 = b - 4*b, -5*b - 4*p = -32. Factor 0*k**2 + 16*k + b*k + 5*k**2.
5*k*(k + 4)
Let i(g) be the third derivative of -g**9/5040 + g**8/1120 + g**7/840 - g**6/120 - 5*g**4/8 + 28*g**2. Let n(p) be the second derivative of i(p). Factor n(v).
-3*v*(v - 2)*(v - 1)*(v + 1)
Let w = -13 + 9. Let y be (-7)/(-28) + (-11)/w. Determine b, given that 0*b**5 + b**4 - b**y - 2*b**5 - 2*b**4 + 3*b**5 + b**2 = 0.
-1, 0, 1
Let u(x) be the first derivative of x**6/24 + 3*x**5/10 - 3*x**4/8 - 7*x**3/3 + 45*x**2/8 - 9*x/2 - 30. Determine j, given that u(j) = 0.
-6, -3, 1
What is y in -132*y + 1125 - 62*y - 106*y + 20*y**2 = 0?
15/2
Let l be ((-134)/26 + 5)/((-12)/13). Find k, given that 0*k**2 - 1/6*k**3 + 0*k + 0 + l*k**4 = 0.
0, 1
Suppose 0 - 2/5*j**2 + 0*j = 0. Calculate j.
0
Suppose 4*v + 3*n = 8, 5*n = -2*v + 7 - 3. Let k(o) be the first derivative of 2*o**3 + v*o - 1/2*o**4 + 1 - 3*o**2. Determine t so that k(t) = 0.
1
Factor -2 + 10*w**3 - 1 - 2*w**4 + 0 + 14*w - 1 - 18*w**2.
-2*(w - 2)*(w - 1)**3
Suppose -2*p = -5 - 1. Factor -26*y**2 + 2*y - 2*y**p + 4*y**3 + 9*y**2 + 13*y**2.
2*y*(y - 1)**2
Let r(i) = -i**3 + 3*i**2 + i + 3. Let p be r(3). Let q be -4 + ((-100)/(-24) - (-3)/p). Factor 0 - 4/3*n - q*n**3 - 2*n**2.
-2*n*(n + 1)*(n + 2)/3
Let q(y) be the third derivative of -y**6/60 + 4*y**5/5 - 55*y**4/4 + 242*y**3/3 + 167*y**2. Factor q(h).
-2*(h - 11)**2*(h - 2)
Let c be (-1)/(-3)*6/4. Suppose 642 - 168 = 158*s. Factor -1/4*n**2 + 1/4*n**4 - 1/2*n + 0 + c*n**s.
n*(n - 1)*(n + 1)*(n + 2)/4
Suppose -a + 4*d + 7 = 0, -2*a = -3*d + d - 8. Let y(s) be the first derivative of 0*s + 2/3*s**a + 2 - s**2. Factor y(v).
2*v*(v - 1)
Let y(h) be the first derivative of -3*h**4/32 + 5*h**3/8 - 9*h**2/8 - 288. Solve y(r) = 0 for r.
0, 2, 3
Let b(r) = -4*r**3 + 9*r**2 - 5*r + 5. Let n(y) be the second derivative of -y**4/12 + y**3/6 - y**2/2 - 10*y. Let l(v) = b(v) + 5*n(v). Factor l(g).
-4*g**2*(g - 1)
Factor 11/4*a**2 - 29/4*a + 1/4*a**3 - 39/4.
(a - 3)*(a + 1)*(a + 13)/4
Let l be (4/3)/(2/9). Let n(x) = x**3 - 4*x**2 - 8*x - 20. Let i be n(l). Determine y, given that 2/7 - 8/7*y**3 - 8/7*y + 12/7*y**2 + 2/7*y**i = 0.
1
Let h = -236 + 241. Suppose -10 = h*k - 20. Factor -5/2*s - 1/2*s**5 - 5*s**3 - 5*s**k - 5/2*s**4 - 1/2.
-(s + 1)**5/2
Factor -23*s + s**2 + 2*s**2 + 119*s - 42*s + 108 - 15*s.
3*(s + 4)*(s + 9)
Let n(f) = -8*f**2 - 16*f. Let p(a) = -a**3 + 15*a**2 + 34*a. Let u(q) = 9*n(q) + 4*p(q). Let u(v) = 0. What is v?
-2, -1, 0
Let z(p) be the first derivative of p**6/360 + p**5/15 + 2*p**4/3 + 8*p**3/3 + 3. Let x(n) be the third derivative of z(n). Factor x(g).
(g + 4)**2
Factor -13/5*n**4 + 1/5*n**2 + 12/5*n**3 + 0 + 0*n.
-n**2*(n - 1)*(13*n + 1)/5
Let k be (-3)/(-30) + (-8 - (-11 + 31/10)). Factor -1/3*o**2 - 1/3*o + k.
-o*(o + 1)/3
Let a(t) = -3*t**4 - 15*t**3 + 27*t**2 - 25*t + 4. Let r(z) = -4*z**4 - 16*z**3 + 27*z**2 - 25*z + 3. Let j(g) = 5*a(g) - 4*r(g). Factor j(k).
(k - 8)*(k - 1)**3
Let f(h) be the second derivative of h**8/4200 + h**7/420 + 2*h**6/225 + h**5/75 - 9*h**3/2 + 9*h. Let d(b) be the second derivative of f(b). Factor d(l).
2*l*(l + 1)*(l + 2)**2/5
Suppose 0 = d - 3, -u + 3*d - 27 = d. Let r(s) = -s**3 - 19*s**2 + 42*s. Let b be r(u). Factor b*i - 8/5 + 2/5*i**2.
2*(i - 2)*(i + 2)/5
Let u(x) be the first derivative of -x**3/9 + 14*x**2/3 + 20*x - 486. What is i in u(i) = 0?
-2, 30
Let m be 3/(-10) + 3/6. Suppose -198*y + 420 = 184 - 556. Factor 1/5*f - 4/5*f**y - 4/5*f**2 + 0 + m*f**5 + 6/5*f**3.
f*(f - 1)**4/5
Factor -175 - 20*c**3 + 25*c**3 + 12*c**2 + 43*c**2 + 115*c.
5*(c - 1)*(c + 5)*(c + 7)
Let o(x) = -3*x**5 - 12*x**4 - 6*x**3 - 24*x**2 - 9*x + 18. Let q(r) = -r**4 - r**3 - r**2 + 1. Let a(f) = o(f) - 18*q(f). Let a(d) = 0. Calculate d.
-1, 0, 1, 3
Let q(m) = 7*m**2 - 2. Let t be q(-1). Suppose -30*c**4 + 40 - 8*c**5 + 60*c - 10*c**2 + 4*c**3 - 59*c**3 + 5*c**5 - 2*c**t = 0. What is c?
-2, -1, 1
Let n(g) = 22*g + 24. Let p be n(-1). Factor -i**p + 5/2 + 1/4*i**3 - 7/4*i.
(i - 5)*(i - 1)*(i + 2)/4
Let p(s) be the second derivative of -s**5/30 + 8*s**4/9 - 28*s**3/9 - 257*s. Determine g, given that p(g) = 0.
0, 2, 14
Let m be (29 + -23 + 305/(-50))/(2/(-8)). Factor -2/5*u + 2/5*u**3 + m*u**2 - 2/5*u**4 + 0.
-2*u*(u - 1)**2*(u + 1)/5
Let s(u) be the first derivative of -18*u**5/35 - 43*u**4/14 - 88*u**3/21 + 12*u**2/7 + 140. Determine o so that s(o) = 0.
-3, -2, 0, 2/9
Factor 30*p**3 + 3/2*p**4 + 81*p**2 + 51/2 + 78*p.
3*(p + 1)**3*(p + 17)/2
Let s(j) be the third derivative of j**6/20 - 26*j**5/15 + 33*j**4/4 + 30*j**3 + 7*j**2 - 14. Factor s(d).
2*(d - 15)*(d - 3)*(3*d + 2)
Let j(r) = r**3 - r + 1. Let f(u) = 4*u**3 + 71 + 8*u**4 + 4*u**2 - 9*u - 59 - 4*u**4 - 3*u. Let x(z) = f(z) - 12*j(z). Factor x(v).
4*v**2*(v - 1)**2
Let d be (-12)/21 + (-28)/(-49). Let h = -60 - -60. Suppose 0 + 0*b + 3/5*b**5 + h*b**3 + d*b**2 + 6/5*b**4 = 0. What is b?
-2, 0
Let b = -41 + 46. Factor -10*o**5 + 0*o**5 + o**b + 6*o**4 + 18*o**2 - 36*o**3 - 3*o + 24*o**4.
-3*o*(o - 1)**3*(3*o - 1)
Let f(u) be the second derivative of 1/135*u**6 - 1/18*u**4 + 11/27*u**3 + 0 - 2/3*u**2 - 1/30*u**5 + 6*u. Suppose f(s) = 0. What is s?
-2, 1, 3
Let g = 1/69 + 89/207. Factor g*i**2 - 2/9*i**3 + 0*i + 0.
-2*i**2*(i - 2)/9
Let d be 20/(-35) + (-60)/(-7). Let g(n) be the third derivative of -1/3*n**4 + 1/60*n**5 + 0 - d*n**2 + 8/3*n**3 + 0*n. Find v such that g(v) = 0.
4
Suppose -26*k = -29*k - 258. Let g = k + 89. Let 3*r + 0 + 3/4*r**3 + g*r**2 = 0. Calculate r.
-2, 0
Suppose -10*b = 2*t - 8*b - 10, -2*b = -2*t - 10. Suppose -6/11 + t*z**3 + 12/11*z**2 + 0*z - 6/11*z**4 = 0. What is z?
-1, 1
Factor 4*v**2 - 8*v**2 - 1707*v + 1659*v.
-4*v*(v + 12)
Let u be ((36/2)/6)/(9/2). Let y(h) be the first derivative of 10 + u*h**3 + 0*h + 1/2*h**2 + 1/4*h**4. Factor y(g).
g*(g + 1)**2
Suppose -4*m - 4*c + 28 = 0, -4*m - 59*c = -57*c - 18. Let q(z) be the third derivative of 0 + 1/240*z**5 + 0*z - 1/16*z**4 + 3/8*z**3 - 8*z**m. Factor q(l).
(l - 3)**2/4
Let q = 7 - 9. Let d be (q/((-5)/(-2) + -3))/2. Find m such that 0*m - 1/3*m**d + 1/3 = 0.
-1, 1
Suppose 24 = -4*j + 8, -4*j - 4 = 4*a. What is r in 1/5 + 1/5*r**4 - 2/5*r**2 - 2/5*r - 2/5*r**5 + 4/5*r**a = 0?
-1, 1/2, 1
Let g(h) = 12*h**2 + h + 14. Let c be g(3). What is a in c*a**3 + 16 - 111*a**3 - 46*a + 60*a**2 - 10*a**4 - 10*a - 24*a**2 = 0?
-2, 2/5, 1, 2
Let w(o) be the third derivative of -1/60*o**5 + 1/120*o**6 - 14*o**2 + 0*o**3 + 0 - 1/12*o**4 + 0*o. Factor w(x).
x*(x - 2)*(x + 1)
Let q = 2129 + -2129. Let p(t) be the second derivative of -1/9*t**3 + 11*t - 1/10*t**5 + 0*t**2 + 1/45*t**6 + 1/6*t**4 + q. Determine i so that p(i) = 0.
0, 1
Let i = -5 + 17. Factor 143 - 21*n - 149 - 3*n**2 - i*n**2.
-3*(n + 1)*(5*n + 2)
Suppose -a + 13 = a + 3*b, -3*a + 4*b + 11 = 0. Suppose -a*z = -10*z. Factor 0 + z*d + 1/2*d**4 + 0*d**2 + 1/2*d**5 + 0*d**3.
d**4*(d + 1)/2
Let g(i) be the second derivative of 1/3*i**3 + 0*i**2 - 25*i + 1/4*i**4 + 0 + 1/20*i**5. Solve g(u) = 0 for u.
-2, -1, 0
Let h(v) be the first derivative of -v**4/3 + 16*v**3/9 - 2*v**2/3 - 8*v - 156. Factor h(z).
-4*(z - 3)*(z - 2)*(z + 1)/3
Let a(n) = 24*n**2 - 9*n - 49. Let l(k) = -5*k**2 - k. Let z(w) = 3*a(w) + 15*l(w). Let z(h) = 0. Calculate h.
-7
Let g(k) be the first derivative of -k**6/135 + 2*k**5/45 - 2*k**4/27 - 43*k + 44. Let p(y) be the first derivative of g(y). Let p(a) = 0. What is a?
0, 2
Let i = 173/8 + -841/40. Let -12/5*b + 12/5 + i*b**2 = 0. Calculate b.
2
Find a, given that -85*a**2 - 20 - 27*a - 55 - 5*a**3 - 128*a = 0.
-15, -1
Let f(p) be the first derivative of -54*p**5/5 - 18*p**4 + 56*p**3 - 32*p**2 - 633. Factor f(k).
-2*k*(3*k - 2)**2*(3*k + 8)
Suppose 0 = r, 26*m + r = 22*m + 8. Factor 2/7*j - 1/7*j**m - 3/7*j**3 + 1/7*j**4 + 0 + 1/7*j**5.
j*(j - 1)**2*(j + 1)*(j + 2)/7
Let z(k) be the second derivative of k**5/60 - 5*k**4/18 + k**3/2 - 3*k + 14. Factor z(o).
o*(o - 9)*(o - 1)/3
Let f(u) = -4*u - 24. Let b be f(-7). Factor -34*c**2 - c + 27*c + 14*c + b*c**2 + 5*c**4 - 15.
5*(c - 1)**3*(c + 3)
Let v(u) = u**2 - u + 1. Let j(q) = -27*q**2 - 75*q. Let t(b) = j(b) - 6*v(b). Factor t(r).
-3*(r + 2)*(11*r + 1)
Let k(n) be the first derivative of -n**5/25 - 3*n**4/5 - 43*n**3/15 - 6*n**2 - 28*n/5 + 333. Solve k(d) = 0 for d.
-7, -2, -1
Fact