1)
Let s = 108 + -96. Solve -33*g + s + 29*g**2 + 22*g**2 - 60*g**2 = 0.
-4, 1/3
Let x be (7/(-504))/(18/(-48)). Let z(s) be the third derivative of -4*s**2 + 1/270*s**5 - x*s**4 + 0*s + 0 + 0*s**3. Factor z(i).
2*i*(i - 4)/9
Factor -1/7*p**4 + 0 - 3/7*p**3 + 1/7*p**5 + 5/7*p**2 - 2/7*p.
p*(p - 1)**3*(p + 2)/7
Factor -12*c**3 - 48 - 272*c**2 - 29 - 44 - 240*c - 188*c - 47.
-4*(c + 1)*(c + 21)*(3*c + 2)
Let y = 11 - 5. Let c be (y/(-4))/((-3)/40). Determine d so that 20 - 3*d**2 - c + 3*d**3 = 0.
0, 1
Let -3/8*w**3 + 3*w - 3/8*w**2 + 9/2 = 0. Calculate w.
-2, 3
Suppose 5*c + 5 = 0, 5*n = 4*n - 4*c - 58. Let a = 56 + n. Factor 8/5 - 2/5*z**3 + 0*z - 6/5*z**a.
-2*(z - 1)*(z + 2)**2/5
Let s(p) be the first derivative of 0*p**2 + 1/50*p**5 + 0*p**4 + 2 + 0*p**3 + 2*p. Let n(o) be the first derivative of s(o). Find q, given that n(q) = 0.
0
Suppose -3 = 2*f + 13. Let b = f + 10. Find m such that m**2 - 4 - b - 1 + 5 - m = 0.
-1, 2
Suppose 22*n = 21*n. Let g be (n/2)/(3/(1 + 2)). Factor 1/8*q**5 + 5/8*q**4 + 1/2*q**2 + 0*q + g + q**3.
q**2*(q + 1)*(q + 2)**2/8
Let i be (1 - 436/(-8))*-2. Let l be (-2)/9 - i/135. Factor 3/5*t + 0 + 6/5*t**2 + l*t**3.
3*t*(t + 1)**2/5
Let d be (((1 + -1)/(-1))/(-4))/3. Let u(k) be the third derivative of 0 + 1/6*k**4 + d*k + 1/3*k**3 + 1/30*k**5 - 3*k**2. Determine g so that u(g) = 0.
-1
Let y = -798 + 798. Let j(n) be the third derivative of 0*n**4 + 0*n + 0 + 1/42*n**8 + 2/105*n**7 + 0*n**5 + 8*n**2 + y*n**3 - 1/30*n**6. Factor j(b).
4*b**3*(b + 1)*(2*b - 1)
Factor -89/6*z - 7/6*z**2 + 13/3.
-(z + 13)*(7*z - 2)/6
Suppose -69 = 4*b + 179. Let p = -60 - b. Suppose 0*k**p + 0 + 0*k**4 + 0*k + 1/4*k**5 - 1/4*k**3 = 0. What is k?
-1, 0, 1
Let l be -3*(3576/(-18))/(-4). Let j = l + 151. Solve -3/4*m**4 - 3/2*m**3 + 3/2*m**j + 3/4*m - 3/4 + 3/4*m**5 = 0.
-1, 1
Let g(f) be the first derivative of -10 + 0*f - 1/30*f**5 + 1/24*f**4 - 1/36*f**6 + 1/18*f**3 + 0*f**2. Find d, given that g(d) = 0.
-1, 0, 1
Let y(x) = -9*x**2 + 393*x - 417. Let n(t) = -t**2 + 49*t - 52. Let w(o) = -33*n(o) + 4*y(o). Determine a, given that w(a) = 0.
-16, 1
Let c(a) = 10*a**2 - 6*a. Suppose 0 = -5*l - 0*l + 20. Let k be l*(-1)/1*-4. Let j(o) = -3*o**2 + 2*o. Let s(d) = k*j(d) + 5*c(d). Factor s(g).
2*g*(g + 1)
Let i = 5768 + -5765. Factor 0*r + 0 - 1/7*r**i + 1/7*r**4 + 0*r**2.
r**3*(r - 1)/7
Let w = -114/17 - -359/51. Factor 1/2 - 4/3*j - w*j**3 + 7/6*j**2.
-(j - 1)**2*(2*j - 3)/6
Let n = 5860 + -5857. Factor -3/5*l**4 + 0 - 1/5*l**2 + 1/5*l - l**n.
-l*(l + 1)**2*(3*l - 1)/5
Let i = 7 + 1. Determine p so that 13*p**3 + 8*p - i*p**3 + 2*p**4 - 11*p**3 = 0.
-1, 0, 2
Let q(m) be the first derivative of 3*m**5/25 + 9*m**4/20 - 14*m**3/5 - 18*m**2/5 + 24*m + 351. Factor q(d).
3*(d - 2)**2*(d + 2)*(d + 5)/5
Let b = -227 + 230. Let i(q) be the second derivative of -2/3*q**2 + 1/2*q**5 - b*q + 11/36*q**4 - 5/18*q**6 - 2/3*q**3 + 0. Let i(z) = 0. Calculate z.
-2/5, 1
Suppose -10 = -2*x - 2. Suppose 54*p + 124*p**3 + 61*p**4 + 56*p - 30*p - 36*p**5 + 264*p**2 - 32 - 125*p**x = 0. What is p?
-2, -1, 2/9, 2
Let q = 93 - 86. Factor q*d**5 - 437*d**4 + 440*d**4 - 5*d**3 + 2*d**3 - 3*d**2 - 4*d**5.
3*d**2*(d - 1)*(d + 1)**2
Let y(d) be the second derivative of d**6/180 + 11*d**5/120 + 19*d**4/72 + d**3/4 - 6*d. Factor y(q).
q*(q + 1)**2*(q + 9)/6
Let z = 267392/11 - 24308. Determine g, given that 10/11*g + 8/11*g**2 + z + 2/11*g**3 = 0.
-2, -1
Suppose 15 = 9*p - 12. Factor 34*v**p - 81 + 33*v**3 - 64*v**3 - 27*v**2 + 81*v.
3*(v - 3)**3
Solve -16/5*a + 2/5*a**2 + 24/5 = 0 for a.
2, 6
Suppose t - 49 = -2*k, 0*k + 74 = 3*k + 2*t. Let u = 27 - k. Solve 8*r**3 + u*r**3 + 4*r + 8*r**2 - 7*r**3 = 0 for r.
-1, 0
Let v(g) = -54*g**3 - 624*g**2 - 244*g - 26. Let b(u) = 110*u**3 + 1250*u**2 + 489*u + 53. Let o(r) = -4*b(r) - 10*v(r). Suppose o(z) = 0. Calculate z.
-12, -1/5
Let w(g) = 2*g + 12. Let n be w(0). Suppose 3*m = 3*i + n, m - 5*i = -4 - 0. Determine y, given that -10*y + 7*y - 12*y**2 - 12*y - 3*y**3 - m = 0.
-2, -1
Let o = -28089925/19 + 1477936. Let z = -481 - o. Let -2/19 - z*c**2 - 4/19*c = 0. Calculate c.
-1
Let z(g) be the first derivative of -3/2*g**2 - 3/20*g**5 + 3/4*g**4 + 1/4*g**3 - 15 + 0*g. Let z(w) = 0. What is w?
-1, 0, 1, 4
Let y(t) be the first derivative of 2*t**3/3 + 13*t**2/2 + 8*t + 13. Let k be y(-6). Factor 0*z**k + 0*z**3 + 0 + 0*z - 2/9*z**4.
-2*z**4/9
Determine a so that 10*a**4 - 22/3*a**2 - 6*a**5 + 0 + 4/3*a + 22/3*a**3 = 0.
-1, 0, 1/3, 2
Let f be 0 + (-2 - -4) - 1. Let y(t) = t**2 + 3*t - 2. Let j be y(f). Factor -3*c**2 + 11*c - 4*c**2 - j + 0*c**2 - 2*c**2.
-(c - 1)*(9*c - 2)
Let y(q) be the third derivative of -q**5/240 - q**4/12 - 7*q**3/24 - 10*q**2 - 2. Let y(h) = 0. What is h?
-7, -1
Let b(p) be the first derivative of 2/15*p - 11 - 1/15*p**4 + 0*p**3 - 2/75*p**5 + 2/15*p**2. Factor b(n).
-2*(n - 1)*(n + 1)**3/15
Let d(p) = -59*p**3 - 110*p**2 - 68*p - 2. Let o(k) = 30*k**3 + 57*k**2 + 34*k + 1. Let s(n) = -4*d(n) - 10*o(n). Factor s(w).
-2*(w + 1)**2*(32*w + 1)
Let t be ((-60)/(-25) + -2)/(202/909). What is b in -t*b**2 + 7/5*b - 2/5 - 1/5*b**4 + b**3 = 0?
1, 2
Let a(d) be the first derivative of -4*d**3/21 + 8*d**2/7 + 48*d/7 - 18. Factor a(j).
-4*(j - 6)*(j + 2)/7
Let v = 6 - 1. Let l be 1/v + 54/30. Suppose k + 0*k**2 - 2*k**2 + 3*k**l + 0*k**2 = 0. Calculate k.
-1, 0
Let b(g) = 20*g**3 + 60*g**2 + 45*g + 5. Let f(v) = -19*v**3 - 59*v**2 - 46*v - 6. Let n(q) = -6*b(q) - 5*f(q). Factor n(o).
-5*o*(o + 1)*(5*o + 8)
Let b be (2/((-12)/6))/((-2)/(-6)). Let q be (-5)/(25/12) + (-9)/b. Factor -3/5*l**2 + 0*l + q*l**3 + 0.
3*l**2*(l - 1)/5
Factor -1/9*s**3 + 845/9 - 299/9*s + 31/9*s**2.
-(s - 13)**2*(s - 5)/9
Let n(v) = -v**2 + 11*v - 25. Let i be n(5). Suppose -i*u + 43 = 33. Let -4*x**u - 2/11*x**4 + 16/11*x**3 + 48/11*x - 18/11 = 0. What is x?
1, 3
Let m(d) be the first derivative of d**6/6 - 11*d**5/5 + 31*d**4/4 + 19*d**3/3 - 70*d**2 + 100*d - 108. Solve m(h) = 0 for h.
-2, 1, 2, 5
Let k(d) be the second derivative of -d**9/45360 + d**8/10080 + d**7/1890 - d**6/270 - d**4/6 - 5*d. Let p(r) be the third derivative of k(r). Factor p(i).
-i*(i - 2)**2*(i + 2)/3
Let o = -12 - -16. Solve 654 + 8*h**3 - 5*h**5 + 3*h**5 - 658 - 6*h + o*h**2 = 0.
-1, 1, 2
Find t such that 92 + 287*t - 12 + 175*t**2 + 43*t = 0.
-8/5, -2/7
Let p be ((-30)/9 - -6)*(77/(-22))/(-7). Solve 0*q**2 + 0 + 0*q - 4*q**3 + 16/3*q**4 - p*q**5 = 0.
0, 1, 3
Let i(t) = -18*t - 34. Let m be i(-2). Let p(j) be the first derivative of -j**m - 3 - j - 1/3*j**3. Let p(g) = 0. What is g?
-1
Let b = 9017/264 + -273/8. Let o = 4/11 - b. Solve -2*g**3 + 0 - o*g - 4/3*g**2 - 1/3*g**5 - 4/3*g**4 = 0.
-1, 0
Let j(q) be the third derivative of 0 - 3/350*q**7 + 0*q**6 + 0*q + 1/20*q**4 - 19*q**2 + 1/840*q**8 - 3/10*q**3 + 13/150*q**5. Find p, given that j(p) = 0.
-1, 1/2, 3
Suppose 1564 = 149*o + 372. Factor -4*l**2 + 1/2*l**3 + o*l + 0.
l*(l - 4)**2/2
Let n(s) = 7*s**2 + 9*s - 18. Let a(f) = -f**2 + 3*f - 1. Let w(o) = 2*a(o) + n(o). Factor w(y).
5*(y - 1)*(y + 4)
Solve 0 + 2/3*f**5 + 44/3*f**3 + 16/3*f**4 + 16*f**2 + 6*f = 0.
-3, -1, 0
Let t(l) be the first derivative of -3 + 2/45*l**3 + 8/15*l**2 + 32/15*l. Factor t(p).
2*(p + 4)**2/15
Let o = 63 - 58. Let s(f) = 15*f**4 + 6*f**3 - 19*f**2 + 3*f + 5. Let g(w) = 7*w**4 + 3*w**3 - 10*w**2 + 2*w + 2. Let q(t) = o*g(t) - 2*s(t). Factor q(p).
p*(p - 1)*(p + 2)*(5*p - 2)
Let h be ((-24)/(-144))/((-2)/(-36))*1. Let y(m) be the first derivative of 1/2*m**2 - h + 7/6*m**3 + 0*m. Suppose y(g) = 0. Calculate g.
-2/7, 0
Determine d so that 4*d**3 - 4*d**4 + 8*d**2 - 8 + 8 + 0*d**3 + 0 = 0.
-1, 0, 2
Let b(m) be the second derivative of -m**6/90 + m**5/15 - m**4/6 - m**3/3 - m. Let a(d) be the second derivative of b(d). Let a(x) = 0. Calculate x.
1
Let u(v) be the first derivative of -v**6/36 + 61*v**5/30 - 104*v**4/3 - 512*v**3/3 + 261. Factor u(i).
-i**2*(i - 32)**2*(i + 3)/6
Let n(f) be the first derivative of -20*f**3/3 + 4*f - 2. Let c(s) = 7*s**2 - 1. Let a(g) = -8*c(g) - 3*n(g). Suppose a(z) = 0. What is z?
-1, 1
Let w = 1617 + -4850/3. Let h(q) be the first derivative of -4/3*q**3 + 4*q + 3*q**2 + w*q**6 - 2*q**4 + 0*q**5 - 15. Let h(j) = 0. What is j?
-1, 1, 2
Suppose 107 = 5*a + 32. Suppose a*r = 16*r - 2, -3*r = h - 8. Facto