 a(b) be the second derivative of 1/30*b**6 + 1/20*b**5 + 0*b**2 + 0 - 1/12*b**4 - t*b**3 + 2*b. Factor a(w).
w*(w - 1)*(w + 1)**2
Let g = 43 - 38. Let k(o) be the second derivative of 0 + 11/40*o**g + 3/4*o**3 - 1/20*o**6 - 1/2*o**2 + 2*o - 5/8*o**4. Suppose k(m) = 0. What is m?
2/3, 1
Let o(f) be the second derivative of -16*f**6/45 + 28*f**5/15 - 25*f**4/18 + f**3/3 + 41*f. Determine r, given that o(r) = 0.
0, 1/4, 3
Suppose 30 = h + 14*h. Let 1/3*b + 2/3 + 1/3*b**4 - b**h - 1/3*b**3 = 0. Calculate b.
-1, 1, 2
Let h**5 - 5/3*h**4 - 1/3*h**3 + 0 - 2/3*h + 5/3*h**2 = 0. What is h?
-1, 0, 2/3, 1
Determine c so that -1/7*c - 1/7*c**2 + 0 = 0.
-1, 0
Let s(o) = o - 5. Let m be s(0). Let b = 10 + m. Factor 2*p**4 + 14*p**5 + 3*p**3 - 5*p**4 - 11*p**b - 3*p**4.
3*p**3*(p - 1)**2
Let p(t) = 9*t**3 - 41*t**2 + 377*t - 1017. Let o(n) = -4*n**3 + 21*n**2 - 189*n + 509. Let v(w) = 7*o(w) + 3*p(w). What is j in v(j) = 0?
8
Let d be (-6)/(-4)*(-6)/9. Let b = 6 + d. Find h such that h**3 - h**b - 2*h**4 - 2*h**3 + 0*h**3 = 0.
-1, 0
Let k(l) = 3*l**4 - 5*l**3 - 5*l**2 + 7*l. Let x(o) = 80*o**4 - 135*o**3 - 135*o**2 + 190*o. Let i(f) = -55*k(f) + 2*x(f). Let i(v) = 0. What is v?
-1, 0, 1
Suppose -16 - 4 = -4*q. Suppose -5*x = q*t - 40, 6*x - x - 34 = -3*t. Factor t*b - b - b + b**2.
b*(b + 1)
Determine w so that -2*w**3 - 21*w + 54*w - 19*w - 12*w = 0.
-1, 0, 1
Let j(b) = b**2 + 13*b + 45. Let v be j(-8). Solve 0 + 6/7*z**4 + 6/7*z**3 + 2/7*z**v + 0*z + 2/7*z**2 = 0 for z.
-1, 0
Let j(o) = -13*o**4 + 5*o**3 + 15*o**2 + o - 8. Let l(b) = b**4 - b**2 - b + 1. Let a(r) = j(r) + 6*l(r). Factor a(h).
-(h - 1)**2*(h + 1)*(7*h + 2)
Let w be 5 - ((-32 - -28) + 3*2). Factor -2/3*i**w + 1/2*i + 1/6 + 0*i**2.
-(i - 1)*(2*i + 1)**2/6
Suppose -3*b = -4*h + 2*b + 21, 3*h - 4*b = 16. Suppose h*k + 7 - 19 = 0. Factor 0 + 0*s + 4/5*s**k - 2/5*s**2.
2*s**2*(2*s - 1)/5
Let m(l) = -27*l**3 - 5*l**2 + 18*l - 1. Let j(t) = 3 + 33*t**3 + 20*t**3 - 16*t**2 + 25*t**2 - 36*t. Let n(u) = 6*j(u) + 10*m(u). Determine k so that n(k) = 0.
-1, 1/4, 2/3
Determine c so that 14*c + 3*c**2 + 2*c**2 + 5*c**3 - 24*c = 0.
-2, 0, 1
Let d(h) be the third derivative of h**7/70 - h**5/5 + 13*h**2. Solve d(p) = 0 for p.
-2, 0, 2
Let q(w) be the first derivative of 5*w**6/3 + 16*w**5/5 + w**4/2 - 4*w**3/3 - 36. Factor q(b).
2*b**2*(b + 1)**2*(5*b - 2)
Let l be (-6)/(-9) + 66/9. Factor -4*c + c**3 - 3*c + l*c + 0*c + 2*c**2.
c*(c + 1)**2
Solve 6/5*j**5 + 4/5*j**4 + 0*j - 16/5*j**2 - 24/5*j**3 + 0 = 0.
-2, -2/3, 0, 2
Let -1/3*u**2 - 1/3*u + 0 = 0. What is u?
-1, 0
Let p(z) be the first derivative of -4/15*z**3 + 6/25*z**5 - 2/5*z - 4 + 3/5*z**2 - 1/5*z**4 - 1/15*z**6. Factor p(f).
-2*(f - 1)**4*(f + 1)/5
Let u(x) be the first derivative of x**5/10 - x**3/3 + 5*x - 7. Let d(h) be the first derivative of u(h). Factor d(k).
2*k*(k - 1)*(k + 1)
Let n(g) be the first derivative of 3 + 2/5*g + 2/25*g**5 - 4/15*g**3 + 1/15*g**6 - 1/5*g**4 + 1/5*g**2. Find b, given that n(b) = 0.
-1, 1
Suppose -5*n + 2*n + x = -6, 5*n - 24 = -3*x. Find p, given that -1/4*p + 1/4*p**n - 1/4*p**2 + 1/4 = 0.
-1, 1
Factor 25/7*j + 0 + 1/7*j**3 - 10/7*j**2.
j*(j - 5)**2/7
Factor 5 + 10*w + 15*w**2 - 8 + 2*w.
3*(w + 1)*(5*w - 1)
Let v(w) be the third derivative of 2*w**7/735 + w**6/70 - 2*w**4/21 + 11*w**2. Solve v(a) = 0.
-2, 0, 1
Solve 8/13*s + 4/13*s**3 - 10/13*s**2 - 2/13 = 0 for s.
1/2, 1
Let l(n) = 8*n - 13. Let i(s) = 7*s - 12. Let d(t) = 6*i(t) - 5*l(t). Let h be d(5). Determine k, given that -k**h - k**3 + 3*k**3 + k**2 = 0.
-1, 0
Let d(q) be the second derivative of q**5/100 - q**3/10 + q**2/2 - 8*q. Let v(k) be the first derivative of d(k). Factor v(a).
3*(a - 1)*(a + 1)/5
Let y(k) be the third derivative of -k**7/280 + k**5/40 + k**3/3 - 8*k**2. Let c(g) be the first derivative of y(g). Find x such that c(x) = 0.
-1, 0, 1
Let v(z) = 9*z**5 + 10*z**4 - 16*z**3 - 44*z**2 - 4. Let x(h) = 8*h**5 + 10*h**4 - 17*h**3 - 43*h**2 - 3. Let g(w) = -3*v(w) + 4*x(w). Factor g(y).
5*y**2*(y - 2)*(y + 2)**2
Suppose 119*u = 117*u. Factor -1/2*r + 0 + r**3 - 1/2*r**5 + 0*r**2 + u*r**4.
-r*(r - 1)**2*(r + 1)**2/2
Let f = -4/629 + 5092/9435. Factor -2/15*o**3 + f*o**2 + 4/15 - 2/3*o.
-2*(o - 2)*(o - 1)**2/15
Suppose -2*u + 0 = -6. Let x be -1 + u/(-9) - -2. Determine h so that 0*h + 4/3*h**3 - x*h**4 + 0 - 2/3*h**2 = 0.
0, 1
Let b(f) = 6*f**2 - f + 3. Let d be b(-3). Let p be 8/d*(-30)/(-12). Determine m so that -p + 1/2*m + 1/2*m**2 - 1/3*m**3 = 0.
-1, 1/2, 2
Let a(t) be the second derivative of t**6/30 - t**5/10 - t**4/4 + 2*t**3/3 + 2*t**2 - 24*t. Factor a(s).
(s - 2)**2*(s + 1)**2
Let z(b) = 2*b - 3. Let p be z(3). Factor 2*r**4 + 2*r**4 - 5*r**4 - 2*r**3 + 4*r**p.
-r**3*(r - 2)
Let s(n) be the third derivative of -n**7/945 - n**6/135 - 2*n**5/135 + 24*n**2. Factor s(c).
-2*c**2*(c + 2)**2/9
Suppose 4*u = 4*f - 56, 2*f + u = -2*u + 23. Let -3*j**5 - f - 6*j**2 + 9*j**3 + 13 = 0. Calculate j.
-2, 0, 1
Let v be -2 - 13*1/(-2). Suppose -1/2*j**5 - v*j**3 - 5/2*j**4 + 0 - j - 7/2*j**2 = 0. Calculate j.
-2, -1, 0
Let y = 44603/22 - 2027. Let d = 125/198 - y. Let d*c**2 + 0 - 2/9*c = 0. Calculate c.
0, 1
Let y(x) be the third derivative of 0*x**5 + 0*x**4 - 1/60*x**6 + 0*x**3 + 0 + 0*x**7 + 3*x**2 + 1/168*x**8 + 0*x. Suppose y(n) = 0. Calculate n.
-1, 0, 1
Factor 3/4*l**3 + 3/4*l**2 - 3/2*l + 0.
3*l*(l - 1)*(l + 2)/4
Let u = -31 + 31. Let v(f) be the first derivative of 0*f - 4/3*f**3 + u*f**2 - 1 - 3*f**4 + 7/5*f**5. Factor v(i).
i**2*(i - 2)*(7*i + 2)
Let q = 86/17 - -13/68. Factor -6*n**2 + 0 + q*n**3 + n + 49/4*n**4.
n*(n + 1)*(7*n - 2)**2/4
Suppose 7*g = 5*g + 4. Suppose 0 = g*f - 4*f. Factor f*a - 2/7*a**4 + 4/7*a**2 + 0*a**3 - 2/7.
-2*(a - 1)**2*(a + 1)**2/7
Let v be (13/(-12))/(-13)*9. Factor -3/4*g - 1/2*g**2 + 1/2 + v*g**3.
(g - 1)*(g + 1)*(3*g - 2)/4
Let t(j) be the second derivative of 1/16*j**4 - 3/40*j**5 + 2*j + 0*j**2 + 1/40*j**6 + 0*j**3 + 0. Factor t(p).
3*p**2*(p - 1)**2/4
Suppose 9 = 2*f + 1. Let v(h) be the first derivative of -2/5*h**5 + 0*h + 2/3*h**3 + 0*h**2 + 2 - 1/2*h**f + 1/3*h**6. Factor v(u).
2*u**2*(u - 1)**2*(u + 1)
Let a(k) = -k**2 - 3*k + 3. Let g be a(-3). Suppose 3*r**3 - 6*r**g + r + r**2 - 1 + 2*r = 0. What is r?
-1, 1/3, 1
Let b(z) = z**2 - 12*z - 13. Let y be b(13). Let m(x) be the third derivative of y + 0*x + 1/54*x**4 - x**2 - 1/27*x**3 - 1/270*x**5. Factor m(c).
-2*(c - 1)**2/9
Suppose 5*l = -5, 2*p = 3*l + 31 + 8. Solve -4*b**4 + 10*b**5 - 2*b**2 - 4*b + p*b**3 + 19*b**4 + 11*b**4 = 0 for b.
-1, 0, 2/5
Let i = 0 + 3. Let x(f) be the first derivative of -1/2*f - 1 + 0*f**2 + 1/6*f**i. Factor x(t).
(t - 1)*(t + 1)/2
Let l = -27 - -73. Let m = l - 136/3. Factor -m*o**2 + 4/3 - 2/3*o.
-2*(o - 1)*(o + 2)/3
Let m = -25 - -15. Let x = m - -10. Factor 2/11*b**3 + 0*b + x + 0*b**2.
2*b**3/11
Let c(m) be the third derivative of m**7/42 + m**6/3 + 11*m**5/6 + 5*m**4 + 15*m**3/2 + 3*m**2 - 3*m. Factor c(s).
5*(s + 1)**2*(s + 3)**2
Let b(c) be the first derivative of c**6/2520 + c**5/420 + c**4/168 - 4*c**3/3 - 2. Let s(i) be the third derivative of b(i). Factor s(m).
(m + 1)**2/7
Factor -16*z**2 + 5*z**5 + 12*z**3 - 16*z - z**5 + 64*z**4 - 48*z**4.
4*z*(z - 1)*(z + 1)*(z + 2)**2
Let q(a) = -a**3 + 6*a**2 - 5*a + 4. Let c be q(5). Suppose c*f = -f + 15. Factor -z**2 - 1/3*z**f - 1/3 - z.
-(z + 1)**3/3
Let c(u) be the third derivative of 0 - 1/210*u**5 + 0*u + 1/7*u**3 + 2*u**2 - 1/42*u**4. Suppose c(h) = 0. What is h?
-3, 1
Let t(y) be the second derivative of -1/48*y**4 - 1/12*y**3 - 4*y + 0 - 1/8*y**2. Find b such that t(b) = 0.
-1
Let q be (7/(-3))/7*0. Let c(d) be the third derivative of 1/72*d**4 + q*d**3 + 0*d - 2*d**2 + 0 + 1/180*d**5. What is n in c(n) = 0?
-1, 0
Let k(h) be the third derivative of 0*h**3 + 1/10*h**5 + 1/30*h**6 + 1/12*h**4 + 0 + 0*h + h**2. Factor k(p).
2*p*(p + 1)*(2*p + 1)
Let r(f) = f**2 - 9*f + 9. Let i be r(8). Let y(w) be the first derivative of w**2 + 0*w**3 - 1/2*w**4 + 0*w + i. Factor y(d).
-2*d*(d - 1)*(d + 1)
Let y(i) be the third derivative of -i**6/660 - i**5/330 + i**4/132 + i**3/33 + 4*i**2. Factor y(b).
-2*(b - 1)*(b + 1)**2/11
Let c(d) be the first derivative of 1/4*d**4 + 0*d + 1/3*d**3 - 7 - 1/5*d**5 - 1/2*d**2. Factor c(x).
-x*(x - 1)**2*(x + 1)
Let q(t) be the 