) be the second derivative of k(a). Factor s(c).
c**2*(c - 1)*(5*c - 2)/2
Let p(t) be the second derivative of -t**7/5040 - t**6/1440 + t**4/4 + 5*t. Let c(s) be the third derivative of p(s). Factor c(l).
-l*(l + 1)/2
Let c(v) be the third derivative of -1/66*v**4 - 1/132*v**6 - 2*v**2 + 0*v - 7/330*v**5 + 0 + 0*v**3. Factor c(n).
-2*n*(n + 1)*(5*n + 2)/11
Suppose s + 3*y + 13 = 0, 0 = -2*s + 6*y - 7*y - 1. Let f = 5 - s. Factor 2/3*r**5 + 0*r**2 + 0*r + 8/3*r**f + 8/3*r**4 + 0.
2*r**3*(r + 2)**2/3
Let q(h) = h + 9. Let c be q(-6). Solve 2/7 + 6/7*z + 6/7*z**2 + 2/7*z**c = 0 for z.
-1
Factor -5*p**4 + 0*p**5 + p**5 - 2*p**2 + 6*p**3 + p**5 - p**4.
2*p**2*(p - 1)**3
Factor -c**4 + 9*c**3 - 8*c**3 + 0*c**4 + 5*c**2 - 5*c**3.
-c**2*(c - 1)*(c + 5)
Let c be (4 + -1)*2/3. Let z(b) be the first derivative of 3/25*b**5 + 1 + 0*b**c + 3/20*b**4 + 1/15*b**3 + 1/30*b**6 + 0*b. Factor z(r).
r**2*(r + 1)**3/5
Let d(w) = w + 2. Let v be d(0). Suppose v*p - j + 2 - 6 = 0, 2*j - 7 = -p. Find g, given that 2*g + g**5 + 3*g**p - 5*g**3 - g = 0.
-1, 0, 1
Find g such that -140*g - 3*g**2 + 134*g + 0*g**2 - 3 = 0.
-1
Let d(c) be the first derivative of 11*c**3 - 15/2*c**2 + 5 - 6*c - 3*c**4. Factor d(h).
-3*(h - 2)*(h - 1)*(4*h + 1)
Let c be ((-11)/55)/((-4)/10). Determine t so that c*t**2 + 1/4 - 3/4*t = 0.
1/2, 1
Factor -1/2 - 1/2*z**2 + z.
-(z - 1)**2/2
Factor -j**4 - 86*j**3 - 2*j**4 + 66*j**3 - 20*j**2 - 2*j**4.
-5*j**2*(j + 2)**2
Let d(s) = 109*s**2 + 1 + s**3 + s + 0*s**3 + s**4 - 108*s**2. Let c(w) = -5*w**4 + 7*w**3 - 5*w**2 - 11*w + 4. Let t(f) = c(f) + 2*d(f). Factor t(u).
-3*(u - 2)*(u - 1)**2*(u + 1)
Factor -2*h**2 + 2*h**4 + 2*h - 2*h**3 + 2*h**2 - 2*h**2.
2*h*(h - 1)**2*(h + 1)
Let l(k) = 3*k - k - 3*k + 2*k + 4. Let u be l(-2). Let -2/5*p**3 + 4/5*p**u - 2/5*p + 0 = 0. Calculate p.
0, 1
Let b = -5 + 0. Let r(j) = -6*j**5 - 3*j**4 + 5*j**3 - 2*j**2 + 6*j. Let d(q) = q**5 + q**4 - q**3 - q. Let n(h) = b*d(h) - r(h). Solve n(o) = 0.
-1, 0, 1
Let a(c) = 21*c**2 - 285*c + 66. Let z(r) = 4*r**2 - 57*r + 13. Let x(b) = -5*a(b) + 24*z(b). Factor x(i).
-3*(i - 6)*(3*i - 1)
Let g(p) be the second derivative of p**7/42 - p**6/15 + 3*p - 6. Let g(x) = 0. What is x?
0, 2
Let a(w) = -w**3 + 3*w**2 + 6*w - 1. Let v be a(4). Let l = 65 - 62. Determine j, given that -2*j + j - 3 - l*j**2 + v*j = 0.
1
Factor -2/9 - 4/9*d**3 + 4/9*d**2 - 2/9*d**4 + 2/9*d**5 + 2/9*d.
2*(d - 1)**3*(d + 1)**2/9
Let x = -9 - -12. Suppose 6*y**2 + 12*y - y**2 - 4*y**2 - 18 - x*y**2 = 0. Calculate y.
3
Let u be 0*((-1)/(-2) - 1). Factor 22*k + u*k + 14*k**3 + 3 + 1 + 32*k**2.
2*(k + 1)**2*(7*k + 2)
Find v, given that 144*v**3 - 1596*v**4 + 247*v**5 - v + 240*v**2 - 47*v + 488*v**5 = 0.
-2/5, 0, 2/7, 2
Let h(i) be the second derivative of -i**6/135 + i**5/90 + i**4/54 - i**3/27 - 8*i. Factor h(w).
-2*w*(w - 1)**2*(w + 1)/9
Let n(g) be the third derivative of g**5/30 - 2*g**4/3 + 4*g**3 - 48*g**2. Let n(m) = 0. What is m?
2, 6
Suppose -3*v + 0*v - 21 + v**2 + 23 = 0. Calculate v.
1, 2
Let n(q) be the second derivative of 5*q**4/48 - 5*q**3/4 - 9*q. Factor n(d).
5*d*(d - 6)/4
Let y(u) be the third derivative of u**8/3360 + u**7/630 + u**6/360 + u**4/24 + u**2. Let l(z) be the second derivative of y(z). Factor l(r).
2*r*(r + 1)**2
Let d be 0 + -1 + 2 - 21/28. Solve -1/2*g**4 + 0 + d*g**3 + 1/4*g**2 + 0*g = 0 for g.
-1/2, 0, 1
Factor 4 + 5*b**2 + 7*b**2 + 7*b**2 + 4*b - 18*b**2.
(b + 2)**2
Let k(u) be the second derivative of 1/9*u**2 + 7/45*u**5 - 1/27*u**6 + 0 - 2/9*u**4 + 4*u + 2/27*u**3. Factor k(y).
-2*(y - 1)**3*(5*y + 1)/9
Factor 2/3*g + 0 + 1/3*g**2.
g*(g + 2)/3
Let o(q) = q**5 + q**2 - q - 1. Let w(b) = 6*b**5 + 8*b**4 + 12*b**3 + 12*b**2 - 2*b - 4. Let v(z) = 4*o(z) - w(z). Factor v(a).
-2*a*(a + 1)**4
Let c be ((-6)/(-16))/(-3 - (-105)/20). Let z(u) be the first derivative of 2 + 0*u**2 - c*u**4 + 2/9*u**3 + 0*u. Suppose z(i) = 0. Calculate i.
0, 1
Solve -1/3*n**3 + 0*n**2 + 2/3 + n = 0 for n.
-1, 2
Let h(m) = m**3 - m - 9. Let d(w) = -w**3 + 8. Let f(x) = -6*d(x) - 5*h(x). Let g(q) = -q**2 - q + 1. Let v(o) = -f(o) - 3*g(o). Find a, given that v(a) = 0.
0, 1, 2
Let c be 4/(2 + -1 + 1). Suppose c = -b + 2*b. Factor -5*s**3 + 4*s**2 + 4*s**3 - b*s**2.
-s**2*(s - 2)
Let u = -9 - -12. Determine q so that q**2 - u*q - q + 4*q = 0.
0
Let g(q) = q**4 + q**3 - q**2 - q. Let f(j) = -j**3 - j**2 + j + 1. Let s(u) = 2*f(u) + 2*g(u). Suppose s(x) = 0. Calculate x.
-1, 1
Let k(l) be the third derivative of -l**5/60 - l**4/24 + 4*l**2. Factor k(r).
-r*(r + 1)
Let d = -23 - -33. Let l be (-3)/d*(-30)/36. What is a in 0*a + 0*a**2 + 0*a**3 + 0 + l*a**5 + 0*a**4 = 0?
0
Let d = 2 + -5. Let a = -1 - d. Factor -2*b**2 - 2*b - 4*b**2 + a*b**2 - 2*b**3.
-2*b*(b + 1)**2
Let o(c) be the third derivative of 0*c**3 + 0*c + 0 - 5*c**2 + 1/16*c**4 - 1/40*c**5. Factor o(u).
-3*u*(u - 1)/2
Let a be 7/(-2) - 7/14. Let c(p) = 3*p**2 - 2*p. Let z(n) = n**2. Let b(d) = c(d) - 2*z(d). Let x(l) = 3*l**2 - 5*l. Let i(g) = a*x(g) + 11*b(g). Factor i(y).
-y*(y + 2)
Let r(f) = 14*f**2 - 4*f + 2. Let q(u) = 29*u**2 - 7*u + 4. Let p(k) = -6*q(k) + 13*r(k). Factor p(l).
2*(l - 1)*(4*l - 1)
Let m = -18 + 20. Suppose 0 + 2/9*w + 2/9*w**3 - 4/9*w**m = 0. What is w?
0, 1
Let p(a) = -a**3 - a**2 + 1. Let l(t) = 5*t**3 + 5*t**2 - 6. Suppose 3*g = 3*x - 33, 5*x - 3*g - 50 = g. Let d(c) = x*p(c) + l(c). Let d(n) = 0. What is n?
-1, 0
Let m(q) = -4*q + 1. Let j be m(-1). Let l(o) be the third derivative of -2*o**2 + 0*o + 0*o**3 + 1/90*o**j + 0 - 1/36*o**4. Factor l(g).
2*g*(g - 1)/3
Let o(j) = -j**5 - j**4 + j**3 - 2*j**2 - 1. Let n(k) = -15*k**5 + 27*k**4 - 39*k**3 + 15*k**2 - 6*k - 6. Let i(u) = -n(u) + 6*o(u). Factor i(v).
3*v*(v - 1)**3*(3*v - 2)
Let f(j) be the first derivative of -j**6/12 + j**5/10 + 5*j**4/8 + j**3/2 + 7. Let f(w) = 0. What is w?
-1, 0, 3
Let j(l) = -l**2 - 4*l + 5. Let b be j(-5). Let d(y) be the first derivative of 2*y**3 + 2/5*y**5 + b*y - 2 + y**2 + 3/2*y**4. Factor d(x).
2*x*(x + 1)**3
Let y(h) be the second derivative of 0 + 3*h**2 - h + 1/4*h**4 - 3/2*h**3. Factor y(l).
3*(l - 2)*(l - 1)
Let t(o) be the third derivative of -o**8/84 + 4*o**7/21 - 5*o**6/6 - 14*o**2. Factor t(m).
-4*m**3*(m - 5)**2
Let y(q) be the second derivative of 5*q + 1/4*q**4 + 0 - 2*q**2 + 0*q**3 - 1/20*q**5. Factor y(g).
-(g - 2)**2*(g + 1)
Factor -h**2 - 4*h + 2*h**3 - 4*h**3 + 4 + 3*h**3.
(h - 2)*(h - 1)*(h + 2)
Let o(q) be the first derivative of -q**6/39 - 2*q**5/65 + 3*q**4/13 + 8*q**3/39 - 8*q**2/13 - 13. Find x, given that o(x) = 0.
-2, 0, 1, 2
Let o(n) be the second derivative of n**5/100 - 2*n**4/15 - 24*n. Suppose o(j) = 0. What is j?
0, 8
Let i = -7 + 1. Let x(q) = 6*q**4 + 2*q**3. Let r(g) = -g**3. Let w(d) = i*r(d) - x(d). Let w(y) = 0. Calculate y.
0, 2/3
Let l(r) be the second derivative of 0 + 0*r**2 - 1/18*r**4 + 1/45*r**6 + 2*r + 0*r**3 + 0*r**5. Find c such that l(c) = 0.
-1, 0, 1
Let d(t) = -6*t**2 + 45*t + 54. Let b(y) = -7*y**2 + 44*y + 55. Let m(a) = -3*b(a) + 4*d(a). Suppose m(u) = 0. What is u?
-1, 17
Let a(x) be the first derivative of -3*x**4/16 - 25*x**3/4 - 429*x**2/8 + 507*x/4 - 13. Factor a(y).
-3*(y - 1)*(y + 13)**2/4
Let i(m) = m - 6. Let b be i(12). Let l(r) be the second derivative of 0*r**2 - r + 1/210*r**7 + 0*r**5 - 1/30*r**3 + 0 + 1/75*r**b - 1/30*r**4. Factor l(v).
v*(v - 1)*(v + 1)**3/5
Let b(r) be the third derivative of -8*r**2 + 0*r - 1/30*r**5 + 0 + 0*r**3 - 1/12*r**4. Factor b(o).
-2*o*(o + 1)
Factor -3/5*a**3 + 0 + 3/5*a + 3/5*a**2 - 3/5*a**4.
-3*a*(a - 1)*(a + 1)**2/5
Let d(x) = -x - 1. Suppose 2*n - 3*w = 2*w + 4, 2*n = -5*w - 16. Let u be d(n). Factor 7/3*g - 2/3 - 5/3*g**u.
-(g - 1)*(5*g - 2)/3
Let 8*d - 15 + 3 - 381*d**2 + 385*d**2 = 0. Calculate d.
-3, 1
Suppose p - 4 = -p. Let 5*h**4 - 2*h - 1 + 5*h - h**5 - 2*h**3 - 2*h**2 - p*h**4 = 0. What is h?
-1, 1
Suppose 3*k = k - 36. Let p = 20 + k. Factor -2/5*s + 0 - 1/5*s**p.
-s*(s + 2)/5
Let o(f) be the second derivative of f**6/480 + f**5/240 - f**4/96 - f**3/24 + 2*f**2 + 5*f. Let n(l) be the first derivative of o(l). Factor n(y).
(y - 1)*(y + 1)**2/4
Let k be 1 - 0/(-5) - 2/(-6). Let m(c) be the first derivative of -24/5*c**5 + 0*c + 3/2*c**4 + 7/3*c**6 + 2 + k*c**3 + 0*c**2. Factor m(n).
2*n**2*(n - 1)**2*(7*n + 2)
Let 