*5 + 0. Factor a(u).
(u - 7)*(u + 1)/4
Let u(f) be the second derivative of 42*f + 0 - 2/3*f**3 - 1/24*f**4 - 4*f**2. Determine x so that u(x) = 0.
-4
Let x(m) be the third derivative of m**7/210 - m**6/120 - m**5/6 - m**4/3 - 32*m**2. Factor x(j).
j*(j - 4)*(j + 1)*(j + 2)
Suppose -2 = -3*y + 4. Let x be (-16)/(-5) - (-183)/(-61). Factor -2/5 + 3/5*d - x*d**y.
-(d - 2)*(d - 1)/5
Let v(n) be the second derivative of 9*n**5/40 - 29*n**4/24 + n**3/2 + 2*n - 26. Solve v(s) = 0.
0, 2/9, 3
Determine t, given that -1/2*t**5 + 0*t - 9/2*t**2 - 15/2*t**3 - 7/2*t**4 + 0 = 0.
-3, -1, 0
Let n(w) = 4*w**2 - 152*w - 150. Let h(k) = 8*k**2 - 306*k - 299. Let y(j) = 2*h(j) - 5*n(j). Factor y(b).
-4*(b - 38)*(b + 1)
Factor 0 - 2/5*t**2 - 2/5*t.
-2*t*(t + 1)/5
Suppose 3*s = 21 - 6. Suppose -s*g + c + 18 = 0, 2*g - 5*c - 1 + 3 = 0. Factor b + g*b**3 - 8*b**3 + 2*b**2 - 2 + b**3 + 2*b**3.
-(b - 2)*(b - 1)*(b + 1)
Let a be ((-39)/26)/(45/(-100)). Factor -4/3 + 2/3*b**4 - 2/3*b**3 - 2*b**2 + a*b.
2*(b - 1)**3*(b + 2)/3
Let r = -47 + 53. Let a be (2/r)/((-120)/(-18) - 5). Factor 0*t**2 + 0 + 0*t + a*t**3.
t**3/5
Let d(b) = 2*b**2 - 49*b + 209. Let z be d(19). Suppose 3*k + k = -3*q - 12, 5*q = 2*k - 20. Factor 1/4*t**3 - 1/4*t**5 + 0 + z*t**2 + k*t**4 + 0*t.
-t**3*(t - 1)*(t + 1)/4
Let d(w) be the first derivative of 39 + 9/5*w + 1/15*w**3 + w**2. Let d(n) = 0. What is n?
-9, -1
Let n = -24376 + 121884/5. Factor -1/5*h**3 - 4/5*h - n*h**2 + 0.
-h*(h + 2)**2/5
Let y(f) be the third derivative of -f**3 + 0*f + 0 - 5/6*f**4 + 3*f**2 - 1/10*f**5. Factor y(q).
-2*(q + 3)*(3*q + 1)
Let a = 113 - 108. Suppose 13*p + 5*h - 25 = 8*p, 2*p = -a*h + 16. Factor 1/4*c**p + 0 + 1/4*c - 1/2*c**2.
c*(c - 1)**2/4
Let o(m) = 5*m**3 - 3*m**2. Let y(q) be the first derivative of -11*q**4/4 + 7*q**3/3 + 31. Let r(v) = -7*o(v) - 3*y(v). Factor r(h).
-2*h**3
Let v(k) be the first derivative of -5*k**6/12 - 11*k**5/5 - 3*k**4/8 + 11*k**3/3 + 2*k**2 - 247. Solve v(s) = 0 for s.
-4, -1, -2/5, 0, 1
Let o(h) be the second derivative of h**4/96 - h**3/12 + h**2/4 - 3*h - 15. Factor o(r).
(r - 2)**2/8
Let g(q) = -3*q - 44. Let w be g(-10). Let p be (-12)/w*(19/2 + -6). Factor 1/2*i**p + 0*i + 0*i**2 + 0 - i**4.
-i**3*(2*i - 1)/2
Let q be (-12 + 0)/(0 + (-5 - -3)). Factor 1128*m**3 - 9*m**2 + q + 3*m**4 - 1131*m**3 + 3*m + 0*m**4.
3*(m - 2)*(m - 1)*(m + 1)**2
Let g(m) = 6*m**3 - 569*m**2 + 12723*m + 13243. Let o(l) = -3*l**3 + 285*l**2 - 6363*l - 6621. Let x(f) = 6*g(f) + 11*o(f). Factor x(c).
3*(c - 47)**2*(c + 1)
Let w(h) be the third derivative of -h**7/3360 + h**6/320 - h**5/80 + h**4/8 + 6*h**2. Let q(m) be the second derivative of w(m). Factor q(d).
-3*(d - 2)*(d - 1)/4
Let l(h) be the third derivative of -h**8/1008 - h**7/105 - h**6/45 + 2*h**2 + 11*h. Factor l(q).
-q**3*(q + 2)*(q + 4)/3
Let k = -42 - -56. Factor -6*x - 36 + k*x**2 - 6*x**2 + 2*x**3 + 0*x**3.
2*(x - 2)*(x + 3)**2
Let f be 60/117 - (-12)/78. Find k such that 0 - f*k**2 - 4/9*k + 2/3*k**4 + 4/9*k**3 = 0.
-1, -2/3, 0, 1
Let o(c) be the second derivative of c**5/15 - 16*c**4/9 + 170*c**3/9 - 100*c**2 + 54*c. Factor o(v).
4*(v - 6)*(v - 5)**2/3
Let h(s) be the second derivative of -23*s**5/70 - 4*s**4/7 - s**3/21 - 80*s + 2. Factor h(b).
-2*b*(b + 1)*(23*b + 1)/7
Let k(q) be the second derivative of 2/11*q**2 + 8/33*q**4 - 7/110*q**5 - 1/3*q**3 + 0 - 26*q. Factor k(d).
-2*(d - 1)**2*(7*d - 2)/11
Factor -2*c + 10939 - 250*c - 11043 + 20*c**2.
4*(c - 13)*(5*c + 2)
Let r(s) be the third derivative of s**9/5292 - s**8/2940 - s**7/735 - 5*s**3/3 - 15*s**2. Let i(p) be the first derivative of r(p). Let i(k) = 0. What is k?
-1, 0, 2
Let o(v) be the first derivative of v**7/2520 + v**6/270 + v**5/72 + v**4/36 + 19*v**3/3 + 2. Let h(j) be the third derivative of o(j). Factor h(f).
(f + 1)**2*(f + 2)/3
Factor 0 - 1/3*g**2 + 1/3*g**4 + 0*g + 0*g**3.
g**2*(g - 1)*(g + 1)/3
Factor -2/25*k**2 - 24/5*k - 72.
-2*(k + 30)**2/25
Let i(u) be the second derivative of u**7/21 + 2*u**6/15 - 3*u**5/10 - 2*u + 19. Factor i(a).
2*a**3*(a - 1)*(a + 3)
Let c = -108 + 112. Factor -307*p + 180 + 65*p**2 + 8*p**c + 50*p**3 + 7*p - 3*p**4.
5*(p - 1)**2*(p + 6)**2
Let u(y) be the first derivative of -2/35*y**5 + 0*y + 7 + 0*y**2 + 0*y**4 + 2/21*y**3. Factor u(n).
-2*n**2*(n - 1)*(n + 1)/7
Let t(v) = 3*v**2 - 11*v + 12. Let a(c) = -c**2 + c - 1. Let q(g) = 4*a(g) + t(g). What is j in q(j) = 0?
-8, 1
Let x(h) be the third derivative of -441*h**8/32 + 63*h**7/5 + 2751*h**6/80 - 1307*h**5/30 + 21*h**4 - 16*h**3/3 - 33*h**2 - 5. Determine t so that x(t) = 0.
-1, 4/21, 1
Let c(k) = -17*k**2 - 11*k + 48. Let g(w) = -5*w**2 - 4*w + 16. Let n(h) = 2*c(h) - 7*g(h). What is x in n(x) = 0?
-8, 2
Suppose -5*k - 109*m = -106*m - 12, 3*k - 2*m - 11 = 0. Let 0 + 18/13*l**k - 4/13*l + 14/13*l**2 = 0. What is l?
-1, 0, 2/9
Let w be 8/56 - 39/(-21). Factor 2/5*f**4 + 0 - 2/5*f**3 - 4/5*f**w + 0*f.
2*f**2*(f - 2)*(f + 1)/5
Suppose 0 = n - 13*n + 48. Let y(i) be the third derivative of 0 + 0*i - 1/16*i**n + 1/240*i**5 + 3/8*i**3 + 6*i**2. Factor y(b).
(b - 3)**2/4
Suppose -11 = 16*o - 75. Let y(p) be the second derivative of 2*p + 0 + 2*p**3 - 1/3*p**o + 2*p**2 - 3/5*p**5. Factor y(b).
-4*(b - 1)*(b + 1)*(3*b + 1)
Factor -194*h**2 + 168*h + 230*h**2 + 1 + 207 - 4*h**3 + 24*h.
-4*(h - 13)*(h + 2)**2
Suppose -230*s - 456*s + 3430 = 0. Let -2/9*f + 4/9*f**3 - 4/9 - 2/9*f**s - 4/9*f**4 + 8/9*f**2 = 0. Calculate f.
-2, -1, 1
Suppose -55 = -2*z - 7. Factor -7*d**3 - z + 3*d**5 + 19*d**3 + 18 - 15*d + 12*d**4 - 6*d**2.
3*(d - 1)*(d + 1)**3*(d + 2)
Suppose 128*h**4 + 41*h + 98*h**2 + 110*h**2 + 268*h**3 + 20*h**5 + 7*h = 0. What is h?
-3, -2, -1, -2/5, 0
Let s(a) = -a**2 - a - 1. Let y(h) = h + 6*h - 7*h**2 + 3*h**3 - 1 - 5*h. Let i(l) = -l + 5. Let t be i(4). Let q(f) = t*s(f) - y(f). Factor q(r).
-3*r*(r - 1)**2
Determine v, given that 4*v**2 + 2*v**2 + 2*v**2 - 5 + 7 - v**2 - 9*v = 0.
2/7, 1
Let a(d) = -65*d - 1296. Let n be a(-20). Factor 2/7*p**n - 6/7 + 0*p**3 - 12/7*p**2 - 16/7*p.
2*(p - 3)*(p + 1)**3/7
Let l(j) be the first derivative of -j**5/100 - 3*j**4/40 + 2*j**3/5 + 6*j**2 + 5. Let t(f) be the second derivative of l(f). Find p, given that t(p) = 0.
-4, 1
Let s(g) be the second derivative of 0*g**2 + 0*g**3 + 0 + 1/36*g**4 - 21*g. Factor s(o).
o**2/3
Let -16*r**2 - 21*r**5 + 24*r**5 + 6*r**4 + 18 - 18*r**3 - 4*r**2 + 15*r - 4*r**2 = 0. Calculate r.
-3, -1, 1, 2
Let w(v) be the second derivative of 3*v**5/80 - v**4/16 - v**3/8 + 3*v**2/8 - 2*v + 15. Determine h, given that w(h) = 0.
-1, 1
Suppose 2*m + 4 = m. Let b(y) = -y - 2. Let l be b(m). Factor -5*o**2 - o**l + 3*o**4 + 3*o**2.
3*o**2*(o - 1)*(o + 1)
Factor 44*u**3 + 17*u**2 + 31*u**2 + 8*u**4 + 5457*u - 5493*u.
4*u*(u + 3)**2*(2*u - 1)
Let t(r) be the second derivative of -5*r**4/12 + 65*r**3/3 - 235*r. Factor t(x).
-5*x*(x - 26)
Let w(m) be the third derivative of -20*m**2 + 0*m**4 + 0*m**6 + 5/1008*m**8 - 1/126*m**7 + 0*m**3 + 0*m**5 + 0 + 0*m. Factor w(l).
5*l**4*(l - 1)/3
Let i(h) be the third derivative of -h**8/2016 + h**7/140 - 29*h**6/720 + 43*h**5/360 - 5*h**4/24 + 2*h**3/9 - 255*h**2. Factor i(v).
-(v - 4)*(v - 2)*(v - 1)**3/6
Let d = 52 - 49. Determine q, given that -36*q + q**5 + 34*q + q**4 - 2*q**5 + 3*q**d - q**2 = 0.
-1, 0, 1, 2
Let j = 1202 + -3548/3. Let v = 20 - j. Suppose 0 - v*g**3 - 2/3*g**2 + 0*g = 0. What is g?
-1, 0
Let b(a) = -a**2 - a - 1. Let s(z) = -9*z**2 + 516*z - 13524. Let f(p) = 4*b(p) - s(p). Suppose f(u) = 0. Calculate u.
52
Let q(l) be the first derivative of 8/7*l - 10/7*l**4 + 8/35*l**5 + 16 - 20/7*l**2 + 22/7*l**3. Find k, given that q(k) = 0.
1/2, 2
Find u, given that 69/2*u**3 + 12 - 147*u + 201/2*u**2 = 0.
-4, 2/23, 1
Let k(q) be the first derivative of -1/3*q**3 - 7*q + 1/12*q**4 + 2 + 1/2*q**2. Let b(z) be the first derivative of k(z). Factor b(f).
(f - 1)**2
Let u(g) = -9 - 5*g - 3*g + 5*g**2 - 8. Let c(y) = -5*y**2 + 7*y + 18. Let w(r) = 2*c(r) + 3*u(r). Determine b, given that w(b) = 0.
-1, 3
Suppose 4*k - 3*y - 26 = 0, -4*y = -5*k + 4*k + 13. Factor u**2 - u + 6 - 3*u**2 + k*u.
-2*(u - 3)*(u + 1)
Suppose 5*x + 0*i - 4 = 3*i, 5*i = 10. Suppose x*n = -0*n + 2*k + 8, 4*n - 5*k = 17. Factor 2/5*c**n + 4/5 - 6/5*c + 0*c**2.
2*(c - 1)**2*(c + 2)/5
Let 46 - 27*p + 14 + 48*