5*y**3 - 45*y**2 - 1. Determine s so that a(s) = 0.
-45, 2/11
Let r(a) = a**3 - 12*a**2 + 2*a. Let x(s) be the second derivative of 25*s**4/12 - 5*s**3/6 - 26*s + 4. Let t(c) = -5*r(c) - 2*x(c). Find i such that t(i) = 0.
0, 2
Solve -1/12*v**2 - 92416/3 - 304/3*v = 0.
-608
Let r(w) be the second derivative of -13/180*w**6 + 2 + 0*w**2 - 23/120*w**5 + 0*w**3 - 34*w - 1/252*w**7 - 11/72*w**4. Factor r(g).
-g**2*(g + 1)**2*(g + 11)/6
Let p(g) = g**3 + g**2 - 6*g + 5. Let y be p(2). Suppose -y*m = 18 - 33. Suppose -5*d**3 - 27*d**2 - 3*d**4 - 9*d**3 + 3*d**m - 7*d**3 = 0. Calculate d.
-3, 0
Find d, given that -1/3*d**2 + 0 + 187/3*d = 0.
0, 187
Let z(n) = -15*n**3 + 1477*n**2 - 36024*n - 37500. Let g(f) = 10*f**3 - 985*f**2 + 24015*f + 25000. Let q(u) = 8*g(u) + 5*z(u). Factor q(l).
5*(l - 50)**2*(l + 1)
Let d(n) be the first derivative of n**5/5 + 73*n**4/16 + 67*n**3/2 + 76*n**2 + 32*n - 118. What is k in d(k) = 0?
-8, -2, -1/4
Let x(f) be the second derivative of -15*f**4 - 23/5*f**5 - 11/15*f**6 + 28 - 27*f**2 - 1/21*f**7 + 3*f - 27*f**3. Let x(n) = 0. Calculate n.
-3, -1
Let t(x) = 5*x**3 - 35*x**2 - 10. Let n(b) be the first derivative of b**4/4 - b**3/3 - b - 45. Let p(w) = 10*n(w) - t(w). Find m, given that p(m) = 0.
-5, 0
Let l(a) be the first derivative of -4*a**3/21 + 90*a**2/7 + 1696*a/7 + 2652. Factor l(r).
-4*(r - 53)*(r + 8)/7
Let w(t) be the third derivative of 0 + 11*t - 1/3*t**4 + 3*t**2 - 1/60*t**5 - 5/2*t**3. Let w(c) = 0. Calculate c.
-5, -3
Let v(y) be the first derivative of 1/2*y**4 + 62 + 6*y + 2*y**5 - 1/2*y**6 + 1/2*y**2 - 16/3*y**3. Solve v(t) = 0 for t.
-1, -2/3, 1, 3
Let f = -513 + 517. Suppose 5*b - 5*u - 11 = -f*u, -4*b + 16 = u. Factor 0 + 1/3*w**b + 0*w**2 + 0*w + 1/3*w**5 - 2/3*w**4.
w**3*(w - 1)**2/3
Let g(d) be the second derivative of -d**7/105 + 11*d**6/30 - 41*d**5/30 + 5*d**4/3 - 25*d**2/2 - d - 25. Let x(h) be the first derivative of g(h). Factor x(k).
-2*k*(k - 20)*(k - 1)**2
Let y(o) be the third derivative of -o**6/288 + 7*o**5/48 - 245*o**4/96 + 5*o**3/3 + 83*o**2. Let n(q) be the first derivative of y(q). Factor n(f).
-5*(f - 7)**2/4
Let i = -836 + 1066. Let g be (1 + 2/(-12))*92/i. Solve 1/3*r**5 + 5/3*r**4 + 10/3*r**3 + g + 10/3*r**2 + 5/3*r = 0.
-1
Factor 726/5*l + 0 + 1/5*l**3 + 77/5*l**2.
l*(l + 11)*(l + 66)/5
Let r = -88699/6 - -29577/2. Factor -r - 1/3*g**2 - 10/3*g.
-(g + 2)*(g + 8)/3
Let x(r) = r**3 - 6*r**2 - 9*r + 17. Let n be x(7). Determine q, given that -q**n + 14*q**2 + 13*q + 0*q**3 - 33*q - q**3 = 0.
0, 2, 5
Let q(d) be the third derivative of 243*d**6/8 + 2169*d**5/2 - 2425*d**4/6 + 60*d**3 + 30*d**2 + 25. Factor q(x).
5*(x + 18)*(27*x - 2)**2
Factor 135*t**2 - 125*t**3 + 3*t**4 - 8*t**4 + 69*t - 29 + 56*t - 101.
-5*(t - 1)**2*(t + 1)*(t + 26)
Let z be -7 + 1 - -5 - (-1 - 5). Solve 6*x**z - x**5 + 17*x**4 - 10*x**3 - 22*x**4 = 0 for x.
-1, 0, 2
Let h(i) = -i**2 + 2. Let z(j) = 4*j**2 + 12*j - 22. Let r = -76 - -75. Let n(x) = r*z(x) - 6*h(x). Factor n(a).
2*(a - 5)*(a - 1)
Factor 31*d**2 + 2 + 2*d**2 - 361*d + 765*d - 369*d.
(d + 1)*(33*d + 2)
Let s(n) be the first derivative of -53*n**2 + 2/3*n**3 - 108*n - 84. Solve s(t) = 0.
-1, 54
Let n(x) be the second derivative of -289/2*x**2 - 69*x - 17/6*x**3 - 1/48*x**4 + 2. Factor n(j).
-(j + 34)**2/4
Factor -2/9*k**2 - 146/9 + 148/9*k.
-2*(k - 73)*(k - 1)/9
Suppose 3*u = -2*s + 12, 3*s - 3 - 4 = u. Suppose 72*n**2 - 1030*n**5 + 53*n**s + 13*n**3 + 1033*n**5 - 69*n - 72*n**4 = 0. Calculate n.
-1, 0, 1, 23
Let z(n) be the third derivative of -n**6/120 - n**5/12 - n**4/12 + 4*n**3/3 - 85*n**2 + 4. Factor z(c).
-(c - 1)*(c + 2)*(c + 4)
Let k be 2300/1173 - (-6)/153. Factor 24/7 + 27/7*g + 3/7*g**k.
3*(g + 1)*(g + 8)/7
Let t be 11*(-28)/35*(-5)/2. Let q(m) = 3*m**3 - 3*m**2 + 4. Let a(u) = 16*u**3 - 15*u**2 + 20. Let d(s) = t*q(s) - 4*a(s). Factor d(b).
2*(b - 2)**2*(b + 1)
Let d = 2213/6620 + 87/1324. Factor 0 + 2/5*w**3 + 0*w - 12/5*w**2 + d*w**4.
2*w**2*(w - 2)*(w + 3)/5
Let o = 1711577 + -15404191/9. Factor -16*n + 288 + o*n**2.
2*(n - 36)**2/9
Let l = -27602 + 414032/15. Find o, given that 0 - 2/15*o**3 - 4/15*o**2 - l*o = 0.
-1, 0
Suppose 1 + 47 = 16*h. Factor 4*p**2 - 3*p**3 + 5*p**h + 8*p**3 - 14*p**3 + 12 + 20*p.
-4*(p - 3)*(p + 1)**2
Let s(y) be the second derivative of -y**4/16 + y**3/4 + 30*y**2 - 921*y. Suppose s(g) = 0. What is g?
-8, 10
Let r(x) be the second derivative of x**6/285 - 7*x**5/190 + 4*x**4/57 + 16*x**3/57 + 725*x. Factor r(o).
2*o*(o - 4)**2*(o + 1)/19
Let w(j) = j**3 - 6*j**2 + 2*j + 17. Suppose 6 = -l + 11. Let q be w(l). Factor -2*z - 10*z**2 + 4*z**q + 4*z**2.
-2*z*(z + 1)
Let m(w) = w**3 + 26*w**2 + 528*w - 2304. Let z(i) = -i**3 - 15*i**2 - 528*i + 2304. Let u(d) = -5*m(d) - 6*z(d). Let u(h) = 0. What is h?
12, 16
Let j(p) be the third derivative of 2*p**7/735 - p**6/70 - 2*p**5/35 + 4*p**4/21 + 5*p**2 - 291*p. Factor j(o).
4*o*(o - 4)*(o - 1)*(o + 2)/7
Let o be ((-1)/(-9))/(283/849). Let s(w) be the third derivative of 0*w - o*w**4 + w**3 - 6*w**2 + 0 + 1/30*w**5. Factor s(b).
2*(b - 3)*(b - 1)
Let u(w) = -4*w**2 + 16*w + 68. Suppose -3*a + 4*m = 0, -4*a + 8*a - 4*m + 4 = 0. Let y(l) = -2*l + 1. Let r(x) = a*y(x) + u(x). Let r(t) = 0. Calculate t.
-2, 8
Let r(w) = 20*w**2 + 5756*w + 5736. Let i(t) = t**2 + 303*t + 302. Let b(l) = -56*i(l) + 3*r(l). Factor b(o).
4*(o + 1)*(o + 74)
Solve -3882 - 1897*d**2 + 497*d + 3382*d + 1900*d**2 = 0.
-1294, 1
What is u in 15*u - 19*u**3 + 32*u**3 + 51*u**2 + 13628*u**4 - 13627*u**4 + 20*u - 55 - 45 = 0?
-5, -4, 1
Let c(a) = -2*a**4 + a. Suppose -12 = 4*l + 2*m, 10*l = 11*l - m + 3. Let v(h) = 3*h**4 + 10*h**3 - 32*h**2 + 30*h. Let j(u) = l*v(u) - 6*c(u). Factor j(t).
3*t*(t - 4)**2*(t - 2)
Let u(a) be the second derivative of -a**4/72 + a**3/18 + 20*a**2/3 - 7084*a. Solve u(y) = 0 for y.
-8, 10
Let x = 922 + -927. Let v be ((-3402)/(-180) + -19)*x/3. Factor 4/3*g**3 + 1/3*g**2 + 1/3*g**4 - 7/6*g - v*g**5 - 2/3.
-(g - 4)*(g - 1)*(g + 1)**3/6
Let q(v) be the third derivative of v**6/600 + 3*v**5/100 + v**4/8 - 5*v**3/6 - 582*v**2 + 5*v. Factor q(d).
(d - 1)*(d + 5)**2/5
Suppose -1/5*t**3 - 13872/5 - 5032/5*t - 139/5*t**2 = 0. What is t?
-68, -3
Let a(k) be the second derivative of 3*k**5/160 + 51*k**4/32 + 99*k**3/16 + 147*k**2/16 + 4*k + 2. Let a(g) = 0. What is g?
-49, -1
Solve -62*d**2 + 61*d - 71*d**2 + 304 - d + 129*d**2 = 0.
-4, 19
Let k(t) be the third derivative of t**7/735 + 3*t**6/35 - 19*t**5/14 + 169*t**4/21 - 172*t**3/7 + t**2 + 156*t. What is h in k(h) = 0?
-43, 2, 3
Factor -7/5 - 11/5*r**2 - 18/5*r.
-(r + 1)*(11*r + 7)/5
Let r(d) be the first derivative of d**4/8 - 121*d**3/6 + 471*d**2/4 - 351*d/2 + 3646. Factor r(t).
(t - 117)*(t - 3)*(t - 1)/2
Let y = -30/427 + 1417/14091. Let i(c) be the second derivative of -1/66*c**4 - y*c**3 + 12/11*c**2 - 24*c + 0. What is a in i(a) = 0?
-4, 3
Let l = 575841 - 575837. Solve -32/5*n**3 - 64/5 - 52/5*n**l + 188/5*n**2 - 32/5*n - 8/5*n**5 = 0.
-4, -1/2, 1
Let z(l) = -7*l**3 + 32*l**2 + 119*l + 100. Let b(t) = -33*t**3 + 159*t**2 + 595*t + 498. Let v(h) = -4*b(h) + 19*z(h). Find s, given that v(s) = 0.
-23, -4, -1
Factor 733 - 303*x - 161*x + 648 + 539 - 4*x**2.
-4*(x - 4)*(x + 120)
Let w = -30721351/3 + 349240322479/34104. Let k = -2/1421 + w. Determine r so that -1/4*r - k*r**3 + 0 - 3/8*r**2 = 0.
-2, -1, 0
Let y(m) be the third derivative of 155/24*m**4 - 93*m**2 + 1/24*m**6 - 11/12*m**5 - 2 + 0*m - 35/2*m**3. Let y(l) = 0. What is l?
1, 3, 7
Let t(f) be the second derivative of 25 - 1/90*f**6 + 1/18*f**3 - 1/12*f**4 + 1/20*f**5 - f + 0*f**2. Factor t(n).
-n*(n - 1)**3/3
Suppose -23*x = -45 - 24. Determine v so that -x*v**2 + 54*v - 3 - 21*v - 27*v = 0.
1
Let a(m) = m**4 - m**2 + 3. Let q(b) = 7*b**4 - 92*b**3 + 1051*b**2 + 92*b - 1043. Let u(t) = -10*a(t) + 2*q(t). Find y, given that u(y) = 0.
-1, 1, 23
Suppose 104*v + 15 = 109*v, -5*v + 15 = 3*g. Let f(t) be the second derivative of -2*t - 3/20*t**5 + 1/2*t**4 + 6*t**2 + 7/2*t**3 + g. Factor f(i).
-3*(i - 4)*(i + 1)**2
Let r(d) = 574*d**2 + 2044*d + 1904. Let z(u) = 1723*u**2 + 6131*u + 5686. Let k(m) = 11*r(m) - 4*z(m). Factor k(j).
-2*(17*j + 30)**2
Let s(k) be the third derivative of k**9/37800 - k**8/3360 + k**7/1050 - k**4/24 - 11*k**3/2 - 42*k**2. Let y(a)