tive of 0*y**5 + 1/36*y**4 + 0 - 1/540*y**6 + 6*y**2 - 7/6*y**3 + 0*y. Let h(o) be the first derivative of a(o). Factor h(n).
-2*(n - 1)*(n + 1)/3
Suppose -14*l + 24 = -8*l. Suppose 0 = -4*k - 2*u + 2, l*k - 4*u - 11 = -3*u. Factor -8/13 - 24/13*w - 10/13*w**k.
-2*(w + 2)*(5*w + 2)/13
Find d, given that -115 - 107*d**2 + 111 + 23*d**2 + 38*d = 0.
1/6, 2/7
Suppose 0 = 3*f - 4*f - 3, 0 = 5*z - 2*f - 16. Let -28*d**2 - 4*d**z + 11*d**2 - 6*d = 0. Calculate d.
-2/7, 0
Factor 52 - 151 + 2*t**2 + 47 + t + 51.
(t + 1)*(2*t - 1)
Find i, given that -5/2*i**3 - 19 - 55/2*i + 49*i**2 = 0.
-2/5, 1, 19
Let g(u) = u**4 - u**2 + u + 1. Let y(j) = -j + 0*j - 2*j + 6*j**3 - 22*j**2 - 8*j**4 - 3 + 32*j**2. Let l(h) = -4*g(h) + 4*y(h). Factor l(s).
-4*(s - 1)**2*(3*s + 2)**2
Let l(m) be the third derivative of m**7/2520 - m**6/360 + m**5/120 + 3*m**4/8 - 10*m**2. Let k(g) be the second derivative of l(g). Factor k(p).
(p - 1)**2
Let t(v) = 24*v + 1. Let s be t(1). Let l be 5/2*40/s. Determine x, given that 9*x**l - 3*x**4 - x**2 + 2*x**5 - 7*x**2 = 0.
-2, 0, 1
Let p(a) be the second derivative of -a**7/147 + a**6/35 + 2*a**5/35 + 42*a. Solve p(s) = 0 for s.
-1, 0, 4
Let i be (4/(-7))/(342/(-399)). Solve -10/3*b + 4/3 + 2/3*b**3 - i*b**4 + 2*b**2 = 0.
-2, 1
Suppose 1 = 5*g - 3*q, -22*q + 27*q - 23 = -4*g. Let x(f) be the first derivative of 6*f**g + 18*f + 2/3*f**3 + 2. Factor x(k).
2*(k + 3)**2
Let m(y) = -y. Let q(j) = 4*j**2 + 3*j - 1. Let w(u) = -6*m(u) - q(u). Suppose w(x) = 0. Calculate x.
-1/4, 1
Let x(m) be the first derivative of 5*m**4/4 - 25*m**3/3 + 10*m**2 + 82. Solve x(t) = 0 for t.
0, 1, 4
Let b(x) be the third derivative of x**8/42 - 29*x**7/105 + 67*x**6/60 - 67*x**5/30 + 29*x**4/12 - 4*x**3/3 + 8*x**2 + 5*x. Factor b(w).
2*(w - 4)*(w - 1)**3*(4*w - 1)
Suppose 4*v + 5*b = 15, -3*b = -3*v - 5 - 4. Find a such that a - 6*a**2 + v*a**2 - 3*a**3 - 5*a + a**3 = 0.
-2, -1, 0
Let w be 68/51*9/(-678). Let p = w + 462/565. Factor 1/5 + 6/5*d**2 + 1/5*d**4 - 4/5*d**3 - p*d.
(d - 1)**4/5
Let f be (-124)/(5 + -3) + 3. Let j = -31 - f. Determine d so that -13*d**2 + j*d**3 + d**2 + d**2 + 8 + 16*d**4 - 28*d - 13*d**2 = 0.
-2, -1, 1/4, 1
Let c(v) be the first derivative of -12/7*v**2 + 7 - 8/7*v - 2/7*v**3 + 5/14*v**4. Factor c(i).
2*(i - 2)*(i + 1)*(5*i + 2)/7
Suppose -151 = -48*n - 55. Factor -1/2*t**4 + 0 + 2*t - 4*t**n + 5/2*t**3.
-t*(t - 2)**2*(t - 1)/2
Let a(u) be the first derivative of -2/5*u**6 - 7/15*u**3 + 11/20*u**4 + 7/25*u**5 + 0*u - 14 + 1/10*u**2. Solve a(o) = 0 for o.
-1, 0, 1/4, 1/3, 1
Let y = 129 - 125. Suppose 6*f = y*f. Determine z so that 0 - 1/2*z**5 - 1/2*z**2 + 1/2*z**3 + f*z + 1/2*z**4 = 0.
-1, 0, 1
Factor 4/3 - 1/9*t**2 - 4/9*t.
-(t - 2)*(t + 6)/9
Let k = -308604/7 + 44088. Solve 90/7*r**4 + 0*r + 0 - 78/7*r**5 - k*r**3 + 0*r**2 = 0 for r.
0, 2/13, 1
Solve 10*w + 3*w**2 - 13 - 11 - 16*w = 0 for w.
-2, 4
Let k(i) be the third derivative of -i**5/30 - 3*i**4/4 + 52*i**3/3 - 356*i**2. Determine y so that k(y) = 0.
-13, 4
Let v = 795 - 760. Factor -49/5*m**5 - 8*m + 4/5 + 29*m**2 + v*m**4 - 47*m**3.
-(m - 1)**3*(7*m - 2)**2/5
Let g(n) be the first derivative of n**6/6 - 5*n**4/4 + 2*n**2 - 115. Solve g(o) = 0.
-2, -1, 0, 1, 2
Find n, given that 36/11*n**4 - 120/11 - 138/11*n**3 + 90/11*n**2 + 144/11*n = 0.
-1, 5/6, 2
Let l(w) be the second derivative of -1/30*w**5 + 0 + 1/9*w**4 + 0*w**3 - 9*w + 0*w**2. Factor l(h).
-2*h**2*(h - 2)/3
Let w be -3 + 5 - (-4)/(-14). Suppose -6*v = 5 - 17. Factor -2/7*g**v - w*g - 18/7.
-2*(g + 3)**2/7
Let j(p) = -2*p - 2*p + 3 + 5*p - 2. Let h(k) = -4*k**2 + 3*k - 9. Let i(s) = h(s) + 5*j(s). Suppose i(t) = 0. What is t?
1
Factor -456 - 197*s**2 + 376*s**2 + 593*s**2 - 68*s**2 - 1132*s - 12*s**3.
-4*(s - 57)*(s - 2)*(3*s + 1)
Let n be -2 - 6*(-2 + 1). Suppose -3*i - 2*q + 3*q + 4 = 0, 2*i + 20 = -5*q. Factor -n + 4 + 2*s + s**2 + i.
s*(s + 2)
Let f(k) be the second derivative of 0 - 3*k + 0*k**2 - 1/15*k**3 - 1/60*k**4. Factor f(r).
-r*(r + 2)/5
Solve -43*b**2 + 80 + 11233*b - 11273*b - 32*b**2 + 40*b**3 - 5*b**4 = 0.
-1, 1, 4
Let z(l) = 6*l + 0*l + 4*l**2 + 1 - 4*l - 4*l. Let f be z(2). Factor 4*s**2 + f*s + 2*s**2 - 10*s + 3*s**3.
3*s*(s + 1)**2
Let y be (5/10)/((-3 + (-172)/(-60))/(-2)). Factor -15/2*k**2 - y*k**3 + 0 - 5/2*k**4 - 5/2*k.
-5*k*(k + 1)**3/2
Let w(d) be the first derivative of d**4/4 + 4*d**3/3 - 109. Let w(i) = 0. Calculate i.
-4, 0
Let o(i) be the first derivative of -1/2*i + 7 + 1/12*i**3 - 1/8*i**2. Let o(y) = 0. Calculate y.
-1, 2
Determine i, given that 48/7 + 8/7*i - 2/7*i**3 - 20/7*i**2 + 2/7*i**4 = 0.
-2, 2, 3
Let u(z) be the third derivative of -z**5/12 + 5*z**4/6 + 25*z**3/6 - 15*z**2 + 10. Solve u(q) = 0.
-1, 5
Factor -4*p**3 + 1/2*p**4 - 16*p - 15*p**2 - 11/2.
(p - 11)*(p + 1)**3/2
Factor -x + x**3 + 1/2*x**4 - 1/2 + 0*x**2.
(x - 1)*(x + 1)**3/2
Let m be ((-4)/130)/(345/(-17940)). Factor 2/5*x**5 - 22/5*x**2 - 24/5*x - 2/5*x**3 + 6/5*x**4 - m.
2*(x - 2)*(x + 1)**3*(x + 2)/5
Let c(l) = 5*l**4 - 5*l**2 - 4. Let n(z) = 48 - 37 - 3*z**3 + 3*z**3 - 14*z**4 + 14*z**2. Let v(q) = 11*c(q) + 4*n(q). Factor v(t).
-t**2*(t - 1)*(t + 1)
Suppose -3*w + 5 = -1. Let k(y) = 3*y - 4. Let z be k(w). Solve -20*x**4 - 2*x**5 + 4*x**2 + 12*x**4 - 12*x**2 - z*x - 12*x**3 = 0 for x.
-1, 0
Let u be (-13 - (-330)/24)*1. Factor -15/8*p - 3/8*p**2 - 3/4 + u*p**3.
3*(p - 2)*(p + 1)*(2*p + 1)/8
Let -488601/7*y + 2097/7*y**2 + 37948011/7 - 3/7*y**3 = 0. What is y?
233
Determine g so that 5256/5*g**2 + 17328/5 - 48*g**3 - 3648*g + 3/5*g**4 = 0.
2, 38
Factor -18 - 3*t**3 - 3*t**2 + 3*t**4 - 18*t**2 + 30*t - 2*t**3 + 2*t**3 + 9*t.
3*(t - 2)*(t - 1)**2*(t + 3)
Let l(k) = 10*k**2 - 252*k - 8706. Let t(u) = 2*u**2 + 2*u + 1. Let a(v) = l(v) - 6*t(v). Factor a(m).
-2*(m + 66)**2
Factor -18/5 - 36*a**2 - 111/5*a - 27/5*a**3.
-3*(a + 6)*(3*a + 1)**2/5
Suppose -r = -9*h + 4*h + 11, 5*h - 27 = -3*r. Suppose -m = 5*j - 6*m - 20, r*m = -j - 6. Factor 1/2*a**j + 0 + 1/2*a.
a*(a + 1)/2
Let j(c) = -7*c**4 - 72*c**3 - 66*c**2 + 52*c + 73. Let f(t) = 6*t**4 + 72*t**3 + 66*t**2 - 57*t - 72. Let n(x) = -4*f(x) - 3*j(x). What is y in n(y) = 0?
-23, -1, 1
Solve 373*h - 546 + 4*h**2 + 210 - 41*h = 0.
-84, 1
Factor 440*l**2 - 857*l**2 + 385*l + 422*l**2 + 750.
5*(l + 2)*(l + 75)
Suppose -6*u = -10*u + 16. Factor 8 - u*i**3 + 7*i + 0*i + 4*i**4 - i - 12*i**2 - 2*i.
4*(i - 2)*(i - 1)*(i + 1)**2
Let m be 5232/9592*(-88)/(-10). Determine o so that -m*o - 3/5*o**2 + 0 = 0.
-8, 0
Suppose -3*k = 226 - 259. Suppose 2*o - 3*p - k - 4 = 0, -3*p - 15 = 5*o. Suppose 2/9*z**4 + 2/9*z**5 + 0 + 0*z**3 + o*z + 0*z**2 = 0. What is z?
-1, 0
Suppose 4*m = 9*m - 15. Let z(j) be the second derivative of 0*j**6 + 1/21*j**7 + 0 + 0*j**2 - 2*j + 0*j**4 + 0*j**m + 0*j**5. Let z(u) = 0. Calculate u.
0
Let t(a) = a**2 + 4*a + 3. Let f be t(4). Let -40*n - f*n**2 - 6 + 9 + 14 + 3 + 25*n**3 = 0. What is n?
-1, 2/5, 2
Suppose -r = 5*d - 15, 10*r + 4*d - 12 = 5*r. Let t(h) be the first derivative of 0*h**2 + 2 - 1/9*h**3 + 1/12*h**4 + r*h. Factor t(f).
f**2*(f - 1)/3
Let n(i) = -6*i**4 + 7*i**3 - 4*i**2 - 12*i. Let v(b) = 2*b**4 + b**3. Let q(w) = -n(w) - 5*v(w). What is k in q(k) = 0?
-3, -1, 0, 1
Let x = 27 + -34. Let j(c) = -c**2 - 4*c + 21. Let h be j(x). Solve -2/7*v + 2/7*v**5 + h + 0*v**3 + 4/7*v**4 - 4/7*v**2 = 0 for v.
-1, 0, 1
Let x be (-1)/9 - (-1496)/6336. Let w(k) be the first derivative of x*k**4 - 1/3*k**2 + 0*k**3 - 1/30*k**5 + 0*k + 6. Factor w(p).
-p*(p - 2)**2*(p + 1)/6
Let i(s) be the first derivative of 4*s**3/15 - 18*s**2/5 + 72*s/5 + 742. Find r, given that i(r) = 0.
3, 6
Let g(r) = 135*r**3 + 15*r**2 - 185*r - 40. Let q(a) = 2*a**2 + 5*a**3 - 23*a + 132 + 12*a**3 - 137. Let w(x) = -3*g(x) + 25*q(x). What is f in w(f) = 0?
-1, -1/4, 1
Let j be -3 + (5 - (-9)/(-3)). Let d be 10 - 7 - 1/j. Factor 21 + 28*g + 3*g**2 + 27 - d*g.
3*(g + 4)**2
Let c(h) be the third derivative of h**7/210 + h**6/60 - h**5/5 + 7*h**4/12 - 5*h**3/6 + h**2 - 34. Let c(m) = 0. What is m?
-5, 1
Let u(h) = 36*h + 975. Let t be u(-27). Let f(n) be the first derivative of -4 - 1/4*n**2 + 1/12*n**t + 0*n. Factor f(y).
y*(y - 2)/4
Let n(j) be the first derivative of 0*j + 5/12*j**4 + 5/36*j**6 + 0*j**2 + 8 + 0*j**3 - 1/2*j**5. Factor n(c).
5*c**3*(c - 2)*(c - 1)/6
Le