be the first derivative of i**7/735 - i**6/420 - i**5/210 + i**4/84 + i**2/2 - 1. Let a(h) be the second derivative of j(h). Factor a(u).
2*u*(u - 1)**2*(u + 1)/7
Let z(f) be the second derivative of f**7/84 - f**6/15 + f**5/10 + f**4/12 - 5*f**3/12 + f**2/2 + f. Factor z(d).
(d - 2)*(d - 1)**3*(d + 1)/2
Let u = 659/3 + -265. Let l = -45 - u. Determine d, given that 0 - 1/3*d**3 + 1/3*d**4 - l*d**2 + 1/3*d = 0.
-1, 0, 1
Let w = 19/39 + -1/3. Suppose -w*f**2 + 4/13*f - 2/13 = 0. Calculate f.
1
Let h(z) be the second derivative of z**6/45 + z**5/20 - z**4/12 + z**3/6 + z. Let p(m) be the second derivative of h(m). Factor p(d).
2*(d + 1)*(4*d - 1)
Let a(x) be the second derivative of 2*x**6/15 + 2*x**5/5 - 7*x. Find g such that a(g) = 0.
-2, 0
Let s = -26 + 31. Suppose x = s*x - 20. Determine m, given that -2/7*m**3 + 0 + 4/7*m**x - 2/7*m + 6/7*m**2 - 6/7*m**4 = 0.
-1, 0, 1/2, 1
Let k = -132 + 398/3. What is y in 4/3*y - 2/3 - k*y**2 = 0?
1
Let p(f) be the second derivative of -f**6/120 - f**5/20 - f**4/12 + 10*f. Factor p(h).
-h**2*(h + 2)**2/4
Suppose -5*x - 41 + 11 = 0. Let u be x/10 + 95/75. Solve -11/3*d**3 + 5*d**2 - 3*d + u + d**4 = 0.
2/3, 1
Let t(r) be the first derivative of r**6/2 - 3*r**5/5 - 15*r**4/4 - 3*r**3 - 21. Factor t(x).
3*x**2*(x - 3)*(x + 1)**2
Suppose -28 = p + 3*p. Let b = -5 - p. Factor 2*h**2 + 2*h - 3*h**2 + 3*h**b.
2*h*(h + 1)
Let l(x) be the first derivative of x**7/5 - 13*x**6/60 + x**5/15 - 2*x**2 + 5. Let y(w) be the second derivative of l(w). Factor y(h).
2*h**2*(3*h - 1)*(7*h - 2)
Suppose -7*u + 2*u = -z + 2, 4*z = -3*u + 8. Let i(p) be the first derivative of 1/3*p**3 + 0*p + 1/4*p**4 + u*p**2 + 3. Factor i(s).
s**2*(s + 1)
Let n(y) = y**2 + 18*y + 17. Let x be n(-17). Let l(r) be the third derivative of -3*r**2 - 1/60*r**5 - 1/6*r**4 + 0*r + x - 2/3*r**3. Factor l(w).
-(w + 2)**2
Find n such that -2*n + 4 - n**2 + 2*n**4 + 4*n**3 + 6*n**3 - 8*n**3 - 5*n**2 = 0.
-2, -1, 1
Let z(m) be the second derivative of m**7/7 + 2*m**6/15 - m**5/10 - m. Factor z(k).
2*k**3*(k + 1)*(3*k - 1)
Let r(i) be the second derivative of i**5/20 - i**4/6 + i. Factor r(a).
a**2*(a - 2)
Let r = 91/3 + -30. Let p be (-1)/((30/12)/(-5)). Determine m, given that -2/3*m - 1/3 - r*m**p = 0.
-1
Let x(c) = -8*c**4 + 6*c**3 + 3*c**2 - c + 5. Let g(z) = 7*z**4 - 6*z**3 - 3*z**2 + 2*z - 4. Let b(y) = -5*g(y) - 4*x(y). Factor b(d).
-3*d*(d - 2)*(d - 1)*(d + 1)
Let a(x) = 2*x**2 - x - 1. Let k(t) = 1 + 0*t + 0 + 2*t - 3*t**2. Suppose 0*n + 4*m = -3*n + 9, -4*n - 3*m = -12. Let d(u) = n*k(u) + 4*a(u). Factor d(w).
-(w - 1)**2
Let f = -633 - -26587/42. Let n(a) be the second derivative of 0 + 2/21*a**3 + f*a**4 + 0*a**2 - 2*a. Determine y so that n(y) = 0.
-2, 0
Suppose -2*f + 8 - 2 = 0. Suppose 5*s - 24 = -2*i, 2*s = -f*i - 1 + 15. Let -2/7*c**3 + 6/7*c**i - 4/7*c + 0 = 0. What is c?
0, 1, 2
Let c(h) be the first derivative of -2*h**6/45 + 7*h**5/30 - h**4/2 + 7*h**3/3 - 5. Let i(g) be the third derivative of c(g). Solve i(j) = 0 for j.
3/4, 1
Let d(j) = 1. Let t(y) = 3*y**2 + 42*y + 142. Let h(r) = 5*d(r) + t(r). Let h(g) = 0. Calculate g.
-7
Determine h so that 0*h**2 + 4/5*h**5 + 0 + 0*h - 2/5*h**3 - 2/5*h**4 = 0.
-1/2, 0, 1
Let h(u) be the first derivative of -u**4/3 + 8*u**3/9 + 2*u**2/3 - 8*u/3 + 13. Find w such that h(w) = 0.
-1, 1, 2
Let t(c) = -c**2 - 3*c + 5. Let b be t(-4). Suppose -4*r = -3*p + 25, -p + b = r + 2. Factor -1/3*f**p + 1/3*f + 1/3*f**2 - 1/3.
-(f - 1)**2*(f + 1)/3
Suppose 0 = 5*s - 25, 3*s = a - 9 + 20. Let m(x) be the second derivative of 1/36*x**a + 0 - 2*x + 1/18*x**3 + 0*x**2. Find z, given that m(z) = 0.
-1, 0
Let f(l) be the first derivative of 0*l**4 + 0*l**2 - 1 - 1/6*l**6 + 0*l + 1/6*l**3 - 3/10*l**5. Determine m so that f(m) = 0.
-1, 0, 1/2
Solve 4*i**2 - 15 + 2*i**3 + 0*i**3 - 2*i + 11 = 0.
-2, -1, 1
Let h = -108925 - -8169491/75. Let d = 3/25 + h. Factor 0*r + 0 + 2/3*r**2 + r**4 + d*r**3.
r**2*(r + 1)*(3*r + 2)/3
Let n = 922/189 - 70/27. Solve -2/7*t**2 + n*t - 32/7 = 0 for t.
4
Let q(w) be the second derivative of -w**6/40 - 3*w**5/40 + 7*w**4/16 - w**3/2 + 17*w. Find a such that q(a) = 0.
-4, 0, 1
Let y(f) = f**3 + 9*f**2 + 7*f - 5. Let p be y(-8). Let i(k) be the first derivative of k**2 - 1/3*k**p - k + 1. Suppose i(o) = 0. What is o?
1
Let b(o) be the third derivative of o**6/1440 + o**5/240 + o**4/96 - 2*o**3/3 - 3*o**2. Let t(x) be the first derivative of b(x). Determine p so that t(p) = 0.
-1
Let j(k) be the first derivative of 0*k + 1/6*k**6 + 1/5*k**5 + 0*k**2 - 1/2*k**4 - 7 + 0*k**3. Suppose j(y) = 0. Calculate y.
-2, 0, 1
Solve 4/9*l**4 + 0*l**2 + 0 + 0*l - 2/9*l**5 - 2/9*l**3 = 0.
0, 1
Let h be (9/3 + -1)*-1. Let x be (-1 - -2) + h/4. Factor 0*f + 0 - x*f**4 + f**3 - 1/2*f**2.
-f**2*(f - 1)**2/2
Factor 0*c**3 - 1/2*c**5 + 0 + 1/2*c**4 + 0*c + 0*c**2.
-c**4*(c - 1)/2
Let g(p) be the third derivative of p**9/26460 - p**8/5880 + p**7/4410 - p**4/4 + 6*p**2. Let b(n) be the second derivative of g(n). What is i in b(i) = 0?
0, 1
Let z(r) be the third derivative of r**7/1470 + r**6/210 + r**5/70 + r**4/42 + r**3/42 - 3*r**2. Factor z(i).
(i + 1)**4/7
Factor -1/2*x + 0 - 3*x**3 + 2*x**2 - 1/2*x**5 + 2*x**4.
-x*(x - 1)**4/2
Let l(v) be the third derivative of 1/420*v**6 - 1/1176*v**8 + 0*v**3 - v**2 + 1/735*v**7 + 0*v + 0*v**4 - 1/210*v**5 + 0. Factor l(i).
-2*i**2*(i - 1)**2*(i + 1)/7
Factor 10*j + 8 - 2*j**3 + 34*j**2 - 50*j - 6*j**3.
-2*(j - 2)**2*(4*j - 1)
Suppose 12 = 216*p - 212*p. What is x in -16/5 - 54*x**p - 556/5*x**2 + 1944/5*x**4 + 184/5*x + 1458/5*x**5 = 0?
-1, 2/9
Factor 0 - 1/4*u**2 + 1/8*u**3 + 1/8*u.
u*(u - 1)**2/8
Let u(w) = -2*w + 9. Let b(c) = -2*c + 10. Let j(t) = 5*b(t) - 6*u(t). Let l be j(3). Factor 1/5 + 3/5*v**l + 4/5*v.
(v + 1)*(3*v + 1)/5
Let w be (-2)/(-4 - (-1 - -2)). Suppose 3*b = -12*b. Factor b - w*f**3 + 4/5*f**2 - 2/5*f.
-2*f*(f - 1)**2/5
Let i(b) be the second derivative of -b**4/24 + b**3/3 + 2*b. Find g, given that i(g) = 0.
0, 4
Find t such that -36*t**5 - 72*t**5 + t + 0*t**2 - 10*t**2 + 56*t**3 - 5*t + 66*t**4 = 0.
-1/2, -2/9, 0, 1/3, 1
Let u be -15*(-2 - 1 - 0). Suppose 3*g - 7*q = -2*q + 35, -u = -5*g + 5*q. Let 0 - 10/3*b**3 + 0*b + 2/3*b**2 + 14/3*b**4 - 2*b**g = 0. What is b?
0, 1/3, 1
Let p(r) be the first derivative of -3*r**5/5 - 6*r**4 - 24*r**3 - 48*r**2 - 48*r - 19. Factor p(g).
-3*(g + 2)**4
Let x = -28 + 39. Suppose -x = -4*j + 1. Factor -2*m**3 + 9*m**4 + j*m**2 - 7*m**2 - 3*m**4.
2*m**2*(m - 1)*(3*m + 2)
Find i, given that -2/5*i**3 - 4/5*i**4 + 0*i**2 - 2/5*i**5 + 0*i + 0 = 0.
-1, 0
Suppose -8 = f - 2*r, 8*f - 3*f + 16 = 4*r. Find k, given that f*k**4 - 3*k**5 - 4*k**4 + 4*k**4 + 3*k**4 = 0.
0, 1
Let q = -153/5 - -1081/35. Suppose 2/7 + q*v**2 - 4/7*v = 0. What is v?
1
Let y(t) = t**3 + 14*t**2 + 12*t - 17. Let d be y(-13). Let l be 9/36 + 1/d. Factor 0*v + l + 2/3*v**2.
2*v**2/3
Suppose 0 = -2*l + 3*l - 2. Determine z so that -2*z**4 - l*z + 2*z + 3*z**4 - z**5 = 0.
0, 1
Let z(t) = -2*t**2 + t + 3. Let a be z(-3). Let r be (4/7)/(a/(-21)). Solve -8/3 - r*y**2 + 8/3*y = 0.
2
Let k be (3 + (-3)/(-2))*2. Suppose 4*t - k = 3. Determine i, given that -1 - i + 4*i**2 - 3 - i + 2*i**t = 0.
-2, -1, 1
Let m(n) be the first derivative of -2*n**5/35 - 2*n**4/7 - 10*n**3/21 - 2*n**2/7 + 13. What is j in m(j) = 0?
-2, -1, 0
Let h(b) be the second derivative of b**6/240 - b**5/40 + b**4/16 - b**3/12 + b**2/16 + 21*b. Factor h(y).
(y - 1)**4/8
Let k(d) = -25*d**2 - 25*d - 4. Let f(q) = q. Let x(o) = 5*f(o) + k(o). Factor x(b).
-(5*b + 2)**2
Let v(c) be the second derivative of c**5/4 + 5*c**4/3 + 5*c**3/2 + 6*c. Factor v(p).
5*p*(p + 1)*(p + 3)
Let j = -5 - -6. Suppose -2 = -f + j. Factor -7*k**2 + 2*k + 2*k**3 + 4 + 2*k + 0*k**f.
(k - 2)**2*(2*k + 1)
Let w(k) = k**3 + 2*k**2 - 3*k - 3. Let x be w(-2). Let j(u) be the third derivative of 1/30*u**4 + 0 + 4*u**2 + 0*u - 1/60*u**5 + 1/30*u**x. Factor j(f).
-(f - 1)*(5*f + 1)/5
Let p be (-27)/(-12) + (-2)/8. Find g such that 4*g**2 + p*g**2 - g**4 - 3*g**2 - 1 - 4*g**5 - g**2 - 4*g + 8*g**3 = 0.
-1, -1/4, 1
Let h(o) be the third derivative of -o**6/8 - o**5/12 + 5*o**4/12 - 2*o**2. Factor h(d).
-5*d*(d + 1)*(3*d - 2)
Let l be 1/1 - (-50 - -9). Let g be (8/(-7))/((-9)/l). Factor -4*m**2 - g - 8*m - 2/3*m**3.
-2*