z**4 + 225/2*z**3 + 0 + 35/2*z**2 - 110*z = 0.
-11, -1, 0, 1, 4
Let k(d) = 3*d**3 + 637*d**2 - 868*d - 848. Let l(p) = -5*p**3 - 635*p**2 + 870*p + 850. Let s(n) = 5*k(n) + 6*l(n). Determine u so that s(u) = 0.
-43, -2/3, 2
Let s(d) be the third derivative of -d**10/75600 + d**8/10080 + 53*d**5/60 + 16*d**2. Let l(h) be the third derivative of s(h). Suppose l(z) = 0. Calculate z.
-1, 0, 1
Let l = -23 - -3. Let q be 4 + 1 - (-12)/l*5. Factor -5*h**q - 2*h - 4*h - 3*h - h.
-5*h*(h + 2)
Let c(z) be the second derivative of 0*z**2 - 1/30*z**6 - 1/10*z**5 + 0 - 48*z + 1/12*z**4 + 1/3*z**3. Let c(a) = 0. Calculate a.
-2, -1, 0, 1
Let k = 69 + -64. Find m, given that -121*m + k*m**2 - 49*m + 1280 + 10*m = 0.
16
Let z(u) be the first derivative of u**5/5 + 521*u**4/4 - 1046*u**3/3 - 8303. Suppose z(w) = 0. What is w?
-523, 0, 2
Let s(n) be the third derivative of n**6/1800 - n**5/100 + 3*n**4/40 - 11*n**3 + 210*n**2. Let i(b) be the first derivative of s(b). Factor i(j).
(j - 3)**2/5
Suppose -3/8*o**2 - 513 + 4107/8*o = 0. Calculate o.
1, 1368
Let d(g) be the first derivative of 4/15*g**5 + 7 - 2/3*g**3 - 5*g**2 + 0*g - 1/6*g**4 + 2/15*g**6. Let w(q) be the second derivative of d(q). Factor w(l).
4*(l + 1)*(2*l - 1)*(2*l + 1)
Let f(t) be the third derivative of t**6/15 + 133*t**5/90 - 133*t**4/36 - 4*t**3/3 + 1014*t**2. Find g, given that f(g) = 0.
-12, -1/12, 1
Let v = 313281/40 + -7832. Let u(s) be the third derivative of -3/20*s**5 + 0 + 0*s + v*s**6 + 0*s**3 + 0*s**4 - 12*s**2. Solve u(m) = 0 for m.
0, 3
Let m(z) = 2*z**2 + 312*z - 5502. Let f be m(16). Suppose 82/17*b + 38/17*b**f + 42/17 - 2/17*b**3 = 0. Calculate b.
-1, 21
Let q(g) be the first derivative of g**4/12 - 4*g**3/3 + 17*g**2/6 + 10*g - 5095. Factor q(d).
(d - 10)*(d - 3)*(d + 1)/3
Suppose -710*s + 934 = -1196. Solve 0*f - 1/6*f**4 + 1/6*f**2 + 0*f**s + 0 = 0.
-1, 0, 1
Find f, given that 18225 - 90*f + 1/9*f**2 = 0.
405
Factor 6136/3*o + 2/3*o**2 + 4706312/3.
2*(o + 1534)**2/3
Suppose 282*x + 1312 - 2981 = -541. Factor 4/3*k**2 + 0 + 1/3*k**3 - 4/3*k - 1/3*k**x.
-k*(k - 2)*(k - 1)*(k + 2)/3
Let m(u) be the third derivative of u**8/420 + 37*u**7/525 - u**6/12 - 107*u**5/150 + 131*u**4/60 - 38*u**3/15 + 2*u**2 - 125*u. Let m(z) = 0. What is z?
-19, -2, 1/2, 1
Let d(g) = -4*g**3 - 23*g**2 - 49*g - 33. Let n(j) = -44*j**3 - 250*j**2 - 538*j - 366. Let h(b) = 34*d(b) - 3*n(b). Factor h(w).
-4*(w + 1)**2*(w + 6)
Let s(z) be the second derivative of 28*z**2 + 1 - 6*z - 1/3*z**4 - 26/3*z**3. What is y in s(y) = 0?
-14, 1
Let j be 1 + 3*(-6)/(-18). Determine p so that -2*p + 142*p**2 + 156*p**j - 317*p**2 = 0.
-2/19, 0
Solve 2528160/7*i + 3/7*i**3 + 5034336/7 + 786*i**2 = 0.
-916, -2
Let h(k) be the third derivative of -k**5/30 - 167*k**4/42 + 32*k**3/7 + 3*k**2 + 3*k + 18. Factor h(t).
-2*(t + 48)*(7*t - 2)/7
Suppose -64*l - 18 + 8 + 26*l**2 + 26*l**2 - 56 - 50*l**2 = 0. Calculate l.
-1, 33
Suppose 0 = 5*j - 2 - 8. Let -12*t**j + 192*t - 32*t - 28*t**3 - 4*t**3 - 5*t**4 + 64 = 0. What is t?
-4, -2/5, 2
Suppose -13 - 111 = -31*k. Let q be (-7)/(-6) - k/(-12). Factor q*v**2 + 3/8*v**3 + 15/8*v + 3/4.
3*(v + 1)**2*(v + 2)/8
Let n(u) be the third derivative of -u**6/300 + 53*u**5/150 + 11*u**4/6 + 1145*u**2. Factor n(s).
-2*s*(s - 55)*(s + 2)/5
Let h = -716 + 815. Let k be 18/33*h/45. Find l such that k - 1/5*l**2 - 1/5*l = 0.
-3, 2
Suppose 432*j + 218 - 1366 = -81*j - 61*j. Factor 19*b**3 - 5*b - 46/3*b**j + 4/3*b**4 + 0.
b*(b - 1)*(b + 15)*(4*b + 1)/3
Suppose -102 = 15*h - 207. Solve 10*i**3 + 2*i**3 - 18*i + 12*i**2 - 7*i**3 - h*i**3 = 0.
0, 3
Suppose -329 = -46*t + 1111 + 32. Let s(o) be the first derivative of -1/24*o**4 - 1/6*o**3 + 0*o**2 - t + 0*o. Factor s(v).
-v**2*(v + 3)/6
Let z(x) = 3*x**2 - x - 1. Let n(u) = -26*u**2 - 378*u - 382. Let h(v) = -n(v) - 10*z(v). Determine o so that h(o) = 0.
-1, 98
Let f(r) be the first derivative of r**4/4 - r**3/3 + r**2/2 - 21*r + 420. Let i be f(3). Factor i + 2/3*s + 1/3*s**2.
s*(s + 2)/3
Suppose 17 = -2219*a + 4455. Factor -15/2*y**2 + y**3 - a + 5/2*y**4 - 8*y.
(y - 2)*(y + 1)**2*(5*y + 2)/2
Let x(n) be the first derivative of n**6/300 + 4*n**5/75 + n**4/12 - n**3/3 - 20*n + 86. Let m(h) be the third derivative of x(h). Factor m(y).
2*(y + 5)*(3*y + 1)/5
Suppose 3*f + 6 = 3*x - 6, 4*f - 16 = -4*x. Let g(p) be the second derivative of p**3 + 0*p**2 + 3/20*p**5 + 0 - 3/4*p**x + 32*p. Find k such that g(k) = 0.
0, 1, 2
Let t(z) be the first derivative of -189*z**5/5 - 173*z**4/2 + 188*z**3/9 - 4*z**2/3 + 87. Solve t(f) = 0 for f.
-2, 0, 2/27, 2/21
Let x(g) = -2*g**2 - 6*g - 2. Let l(b) = -12*b**2 - 4263*b - 525. Let c(j) = -l(j) - 6*x(j). Suppose c(a) = 0. Calculate a.
-179, -1/8
Let f(n) = n**3 - n**2 + 6*n - 1. Let g be f(2). Factor 4*o**5 - 45 + 15*o**3 + o - 7*o**2 - 13*o**4 + 30 + g.
o*(o - 1)**3*(4*o - 1)
Suppose 3*m - 6 = c, -2*m + 2*c - 6 = -5*m. Factor 64*z - 116*z**3 + 152*z**m + 0*z**4 + 14*z**3 + 28*z**4 - 142*z**3.
4*z*(z - 8)*(z - 1)*(7*z + 2)
Let h = -195 + 202. Suppose 30 = h*q + 9. Factor d + 4*d**2 + 7/3*d**q - 2/3.
(d + 1)**2*(7*d - 2)/3
Let i(a) be the third derivative of -a**7/30 - 2*a**6/15 + 7*a**5/15 + 8*a**4/3 + 69*a**2 + 6. Factor i(f).
-f*(f - 2)*(f + 2)*(7*f + 16)
Let n(t) = -t**3 + 3*t**2 + t + 16. Let d be n(4). Factor -32*k**5 + 0*k**4 - k**4 - 1266*k - 27*k**4 + 1266*k + d*k**3.
-4*k**3*(k + 1)*(8*k - 1)
Let x(t) = 27*t. Let k(l) = 5*l**2 - 26*l + 12. Let g(r) = -4*r**2 + 26*r - 9. Let s(d) = 4*g(d) + 3*k(d). Let y(b) = 3*s(b) - 2*x(b). Factor y(w).
-3*w*(w - 8)
Let h(u) = -136*u - 6797. Let n be h(-50). Factor 20 + 163/5*r**n + 23/5*r**4 + 361/5*r**2 + 64*r + 1/5*r**5.
(r + 1)**3*(r + 10)**2/5
Determine c, given that 1500 - 650*c + 18*c**3 - 2*c**4 - 5668*c**2 + 2843*c**2 + 2855*c**2 = 0.
-6, 5
Let g(u) be the first derivative of -u**4/30 + 98*u**3 - 108045*u**2 + 52942050*u - 742. Let g(t) = 0. Calculate t.
735
Solve -188*o**2 - 44563002 + 44563002 - 2*o**3 = 0.
-94, 0
Suppose -17*v - 4*t - 18 = -22*v, -2*v = -4*t - 12. Let i(y) be the first derivative of 6*y + 9/2*y**v + 0*y**3 - 3/4*y**4 + 12. Find q such that i(q) = 0.
-1, 2
Let l = -4455/7 - -58167/91. Factor 0 + 22/13*s**2 - 2/13*s**3 - l*s.
-2*s*(s - 9)*(s - 2)/13
Let q be (-2)/(-4)*2 + (-14 - -3). Let d(x) = 2*x**2 + 19*x - 6. Let r be d(q). Factor -21*h**4 + 6*h**4 + 12*h**r.
-3*h**4
Suppose 74*a + 3245 = 3541. Factor 11/6*j**3 - 1/6*j**a + 0 - 35/6*j**2 + 25/6*j.
-j*(j - 5)**2*(j - 1)/6
Let n(x) = -4*x**2 - x - 2. Let s(q) = -5*q**2 - q - 2. Let p(k) = -6*n(k) + 5*s(k). Let r be p(0). Determine f so that 5*f - 6*f**2 + 4*f**2 - 6 + f**r = 0.
2, 3
Suppose -1012*k**2 - 24*k**5 + 4988*k**3 - 1580*k**4 + 164 + 36 + 168*k**5 - 380*k - 2360*k**2 = 0. What is k?
-1/4, 2/9, 1, 5
Let u(y) be the third derivative of 0 + 0*y**3 + 0*y + 1/270*y**5 + 10*y**2 + 1/1512*y**8 + 1/54*y**4 - 1/180*y**6 - 1/945*y**7. Find n, given that u(n) = 0.
-1, 0, 1, 2
Let k be ((-1280)/(-40))/(2*-1). Let l(m) = -6*m - 96. Let b be l(k). What is j in b*j - 2/11*j**2 + 2/11 = 0?
-1, 1
Let m = 6/8479 + 186508/42395. Factor 2/5*a**3 + m*a - 24/5*a**2 + 0.
2*a*(a - 11)*(a - 1)/5
Determine t so that 22/5*t**4 + 38/5*t - 36/5*t**3 - 2/5*t**5 - 4/5*t**2 - 18/5 = 0.
-1, 1, 9
Let l = 112696 + -450777/4. Factor -l*x - 1/4*x**3 - 3/4 - 5/4*x**2.
-(x + 1)**2*(x + 3)/4
Factor -19/3*j**2 - 1 + 10/3*j**3 - 32/3*j.
(j - 3)*(j + 1)*(10*j + 1)/3
Let g be (46 + -45)/(102/952). Factor 8/3*k**3 + 52/3*k**2 + g - 74/3*k - 16/3*k**4 + 2/3*k**5.
2*(k - 7)*(k - 1)**3*(k + 2)/3
Let d be ((-2)/(-4))/(7 - (16 + -11)). Let q = 8 - 11/2. Factor q*n + d*n**2 + 25/4.
(n + 5)**2/4
Suppose -19*a - 4 = -15*a, 0 = f + a - 1. Let r(m) be the second derivative of 1/6*m**4 + 0 + 15*m - m**f + 0*m**3. Solve r(d) = 0.
-1, 1
Let n = -422 + 426. Suppose -n*v + 8*x = 11*x - 3, -5*v + 1 = x. Let 1/8*p**2 + v + 0*p = 0. What is p?
0
Let q(w) = -4*w**2 - 58*w + 5. Let p be q(-15). Let m be (-30)/(-12)*(-2)/p. Factor 0 - 2/5*t - m*t**3 - 3/5*t**2.
-t*(t + 1)*(t + 2)/5
Let w(j) = -3*j**2 - 8*j. Suppose -3*x + 8*x = 20. Let f(s) = -8*s**2 - 24*s. Let r(y) = x*f(y) - 11*w(y). What is c in r(c) = 0?
0, 8
Let v(d) be the third derivative of -d**8/84 - 22*d**7/105 + 21*d**6/5 + 434*d**5/15 + 451*d**4/6 + 102*d**3 + 157*d**2 - 7*d. Det