/3. Let u(o) = -8*o**3 - o + 6*o**3 + 0*o. Let p(z) = -3*z**3 + z**2 - 2*z. Let b(n) = y*u(n) - 3*p(n). Factor b(d).
d*(d - 2)*(d - 1)
Suppose 41*p = 30*p. Let n(u) be the first derivative of 6 - 1/8*u**3 + p*u - 3/32*u**4 + 0*u**2. Suppose n(k) = 0. What is k?
-1, 0
Suppose -123*i + 28*i - 115 = -305. Factor 1/6*z**i - 7/3*z + 49/6.
(z - 7)**2/6
Factor 0 - 1520/7*s**2 - 800/7*s - 2/7*s**5 + 76/7*s**4 - 642/7*s**3.
-2*s*(s - 20)**2*(s + 1)**2/7
Suppose -x - 4*i = -24, -8*i - 24 = 3*x - 12*i. Factor -4/9*h**4 - 4/3*h**3 + 0 + x*h + 0*h**2.
-4*h**3*(h + 3)/9
Factor 0 - 1/2*z + 6*z**3 + 1/2*z**2.
z*(3*z + 1)*(4*z - 1)/2
Let c be 1485/(-115) - (-182)/14. Factor 2/23*h**3 + 0 + c*h**2 - 4/23*h.
2*h*(h - 1)*(h + 2)/23
Solve 68 - 39*m + 56 + 3*m**2 - 236 + 70 = 0.
-1, 14
Let t = 149/580 - 1/145. Let l(b) be the third derivative of 0 + 0*b**3 + 0*b + 2*b**2 + t*b**5 - 1/4*b**4 + 7/40*b**6. Suppose l(j) = 0. Calculate j.
-1, 0, 2/7
Let z(b) = b**2 - b - 4. Let r be z(0). Let n = r - -5. Suppose 3*f**4 + 0 + 2*f - 3*f**4 + n - 2*f**3 - f**4 = 0. What is f?
-1, 1
Let d(v) = -5*v**5 - 11*v**4 + 2*v**3 + 60*v**2 + 44*v. Let i(q) = -5*q**5 - 10*q**4 + 60*q**2 + 45*q. Let r(c) = -5*d(c) + 4*i(c). Factor r(p).
5*p*(p - 2)*(p + 1)*(p + 2)**2
Suppose 7*u + 1 - 22 = 0. Let f(k) be the second derivative of -1/30*k**4 + 3*k - 1/75*k**6 + 0*k**2 + 1/25*k**5 + 0 + 0*k**u. Factor f(v).
-2*v**2*(v - 1)**2/5
Factor 1824/5*u + 292/5*u**2 + 576/5 + 12/5*u**3.
4*(u + 12)**2*(3*u + 1)/5
Let x(b) be the first derivative of -b**5/5 + 5*b**4/3 + 4*b**3 + 11*b + 31. Let y(n) be the first derivative of x(n). Factor y(d).
-4*d*(d - 6)*(d + 1)
Let p(z) = -45*z**3 - 121*z**2 - 74*z - 24. Let y(l) = -11*l**3 - 30*l**2 - 19*l - 6. Let q(r) = -6*p(r) + 26*y(r). Factor q(i).
-2*(i + 1)*(i + 2)*(8*i + 3)
Let q(z) = z**3 + 6*z**2 - 11*z + 6. Let m be q(-8). Let f = -31 - m. Factor -7*i**5 - 16*i - 348*i**4 - 52*i**f - 48*i**2 + 324*i**4 + 3*i**5.
-4*i*(i + 1)**2*(i + 2)**2
Let q = 121 - 96. Factor 26*x - 55*x + q*x + 4*x**2.
4*x*(x - 1)
Suppose 2*b - 14 = -3*p, -5*b = 5*p - 30 - 0. Factor -b*o**3 + 2*o**3 + 4*o**3 - o**2 + o**4 - 2*o.
o*(o - 1)*(o + 1)*(o + 2)
Let a(w) be the third derivative of -1/340*w**6 + 0 - 10*w**2 - 1/204*w**4 + 0*w**3 + 0*w - 1/1785*w**7 - 1/170*w**5. Determine o, given that a(o) = 0.
-1, 0
Let h(g) be the third derivative of 2/105*g**7 + 0*g**3 + 0 + 5*g**2 + 0*g**4 + 0*g + 1/15*g**5 + 1/15*g**6. Factor h(n).
4*n**2*(n + 1)**2
Let q(f) be the first derivative of -f**6/36 - f**5/15 + 3*f**4/8 + f**3/9 - 2*f**2/3 + 295. Let q(a) = 0. Calculate a.
-4, -1, 0, 1, 2
Let a(r) be the second derivative of r**6/120 - r**5/30 + r**4/24 - 19*r**2/2 + 4*r. Let w(y) be the first derivative of a(y). Factor w(g).
g*(g - 1)**2
Let z(x) = -x**2 + 563*x + 15683. Let g(p) = 1125*p + 31365. Let c(j) = -3*g(j) + 5*z(j). Factor c(t).
-5*(t + 56)**2
Let r = -9655/189 - -1387/27. Find m, given that -16/7 - 4/7*m + r*m**2 = 0.
-2, 4
Factor -2/3*w**2 + 0*w - 5/6*w**3 + 0 - 1/6*w**4.
-w**2*(w + 1)*(w + 4)/6
Let u(v) be the second derivative of v**6/30 + 7*v**5/10 + 3*v**4 + 17*v**3/3 + 11*v**2/2 + 71*v. Suppose u(m) = 0. What is m?
-11, -1
Let l(v) = 9*v**2 - v. Let r(o) = 220*o**2 + 260*o - 810. Let f(h) = -25*l(h) + r(h). Let f(n) = 0. Calculate n.
3, 54
Suppose -u - 5*h + 103 = 0, -3*u + 515 = 2*u + 4*h. Suppose 95 = -4*d + u. Solve 2/3*w**4 + 4/3*w**3 - d*w**2 - 8/3*w + 8/3 = 0 for w.
-2, 1
Let d = 502 + -498. Let h(q) be the third derivative of 0*q**5 + 0*q**3 - q**2 + 0*q**6 + 1/140*q**7 + 0*q**d + 0 + 0*q. Factor h(a).
3*a**4/2
Suppose 0 = 35*g - 30*g - r - 9, 5*r - 30 = 0. Suppose 0 + 3/4*d**2 - 3/4*d**g - 1/4*d + 1/4*d**4 = 0. What is d?
0, 1
Let s(l) be the third derivative of l**5/360 + l**4/48 + 2*l**2 + 15*l. Determine n, given that s(n) = 0.
-3, 0
Let c(b) be the second derivative of -44/3*b**3 + 0 - 1/3*b**4 - 242*b**2 + 11*b. Factor c(y).
-4*(y + 11)**2
Let 36 - 20 + 6*g**2 + 65*g - g**2 + 44 = 0. Calculate g.
-12, -1
Find z such that 0 + 0*z - 3/4*z**4 - 1/2*z**5 + 1/4*z**2 + 0*z**3 = 0.
-1, 0, 1/2
Let l(w) = 6*w**3 - 22*w**2 - 19*w. Let b(o) = o**3 - 2*o**2 - o. Let u(g) = -28*b(g) + 4*l(g). Factor u(i).
-4*i*(i + 2)*(i + 6)
Let f = -50 - -53. Factor -5*u**2 + u**3 + 6*u**2 + 0*u**f.
u**2*(u + 1)
Let n(o) = -o**2 - 6*o + 0*o**2 + 0*o + 2*o**2. Let f(k) = k**2 - 7*k. Let s(g) = -4*f(g) + 5*n(g). Factor s(y).
y*(y - 2)
Let v be 5*((2 - 1) + (2 - 2)). Factor -3*o**2 + 0*o**2 - o**2 + o**2 - 2 + v*o.
-(o - 1)*(3*o - 2)
Let d(n) be the third derivative of -n**7/3780 - n**6/216 + 5*n**4/12 + 24*n**2. Let c(w) be the second derivative of d(w). Find t, given that c(t) = 0.
-5, 0
Suppose 2*f - 4 = -0*f. Determine l, given that -5*l**5 - 2*l**f + 2*l**4 - 1272*l + 1273*l + 4*l**5 = 0.
-1, 0, 1
Let j = 83111/221672 + 2/27709. Factor -9/2 + 75/8*b + j*b**3 - 21/4*b**2.
3*(b - 12)*(b - 1)**2/8
Let b = 1/2846 + 1411/34152. Let k(j) be the second derivative of 0 - 3*j - b*j**4 - 1/80*j**5 + 0*j**2 - 1/24*j**3. Factor k(y).
-y*(y + 1)**2/4
Let a(h) be the first derivative of h**5/15 + h**4/3 - 15*h**2/2 - 14. Let d(l) be the second derivative of a(l). Factor d(o).
4*o*(o + 2)
Let j = -83/2 - -14. Let r = j + 28. Factor -1/2*p + r + 1/2*p**3 - 1/2*p**2.
(p - 1)**2*(p + 1)/2
Let a(v) = 4*v**2 + 2*v - 1. Let s be a(1). Solve -1/4*b - 1/2*b**2 + 1/2*b**4 + 0 + 1/4*b**s + 0*b**3 = 0 for b.
-1, 0, 1
Let j = -337/284 - -244/71. Solve 7/4*h**2 - 5/4*h**4 - 1/2 - j*h**3 + 9/4*h = 0 for h.
-2, -1, 1/5, 1
Let u(t) be the second derivative of 31*t + 0 - 75/16*t**4 - 1/8*t**2 + 5/4*t**3. Determine c, given that u(c) = 0.
1/15
Let o(v) = v - 1. Let z(b) = 6*b - 4. Let i(c) = -4*o(c) + z(c). Let h be i(1). Factor h*u**2 - 4*u**4 - 6*u**2 - 6*u**3 - u**5 - u + 0*u**4.
-u*(u + 1)**4
Let w(l) = 9*l**2 + 23*l + 63. Let u(b) = -4*b**2 - 12*b - 31. Let m(p) = -7*u(p) - 3*w(p). Let q be m(-13). Factor -1/2 - 1/4*x**q + 3/4*x.
-(x - 2)*(x - 1)/4
Solve 29/5*s**2 - 1/5*s**3 + 196/5 - 224/5*s = 0 for s.
1, 14
Let u = -61/288 - -21/32. Let i be (-82)/(-126) - 12/28. Factor 2/9 + i*v**2 - u*v.
2*(v - 1)**2/9
Let g = 853/3010 + 1/430. Let r = -308 - -2160/7. Suppose -2/7 - g*v**2 + r*v = 0. Calculate v.
1
Determine m, given that 0 - 2/9*m - 2/9*m**2 = 0.
-1, 0
Let p = 2 - -2. Suppose x + 2*c = p*c + 16, -2*c = -3*x + 44. What is a in 25*a**4 + a**3 - 20*a**5 + x*a**3 - 5*a + 10*a**2 - 35*a**2 + 10*a = 0?
-1, 0, 1/4, 1
Determine l so that -5*l**2 + 0 - 35/3*l**5 + 25*l**4 + 0*l + 95/3*l**3 = 0.
-1, 0, 1/7, 3
Let l be 8 - 7 - (2/1)/(-2). Let u(x) be the first derivative of -l + 2/3*x**3 - 2*x + 0*x**2. Determine a, given that u(a) = 0.
-1, 1
Let m(i) be the first derivative of i**6/720 + 11*i**5/120 + 121*i**4/48 - 6*i**3 + 5. Let p(j) be the third derivative of m(j). Find l, given that p(l) = 0.
-11
Let d be ((-9)/6)/(21/(-364)). Factor 2*c + 4 + 28*c**2 - d*c**2 - 4.
2*c*(c + 1)
Let r be 176/(-5) + 8/40. Let t be ((-110)/15 - -4)*12/r. Factor -4/7*z**2 + t - 4/7*z.
-4*(z - 1)*(z + 2)/7
Factor -88*l**2 - 13*l - 9 - 5*l + 84*l**2 - 14*l - 39.
-4*(l + 2)*(l + 6)
Let d(q) be the second derivative of q**7/252 + q**6/90 - 7*q**5/120 + q**4/18 + 49*q - 2. Find h such that d(h) = 0.
-4, 0, 1
Let i(s) be the second derivative of s**6/10 - s**5/4 - 23*s**4/6 - 14*s**3/3 + 20*s**2 + 5*s + 10. Factor i(t).
(t - 5)*(t + 2)**2*(3*t - 2)
Let g(m) be the third derivative of 2*m**7/175 - 31*m**6/200 + 17*m**5/20 - 12*m**4/5 + 18*m**3/5 - 273*m**2. Let g(q) = 0. What is q?
3/4, 2, 3
Let p be (0 - (-3005)/(-860)) + 4. Let h = p + -1/172. Solve i**3 - 3/2*i**4 + 1/2*i**5 - 3/2*i + h + i**2 = 0 for i.
-1, 1
Let m(z) be the third derivative of -z**7/210 + z**6/30 - z**5/20 - z**4/6 + 2*z**3/3 + 25*z**2. Factor m(k).
-(k - 2)**2*(k - 1)*(k + 1)
Let b(z) be the second derivative of -98*z**6/15 + 28*z**5/5 + 64*z**4 - 224*z**3/3 + 32*z**2 + 4*z - 17. What is l in b(l) = 0?
-2, 2/7, 2
Let k(o) = 7*o**4 + 98*o**3 + 766*o**2 + 2*o + 2. Let i(x) = 9*x**4 + 99*x**3 + 765*x**2 + 3*x + 3. Let v(c) = -2*i(c) + 3*k(c). Let v(n) = 0. What is n?
-16, 0
Let r(q) be the first derivative of 3*q**6/2 + 39*q**5/5 + 51*q**4/4 + 3*q**3 - 12*q**2 - 12*q - 94. Solve r(n) = 0 for n.
-2, -1, 2/3
Determine r, given that -2/17*r**2 + 168/17*r - 3528/17 = 0.
