
Let x(g) be the third derivative of g**9/30240 + g**8/2880 + g**7/720 + g**6/360 - g**5/30 - 7*g**2. Let n(k) be the third derivative of x(k). Factor n(f).
(f + 1)*(f + 2)*(2*f + 1)
Let j(b) = b. Let l be j(5). Suppose o = l*o. Let 16/5*g**3 + o + 4/5*g - 14/5*g**2 - 6/5*g**4 = 0. What is g?
0, 2/3, 1
Let g(f) be the second derivative of -f**4/30 + 4*f**3/15 + 12*f. Factor g(t).
-2*t*(t - 4)/5
Let s(u) be the second derivative of 3*u + 0*u**2 + 2/5*u**5 + 2/3*u**3 - 5/6*u**4 + 0 - 1/15*u**6. Find y, given that s(y) = 0.
0, 1, 2
Let m(b) = -48*b**3 - 210*b**2 - 357*b - 141. Let y(c) = 7*c**3 + 30*c**2 + 51*c + 20. Let u(d) = 4*m(d) + 27*y(d). Let u(g) = 0. Calculate g.
-8, -1
Let g(o) be the third derivative of 0 + 1/96*o**4 + 0*o**3 + 1/240*o**5 + 0*o - o**2 - 1/840*o**7 - 1/480*o**6. Factor g(f).
-f*(f - 1)*(f + 1)**2/4
Let x(h) be the second derivative of 1/36*h**4 + 5*h + 1/6*h**2 - 1/9*h**3 + 0. Factor x(a).
(a - 1)**2/3
Let h(z) = 3*z**4 + 2*z**3 - 3*z**2 + 2*z - 2. Let q(w) = -7*w**4 - 5*w**3 + 7*w**2 - 5*w + 5. Let n(j) = 15*h(j) + 6*q(j). Factor n(x).
3*x**2*(x - 1)*(x + 1)
Let w(r) be the first derivative of -16*r**3/3 - 26*r**2 - 12*r - 11. Factor w(t).
-4*(t + 3)*(4*t + 1)
Let s be 20/9 - (-1 + 88/72). Let -1 + 4/3*b - 1/3*b**s = 0. Calculate b.
1, 3
Let j(i) be the third derivative of i**8/560 + i**7/350 - i**6/200 - i**5/100 + 12*i**2. Suppose j(h) = 0. Calculate h.
-1, 0, 1
Suppose -6 = 4*b - 7*b. Let -14 - 17 - 40*z - 12*z**b + 19 = 0. Calculate z.
-3, -1/3
Suppose 2 - 4 = -4*w - 2*u, 3*w = 3*u - 21. Let v be w/((-18)/(-3)) - -1. Solve v*f**2 + 8/3*f + 8/3 = 0 for f.
-2
Let a(p) = 3*p**3 + p**3 - 5*p**3 + p + 2. Let r be a(0). Factor -10*h**2 + 2*h**2 - r*h - 9*h**3 + 3*h**3.
-2*h*(h + 1)*(3*h + 1)
Suppose 0 = -3*g - 9 + 9. Factor g - 3/4*r**3 + 0*r - 3/2*r**2.
-3*r**2*(r + 2)/4
Let q = -12/5 + 41/15. Factor q*x**2 + 0 - 2/3*x.
x*(x - 2)/3
Let s(i) be the third derivative of i**8/6720 - i**7/1680 + i**6/1440 + i**3/6 + 5*i**2. Let z(w) be the first derivative of s(w). Determine p so that z(p) = 0.
0, 1
Let y(s) be the third derivative of 0*s**3 + 0*s + 1/60*s**4 + 0 + 2/75*s**5 + s**2. Let y(x) = 0. Calculate x.
-1/4, 0
Let k(g) be the first derivative of 0*g**2 - 1/2*g**6 + 9/5*g**5 + g**3 - 1 + 0*g - 9/4*g**4. Factor k(l).
-3*l**2*(l - 1)**3
Let j be (1 - -1) + (-16 - -16). Factor 0 + 3/5*o - 3/5*o**4 + 3/5*o**j - 3/5*o**3.
-3*o*(o - 1)*(o + 1)**2/5
Let q(x) be the third derivative of -x**7/840 + x**6/160 - x**5/80 + x**4/96 - 4*x**2. Factor q(m).
-m*(m - 1)**3/4
Let f = -67/3 + 23. Factor 2/3 - 2/3*l**2 - 2/3*l + f*l**3.
2*(l - 1)**2*(l + 1)/3
Suppose 3*z + 9 = 3*q, 10*z = 5*z + 4*q - 12. Factor -1/2*k**3 + 1/2*k**5 + 1/2*k**2 - 1/2*k**4 + z*k + 0.
k**2*(k - 1)**2*(k + 1)/2
Factor 8*m**3 + 0*m + 16/9*m**2 + 14/9*m**5 + 20/3*m**4 + 0.
2*m**2*(m + 2)**2*(7*m + 2)/9
Let p(y) = -5*y**5 + 11*y**4 - 2*y**3 - 12*y**2 - 2. Let f(g) = -66*g**5 + 144*g**4 - 27*g**3 - 156*g**2 - 27. Let u(d) = -2*f(d) + 27*p(d). Factor u(q).
-3*q**2*(q - 2)**2*(q + 1)
Let t(h) be the third derivative of -h**5/20 - 3*h**4/8 - h**3 + 5*h**2. Find k, given that t(k) = 0.
-2, -1
Let x be (-34)/108 - (-2)/4. Let a(o) be the second derivative of 0 + 2*o + 1/9*o**2 + 1/27*o**4 + 4/45*o**5 - x*o**3. Suppose a(v) = 0. Calculate v.
-1, 1/4, 1/2
Let h(o) be the third derivative of 0*o - 1/315*o**7 + 7*o**2 - 1/72*o**6 + 0 + 0*o**3 + 1/90*o**5 + 0*o**4 + 5/1008*o**8. Suppose h(t) = 0. What is t?
-1, 0, 2/5, 1
Factor 5*r**2 - 15*r**4 + 3*r**2 + 11*r**4 - 4.
-4*(r - 1)**2*(r + 1)**2
Let x = 11 - 32. Let v be (-78)/x + (-4)/(-14). Factor -v*l**2 - 4*l**2 - 2*l + 6*l**2 + 4*l**2.
2*l*(l - 1)
Let y(s) be the third derivative of s**6/600 + s**5/100 + s**4/60 - 10*s**2. Suppose y(c) = 0. Calculate c.
-2, -1, 0
Let y(b) be the first derivative of -b**5/10 + b**4/4 - b**3/6 + 12. Suppose y(a) = 0. Calculate a.
0, 1
Let r(l) be the second derivative of l**5/40 - l**4/12 + l**3/12 + 6*l. Factor r(i).
i*(i - 1)**2/2
Let m = 790079/45 - 35113/2. Let b = 7/18 + m. Find r, given that -b*r**2 - 2/5 - 2/5*r**3 - 6/5*r = 0.
-1
Let z = 20 + -42. Let k(v) = 8*v**4 - 14*v**3 + 2*v**2 + 4*v + 2. Let j(c) = -39*c**4 + 69*c**3 - 10*c**2 - 20*c - 11. Let q(x) = z*k(x) - 4*j(x). Factor q(w).
-4*w*(w - 1)**2*(5*w + 2)
Let c be 15/(-3) - (-95)/15. Determine l so that -10/3*l**3 - c*l**4 + 2/3*l + 2/3 - 2*l**2 = 0.
-1, 1/2
Let h be (-20)/15*1/(-2). Let m = 4/71 - -272/213. What is a in m*a - 2/3 - h*a**2 = 0?
1
Let z = -9 + 12. Let v(g) be the first derivative of -1/2*g**2 + 2*g - 1 + 3/4*g**4 - 4/3*g**z. Determine c, given that v(c) = 0.
-2/3, 1
Let o = 1159/4 + -579/2. Factor -o*d**3 - 27/4*d - 9/4*d**2 - 27/4.
-(d + 3)**3/4
Let r(m) be the first derivative of -m**6/45 + 2*m**5/15 - m**4/3 + 4*m**3/9 - m**2/3 + 3*m + 2. Let a(f) be the first derivative of r(f). Solve a(q) = 0.
1
Let v(c) be the first derivative of 2*c**5/15 - c**4/6 - 2*c**3/3 + c**2/3 + 4*c/3 + 7. Let v(p) = 0. What is p?
-1, 1, 2
Let 0*x**2 + 0*x + 2/5*x**3 - 2/5*x**5 + 0 + 0*x**4 = 0. What is x?
-1, 0, 1
Let w(u) be the third derivative of 0*u**4 - 1/40*u**6 + 0 + 1/20*u**5 - 4*u**2 + 0*u + 0*u**3. Factor w(d).
-3*d**2*(d - 1)
Let a(r) be the third derivative of 4/3*r**3 + 1/2*r**4 + 0*r**5 + 0*r - 1/30*r**6 - 4*r**2 + 0. Suppose a(c) = 0. Calculate c.
-1, 2
Let m(t) = 2*t**2 - 4*t - 4. Let y(r) = r**2. Let f(l) = -m(l) + 3*y(l). Let f(i) = 0. What is i?
-2
Suppose -m + 10 = -0*m. Let u = -6 + m. Factor -11/2*n**3 + 13/4*n**u - 3/4*n**5 + 9/2*n**2 + 1/4 - 7/4*n.
-(n - 1)**4*(3*n - 1)/4
Let b = -4 - -6. Suppose -q = -g + 20, 4*q = -2*g + b + 38. Factor 80*r**4 - 66*r**3 + g*r**2 - 2*r + r**5 + 4*r**5 - 37*r**5.
-2*r*(r - 1)**2*(4*r - 1)**2
Suppose 2*z + f - 4*f - 10 = 0, 3*f = 0. Factor -3*k + z + 3*k**2 - 15 + 10.
3*k*(k - 1)
Let j(q) be the first derivative of 0*q**4 + 3 + 0*q**2 - 1/5*q + 2/15*q**3 - 1/25*q**5. Find m such that j(m) = 0.
-1, 1
Find o, given that -1/2*o**4 + 1/2*o - 1/2*o**3 - 1 + 3/2*o**2 = 0.
-2, -1, 1
Let m(u) be the second derivative of -4*u**5/5 - 7*u**4/6 - 8*u. Let k(q) = q**3 + q**2. Let y(g) = 36*k(g) + 2*m(g). Solve y(r) = 0.
-2, 0
Let m(g) be the first derivative of -9*g**4/10 - 4*g**3/5 - g**2/5 + 2. Factor m(i).
-2*i*(3*i + 1)**2/5
Let s(p) be the second derivative of -p**6/60 + p**5/20 - 8*p. Factor s(l).
-l**3*(l - 2)/2
Let r(k) = 2*k**2 + 17*k - 4. Let h be r(-9). Let q(s) be the first derivative of 0*s**4 - 2/35*s**h + 0*s**2 - 2/7*s + 4 + 4/21*s**3. Factor q(j).
-2*(j - 1)**2*(j + 1)**2/7
Let k be (-58)/(-10) - (-10 - -5 - -10). Find g, given that k*g**2 + 0 + 4/5*g**3 + 1/5*g**4 + 0*g = 0.
-2, 0
Suppose -o + 0 + 2 = 0. Let n(b) = b**2 + 2*b**3 - o - b + 0*b**3 + b**3 + 3. Let x(c) = -c**3 - 1. Let i(m) = -n(m) - 2*x(m). Factor i(w).
-(w - 1)*(w + 1)**2
Suppose 2*m = 2*m + 10*m. Let w(r) be the third derivative of 0 + 0*r**5 + m*r**4 - r**2 + 1/60*r**6 + 0*r + 0*r**3 + 4/105*r**7. Let w(v) = 0. Calculate v.
-1/4, 0
Solve 0*c**2 + 3*c**2 - 5*c - 2*c**2 + 4 + 0 = 0.
1, 4
Let n(m) be the third derivative of -1/10*m**7 + 0*m**3 + 5/112*m**8 + 0 + 0*m**4 + 0*m**5 + 0*m + 4*m**2 + 1/20*m**6. What is j in n(j) = 0?
0, 2/5, 1
Let f be ((-4)/3)/((-4)/6). Factor 0*t - 2*t - t**f + t**3 + 0*t**2.
t*(t - 2)*(t + 1)
Factor -1/12*m**2 - 1/6*m - 1/12.
-(m + 1)**2/12
Let y(f) be the first derivative of -f**4/4 + 3*f**2/2 + 2*f + 5. Factor y(a).
-(a - 2)*(a + 1)**2
Let z(i) = -22*i + 418. Let q be z(19). Factor 9/7*p**4 - 12/7*p**5 + 3/7*p**3 + q*p + 0 + 0*p**2.
-3*p**3*(p - 1)*(4*p + 1)/7
Let k(j) be the second derivative of 5*j**7/14 - 4*j**6/5 + 3*j**5/20 + j**4/2 + 7*j. Factor k(n).
3*n**2*(n - 1)**2*(5*n + 2)
Let r(j) be the second derivative of -j**7 + 8*j**6/15 + 44*j**5/5 - 16*j**4/3 - 16*j**3/3 + 36*j - 2. Solve r(d) = 0.
-2, -2/7, 0, 2/3, 2
Let x(m) = 4*m**3 - 17*m**2 + 17*m - 4. Let w(t) = 2*t**3 - 9*t**2 + 9*t - 2. Let v(p) = 5*w(p) - 3*x(p). Factor v(i).
-2*(i - 1)**3
Factor -1/3*t + 0 - 1/6*t**2.
-t*(t + 2)/6
Suppose -3*b + 2*b + 17 = 5*c, 3 = -b. Let m(p) be the first derivative of -1/20*p**c + 2/15*p**3 - 1/10*p**2 + 0*p - 1. What is d in m(d) = 0?
0, 1
Let w(l) = -6*l**3 - 5*l**2. Let q(r) = -2*r**3 - 2*r**2. Let z(g) = -17*q(g) + 6*w(g). Factor z(m).
-2*m**2*(m - 2)
Factor 4 - 8 