41. Let t(a) = 5*a**2 + 5*a - 8. Let v(f) = 11*t(f) - 2*z(f). Suppose v(n) = 0. What is n?
-2, 1
Factor 0 + 6/5*m**5 - 9/5*m**4 + 3/5*m**3 + 0*m + 0*m**2.
3*m**3*(m - 1)*(2*m - 1)/5
Let p = 325555/9 - 36029. Let g = 144 - p. Solve 4/9*w**3 + 8/9*w**4 + 0 - 8/9*w**2 + g*w - 2/3*w**5 = 0.
-1, 0, 1/3, 1
Let d(k) be the third derivative of 2*k**7/105 - k**6/30 - k**5/5 + k**4/6 + 4*k**3/3 - 6*k**2. Factor d(n).
4*(n - 2)*(n - 1)*(n + 1)**2
Let r(k) be the second derivative of -k**6/75 + 3*k**5/50 - k**4/10 + k**3/15 + 6*k - 4. Factor r(p).
-2*p*(p - 1)**3/5
Let g(n) be the second derivative of 0 + 0*n**2 + 0*n**4 + 0*n**3 - 5*n - 1/5*n**5 + 1/15*n**6 + 1/21*n**7. Factor g(a).
2*a**3*(a - 1)*(a + 2)
Let v(l) be the first derivative of -3 + 2/5*l**3 - 2/25*l**5 - 8/5*l + 1/5*l**4 - 4/5*l**2. Solve v(g) = 0 for g.
-1, 2
Let l(q) be the second derivative of q**6/120 - q**4/8 + q**3/3 + 3*q**2/2 - 3*q. Let o(j) be the first derivative of l(j). Factor o(k).
(k - 1)**2*(k + 2)
Let o(q) be the third derivative of -q**6/480 + q**4/32 + q**3/12 - 25*q**2. Factor o(h).
-(h - 2)*(h + 1)**2/4
Let d(g) be the second derivative of -g**7/294 + g**5/20 - g**4/14 + 2*g - 14. Determine b, given that d(b) = 0.
-3, 0, 1, 2
Suppose -558*r + 561*r = 6. Determine s so that 16/3*s - 4/3*s**r - 16/3 = 0.
2
Let h(p) be the third derivative of -p**7/420 + 7*p**6/240 + 25*p**2. Factor h(s).
-s**3*(s - 7)/2
Let t(x) be the third derivative of 0 - 1/40*x**5 + 0*x - 1/16*x**4 + 0*x**3 + 5*x**2. Factor t(m).
-3*m*(m + 1)/2
Let d = 56 - 52. What is q in 6/5*q**2 + 2/5 + 2*q**3 - 8/5*q**d - 2*q = 0?
-1, 1/4, 1
Let w(t) be the second derivative of -5*t**7/126 + 4*t**6/45 + t**5/15 - 5*t**4/18 + t**3/18 + t**2/3 - 6*t. Determine j, given that w(j) = 0.
-1, -2/5, 1
Solve 2/7*n - 4/7 + 2/7*n**2 = 0.
-2, 1
Let j(q) be the second derivative of -q**5/90 - q**4/27 - q**3/27 - 9*q. Factor j(c).
-2*c*(c + 1)**2/9
Let h(w) be the third derivative of w**6/120 + 3*w**5/10 - 13*w**4/8 + 11*w**3/3 + 13*w**2. Let y be h(-20). Factor 0 + x + 1/2*x**y.
x*(x + 2)/2
Let p(z) be the first derivative of 3*z**4/2 - 7*z**3 + 9*z**2/2 + 21. Solve p(n) = 0 for n.
0, 1/2, 3
Suppose 8*k - 10*k = -4. Solve 2/3*n**k - n + 1/3*n**3 + 0 = 0.
-3, 0, 1
Factor -x**3 + 3*x**5 + 8*x**4 + 0*x**3 + 4*x**3 - 2*x**4.
3*x**3*(x + 1)**2
Let c(x) be the second derivative of -1/4*x**2 + 3*x + 0 - 1/40*x**5 + 1/24*x**4 + 1/12*x**3. Factor c(p).
-(p - 1)**2*(p + 1)/2
Let i be 1/(-6)*48/(-42). Let k(a) be the first derivative of 4/7*a + 1 - 1/14*a**4 + 1/7*a**2 - i*a**3. Factor k(x).
-2*(x - 1)*(x + 1)*(x + 2)/7
Let y = 4 - 2. Let l be (-11)/33*(-3)/2. Factor 0 + 1/2*u**3 - u**y + l*u.
u*(u - 1)**2/2
Let d(n) = 19*n**3 + 79*n**2 + 36*n - 6. Let j(s) = 18*s**3 + 78*s**2 + 37*s - 7. Let a(o) = -7*d(o) + 6*j(o). Factor a(t).
-5*t*(t + 3)*(5*t + 2)
Let w(o) be the third derivative of o**5/330 - 7*o**4/132 - 8*o**2. Factor w(i).
2*i*(i - 7)/11
Let g(v) be the first derivative of -4/9*v + 1/27*v**6 + 3 + 4/27*v**3 + 1/3*v**2 + 0*v**5 - 2/9*v**4. Solve g(f) = 0 for f.
-2, -1, 1
Let c(d) be the first derivative of -4*d**4 + 4*d**3 - 3 - 2*d + 6/5*d**5 + 0*d**2. Factor c(t).
2*(t - 1)**3*(3*t + 1)
Suppose 0 = -c + 2*t - 8, -t = -4*t + 12. Factor 2/9*j**3 + c + 0*j**2 - 2/9*j.
2*j*(j - 1)*(j + 1)/9
Suppose -4*t - 12 = -4*i + 8*i, i = t - 3. Let v(o) be the third derivative of 2*o**2 - 1/24*o**4 + t*o**5 + 0*o + 1/120*o**6 + 0*o**3 + 0. Factor v(z).
z*(z - 1)*(z + 1)
Let c be -11 - -12 - (-11)/1. Factor -12*w - 3 - c*w**3 - 18*w**2 - 26*w**4 + 40*w**4 - 17*w**4.
-3*(w + 1)**4
Factor -158*n - 4 + 6*n**3 + 152*n - 2*n**2 - 2*n**4 + 5 + 3.
-2*(n - 2)*(n - 1)**2*(n + 1)
Let k be 70/20 - 6/(-4). Let a(x) be the second derivative of 0 + 0*x**2 + 11/60*x**k + x - 1/14*x**7 + 1/9*x**4 - 2/9*x**3 - 1/15*x**6. Solve a(l) = 0.
-1, 0, 2/3
Suppose 3*j = -2*m - 1, 2 = -4*m - 2*j + 12. Suppose -m*z + z = -4*h - 16, 0 = -2*z - 3*h + 22. Factor 0*o**4 - 12*o**2 - 2 + 5*o**3 - 2*o**4 + z*o + 3*o**3.
-2*(o - 1)**4
Let t = -6 + -54. Let b be (1/(-3))/(10/t). What is z in -1/3*z - 8/3*z**3 - 5/3*z**b - 4/3*z**4 + 0 = 0?
-1, -1/2, 0
Let a(w) be the second derivative of -w**4/12 + 2*w**2 - 21*w. Determine j, given that a(j) = 0.
-2, 2
Let f = 49 - 46. Determine i so that 1/4*i**4 - 1/4*i + 1/4*i**f + 0 - 1/4*i**2 = 0.
-1, 0, 1
Let i(m) be the first derivative of 1 - 1/12*m**4 + 0*m**2 + 0*m + 0*m**3 - 1/3*m**5 - 2/9*m**6. Solve i(x) = 0.
-1, -1/4, 0
Let d(p) be the first derivative of -9*p**4/8 + p**3 + 15*p**2/4 - 6*p + 27. Factor d(x).
-3*(x - 1)**2*(3*x + 4)/2
Suppose 0 = -j - 2*j + 4*r + 28, -3*r = 2*j + 4. Determine b so that -2 + 6 + 0*b + b**4 - 2*b**3 - 3*b**2 + 0*b**3 + j*b = 0.
-1, 2
Suppose 4*m - 2*m = 0. Let d be (-7)/((-2)/8 - m). Find j, given that 30*j**3 - j**2 + 2*j**2 - j**2 - j**2 - 2*j - d*j**5 + j**4 = 0.
-1, -1/4, 0, 2/7, 1
Let m be ((-4)/14)/(876/(-511)). Find d such that -1/3*d**2 - m*d**3 + 1/3 + 1/6*d = 0.
-2, -1, 1
Let x(a) be the third derivative of 0 - 1/6*a**4 - 4*a**2 + 2/3*a**3 + 0*a + 1/60*a**5. Solve x(b) = 0 for b.
2
Let d(q) be the first derivative of 0*q + 19*q**4 - 8*q**2 - 8*q**3 + 174/5*q**5 + 15*q**6 + 1. Determine j, given that d(j) = 0.
-1, -2/3, 0, 2/5
Let l(z) = z**3 + 9*z**2 + 6*z. Let c(s) = s**2 + s. Let w(y) = 40*c(y) - 5*l(y). Solve w(u) = 0 for u.
-2, 0, 1
Suppose 2*d = 5*d + 3*d. Factor 1/6*v**3 + 0*v + d*v**2 + 0 + 0*v**4 - 1/6*v**5.
-v**3*(v - 1)*(v + 1)/6
Let z(t) be the second derivative of 2*t**7/21 - t**5/5 + 34*t. Factor z(j).
4*j**3*(j - 1)*(j + 1)
Let d(r) be the first derivative of r**4/9 - 2*r**3/27 + 11. Solve d(z) = 0 for z.
0, 1/2
Let v(m) = m**3 + 2*m**2 - 3*m + 2. Suppose q = 2 - 5. Let h be v(q). Factor 2/7*o**h + 0 + 2/7*o.
2*o*(o + 1)/7
Let n(g) = g**3 + 8*g**2 + 18*g + 15. Let d be n(-5). Factor 16/3 + d*y - 8/3*y**2 + 1/3*y**4 + 0*y**3.
(y - 2)**2*(y + 2)**2/3
Let m(y) be the second derivative of -y**6/60 - y**5/15 - y**4/12 - y**2 - 4*y. Let r(a) be the first derivative of m(a). Determine p so that r(p) = 0.
-1, 0
Let f be 2*6/((-72)/(-30)). Let 18/5*s**3 + 6/5*s**2 - 9/5 + 3/5*s**4 - 3/5*s**f - 3*s = 0. Calculate s.
-1, 1, 3
Let k(w) be the first derivative of w**3/6 - w**2/4 + 5. Factor k(t).
t*(t - 1)/2
Factor -879*f**3 + 66*f**2 - 8 + 862*f**3 - 8*f - 52*f.
-(f - 2)**2*(17*f + 2)
Let m = -221 + 223. Let w(r) be the third derivative of 1/84*r**4 + 0 - 1/21*r**3 + 2*r**m + 1/210*r**5 + 0*r - 1/420*r**6. Factor w(t).
-2*(t - 1)**2*(t + 1)/7
Let c(u) be the first derivative of u**6/120 - u**5/80 - 3*u - 3. Let x(o) be the first derivative of c(o). Factor x(k).
k**3*(k - 1)/4
Suppose -19*b - s = -17*b - 3, -3*b + 12 = -s. Factor -2*n**2 + 16/5*n + 2/5*n**b - 8/5.
2*(n - 2)**2*(n - 1)/5
Let q(u) be the third derivative of -u**7/1680 - u**6/1440 - u**3/6 + 2*u**2. Let d(l) be the first derivative of q(l). Factor d(p).
-p**2*(2*p + 1)/4
Let k(o) = -o**3 - 21*o. Let y(p) = -p**2 + 7*p - 6. Let g be y(4). Suppose 0 - g = -3*v. Let u(x) = -4*x. Let r(z) = v*k(z) - 11*u(z). Factor r(j).
-2*j*(j - 1)*(j + 1)
Let z be 5 - (0 - (-3 - -2)). Factor l**2 + 1 + 0*l**2 - z*l + 2*l.
(l - 1)**2
Let l(b) be the second derivative of b + 0*b**2 + 1/42*b**4 + 0 + 1/21*b**3. Factor l(n).
2*n*(n + 1)/7
Let k(g) be the third derivative of g**9/2016 - g**8/560 + g**7/560 + 4*g**3/3 + 6*g**2. Let a(t) be the first derivative of k(t). Factor a(h).
3*h**3*(h - 1)**2/2
Determine c so that 21/5*c + 26/5*c**3 + 1 + 9/5*c**4 + 1/5*c**5 + 34/5*c**2 = 0.
-5, -1
Suppose 103 = 11*r + 70. Solve 2/3*q**2 - 4/9*q - 2/9*q**r + 0 = 0 for q.
0, 1, 2
Let v(q) be the second derivative of 0*q**3 - 1/45*q**5 + 0 - q**2 - 1/36*q**4 - 3*q. Let o(g) be the first derivative of v(g). Solve o(f) = 0.
-1/2, 0
Factor 0*w**2 + 5/4*w**5 + w**3 + 0*w + 3*w**4 + 0.
w**3*(w + 2)*(5*w + 2)/4
Let -1/4*t - 1/4*t**2 + 0 = 0. What is t?
-1, 0
Let j be (-2)/(-2*(-4)/(-12)). Suppose j*h + 5 = -h - i, -3*i - 15 = -4*h. Let 1/4*d**2 + h*d + 0 - 1/2*d**3 = 0. What is d?
0, 1/2
Let b = -301 - -303. Determine p so that 5/4*p**4 - 3/4*p - 7/4*p**b + 1/2 + 3/4*p**3 = 0.
-1, 2/5, 1
Suppose -4*r + 15 = y, 3*r + 2*y + 3 = 13. Factor -34*k**4 - 8*k**3 + 69*k**r + 4*k**5 - 31*k**4.
4*k**3*(k - 1)*(k + 2)
Determine u, given that -3*u**3 - 3*u**3 + 3*u**3 - 6*u**2