 d(i) be the third derivative of -i**5/60 + i**3/6 + i**2. Let f be 3*1*(-3)/(-9)*1. Let z(c) = 3*c**2 - 3. Let r(j) = f*z(j) + 6*d(j). Factor r(s).
-3*(s - 1)*(s + 1)
Let i(a) be the third derivative of -a**6/20 - a**5/60 + a**4/24 + a**3/6 - a**2. Let g be i(-1). Factor 0*f - 17*f**2 + g*f**2 + 3*f**3 + 14*f - 2*f.
3*f*(f - 2)**2
Let g be (-3)/(-6) - 9/(-2). Suppose -b = 2 - g. Factor -o**3 + b*o**4 + 8*o**3 - 3 - 6*o - o**3.
3*(o - 1)*(o + 1)**3
Let x(o) = o**3 + o**2 - 22*o - 6. Let u be x(-5). Factor 3*b**4 + 6*b**3 + b**2 - 7*b**3 + b**5 + u*b**3.
b**2*(b + 1)**3
Let u(b) = 3*b**4 + 30*b**3 - 7*b**2 + 13. Let v(n) = -n**4 - 15*n**3 + 4*n**2 - 6. Let g = 71 - 65. Let o(s) = g*u(s) + 13*v(s). Factor o(i).
5*i**2*(i - 2)*(i - 1)
Let l be 1*(6 + 2) + 12 + -16. What is w in 4/3 + 7/3*w - 2/3*w**l - 8/3*w**3 - 2/3*w**2 + 1/3*w**5 = 0?
-1, 1, 4
Let t = -1725 + 1725. Suppose 0 + t*m - 2/5*m**3 + 2/5*m**2 = 0. What is m?
0, 1
Let v(d) be the third derivative of -d**5/150 + 17*d**4/20 - 98*d**3/15 + 9*d**2 - 11. Factor v(a).
-2*(a - 49)*(a - 2)/5
Suppose 6*c + c = 14. What is k in -20*k**c + 4 + 4*k**4 + 11 + 1 = 0?
-2, -1, 1, 2
Let c(d) be the third derivative of d**5/12 - 275*d**4/12 + 15125*d**3/6 - 47*d**2. Factor c(v).
5*(v - 55)**2
Let z(m) = 2*m**2 - 24*m + 7. Let p be z(12). Determine c, given that -9*c**2 - 10*c + p*c + 12*c**2 = 0.
0, 1
Let m = 2/387 + 119/1935. Let b(p) be the second derivative of 1/90*p**4 + 0*p**2 - 6*p + m*p**3 + 0. Let b(v) = 0. What is v?
-3, 0
Let s(a) be the third derivative of a**7/630 - a**5/60 - a**4/36 + a**2 + 19. Let s(b) = 0. Calculate b.
-1, 0, 2
Suppose -32/9*l + 32/3 + 2/3*l**4 + 16/9*l**3 - 2/9*l**5 - 16/3*l**2 = 0. What is l?
-2, 2, 3
Let j(x) = -3*x**5 - 6*x**4 - 6*x**3 - 2*x**2 - x - 1. Let m(f) = -f**5 - f - 1. Let t(d) = -2*j(d) + 2*m(d). Factor t(u).
4*u**2*(u + 1)**3
Suppose 0 = -41*l + 82*l. Let o(x) be the second derivative of -4*x + 0 + 0*x**3 + l*x**2 - 1/32*x**4. Let o(h) = 0. Calculate h.
0
Let c = -413/8 - -2915/56. What is h in 0*h**3 - c - 8/7*h + 1/7*h**4 - 6/7*h**2 = 0?
-1, 3
Let r = 74 - 50. Let x be (r/39*1)/1. Solve 4/13 - 2/13*f**3 + x*f**2 - 10/13*f = 0.
1, 2
Let f(q) be the second derivative of -5/6*q**3 - 1/80*q**5 + 0 + 1/720*q**6 - 5*q + 0*q**4 + 0*q**2. Let w(n) be the second derivative of f(n). Factor w(g).
g*(g - 3)/2
Let j(a) be the first derivative of a**6/36 + a**5/6 - 3*a**4/8 - 53*a**3/18 + 2*a**2/3 + 8*a - 119. Find b such that j(b) = 0.
-4, -1, 1, 3
Let g be ((252/(-14))/(-6))/((-3)/(-2)). Factor 0*f**g - f + 1/3*f**3 - 2/3.
(f - 2)*(f + 1)**2/3
Let c(w) = -w - 2. Let h be c(-7). Let -24*k**4 + 5*k**h + 4*k**5 - 9*k**4 - 8*k**3 + 12*k**2 + 32*k**3 = 0. Calculate k.
-1/3, 0, 2
Let n(f) = f**3 + 4*f**2 - 1. Let y be n(3). Let l = y - 60. Find g such that 2/7*g**l + 16/7*g + 32/7 = 0.
-4
Let l = 929/5660 - 4/283. Let x(v) be the second derivative of -1/4*v**4 + l*v**5 + 2*v + 0 - v**3 + 0*v**2. Let x(j) = 0. What is j?
-1, 0, 2
Let c(w) be the second derivative of 1/18*w**4 + 0*w**3 + 0*w**2 + 8*w + 1/20*w**5 + 1/90*w**6 + 0. Factor c(n).
n**2*(n + 1)*(n + 2)/3
Let u(o) be the first derivative of -o**3/15 - 3*o**2/10 - 115. Factor u(m).
-m*(m + 3)/5
Let w(y) be the third derivative of y**8/6720 - y**6/720 - y**4/3 - 8*y**2. Let o(g) be the second derivative of w(g). Factor o(u).
u*(u - 1)*(u + 1)
Factor 2*h + 5896 + 46*h - 5896 - 2*h**2.
-2*h*(h - 24)
Let k(s) be the second derivative of -s**4/6 + 80*s**3/3 - 1600*s**2 - 107*s. Factor k(y).
-2*(y - 40)**2
Let p(f) be the second derivative of f**10/4032 + f**9/864 + 5*f**8/2688 + f**7/1008 - 13*f**4/4 + 33*f. Let l(t) be the third derivative of p(t). Factor l(g).
5*g**2*(g + 1)**2*(3*g + 1)/2
Let j(c) be the third derivative of c**7/1890 - c**6/1080 - 7*c**5/540 + c**4/216 + c**3/9 + 3*c**2 - 82. Solve j(d) = 0 for d.
-2, -1, 1, 3
Factor -3/4*d**3 + 1/4*d**5 + 0 + 1/4*d**4 - 1/4*d**2 + 1/2*d.
d*(d - 1)**2*(d + 1)*(d + 2)/4
Let m(r) be the second derivative of r**4/4 - 61*r**3/18 - 7*r**2/3 - 68*r + 1. What is u in m(u) = 0?
-2/9, 7
Let d(q) be the third derivative of 0 + 3*q**3 + 1/270*q**5 + 0*q + 1/6*q**4 - 9*q**2. Factor d(z).
2*(z + 9)**2/9
Let z be -4 - -6*(-2 + 3). Let r(a) = a**2 - 2*a + 3. Let b be r(z). Factor -2*j**3 + j**4 + 6*j**3 + 12*j**2 + 4*j + j**b - 4*j**2.
j*(j + 1)*(j + 2)**2
Let w(i) = -i + 4. Let a be w(1). Factor -2*u**5 + 6*u**5 - 114*u**a + 102*u**3 - 8*u**2.
4*u**2*(u - 2)*(u + 1)**2
Let g = 154 - 153. Let d be (6 + -5)*(g + 1). Suppose -3/7 - 1/7*w**d - 4/7*w = 0. What is w?
-3, -1
Let q(n) be the third derivative of -n**6/90 + n**5/15 - n**4/6 + 13*n**3/6 + 22*n**2. Let x(i) be the first derivative of q(i). Solve x(c) = 0.
1
Let l(f) be the second derivative of -f**7/735 - f**6/60 - 11*f**5/210 - 5*f**4/84 - 3*f**2 + 45*f. Let o(k) be the first derivative of l(k). Factor o(n).
-2*n*(n + 1)**2*(n + 5)/7
Let g(q) be the second derivative of -3/100*q**5 + 6*q + 0 + 0*q**2 - 3/20*q**4 - 1/5*q**3. What is r in g(r) = 0?
-2, -1, 0
Let q(p) be the second derivative of -p**5/50 + 19*p**4/10 - 361*p**3/5 + 6859*p**2/5 + 3*p - 8. Factor q(u).
-2*(u - 19)**3/5
Let t be (1 - 3/9)/(2/9). Factor 21*s**2 - 36*s**t - 33*s + 68*s**3 - 35*s**3 + 15.
-3*(s - 5)*(s - 1)**2
Factor 7/4*p**4 + 0*p + 0 - p**2 + 3*p**3.
p**2*(p + 2)*(7*p - 2)/4
Let b(x) be the third derivative of x**5/30 + 11*x**4/6 - 4*x**2 + x. Determine m, given that b(m) = 0.
-22, 0
Let l(w) be the second derivative of 1/26*w**4 - 1/130*w**5 + 0 + 0*w**3 + 0*w**2 - 20*w. Factor l(o).
-2*o**2*(o - 3)/13
Let k(j) be the third derivative of -2*j**7/525 + 4*j**6/75 + 19*j**5/75 + j**4/3 - 3*j**2 - 10*j. Factor k(v).
-4*v*(v - 10)*(v + 1)**2/5
Factor -5*s + s**2 + 12*s - 1039 + 1049.
(s + 2)*(s + 5)
Let z be (1 - (-29)/(-50)) + (-28)/(-350). Let -1/2*w**3 + 1 - w**2 + z*w = 0. What is w?
-2, -1, 1
Let h be (5 - (1 + -5))*5/15. Find r such that -1/4*r**h - 1/4 + 1/4*r + 1/4*r**2 = 0.
-1, 1
Let n(t) = -6*t**2 + 53*t - 40. Let j be n(8). Let v(z) be the third derivative of -1/240*z**5 + 1/24*z**3 + j*z + 3*z**2 + 0 + 0*z**4. Let v(u) = 0. What is u?
-1, 1
Suppose 0 = 2*f - 4*c - 2 - 6, 5*f + c = 53. Let x be (-3)/((-90)/(-8)) - (-6)/f. Suppose x + 1/3*n**2 + 2/3*n = 0. What is n?
-1
Let l be (-2)/(-21) - 24/(-189). Solve 1/9*n**2 + l + 1/3*n = 0.
-2, -1
Let n(x) be the third derivative of x**9/1008 - x**8/280 - x**7/280 + x**6/60 - 7*x**3 - 9*x**2. Let z(l) be the first derivative of n(l). Factor z(c).
3*c**2*(c - 2)*(c - 1)*(c + 1)
Factor -18*g - 16*g**2 - 3 - 14 - 10 + 13*g**2 + 0.
-3*(g + 3)**2
Let b = -125 + 125. Suppose 3*p - a - 5 = b, -5*p + 3*a = -5 + 2. Factor 6/7*y**2 - 2/7*y**p + 0 - 4/7*y.
-2*y*(y - 2)*(y - 1)/7
Let i(s) be the second derivative of -s**4/4 + 34*s**3 - 1734*s**2 + 105*s - 1. Factor i(l).
-3*(l - 34)**2
Let x(v) be the first derivative of -v**3/33 + v**2/22 + 12*v/11 + 651. Suppose x(i) = 0. What is i?
-3, 4
Suppose 0 = -m - 3*m + 12. Solve -4*r**3 + 3*r**m - 2*r**2 + 0*r**2 = 0 for r.
-2, 0
Let v be (2 - -3)*(-1 - 5 - -7). Let l(w) be the first derivative of 8/21*w**3 - 9 - 1/21*w**6 - 1/7*w**2 + 8/35*w**v + 0*w - 3/7*w**4. Factor l(r).
-2*r*(r - 1)**4/7
Let -7/2*s + 3 + 1/2*s**2 = 0. Calculate s.
1, 6
Find c, given that -42*c**4 - 245/6*c**5 + 86/3*c**3 + 1 + 41*c**2 + 73/6*c = 0.
-1, -3/5, -2/7, -1/7, 1
Let y(n) be the second derivative of 2/5*n**5 + 8/3*n**4 - 4/15*n**6 - 15*n - 2/21*n**7 + 4*n**2 + 0 + 14/3*n**3. Determine m so that y(m) = 0.
-1, 2
Let v(w) be the first derivative of 5/48*w**3 + 1/16*w**2 - 6 - 3*w + 1/24*w**4. Let y(f) be the first derivative of v(f). Factor y(l).
(l + 1)*(4*l + 1)/8
Determine s, given that 4/3*s**4 - 16/3*s**3 + 0 - 4/3*s**2 + 16/3*s = 0.
-1, 0, 1, 4
Let w(v) be the first derivative of 2*v**5/25 - 14*v**3/15 - 6*v**2/5 + 30. Factor w(p).
2*p*(p - 3)*(p + 1)*(p + 2)/5
Let r = -10 + 7. Let d be 2/((r/2)/(-3)). Factor 2*n**2 + 15*n**4 + 9*n**3 + n**3 - n**5 + 9*n**5 + n**d.
2*n**2*(n + 1)*(2*n + 1)**2
Suppose 2*c = -34 + 4. Let b be (-20)/70*(1 + c). Suppose -4/5*s + 2/5*s**2 - 2/5*s**b + 0 + 4/5*s**3 = 0. What is s?
-1, 0, 1, 2
Let a(n) be the third derivative of -1/12*n**4 + 2/105*n**7 + 13*n**2 + 1/168*n**8 + 0*n**3 - 1/15*n**5 + 0*n**6 + 0*n + 0. Factor a(s).
2*s*(s - 1)*(s + 1)**3