**3.
-3*(n - 1)*(n + 9)**2/5
Let u = 1180083/65 + -235884/13. What is m in -u*m + 18/5 + 21/5*m**2 = 0?
3/7, 2
Let h be ((-106)/(-4) + 7475/(-325))*12/70. Let h*i**2 + 3/5*i**3 + 0 - 6/5*i = 0. Calculate i.
-2, 0, 1
Let 11*h**3 + 13*h**4 - 21*h**3 - 1620*h + 1425*h**2 - 8*h**4 + 148*h**3 + 52*h**3 = 0. Calculate h.
-27, -12, 0, 1
Determine d, given that 3/10*d**4 - 26/5*d**3 - 24/5 + 0*d**2 + 1/2*d**5 + 64/5*d = 0.
-3, -2, 2/5, 2
Let p(k) = -4*k - 124. Let r be p(27). Let i = -232 - r. Determine h, given that 0*h + 0*h**3 + i + 0*h**4 - 4/7*h**5 + 0*h**2 = 0.
0
Suppose 50*s = 52*s - 2*x - 6, 2*x + 9 = 3*s. Factor -13*t + 23 + 169*t + 4 + 129*t**2 + 9 + 30*t**s.
3*(t + 2)**2*(10*t + 3)
Let r(k) be the second derivative of 3*k**5/80 - k**4/4 + 5*k**3/8 - 3*k**2/4 - 61*k - 2. What is t in r(t) = 0?
1, 2
Let y(m) be the first derivative of -3*m**4/4 + 5*m**3 + 156*m**2 + 3133. Factor y(s).
-3*s*(s - 13)*(s + 8)
Solve -101/5*s + 3/5*s**5 - 6 - 22/5*s**3 - 104/5*s**2 + 14/5*s**4 = 0.
-5, -1, -2/3, 3
Let h(o) = o + 27. Let u be h(-8). Let q = 22 - u. Determine f, given that -2*f**2 + f**2 + 5*f + 2*f**2 - f**3 + q = 0.
-1, 3
Let y(b) be the third derivative of -28*b**2 - 1/840*b**8 + 0*b - 2/75*b**5 - 2/5*b**3 + 2/525*b**7 + 0 - 13/60*b**4 + 1/50*b**6. Find h, given that y(h) = 0.
-1, 2, 3
Solve -38/9*m**4 + 2/9*m**3 + 170/9*m**2 - 4 + 34/3*m - 8/9*m**5 = 0.
-3, -1, 1/4, 2
Suppose 949*y + 946*y = 1899*y - 8. Suppose 12/5 - 14/5*r + 2/5*r**y = 0. Calculate r.
1, 6
Suppose -4*c + 24 = j, 4*j + 2*c - 66 = c. Determine a so that -8*a**5 + j*a + 66578 + 28*a**3 + 18*a**4 - 66578 - 72*a**2 = 0.
-2, 0, 1/4, 2
Let j(f) = 2*f**4 + f**2 - f - 1. Let u(b) = -b**4 + 6485*b**3 + 2*b**2 - 2*b - 2. Let l(w) = 2*j(w) - u(w). Factor l(h).
5*h**3*(h - 1297)
Let l = 278078/3 - 92680. Factor -2/3*i**2 - 40/3*i - l.
-2*(i + 1)*(i + 19)/3
Let n(v) = v**2 + 25*v + 78. Let f be n(-21). Let p be (-2 - -6)*(1 - (-5)/f). Factor -b - 1/3*b**2 - p.
-(b + 1)*(b + 2)/3
Suppose 14*w = 155*w + 76*w - 13888. Let q(l) be the first derivative of -36 + w*l - 56*l**2 - 13/4*l**4 + 20*l**3 + 1/5*l**5. Suppose q(c) = 0. What is c?
1, 4
Let z(f) be the first derivative of 0*f**2 + 21 + 1/18*f**4 + 2/9*f**3 + 17*f. Let n(c) be the first derivative of z(c). Factor n(d).
2*d*(d + 2)/3
Solve 2/9*v**2 + 4152962/9 + 5764/9*v = 0 for v.
-1441
Let d(m) be the first derivative of 0*m + 1/2*m**3 + 13/2*m**2 + 1/40*m**6 + 3/8*m**4 + 3/20*m**5 - 25. Let j(y) be the second derivative of d(y). Factor j(l).
3*(l + 1)**3
Suppose -14*q + 127 = 29. Suppose n - q*n = 3*n. Factor 0 + 0*l + 3/5*l**3 + 0*l**2 - 3/5*l**5 + n*l**4.
-3*l**3*(l - 1)*(l + 1)/5
Factor -1801*v**2 - 5841725401/3 - 3243601*v - 1/3*v**3.
-(v + 1801)**3/3
Let g = -267882 + 267890. Factor 4*h**4 + g*h + 1/2*h**5 + 12*h**3 + 0 + 16*h**2.
h*(h + 2)**4/2
Let q(a) = 8*a**4 + 182*a**3 + 784*a**2 + 620*a. Let m(w) = w**4 - w**3 - w**2 + 2*w. Let f(s) = 10*m(s) - q(s). Factor f(x).
2*x*(x - 100)*(x + 1)*(x + 3)
Suppose -2*y - 7748 = 2*i - 7840, -104 = -2*i + 4*y. What is u in -22/3*u**4 + 0 + 88/3*u**2 - i*u + 28/3*u**3 + 2/3*u**5 = 0?
-2, 0, 2, 9
Suppose 3*w + 5*g = 2*w + 18, 0 = -4*w - 4*g + 24. Determine k so that -15*k**4 - 3*k**5 + 74*k**w - 62*k**3 + 6*k**4 = 0.
-4, 0, 1
Let -1534/7*a**3 - 4232/7 - 862*a**2 - 102/7*a**4 - 2/7*a**5 - 8832/7*a = 0. What is a?
-23, -2, -1
Let f be 1 + 1 + 2 - (-29464)/(-18415). Factor 0*b + 0 + 4/5*b**3 - f*b**2.
4*b**2*(b - 3)/5
Let i(d) be the third derivative of d**5/40 - 479*d**4/16 - 120*d**3 + 1611*d**2. Factor i(a).
3*(a - 480)*(a + 1)/2
Suppose -u + 211*t + 8 = 212*t, 3*t - 22 = -2*u. Factor -14/5*p**u + 0 - 4/5*p.
-2*p*(7*p + 2)/5
Let a(b) = 3*b**2 + 5*b. Let t be (-42)/(-9)*3/2. Let p(u) = t*u - 5*u - 2*u**2 - 5*u. Let h(q) = -6*a(q) - 10*p(q). Factor h(r).
2*r**2
Let y = -106951/1260 + 764/9. Let c(x) be the second derivative of 0 - 1/42*x**3 + 1/42*x**4 - 5*x - 1/7*x**2 + y*x**5. Solve c(u) = 0.
-2, -1, 1
Let v be -8 + -4 + 104/6. Let c(k) be the first derivative of 19 + 7/2*k**4 + 0*k + v*k**3 + 4/3*k**2 - 98/15*k**5. Find y such that c(y) = 0.
-2/7, 0, 1
Let q(r) be the third derivative of r**8/1680 + 4*r**7/525 - 17*r**6/600 - 17*r**5/25 - 3*r**4/2 - 416*r**2 - r. What is n in q(n) = 0?
-6, -1, 0, 5
Let i(f) be the second derivative of -2401*f**5/20 - 2989*f**4/12 - 104*f**3 - 18*f**2 + 6*f - 13. Let i(m) = 0. What is m?
-1, -6/49
Let v be 4/(-14) - ((-2772)/98 + -8). Factor 16222*i**2 + 0*i**4 - v*i**3 - 16255*i**2 - 3*i**4.
-3*i**2*(i + 1)*(i + 11)
Let n = 704061/1126472 - 2/140809. Factor -1/8*y**3 + 3/8 - 7/8*y + n*y**2.
-(y - 3)*(y - 1)**2/8
Let w(m) = 5*m**4 + 347*m**3 + 1327*m**2 + 1657*m + 654. Let l(u) = 15*u**4 + 1040*u**3 + 3975*u**2 + 4970*u + 1960. Let f(z) = 3*l(z) - 10*w(z). Factor f(s).
-5*(s + 1)**2*(s + 2)*(s + 66)
Let v(g) be the third derivative of 0 + 0*g - 3/16*g**4 - 1/240*g**6 - 121*g**2 - 1/20*g**5 + 0*g**3. Find k, given that v(k) = 0.
-3, 0
Let t(y) be the second derivative of y**4/78 + 27*y**3/13 + 308*y**2/13 + 37*y - 121. Determine x, given that t(x) = 0.
-77, -4
Let -1354/15*y**2 - 4708/15*y - 368/15 - 10/3*y**3 = 0. Calculate y.
-23, -4, -2/25
Solve -717409/2 + 108416*h - 9039*h**2 - 1/2*h**4 + 128*h**3 = 0.
7, 121
Let d = -636260 - -1272531/2. Suppose -13 + d*v + 1/2*v**2 = 0. What is v?
-13, 2
Let s = 381 - 374. Suppose -3*b**4 - s*b**3 - 27*b**3 - 57*b**2 - 27*b + b**3 = 0. What is b?
-9, -1, 0
Let l(d) be the second derivative of -d**5/80 + 17*d**4/12 - 50*d**3 + 792*d**2 + 462*d. Factor l(u).
-(u - 44)*(u - 12)**2/4
Determine h, given that -214/11*h**2 - 2/11*h**4 - 38/11*h**3 - 322/11*h - 144/11 = 0.
-9, -8, -1
Let c(y) be the first derivative of 97 - 2/3*y**3 + 28*y - 13*y**2. Let c(k) = 0. What is k?
-14, 1
Let w(k) be the second derivative of k**5/20 + 2*k**4/3 - 25*k**3/2 + 63*k**2 - 1216*k. Solve w(j) = 0.
-14, 3
Let b(v) be the second derivative of 1/16*v**5 + 0 + 0*v**2 - 5/48*v**4 + 24*v + 0*v**3. Factor b(r).
5*r**2*(r - 1)/4
Let y(u) be the first derivative of -1/2*u**4 - 2*u**3 + 6*u + u**2 - 9. Find k such that y(k) = 0.
-3, -1, 1
Suppose 0*o = 3*o. Suppose -4*m + f + 673 = o, -3*f + 163 = m - 5*f. Factor -6 - 80*s**4 - 50*s - 200*s**3 - m*s**2 + 5 - 4 + 4*s**2.
-5*(s + 1)**2*(4*s + 1)**2
Let q(f) be the second derivative of -13/6*f**3 + 1/15*f**6 + 19/12*f**4 - 2*f - 6 - 11/20*f**5 + 3/2*f**2. What is j in q(j) = 0?
1/2, 1, 3
Let o(g) be the second derivative of 1/3*g**4 + 48*g**2 - 20/3*g**3 + 0 + 98*g. Factor o(x).
4*(x - 6)*(x - 4)
Let h(p) be the second derivative of p**5/80 + 13*p**4/24 - 105*p**3/8 + 2*p - 107. Determine q so that h(q) = 0.
-35, 0, 9
Suppose 3*v = h + 17, -3*v - 11*h = -10*h - 13. Factor -p**5 - 447*p**3 - 3*p**v + 443*p**3 - 8*p**4.
-4*p**3*(p + 1)**2
Let m(f) = 2*f**3 + f**2 + f - 2. Let s(l) = 9*l**3 - 258*l**2 + 1427*l - 2074. Let w(d) = 2*m(d) - s(d). Determine x, given that w(x) = 0.
3, 46
Let b(s) = 49*s**2 + 1298*s + 417328. Let p(w) = 8*w**2 + w + 2. Let v(y) = -b(y) + 6*p(y). Factor v(h).
-(h + 646)**2
Let y(p) be the third derivative of -p**5/12 + 55*p**4/3 - 1600*p**3/3 + 4*p**2 + 5*p - 7. Factor y(h).
-5*(h - 80)*(h - 8)
What is g in -1/6*g**4 + 36*g**2 + 232/3*g + 7/2*g**3 + 0 = 0?
-4, 0, 29
Factor 2/3*v + 1/9*v**2 + 1.
(v + 3)**2/9
Let d = -124012 + 124015. Factor -3/2*i - 27/2*i**2 + 3/2*i**d + 27/2.
3*(i - 9)*(i - 1)*(i + 1)/2
Let m(g) = -5*g**4 + 37*g**3 - 138*g**2 + 146*g - 2. Let n(f) = 6*f**4 - 36*f**3 + 138*f**2 - 147*f + 3. Let x(b) = -3*m(b) - 2*n(b). Factor x(j).
3*j*(j - 8)*(j - 3)*(j - 2)
Determine v, given that 108*v - 632*v + 1694 + 8*v**2 - 1958 = 0.
-1/2, 66
Let m(k) = -308*k**2 + 1000*k - 148. Let w = -140 + 137. Let s(r) = -44*r**2 + 143*r - 21. Let y(p) = w*m(p) + 20*s(p). Factor y(z).
4*(z - 3)*(11*z - 2)
Let r(d) be the first derivative of -195 - 15/2*d**2 - 15/2*d**4 + 0*d**5 + 5/6*d**6 + 0*d + 40/3*d**3. Factor r(l).
5*l*(l - 1)**3*(l + 3)
Factor 10 + 1/3*j**3 + 32/3*j**2 + 61/3*j.
(j + 1)**2*(j + 30)/3
Suppose 2*s - 4*t = 94, 42*s - 43*s + 77 = 4*t. Let f = -111/2 + s. What is o in -3/2*o**2 - f*o + 0 = 0?
-1, 0
Let c(m) = -10*m - 8*m + m**2 + 30*m + 3*m**2. Let k be c(-3). Find g such that 2/3*g**2 + 4/3*g + k - 4/3*g**3 - 2/3*g**4 = 0.
-2, -1, 0, 1
Let y(b) be the third derivati