) be the second derivative of -l**7/5040 - l**6/180 - l**5/15 - l**4/6 - 8*l. Let i(n) be the third derivative of u(n). Factor i(x).
-(x + 4)**2/2
Let l = -54 - -487/9. Let j(r) be the second derivative of -l*r**2 - r + 1/27*r**4 - 1/45*r**5 + 1/27*r**3 + 0 - 1/135*r**6 + 1/189*r**7. Factor j(h).
2*(h - 1)**3*(h + 1)**2/9
Let o = 491 + -488. Factor 1/4*r**o - 1/2*r + 0 + 1/4*r**2.
r*(r - 1)*(r + 2)/4
Factor -13 - 2 + 1 - 3*r**2 + 36*r**3 - 36*r - 12*r**4 + 2.
-3*(r - 2)**2*(2*r + 1)**2
Suppose -3*h - 6 = 42. Let y = -11 - h. Solve -1/3*b**y + 0 + b**4 + 0*b + 1/3*b**2 - b**3 = 0 for b.
0, 1
Let s(t) be the first derivative of -t**3/12 - 7*t**2/8 - 3*t/2 + 1. Determine w, given that s(w) = 0.
-6, -1
Factor -t**3 + 15 + 9*t + 4*t**3 + 9*t**2 - 12.
3*(t + 1)**3
Let x(o) be the first derivative of -o**6/720 + o**5/40 - 3*o**4/16 + o**3 - 3. Let r(s) be the third derivative of x(s). Factor r(q).
-(q - 3)**2/2
Find f, given that -12/17*f**5 + 4/17*f + 2/17*f**4 + 0 + 22/17*f**2 + 32/17*f**3 = 0.
-1, -1/2, -1/3, 0, 2
Let a(s) be the third derivative of 1/30*s**5 + 2*s**2 - 7/24*s**4 + 1/2*s**3 + 0*s + 0. Let a(i) = 0. Calculate i.
1/2, 3
Let y = -133 + 133. Let q(w) be the first derivative of y*w**3 - 1/4*w**2 - 4 + 1/8*w**4 + 0*w. Factor q(u).
u*(u - 1)*(u + 1)/2
Let g(u) be the second derivative of 1/3*u**2 + 0 - 1/36*u**4 - 5*u + 1/18*u**3. What is r in g(r) = 0?
-1, 2
Let n(c) be the third derivative of 0*c - 1/6*c**4 + 0 + 0*c**3 + 1/15*c**5 + c**2. Factor n(g).
4*g*(g - 1)
Suppose -8 = -5*d + 2. Let b(i) be the first derivative of 0*i**5 + 0*i**3 + 1/27*i**6 + 1 + 0*i - 1/9*i**4 + 1/9*i**d. Factor b(j).
2*j*(j - 1)**2*(j + 1)**2/9
Let j(a) be the first derivative of 6/35*a**5 + 0*a**2 + 6 - 1/21*a**6 + 0*a - 3/14*a**4 + 2/21*a**3. Factor j(w).
-2*w**2*(w - 1)**3/7
Factor 1/4*l**3 - 4 - 3*l + 0*l**2.
(l - 4)*(l + 2)**2/4
Suppose 0 = 5*c + 23 + 12. Let s be -5 - c - (-14)/(-8). Factor 0*d - 1/2*d**4 - 1/4*d**5 + 0 - s*d**3 + 0*d**2.
-d**3*(d + 1)**2/4
Let s = -3 - 0. Let l be (-1)/s - (-2)/6. Factor -4/3*q + l + 2/3*q**2.
2*(q - 1)**2/3
Let i(z) = -z**5 + z**3 + z**2 - 1. Let b(y) = 4*y**5 - y**4 - 3*y**3 - 3*y**2 - y + 4. Let w(l) = b(l) + 5*i(l). Find t such that w(t) = 0.
-1, 1
Let f be (-5)/(-3) - (20 - 20). Factor -f*l**2 - 8/3*l + 4/3.
-(l + 2)*(5*l - 2)/3
Let m = -9/46 + 237/506. Let d = 13/33 + m. Factor -d*c + 0 + 2/3*c**2.
2*c*(c - 1)/3
Suppose 4*r - 2*r - 48 = 0. Factor 5*h**4 - r*h - 16*h**3 + 12*h**2 + 6*h**2 + 1 + 16*h.
(h - 1)**3*(5*h - 1)
Let m = -5075/9 + 564. What is k in 0 - m*k - 1/9*k**4 - 1/3*k**3 - 1/3*k**2 = 0?
-1, 0
Let j be (-4 - -2 - 8/(-5))/(-2). Factor j*i + 1/5*i**3 - 2/5*i**2 + 0.
i*(i - 1)**2/5
Find a such that 2/7*a - 2/7*a**3 + 22/7 - 22/7*a**2 = 0.
-11, -1, 1
Let u(q) be the second derivative of q**7/126 + q**6/90 - q**5/30 - q**4/18 + q**3/18 + q**2/6 - 5*q. Suppose u(k) = 0. What is k?
-1, 1
Let q = 11 + -32/3. Let x(c) be the second derivative of -2*c + 0 + 1/9*c**3 - q*c**2 + 1/18*c**4 - 1/30*c**5. Find z such that x(z) = 0.
-1, 1
Let j(d) be the third derivative of 0*d + 0 + 1/40*d**4 + 1/100*d**5 - 6*d**2 + 0*d**3. Factor j(f).
3*f*(f + 1)/5
Let y be (-24)/(-90)*(-10)/(-4). Let c(l) be the first derivative of -2 - 4/3*l**3 + y*l - 1/2*l**2 - 7/12*l**4. Let c(o) = 0. Calculate o.
-1, 2/7
Let p(j) be the first derivative of -2*j**3/3 + j**2 - 3. Factor p(t).
-2*t*(t - 1)
Let r(g) = g + 7. Let q(y) = 2*y + 15. Let d(b) = -6*q(b) + 13*r(b). Let s(m) = 0 + 0*m + m**2 + 1 + m. Let u(k) = d(k) - s(k). Factor u(i).
-i**2
Let l be 2/((-99)/44 + 4). Determine x, given that 0 + 0*x + 16/7*x**3 - 10/7*x**4 - l*x**2 + 2/7*x**5 = 0.
0, 1, 2
Let r(a) be the third derivative of -a**6/360 + a**5/90 + a**4/72 - a**3/9 + 5*a**2. Factor r(s).
-(s - 2)*(s - 1)*(s + 1)/3
Let w(p) = p**2 - 24*p + 82. Let s be w(4). Determine z so that -z**5 + 7/5*z**4 + 4/5 - 8/5*z + 13/5*z**3 - 11/5*z**s = 0.
-1, 2/5, 1, 2
Let 0 + 1/3*p**4 + 1/3*p - 1/3*p**2 - 1/3*p**3 = 0. Calculate p.
-1, 0, 1
Let m be (-196)/(-84) - 2/(-3). Factor -4/5*i**m + 1/5 - 7/5*i**2 - 2/5*i.
-(i + 1)**2*(4*i - 1)/5
Solve -2*i + 6*i**2 - 4*i - 1 + 5 - 4*i**2 = 0.
1, 2
Let z = 57/2 - 111/4. Let 0 + 3/4*v**4 + 0*v - 3/4*v**5 - z*v**2 + 3/4*v**3 = 0. Calculate v.
-1, 0, 1
Let m(k) be the second derivative of k**6/6 - 7*k**5/2 + 30*k**4 - 400*k**3/3 + 320*k**2 + 12*k. Factor m(b).
5*(b - 4)**3*(b - 2)
Let w be 12/(-4)*(102/27 - 4). Factor -4/3*o + w - 2*o**2.
-2*(o + 1)*(3*o - 1)/3
Let h(x) be the third derivative of -x**9/100800 + x**8/16800 - x**7/8400 - x**5/15 + 2*x**2. Let v(a) be the third derivative of h(a). Factor v(d).
-3*d*(d - 1)**2/5
Let p be (-3)/((-4)/(-4) + -2). What is y in 3*y**4 + 2/3*y**5 + 11/3*y**p + 0 + 0*y**2 - 4/3*y = 0?
-2, -1, 0, 1/2
Suppose 39 - 207 = -7*w. Factor 32*h**3 + w*h**2 + 1/2 + 6*h.
(4*h + 1)**3/2
Suppose -5*c - 5*o + 35 = 0, 3*c = -0*c + 3*o - 9. Suppose 0*b**c + b**2 + 11*b**3 + 5*b**2 - 2*b**3 - 3*b = 0. What is b?
-1, 0, 1/3
Let a(o) be the first derivative of -o**6/360 + o**5/60 - o**4/24 - o**3 - 4. Let d(n) be the third derivative of a(n). Factor d(u).
-(u - 1)**2
Let b(x) be the third derivative of -x**6/240 + 11*x**5/240 - x**4/8 - 3*x**3/8 + 4*x**2. Factor b(i).
-(i - 3)**2*(2*i + 1)/4
Let y(u) = -3*u**4 - 3*u**2 + 3*u**3 + 4*u + 4 - u**4 + 0*u**3. Let i(m) = m**2 - m - 1. Let x(w) = 4*i(w) + y(w). Find p such that x(p) = 0.
-1/4, 0, 1
Let j(k) = -2*k**4 - k**3 - k**2 + 3*k. Let r(l) = -2*l**4 - 2*l**3 - 2*l**2 + 2*l. Let h(u) = -4*j(u) + 5*r(u). Factor h(a).
-2*a*(a + 1)**3
Let p = -12 - -14. Let t(f) be the first derivative of 1 + 10/3*f**3 - 6/5*f**5 - f**p + 1/2*f**4 - 4*f. What is r in t(r) = 0?
-1, -2/3, 1
Let b(r) be the first derivative of 5*r**3/3 - 5*r**2/2 - 30*r + 8. Factor b(f).
5*(f - 3)*(f + 2)
Suppose 0*w + 2*w = 6. What is n in 324*n + 25*n**3 + w*n**4 + 162*n**2 + 315 - n**3 + 12*n**3 - 72 = 0?
-3
Let u(s) = 2*s - 4. Let m be u(4). Factor 4*x**m - 2*x**3 - x**4 - 4*x**4.
-x**3*(x + 2)
Let i be (-72)/(-16) + 1/(-2). Let c(s) be the second derivative of -1/36*s**i + 0*s**3 + 0*s**2 - s - 1/30*s**5 - 1/90*s**6 + 0. Factor c(l).
-l**2*(l + 1)**2/3
Let t(d) be the first derivative of 0*d + 0*d**2 + 2 + 2/21*d**3. Factor t(i).
2*i**2/7
Let j = -86/3 - -30. Factor 0 + j*y - 2*y**2.
-2*y*(3*y - 2)/3
Suppose 0 + 1/2*w + w**2 = 0. What is w?
-1/2, 0
Solve -3/5 + 4/5*n - 1/5*n**2 = 0 for n.
1, 3
Let m be (1 + 0)*(-24)/3660. Let w = 1226/915 + m. Solve 2/9*y**2 + 2 + w*y = 0.
-3
Let o = -16 - -5. Let f = o + 11. Factor 0 + 0*r**2 + 2/9*r**3 + f*r.
2*r**3/9
Determine a so that 4*a**5 + 0 - 2 + 5*a**2 + 2*a**4 - 8*a**4 - 4*a**3 + 3*a**2 = 0.
-1, -1/2, 1
Let o(p) be the third derivative of -p**10/756000 - p**9/302400 - p**5/60 + 3*p**2. Let u(j) be the third derivative of o(j). Factor u(x).
-x**3*(x + 1)/5
Let i(x) be the second derivative of x**7/21 - 8*x**6/15 + 13*x**5/10 + 13*x**4/3 - 64*x**3/3 + 32*x**2 + 15*x - 2. Solve i(o) = 0.
-2, 1, 4
Let j be 1*2 - (11 - 1). Let y be j/6*(5 + -8). Determine o, given that 2*o**3 - 2*o**4 - y*o**4 + 4*o**2 + 4*o**4 = 0.
-1, 0, 2
Let s = 8 + -6. Let d be (-14)/(-105)*(-15)/(-9). Let -4/9*q - 2/9*q**s - d = 0. Calculate q.
-1
Let x(o) be the second derivative of -o**5 - 55*o**4/12 - 25*o**3/6 + 5*o**2 + 2*o - 18. Factor x(w).
-5*(w + 1)*(w + 2)*(4*w - 1)
Determine z so that -14/3*z**3 + 46/3*z**2 - 40/3*z + 8/3 = 0.
2/7, 1, 2
Let a(r) = -13*r**4 + 4*r**3 - 7*r + 7. Let q(t) = 7*t**4 - 2*t**3 + 4*t - 4. Let u(j) = 4*a(j) + 7*q(j). Factor u(d).
-d**3*(3*d - 2)
Let x(w) be the third derivative of w**7/1680 + w**6/360 + w**5/240 + w**3/2 + 2*w**2. Let m(g) be the first derivative of x(g). Factor m(i).
i*(i + 1)**2/2
Suppose 4*g + 0*y + 4*y = 4, 2*y - 8 = 4*g. Let u be (g/6)/(2/(-8)). Determine o, given that o**2 + 1/3*o - 1/3*o**3 - u*o**4 - 1/3 = 0.
-1, 1/2, 1
Let r(g) be the third derivative of g**9/30240 - g**5/20 + 6*g**2. Let h(p) be the third derivative of r(p). Factor h(j).
2*j**3
Let a(w) be the first derivative of 2*w**5/35 - 2*w**4/7 + 4*w**3/7 - 4*w**2/7 + 2*w/7 - 15. Let a(d) = 0. Calculate d.
1
Let f(o) be the second derivative of -o**4/42 + o**3/21 + 2*o**2/7 - 5*o. Solve f(g) = 0 for g.
-1, 2
Let y(s) be the second derivative of -1/48*s**4 - 2*s - 1/4*s**2 - 1/8*s**