2*u*(u - 1)**3*(u + 1)/5
Suppose 52/9*m**4 - 80/9*m**3 + 0 + 44/9*m**2 - 10/9*m**5 - 2/3*m = 0. What is m?
0, 1/5, 1, 3
Let s(f) be the third derivative of f**6/360 + 19*f**5/180 + 35*f**4/72 + 17*f**3/18 - 9*f**2. Determine t so that s(t) = 0.
-17, -1
Let t(w) be the first derivative of w**2 - 7*w - 1. Let c be t(5). Determine d so that -2*d**2 + 16 - 3*d + 0*d**2 + 5*d**2 + c*d**3 - 19 = 0.
-1, 1
Let q = -96 - -101. Suppose 11*k - 13*k = q*v + 4, -5*k = -3*v - 21. Factor 1/4*m**k - 1/4*m + 0*m**2 + 0.
m*(m - 1)*(m + 1)/4
Let j(n) be the first derivative of 2*n**5/5 + n**4 - 14*n**3/3 - 20*n**2 - 24*n - 204. Factor j(b).
2*(b - 3)*(b + 1)*(b + 2)**2
Suppose y + n = 4, -4*y = -0*n - n - 11. Let f(x) = 12*x**3 + 9*x**2 - 3. Let v(p) = p**4 + 24*p**3 + 18*p**2 - 5. Let c(b) = y*v(b) - 5*f(b). Factor c(g).
3*g**2*(g + 1)*(g + 3)
Suppose -2*v + v = -27. Suppose 5 = h - v. Find a such that a**4 - 4 - 23*a**4 + 2 - 13*a - 38*a**3 - 5*a**5 - h*a**2 = 0.
-1, -2/5
Suppose -2/7*w**3 - 10366/7*w - 290/7*w**2 + 10658/7 = 0. What is w?
-73, 1
Let j(o) be the third derivative of -5*o**7/6 + 11*o**6/4 - 23*o**5/12 - 5*o**4/2 + 10*o**3/3 - 74*o**2. Suppose j(k) = 0. Calculate k.
-2/5, 2/7, 1
Solve 1/10*c**4 - 24/5 - 3/10*c**2 + 28/5*c - 3/5*c**3 = 0.
-3, 1, 4
Suppose -6*z - 219 = -21. Let h = 35 + z. Factor -3/7*w - 6/7 + 3/7*w**h.
3*(w - 2)*(w + 1)/7
Factor 5/2*v - 6*v**2 + 2*v**4 + 1/2*v**3 + 1.
(v - 1)**2*(v + 2)*(4*v + 1)/2
Let t be (222/(-30) - -8) + 6 + 305/(-50). Factor 2 - 9/2*b + 3*b**2 - t*b**3.
-(b - 4)*(b - 1)**2/2
Let j(w) be the first derivative of 5/48*w**4 + 0*w + 3*w**2 + 1 + 0*w**3 - 1/24*w**5. Let l(z) be the second derivative of j(z). Suppose l(v) = 0. Calculate v.
0, 1
Let h(b) be the second derivative of b**9/30240 - b**8/6720 + b**7/5040 - b**4/3 - 16*b. Let u(k) be the third derivative of h(k). Factor u(c).
c**2*(c - 1)**2/2
Let q(v) be the third derivative of 2*v**7/105 - 3*v**5/5 - 2*v**4/3 + 8*v**3 + 3*v**2. Factor q(m).
4*(m - 3)*(m - 1)*(m + 2)**2
Suppose -4/3 - 1225/3*w**2 - 140/3*w = 0. Calculate w.
-2/35
Let m(v) be the second derivative of v**7/210 - v**6/75 - 21*v**5/100 - 11*v**4/30 + 2*v**3/3 + 12*v**2/5 - 80*v - 2. Let m(y) = 0. What is y?
-2, -1, 1, 6
Let o(k) be the first derivative of -5*k**4/4 + 55*k**3/3 - 195*k**2/2 + 225*k + 30. Factor o(i).
-5*(i - 5)*(i - 3)**2
Let n(i) = -3*i**2 - 21*i - 26. Let v(g) = 2*g**2 + 22*g + 26. Let j(y) = 3*n(y) + 4*v(y). Factor j(q).
-(q - 26)*(q + 1)
Let o = 75419/588 - 513/4. Let v(l) be the second derivative of -o*l**7 - 2/105*l**6 + 4/21*l**3 + 2*l + 0 + 5/21*l**4 + 3/35*l**5 + 0*l**2. Factor v(j).
-4*j*(j - 2)*(j + 1)**3/7
Let l = -78 - -78. Let b be -1 + 4 - (l + 3). Find u, given that -1/2*u**3 + 1/2*u**5 + b + 0*u + 0*u**4 + 0*u**2 = 0.
-1, 0, 1
Suppose 12 = 4*o - 0. Solve n**o + n + 0*n - 3*n + n = 0 for n.
-1, 0, 1
Suppose 2*s - 60 = -3*s. Let r(l) = l**2 - 13*l + 14. Let a be r(s). Factor u**a + 0*u - 3/2*u**3 + 0 + 1/2*u**4.
u**2*(u - 2)*(u - 1)/2
Let g be -5*1 + (4 - 2). Let o = 8 + g. Factor -12*p**2 - o + 5 + 0*p**2 + 3 + 9*p.
-3*(p - 1)*(4*p + 1)
Let s be (10/15*-5)/(20/(-24)). Determine t so that -2/5*t**2 + 0 + 2/5*t**3 + 2/5*t**s - 2/5*t = 0.
-1, 0, 1
Let q = -132/179 - -2949/358. Factor -25/2*g - 5/6*g**3 - 125/6 + q*g**2.
-5*(g - 5)**2*(g + 1)/6
Factor 3*s**3 + 0 + 7/3*s**2 + 5/3*s**4 + 1/3*s**5 + 2/3*s.
s*(s + 1)**3*(s + 2)/3
Let a(g) be the second derivative of -3*g - 1/42*g**4 + 0 - 2/7*g**2 - 1/7*g**3. Determine l so that a(l) = 0.
-2, -1
Let f(v) = v - 6. Let t be f(9). Let -40*m**2 - 17*m**3 + 3*m**5 - 45*m + 23*m**3 + 12*m**5 - 10 + 50*m**4 + 24*m**t = 0. Calculate m.
-2, -1, -1/3, 1
Factor 165*d - 83*d - 6*d**2 - 98*d + 2*d**4 - 6*d**2 - 6.
2*(d - 3)*(d + 1)**3
Let f(v) = v**2 + 14*v + 18. Let r be f(-13). Factor -5 - 5*d**3 - 5*d**4 + r.
-5*d**3*(d + 1)
Let t(c) be the first derivative of 4/3*c**3 + 8*c + 13 + 6*c**2. Determine z, given that t(z) = 0.
-2, -1
Let z(d) = 5*d**2 - 42. Let u(h) = 15*h**2 - 127. Let n(g) = 3*u(g) - 8*z(g). Solve n(s) = 0.
-3, 3
Let l(c) be the second derivative of -8*c + 1/5*c**3 + 5*c**2 + 0 - 1/100*c**5 + 1/40*c**4. Let n(g) be the first derivative of l(g). Factor n(k).
-3*(k - 2)*(k + 1)/5
Let y(u) be the first derivative of -1/16*u**4 + u + 0*u**2 - 1/4*u**3 + 1. Factor y(n).
-(n - 1)*(n + 2)**2/4
Let u(i) = i**2 + 6*i + 6. Let b be u(8). Suppose b = 4*c - 122. Determine v so that 106*v**5 - v**3 + 12*v - 210*v**4 + c*v**2 + 41*v**5 - 8*v**3 = 0.
-2/7, 0, 1
Let g(x) be the second derivative of x**6/360 - x**5/80 - x**4/24 - 13*x**3/3 + 21*x. Let i(v) be the second derivative of g(v). Factor i(y).
(y - 2)*(2*y + 1)/2
Let z(o) = 14*o + 112. Let l be z(-8). Let j(h) be the first derivative of -2/9*h**3 + 2/15*h**5 + l*h**4 + 3 + 0*h**2 + 0*h. Factor j(p).
2*p**2*(p - 1)*(p + 1)/3
Let x(p) be the first derivative of p**6/720 - p**5/80 + p**4/24 + 4*p**3/3 + 9. Let i(l) be the third derivative of x(l). Find t, given that i(t) = 0.
1, 2
Let z(x) be the first derivative of 6/5*x**2 + 0*x + 15 - 1/2*x**4 + 26/15*x**3. Determine t, given that z(t) = 0.
-2/5, 0, 3
Let i(x) be the third derivative of x**7/3780 - x**6/270 + x**5/60 - x**4/27 - 7*x**3/2 + 3*x**2. Let w(p) be the first derivative of i(p). Factor w(n).
2*(n - 4)*(n - 1)**2/9
Find t, given that 0*t + 1/6*t**3 - 5*t**2 + 0 = 0.
0, 30
Let u(b) = 4*b**5 - 6*b**4 + 14*b**3. Let h(y) = 39 - 39 - 26*y**3 + 17*y**4 - 11*y**5 - 15*y**3. Let x(l) = 6*h(l) + 17*u(l). Determine o, given that x(o) = 0.
-2, 0, 2
Let p be (-82)/(-8) + (-33)/(-44). Suppose -1 + p = 5*y. Let 4*n - 12*n**2 - 6*n + 4*n**y = 0. Calculate n.
-1/4, 0
Let f(g) be the first derivative of 2*g**3/27 + 8*g**2/9 + 32*g/9 + 147. Solve f(z) = 0.
-4
Suppose -a**2 + 4*a**3 - 7*a**2 + 49*a - 12 + 20*a**2 + 50*a - 103*a = 0. What is a?
-3, -1, 1
Let p(j) = 3*j**3 + j**2 + j + 1. Let c be p(-2). Let b be (10/6)/((-7)/c). Factor 3*t**2 - b*t**3 + 9*t**2 - 10*t - 2*t + 2*t**3.
-3*t*(t - 2)**2
Let r(b) be the first derivative of -5*b + 13 - 1/3*b**3 - 3*b**2. Factor r(g).
-(g + 1)*(g + 5)
Let 8*k**2 - 10*k + 18 + k**5 + 4*k**3 + 32*k**3 - 27*k - 20*k**4 - 6*k**2 = 0. Calculate k.
-1, 1, 18
Suppose -7*t + 13 - 55 = 0. Let j be 0 + t/10 + 119/140. Factor -1/4*o**2 + j*o**4 + 1/2*o**3 + 0 - 1/2*o.
o*(o - 1)*(o + 1)*(o + 2)/4
Let d(m) = 59*m**2 - 6*m - 8. Let y(t) = -5*t**2. Let x(i) = -2*d(i) - 18*y(i). Factor x(b).
-4*(b - 1)*(7*b + 4)
Let y be 3*(140/63 + 4/(-9)). Factor 2 + 10/3*z - y*z**2.
-2*(z - 1)*(8*z + 3)/3
Let i(h) = -h**2 - h - 1. Let c(l) = 4*l**2 + 2*l + 13. Let k(w) = -c(w) - 6*i(w). Let r(v) = -1. Let a(t) = -2*k(t) + 14*r(t). Factor a(b).
-4*b*(b + 2)
Let c = 2/121 + 355/484. Suppose 3/4*g**3 - 3/4 + 3/4*g**2 - c*g = 0. Calculate g.
-1, 1
Let b(w) = -w**4 + 9*w**3 - 7*w**2 - 9*w - 2. Let a(t) = 2*t**4 - 14*t**3 + 10*t**2 + 14*t + 4. Let x(q) = -5*a(q) - 8*b(q). Determine p so that x(p) = 0.
-2, -1, 1
Let z(d) be the first derivative of 2/3*d**3 - 12 + 0*d - 2*d**2. Let z(m) = 0. Calculate m.
0, 2
Factor 2/3*k**4 + 0 + 96*k + 32/3*k**3 + 56*k**2.
2*k*(k + 4)*(k + 6)**2/3
Let c(f) be the first derivative of 2*f**5/5 + 5*f**4/2 + 6*f**3 + 7*f**2 + 4*f + 104. Factor c(t).
2*(t + 1)**3*(t + 2)
Let y be (-2)/(5/(-116)*-4). Let a = 12 + y. Factor -8/5*b + a*b**4 + 0*b**2 + 0 + 6/5*b**3.
2*b*(b - 1)*(b + 2)**2/5
Let j(p) = -2*p**2 - 10. Let r be j(0). Let i = r - -31. Let f(m) = -m**2 - 5*m - 4. Let n(k) = -3*k**2 - 16*k - 13. Let w(u) = i*f(u) - 6*n(u). Solve w(x) = 0.
-2, -1
Let s = -65 - -85. Solve 16*a**4 - 34*a**4 + 4*a**2 - 6*a**3 + 0*a**2 + s*a**4 = 0 for a.
0, 1, 2
Let h(k) be the second derivative of k**6/420 + k**5/105 + k**4/84 + 3*k**2/2 + 11*k. Let m(j) be the first derivative of h(j). Factor m(q).
2*q*(q + 1)**2/7
Let o = 5482/5 + -1096. Factor 0*n**4 - 2/5*n**5 + 0*n**2 - o*n + 4/5*n**3 + 0.
-2*n*(n - 1)**2*(n + 1)**2/5
Let w(h) be the first derivative of -h**6/2 - 5*h**5/4 + 5*h**4/3 + 10*h**3/3 - 24*h - 27. Let i(t) be the first derivative of w(t). Solve i(l) = 0 for l.
-2, -2/3, 0, 1
Suppose 13*f - 80 = 17*f. Let y be 10/21*(-72)/f. What is m in 3/7 + 3/7*m**4 + 18/7*m**2 - 12/7*m**3 - y*m = 0?
1
Find r, given that -4*r**4 + 40*r**2 + 42*r**2 - 47 + 61 + 52 - 38*r**3 + 182*r = 0.
-11, -1, -1/2, 3
