0 + v**4/2 + 3*v**3/2 - 5*v**2/2 - 4. Let i(z) be the second derivative of n(z). Find u, given that i(u) = 0.
-3, -1
Let m(a) be the third derivative of -a**8/336 + a**7/147 + a**6/210 - a**5/42 + a**4/56 - 42*a**2. Determine g, given that m(g) = 0.
-1, 0, 3/7, 1
Let k = 2 + 12. Let q = 18 - k. Factor -1/4*g**2 + 0*g + 1/4*g**q + 0 + 0*g**3.
g**2*(g - 1)*(g + 1)/4
Let t(w) = w**3 - w + 1. Let h(j) = -3*j**3 - 8*j**2 + 3*j + 9. Let v(y) = -h(y) + t(y). Factor v(a).
4*(a - 1)*(a + 1)*(a + 2)
Let x(i) = i**2 - 9*i - 7. Let v be x(10). Suppose -v*h = -h. Factor -1/4*g**3 + 0*g**2 + 0*g + h - 1/4*g**4.
-g**3*(g + 1)/4
Determine q so that 0*q**2 + 2/5*q**3 + 0 - 2/5*q = 0.
-1, 0, 1
Let d(m) be the first derivative of -2/5*m**5 + 2*m**4 - 7/2*m**3 - m - 1 + 11/4*m**2. Let d(s) = 0. Calculate s.
1/2, 1, 2
Let g be (3/78)/(1/(-4))*-1. Factor 0 - g*y**2 - 4/13*y.
-2*y*(y + 2)/13
Suppose -2*v + 155 = -r, -3*v + r = -3*r - 240. Let w be v/95*(-5)/(-2). Factor -1/3*k**w + k - 2/3.
-(k - 2)*(k - 1)/3
Let v(o) be the first derivative of 4 + 1/12*o**3 + 1/4*o**2 + 1/4*o. Solve v(j) = 0.
-1
Let f(l) be the second derivative of l**6/90 - 2*l**5/15 + 23*l**4/36 - 14*l**3/9 + 2*l**2 - l + 12. Solve f(m) = 0 for m.
1, 2, 3
Factor 8*v**3 + 0*v**3 - 35*v**2 + 25*v - 15*v**3 - 13*v**3 + 30.
-5*(v - 1)*(v + 2)*(4*v + 3)
Let d(p) = p**2 + 9*p - 8. Let i be d(-10). Let w(u) be the first derivative of 0*u + 1/3*u**i - 1 - 2/9*u**3. Find a such that w(a) = 0.
0, 1
Let w(z) be the third derivative of 0 + 0*z - 1/6*z**4 - 1/160*z**6 + 13/240*z**5 + 1/6*z**3 - 6*z**2. Solve w(b) = 0 for b.
1/3, 2
Let s(q) be the third derivative of -1/10*q**5 - 1/6*q**4 + 0 + 2*q**2 + 0*q - 1/60*q**6 + 0*q**3. Factor s(c).
-2*c*(c + 1)*(c + 2)
Let i = 644 - 642. Factor 0*f**3 + 0*f**4 + 0*f**i + 1/4*f**5 + 0*f + 0.
f**5/4
Let j be (-20)/15*(-6)/4. Factor 0 + 0*o - 2/11*o**3 + 0*o**j - 2/11*o**4.
-2*o**3*(o + 1)/11
Let p be 48/80 - 94/165. Let b(u) be the second derivative of 1/66*u**4 + 0*u**2 - p*u**3 + 3*u + 0. Factor b(r).
2*r*(r - 1)/11
Factor 4 - 8*d**3 + 23*d**2 - 26*d**2 + 11*d + d + 3*d**4.
(d - 2)**2*(d + 1)*(3*d + 1)
Let t(r) = r**2 + r + 1. Let n(u) = -4*u**3 + 3*u**2 - 3*u - 2. Let i(q) = n(q) + 2*t(q). Factor i(a).
-a*(a - 1)*(4*a - 1)
Suppose -4*s + 1 = s - b, -s = -4*b - 4. Let g(m) be the second derivative of s - 1/60*m**4 + 1/15*m**3 + m - 1/10*m**2. Determine d so that g(d) = 0.
1
Let q(s) be the first derivative of -2*s**3/15 - 9. Factor q(v).
-2*v**2/5
Suppose -4*p + 22 = 2. Suppose -2*r - 21 = -p*j, j - 20 = -5*r - j. Let 0*s**r + 1/2*s**3 + 0*s + 0 = 0. What is s?
0
Let d(s) = -s**3 - s - 1. Let v(i) = 10*i**3 - 32*i**2 + 34*i + 40. Let a(b) = -4*d(b) - v(b). Factor a(h).
-2*(h - 3)**2*(3*h + 2)
Suppose 9 = -2*z - 1. Let q(a) = a**2 + 5*a + 5. Let g be q(z). Factor -x**4 + 2*x**5 - x**4 + 0*x**g.
2*x**4*(x - 1)
Let b(t) = -t**5 - t**4 + t**3 - t**2 + t - 1. Let z(r) = -25*r**4 - 45*r**3 + 35*r**2 + 40*r + 5. Let l(s) = 5*b(s) + z(s). Suppose l(q) = 0. Calculate q.
-3, -1, 0, 1
Let t(q) = -2*q**4 - 4*q**3 + 27*q**2 - 5*q - 40. Let h(d) = 4*d**4 + 8*d**3 - 55*d**2 + 11*d + 80. Let y(p) = -3*h(p) - 5*t(p). What is v in y(v) = 0?
-5, -1, 2
Let b(i) be the first derivative of -i**4/18 - 4*i**3/9 - 4*i**2/3 - 5*i - 7. Let q(v) be the first derivative of b(v). Find z such that q(z) = 0.
-2
Let l(q) be the second derivative of -4*q**5 + 10*q**4/3 - 5*q**3/6 + 14*q. Factor l(j).
-5*j*(4*j - 1)**2
Let t(f) be the second derivative of f**4/20 - f**3/5 + 3*f**2/10 - 8*f. Find o, given that t(o) = 0.
1
Let -16/5 - 52/5*k**4 - 4*k**5 + 4/5*k**3 + 16/5*k + 68/5*k**2 = 0. Calculate k.
-2, -1, 2/5, 1
Let r(k) be the first derivative of 5*k**3/3 - 5*k**2/2 - 4. Let r(o) = 0. What is o?
0, 1
Let p(k) be the first derivative of 4*k**5/15 + 17*k**4/12 + 8*k**3/3 + 13*k**2/6 + 2*k/3 + 2. Factor p(g).
(g + 1)**2*(g + 2)*(4*g + 1)/3
Let z(f) be the second derivative of 1/15*f**3 + 0*f**2 - 2*f + 1/60*f**4 + 0. Determine k so that z(k) = 0.
-2, 0
Let u(s) be the second derivative of 0 + 1/12*s**3 - 4*s + 1/6*s**4 + 1/84*s**7 - 1/30*s**6 - 1/2*s**2 - 1/20*s**5. Suppose u(c) = 0. Calculate c.
-1, 1, 2
Let a(j) be the third derivative of j**9/151200 - j**8/50400 - j**5/15 - 4*j**2. Let h(v) be the third derivative of a(v). Determine c, given that h(c) = 0.
0, 1
Let j(f) be the second derivative of f**6/120 - f**5/60 - f**4/12 + f**2 - 4*f. Let x(h) be the first derivative of j(h). Suppose x(z) = 0. What is z?
-1, 0, 2
Let r = 41 + -39. What is j in 10*j - r - 25/2*j**2 = 0?
2/5
Factor -2*o**4 + 3*o**5 + 2*o**4 - 2*o - 3*o**2 + 4*o**4 + 3*o**3 + 3*o**4.
o*(o + 1)**3*(3*o - 2)
Let t be (-105)/(-300) - (12/(-5) - -2). Suppose i + 4*i = 0. Factor 1/4*o**4 + t*o**3 + 0 - o + i*o**2.
o*(o - 1)*(o + 2)**2/4
Let w(q) be the third derivative of q**5/120 - 5*q**4/24 + 25*q**3/12 + 3*q**2. Factor w(t).
(t - 5)**2/2
Let c(b) be the second derivative of b**6/3 + 8*b**5/15 - 11*b**4/18 - 16*b**3/9 - 4*b**2/3 + 25*b. Suppose c(k) = 0. Calculate k.
-1, -2/3, -2/5, 1
Let c(p) be the second derivative of p**9/3024 - p**8/840 + p**7/840 - 5*p**3/3 - 5*p. Let r(z) be the second derivative of c(z). Determine i so that r(i) = 0.
0, 1
Let v(h) = 10*h**3 + 24*h**2 + 16*h + 2. Let l(a) = 30*a**3 + 72*a**2 + 47*a + 5. Let d(y) = -2*l(y) + 7*v(y). Let d(p) = 0. What is p?
-1, -2/5
Let w(z) be the third derivative of 1/60*z**4 - 1/300*z**6 + 0*z + 0 + 1/150*z**5 - z**2 - 1/15*z**3. Determine o, given that w(o) = 0.
-1, 1
Find j such that -106*j + j**3 + 3*j**2 + 7*j**2 + 106*j = 0.
-10, 0
Let d(z) be the second derivative of -7*z**5/50 - 2*z**4/5 - z**3/5 + 2*z**2/5 - 3*z. Factor d(x).
-2*(x + 1)**2*(7*x - 2)/5
Let f(d) be the first derivative of -3*d**3 - 9/20*d**5 + 1 - 2*d + 13/8*d**4 + 3*d**2 + 1/20*d**6. Let k(z) be the first derivative of f(z). Factor k(p).
3*(p - 2)**2*(p - 1)**2/2
Factor 0*w + 2/9*w**2 + 0.
2*w**2/9
Let g(r) be the second derivative of r**5/20 - r**3/2 - r**2 + 6*r. Factor g(c).
(c - 2)*(c + 1)**2
Let u be (0 - 4)/(2/(-3)). Let b(w) be the second derivative of -1/40*w**5 - 1/24*w**4 + 0 + 1/12*w**3 + 2*w + 0*w**2 + 1/60*w**u. Find l such that b(l) = 0.
-1, 0, 1
Let q = -10/29 - -59/87. Let z(d) be the second derivative of 4*d - 1/12*d**4 + 0*d**2 - q*d**3 + 0. Factor z(b).
-b*(b + 2)
Let t(c) = -29*c**2 + 1. Let r be t(1). Let n = r + 30. Factor 1/2*w + 1/2 - 1/2*w**n - 1/2*w**3.
-(w - 1)*(w + 1)**2/2
Suppose -3*o**3 + 6*o**4 - o**2 - 11*o**3 + 5*o**2 = 0. Calculate o.
0, 1/3, 2
Factor -5*g**5 + 20*g**2 - 96*g**3 + 96*g**3 - 15*g**4.
-5*g**2*(g - 1)*(g + 2)**2
Let l(i) be the first derivative of i**7/840 + i**6/360 - i**5/120 - i**4/24 + i**3/3 - 5. Let h(u) be the third derivative of l(u). Factor h(q).
(q - 1)*(q + 1)**2
Let t(d) be the second derivative of d**5/10 + 5*d**4/24 + d**3/12 - d. Factor t(m).
m*(m + 1)*(4*m + 1)/2
Let y be (4/(-7))/((-42)/49). Factor 4/3*r**2 + 2*r + y.
2*(r + 1)*(2*r + 1)/3
Solve 3/2*h**2 - 3/2*h**3 + 0 + 1/2*h**4 - 1/2*h = 0 for h.
0, 1
Suppose 8*n - 7*n = -2*r + 2, -1 = -n - 3*r. What is m in 0*m - 6/5*m**3 + 0 - 3/5*m**n - 3/5*m**2 = 0?
-1, 0
Determine f so that 1/6*f**2 + 1/6*f**5 + 0 - 1/6*f**4 - 1/6*f**3 + 0*f = 0.
-1, 0, 1
Let p(z) be the second derivative of 0*z**2 + 1/6*z**4 + 0 - 2*z - 2/3*z**3. Factor p(s).
2*s*(s - 2)
Let d(s) be the first derivative of s**5/5 - 5*s**4/4 + 7*s**3/3 - 3*s**2/2 + 38. Solve d(c) = 0.
0, 1, 3
Let p = -194 - -196. Let s = -1 - -2. Factor -1/4*z**p - s + z.
-(z - 2)**2/4
Let o(j) = 10*j**5 + 9*j**4 + 3*j**3 + j**2 + 3*j + 3. Let q(w) = 21*w**5 + 17*w**4 + 6*w**3 + 3*w**2 + 7*w + 7. Let k(n) = 14*o(n) - 6*q(n). Factor k(y).
2*y**2*(y + 1)**2*(7*y - 2)
Let a(o) be the third derivative of o**7/6300 - o**6/900 + o**5/300 + o**4/6 + o**2. Let q(y) be the second derivative of a(y). Suppose q(g) = 0. What is g?
1
Let m = 2/41 + 37/82. Let v(a) be the first derivative of 1/12*a**3 + 3/8*a**2 + m*a - 1. Factor v(g).
(g + 1)*(g + 2)/4
Let t(x) be the second derivative of -x**4/12 + x**3/6 + x**2 - 8*x. Suppose t(l) = 0. Calculate l.
-1, 2
Let a(h) = 5*h**2 - 8*h + 5. Let k(p) = -26*p**2 + 41*p - 26. Let g(s) = -11*a(s) - 2*k(s). Factor g(d).
-3*(d - 1)**2
Let 5*i**2 - 3*i**2 + 0*i**2 + i**2 + 6*i = 0. What is i?
-2, 0
Factor 14/11*h**4