y(d).
-d**2*(d - 2)*(d + 2)/3
Let t(j) be the first derivative of 2*j**3/3 + 929*j**2 - 1860*j - 438. Factor t(l).
2*(l - 1)*(l + 930)
Let g = -451 + 455. Let x(y) = -5*y**4 + 4*y**3 - 6*y**2 + 16*y - 1. Let z(d) = 9*d**4 - 9*d**3 + 15*d**2 - 32*d + 3. Let v(h) = g*z(h) + 7*x(h). Factor v(c).
(c - 5)*(c - 1)**3
Factor -54*m**3 + 0 + 2/5*m