t n be (6/(90/(-35)) + (-63)/(-189))/(-1). Determine f so that -34/11*f - 2/11*f**5 + 56/11*f**n + 8/11 - 4*f**3 + 16/11*f**4 = 0.
1, 4
Suppose 50*x - 84*x = 0. Let m(w) be the third derivative of 0 + 1/280*w**6 + 0*w + 3/140*w**5 - 1/14*w**4 - 8*w**2 + x*w**3. Factor m(z).
3*z*(z - 1)*(z + 4)/7
Let y(l) be the first derivative of -9 + 5/6*l**3 + 5/12*l**4 + 0*l**2 + 2*l. Let r(m) be the first derivative of y(m). Suppose r(f) = 0. What is f?
-1, 0
Factor -136 - 4864*c**3 + 17328*c**2 - 292*c**4 - 4*c**5 + 104 + 32.
-4*c**2*(c - 3)*(c + 38)**2
Let k(q) = q - 1. Let v(h) = h - 2. Let c(s) = s**2 + 4*s + 28. Let m(f) = c(f) + 5*v(f). Let a(w) = -15*k(w) - 3*m(w). Factor a(l).
-3*(l + 1)*(l + 13)
Suppose 160*v - 162*v + 32 = 0. Suppose v*o - 29*o = -16*o. Find a, given that 0*a + o*a**2 + 2/9*a**3 + 0 = 0.
0
Let l(z) be the first derivative of 9*z**4/16 - 73*z**3/4 - 75*z**2/4 + 631. Factor l(j).
3*j*(j - 25)*(3*j + 2)/4
Let q(o) = -20*o**2 - 4059*o + 205. Let d be q(-203). What is z in -4/5*z**d - 48/5 + 52/5*z = 0?
1, 12
Factor -131*u**3 - 88*u + 537*u**2 + 128*u**3 - 934*u - 40*u.
-3*u*(u - 177)*(u - 2)
Let m(z) be the second derivative of -z**7/630 - z**6/135 - z**5/90 + 37*z**3/6 - 55*z. Let c(g) be the second derivative of m(g). Factor c(n).
-4*n*(n + 1)**2/3
Suppose -32/7 - 12*m - 74/7*m**2 - 2/7*m**4 - 24/7*m**3 = 0. Calculate m.
-8, -2, -1
Let i(d) be the first derivative of -d**6/120 + d**5/6 - 4*d**4/3 + 16*d**3/3 - 27*d**2 + 114. Let l(a) be the second derivative of i(a). Factor l(h).
-(h - 4)**2*(h - 2)
Let u(h) = h**5 + 3*h**4 - h**3 + h**2 + 1. Let s(l) = 12*l**5 - 54*l**4 + 1310*l**3 - 9186*l**2 + 23958*l + 10. Let m(v) = 2*s(v) - 20*u(v). Factor m(j).
4*j*(j - 11)**3*(j - 9)
Let f be 5/3*(-30 + (-156)/(-5)). Let -1/2*a**f + 0*a + 25/2 = 0. Calculate a.
-5, 5
Suppose -15*q = -12*q - 6, 0 = -2*g - 4*q - 2080. Let z = -11476/11 - g. Solve 0*i + 0 - 2/11*i**3 - z*i**2 = 0 for i.
-4, 0
Let w(d) = -8*d**3 - 379*d**2 - 4402*d + 4779. Let a(t) = -4*t**3 - 190*t**2 - 2200*t + 2390. Let g(f) = -5*a(f) + 2*w(f). Factor g(u).
4*(u - 1)*(u + 23)*(u + 26)
Let u(t) be the second derivative of 41*t**7/2 + 573*t**6/5 + 2559*t**5/20 - 577*t**4/2 - 570*t**3 + 12*t**2 - 151*t. Suppose u(r) = 0. What is r?
-2, -1, 2/287, 1
Let k = 30/23203 + 139068/116015. Factor 4/5*n**2 - k - 2/5*n.
2*(n + 1)*(2*n - 3)/5
Let z(r) be the first derivative of r**6/2 + 933*r**5/5 + 2781*r**4/4 + 925*r**3 + 462*r**2 + 8180. What is a in z(a) = 0?
-308, -1, 0
Let w(g) be the second derivative of g**6/300 - g**5/50 - g**4/6 + 3*g**2 - 2*g. Let l(o) be the first derivative of w(o). Factor l(u).
2*u*(u - 5)*(u + 2)/5
Suppose 21*j - 20 = 64. Suppose -r**j + 12*r - 3*r**2 + 0 + 3*r**2 - 4*r**3 - 9 + 2*r**2 = 0. What is r?
-3, 1
Let q(b) be the first derivative of 2*b**5/25 - 251*b**4/5 + 127994*b**3/15 - 249996*b**2/5 + 496008*b/5 + 1074. Determine l so that q(l) = 0.
2, 249
Suppose -o + 3*o = 8. Let j(t) = 54*t**3 - 53*t**2 - 9*t + 6. Let k(u) = -u**2 - 2*u + 2. Let x(i) = o*k(i) - 2*j(i). Factor x(f).
-2*(f - 1)*(6*f - 1)*(9*f + 2)
Suppose 3668 - 3703 = -7*s. Let q(i) be the third derivative of 0*i + 1/64*i**4 + 18*i**2 + 1/160*i**s - 1/8*i**3 + 0. Factor q(y).
3*(y - 1)*(y + 2)/8
Determine z so that 443*z - 1563 + 202*z + 302*z + 613*z + 3*z**2 = 0.
-521, 1
Let k = -16937 + 16940. Determine v so that 2/7*v**k + 4/7*v**2 - 16/7 - 8/7*v = 0.
-2, 2
Find l such that 24*l**3 - 8*l**3 - 679878*l**2 + 679866*l**2 - 4*l**4 = 0.
0, 1, 3
Let i(u) be the first derivative of -7/12*u**3 - 76 - 3*u - 1/8*u**4 + 5/2*u**2 + 1/20*u**5. Factor i(g).
(g - 2)**2*(g - 1)*(g + 3)/4
Let k(a) be the first derivative of 4*a**3/21 + 278*a**2/7 + 1632*a/7 - 12992. Factor k(n).
4*(n + 3)*(n + 136)/7
Let -565*t**5 + 545*t**5 - 19 + 118*t**2 + 944*t - 365 + 248*t**4 - 756*t**3 + 186*t**2 = 0. Calculate t.
-1, 2/5, 2, 3, 8
Let t(i) be the first derivative of 0*i**2 - 5/3*i**3 + 5/4*i**4 + 18 + 0*i. Determine q so that t(q) = 0.
0, 1
Let k be 148894/108597 - 2/53. Let j(w) be the first derivative of k*w**3 + 0*w + 22 + 0*w**2 - 2*w**4. Factor j(r).
-4*r**2*(2*r - 1)
Let b be (5 - 7) + 0 + 8. Let c be ((-20)/50)/((-2)/b). Find z such that -4/5 - c*z - 2/5*z**2 = 0.
-2, -1
Let j be 1 - (-480)/(-722) - (-481)/(-1443). Let u = 1069/7581 + j. Factor -u*p**2 - 6/7 + p.
-(p - 6)*(p - 1)/7
Let l(p) be the second derivative of 0*p**2 - 1/90*p**6 + p**3 + 1/30*p**5 + 7/12*p**4 - 5 + 2*p. Factor l(u).
-u*(u - 6)*(u + 1)*(u + 3)/3
Let j(l) = 726*l - 261358. Let d be j(360). Factor 18*r - 2/3*r**3 - 36 + 0*r**d.
-2*(r - 3)**2*(r + 6)/3
Suppose 4*g = -3*b + 27, -7*b + 74 = -2*b - 3*g. Suppose -b*p - 41 = -67. Solve 3*u + 9/7*u**5 + 3/7 + 66/7*u**3 + 54/7*u**p + 39/7*u**4 = 0 for u.
-1, -1/3
Let w(h) be the third derivative of -h**5/120 + 125*h**4/6 - 62500*h**3/3 - 1771*h**2. Factor w(q).
-(q - 500)**2/2
Let u(n) = -14*n**2 - 58*n + 20. Let i be u(-4). Let q(r) be the second derivative of -1/30*r**5 + 1/18*r**4 - i*r + 0*r**2 + 0*r**3 + 0. Factor q(x).
-2*x**2*(x - 1)/3
Solve 84 - 7*m + 4*m - 8*m - 3*m**2 + 58*m - 11*m = 0.
-2, 14
Let n be ((4 - 1) + 26/(-6))*-6. Suppose -n*p + 8 = -4*p. Find t such that -4 + 6*t**p - 26*t - 12 - 4 = 0.
-2/3, 5
Let v(f) be the first derivative of 25*f**6/4 + 129*f**5/2 - 267*f**4/8 + 9*f**3/2 - 1976. Factor v(l).
3*l**2*(l + 9)*(5*l - 1)**2/2
Let d(q) be the third derivative of -q**6/75 - 29*q**5/150 + 17*q**4/30 + 16*q**3/3 - 21*q**2 + 21. Suppose d(o) = 0. Calculate o.
-8, -5/4, 2
Let p(t) be the first derivative of -t**6/27 - 116*t**5/45 - 614*t**4/9 - 2608*t**3/3 - 5760*t**2 - 19200*t + 2926. Factor p(a).
-2*(a + 6)**3*(a + 20)**2/9
Solve -308025/4 - 1/4*o**2 + 555/2*o = 0.
555
Let q = 1871839 + -2964992809/1584. Let b = 1/176 + q. Solve 2/9*o + 1/9*o**2 + b = 0.
-1
Suppose 3*m = 2*o + 1112, -5*m + o + 1397 = -454. Let j = m - 368. Factor -2/21*n + 2/21*n**j + 0.
2*n*(n - 1)/21
Let v(d) = 2*d**3 + 7*d**2 - 13*d + 3. Suppose -77*r = -80*r - 9. Let h(a) = 5*a**3 + 21*a**2 - 38*a + 8. Let j(n) = r*h(n) + 8*v(n). Find o such that j(o) = 0.
0, 2, 5
Solve 543*k**4 - 393129 - 206*k**5 - 1543907*k + 50515*k + 202*k**5 + 6148*k + 335210*k**2 - 23376*k**3 = 0 for k.
-1/4, 11, 57
Let v be (-4920)/(-6888) + (-5374)/(-42) + 2. Factor 2/3*y**4 + v - 12*y**3 - 168*y + 218/3*y**2.
2*(y - 7)**2*(y - 2)**2/3
Let g(t) = 5*t**4 + t**3 + 7*t**2 - 7*t + 6. Let l(u) = -4*u**4 - 2*u**3 - 5*u**2 + 7*u - 6. Suppose 90 = -3*y - 15*y. Let h(s) = y*g(s) - 6*l(s). Factor h(z).
-(z - 6)*(z - 1)**2*(z + 1)
Let t = -9219 + 9221. Let v(l) be the second derivative of 0*l**t + 44*l - 2/15*l**3 + 0 - 1/10*l**4 - 1/50*l**5. Factor v(i).
-2*i*(i + 1)*(i + 2)/5
Let u(y) = -4*y**2 + 58*y - 146. Let t be u(11). What is c in 48 - t*c + 1/3*c**2 = 0?
12
Let v be (-7 - (-135)/20)*-20. Let m(g) be the second derivative of 0 - 1/5*g**v + 0*g**3 - 12*g + 0*g**2 - 1/3*g**4. Factor m(k).
-4*k**2*(k + 1)
Let f(l) be the first derivative of l**5/3 - 29*l**4/4 + 184*l**3/9 - 10*l**2 + 5941. Determine n, given that f(n) = 0.
0, 2/5, 2, 15
Factor 1/3*v**3 + 6724/3 + 6560/3*v - 163/3*v**2.
(v - 82)**2*(v + 1)/3
Let m be 60/72*6*1. Factor -19*p**5 - 4*p**3 + 0*p - 7*p + 10*p - 2*p**4 + 20*p**m + 2*p**2.
p*(p - 3)*(p - 1)*(p + 1)**2
Let k be (-30)/(-1) - ((6 - 12) + 6 + -5). Let g(s) be the second derivative of 2/15*s**3 + k*s + 1/5*s**4 + 0 - 1/25*s**5 - 6/5*s**2. Factor g(f).
-4*(f - 3)*(f - 1)*(f + 1)/5
Let t(d) = -32*d**2 + 1468*d + 2804. Let a(f) = -15*f**2 + 735*f + 1410. Let g(z) = 13*a(z) - 6*t(z). Solve g(r) = 0.
-2, 251
Let q(c) be the first derivative of -c**6/18 - 17*c**5/3 - 1847*c**4/12 - 1679*c**3/9 + 308*c**2 + 588*c + 4500. Let q(m) = 0. What is m?
-42, -1, 1
Let c(f) be the second derivative of -42*f**3 - 5/2*f**4 - 68*f - 1/20*f**5 - 2 - 196*f**2. Factor c(s).
-(s + 2)*(s + 14)**2
Let l(m) be the first derivative of 0*m + 1/26*m**4 + 118 + 0*m**2 - 2/13*m**3. What is g in l(g) = 0?
0, 3
Let y(h) be the first derivative of h**4/10 - 142*h**3/15 - 1158. Factor y(w).
2*w**2*(w - 71)/5
Let x(r) = -9*r**2 - 11*r + 5. Let b be 34/(-187) - 57/(-11). Let h(n) = 7*n**2 + 10*n - 4. Let p(c) = b*h(c) + 4*x(c). Determine y, given that p(y) = 0.
0, 6
Solve -14*b**3 - 19*b - 21*b - 8308*b**2 - 11*b**3 + 8238*b**2 = 0 for b.
-2, 