
Let n = -19 + 19. Let f(j) be the first derivative of 0*j**2 + 2/21*j**3 - 1/7*j**4 - 1 + n*j + 2/35*j**5. Factor f(v).
2*v**2*(v - 1)**2/7
Let k(w) be the first derivative of 5/3*w**3 - 1/2*w**4 - w**5 + w**2 - 1 + 0*w. Factor k(g).
-g*(g - 1)*(g + 1)*(5*g + 2)
Let y(n) be the third derivative of -n**5/100 - n**4/40 - n**2. Determine t, given that y(t) = 0.
-1, 0
Let t(c) be the first derivative of -c**5/5 + 9*c**4/4 - 22*c**3/3 + 32*c - 24. Factor t(f).
-(f - 4)**2*(f - 2)*(f + 1)
Factor 0 - 2/9*u**2 + 2/9*u**3 - 4/9*u.
2*u*(u - 2)*(u + 1)/9
Let v(g) = 2*g**2 + 2*g - 2. Let a be v(1). Let s(o) be the second derivative of -1/6*o**a - 1/9*o**3 - 1/36*o**4 + 0 - 2*o. Factor s(d).
-(d + 1)**2/3
Let m(b) = -b**5 + b**4 + b**2 + b - 1. Let j(q) = -5*q**5 + 10*q**4 + 3*q**3 + 2*q**2 + 2*q - 6. Let i(p) = 5*j(p) - 30*m(p). Factor i(n).
5*n*(n - 1)*(n + 1)*(n + 2)**2
Let d(i) be the first derivative of 2*i**3/27 + 2*i**2/9 + 2*i/9 - 13. Factor d(j).
2*(j + 1)**2/9
Factor 0*m + 0*m**4 - 2/3*m**5 + 2*m**3 - 4/3*m**2 + 0.
-2*m**2*(m - 1)**2*(m + 2)/3
Let a be ((-1)/(-2))/((-10)/(-160)). Suppose -i + 3 = p - 1, -4*i + 2*p = a. Let -2/5*m**2 + i + 9/5*m**3 + 0*m - 7/5*m**4 = 0. What is m?
0, 2/7, 1
Let y be 3 - (-5)/((-80)/596). Let j = -34 - y. Find i such that j*i**2 - 1/4 + 1/4*i - 1/4*i**3 = 0.
-1, 1
Let c be ((-1)/2)/((140/(-15))/14). Factor 0*m - 3/4*m**2 + 0 - 3/2*m**3 - c*m**4.
-3*m**2*(m + 1)**2/4
Suppose 2 = 5*j - 3*j. Suppose -s + j = -1. Find a such that 0*a - 2*a - 2*a**s - 2 - 2*a = 0.
-1
Let x(k) = 6*k**2 - 6. Let a(m) = 5*m**2 - 5. Let t(n) = -3*a(n) + 2*x(n). Factor t(l).
-3*(l - 1)*(l + 1)
Let m(v) be the first derivative of -v**7/420 + v**5/60 - v**3/12 - v**2/2 - 1. Let i(q) be the second derivative of m(q). Let i(x) = 0. Calculate x.
-1, 1
Let h(s) = -162*s**3 + s**2 + s - 1. Let n be h(1). Let c = -1755/11 - n. Suppose -c*d + 196/11*d**3 + 98/11*d**4 - 8/11 + 90/11*d**2 = 0. Calculate d.
-1, -2/7, 2/7
Let d(p) be the first derivative of 3*p**4/4 + 5*p**3 + 12*p**2 + 12*p + 9. Let d(u) = 0. What is u?
-2, -1
Let v = -78 + 83. Factor -v*p**2 + 1 - 1/2*p - 2*p**3 + 4*p**4 + 5/2*p**5.
(p - 1)*(p + 1)**3*(5*p - 2)/2
Suppose -11 + 2 = -3*f. Factor -2*r**f - r**2 - 2*r**2 - 2*r**3 - r**4 + r**3 - r.
-r*(r + 1)**3
Suppose 3*c - 4 = -c. Let v(u) = u**3 - u. Let m(l) = l**3 + 9*l + 0 + 6*l**2 + 1 + l**4 - 2*l**3. Let s(b) = c*m(b) + 5*v(b). Let s(p) = 0. Calculate p.
-1
Let x be 2/(-16)*(6/(-3))/4. Let k(i) be the second derivative of 0 + 0*i**2 + 1/24*i**3 + 2*i + 3/80*i**5 - 1/120*i**6 - x*i**4. Factor k(g).
-g*(g - 1)**3/4
Let b(i) = 2*i**4 + i**3 + 6*i**2 - 9*i + 7. Let k(l) = -2*l**4 - 4*l**4 + 0*l**4 + 5*l**4 - 3*l**2 + 4*l - 3. Let m(h) = -6*b(h) - 14*k(h). Factor m(f).
2*f*(f - 1)**3
Let d be 3*((-8)/6)/(-2). Factor 3*a**2 + 0*a**2 - 4*a**2 - 2*a + 5*a**2 - d*a**3.
-2*a*(a - 1)**2
Let p(n) be the second derivative of 0 - 1/3*n**2 + 1/9*n**3 + 1/18*n**4 - 1/30*n**5 + n. Let p(a) = 0. Calculate a.
-1, 1
Suppose 5*k - 2*c - 21 = c, 4*k - 5*c - 22 = 0. Suppose 0 = -k*v - a + 1, 5*v = 3*a + 5 + 20. Factor -2*j**2 + 14*j - 14*j - v*j**3.
-2*j**2*(j + 1)
Let a be -1*(1 + 1)*-1. Let y(q) be the first derivative of -1 + a*q + 9/2*q**3 + 27/16*q**4 + 9/2*q**2. What is l in y(l) = 0?
-2/3
Let i(y) be the third derivative of -y**7/10080 + y**4/6 + 4*y**2. Let h(a) be the second derivative of i(a). Determine f so that h(f) = 0.
0
Let b(j) be the first derivative of 3*j**5/5 - 3*j**4/2 - j**3 + 3*j**2 - 3. Factor b(g).
3*g*(g - 2)*(g - 1)*(g + 1)
Factor -4*q + 4*q - 5*q - 3*q + 4*q**2 - 12.
4*(q - 3)*(q + 1)
Let f(i) be the first derivative of -i**5/180 + i**4/18 - 2*i**3/9 + 3*i**2/2 + 3. Let z(u) be the second derivative of f(u). Factor z(v).
-(v - 2)**2/3
Let v be (-105)/98*32/(-40). Determine x so that v*x + 10/7*x**2 - 4/7 = 0.
-1, 2/5
Let -2/11 + 0*j - 2/11*j**4 + 4/11*j**2 + 0*j**3 = 0. Calculate j.
-1, 1
Let h = -98 + 104. Let g(w) be the second derivative of 0 + w - 1/9*w**3 + 1/30*w**5 + 0*w**2 + 1/45*w**h - 1/18*w**4. Solve g(a) = 0.
-1, 0, 1
Factor 2/19*a + 26/19*a**3 + 0 - 12/19*a**4 - 16/19*a**2.
-2*a*(a - 1)**2*(6*a - 1)/19
Let i = 40 - 32. Let d(h) be the third derivative of -1/336*h**i + 1/60*h**6 - 1/24*h**4 + 0*h**3 + 0 + 0*h**5 + h**2 + 0*h**7 + 0*h. Find c such that d(c) = 0.
-1, 0, 1
Let z(g) be the second derivative of -g**7/9 + g**6/9 + g**5/15 + 5*g. Find k such that z(k) = 0.
-2/7, 0, 1
Determine b so that -375 + 8*b**3 - 4*b**5 + 375 - 4*b = 0.
-1, 0, 1
Let p = -58 + 58. Let q(g) be the third derivative of p*g**4 + 0*g**3 + 1/45*g**5 + 0 + 0*g - 1/315*g**7 + 3*g**2 + 1/180*g**6. Factor q(x).
-2*x**2*(x - 2)*(x + 1)/3
Let l(z) = -z**3 - z**2 - z + 1. Let b(p) = -27*p**3 + p**2 + 5*p + 3. Let h(i) = -b(i) + 3*l(i). Factor h(s).
4*s*(2*s + 1)*(3*s - 2)
Let i(x) be the second derivative of -x**4/6 - 4*x**3/3 - 3*x**2 - 4*x. Factor i(n).
-2*(n + 1)*(n + 3)
Let h be (-14)/(-4)*(-30)/195. Let w = h + 101/91. Factor 6/7*n - w - 2/7*n**2.
-2*(n - 2)*(n - 1)/7
Let f be (4 + -2)/(-2)*-2. Find t such that -4/9 + 2/9*t**f - 2/3*t + 2/3*t**3 + 2/9*t**4 = 0.
-2, -1, 1
Let q be 1/(-3) + (-52)/(-12). Let o be (-11)/(-14) - q/14. Find m, given that -o*m + 1/4 + 1/4*m**2 = 0.
1
Factor 2 - 1 - 3*l**2 - 4 - 6*l.
-3*(l + 1)**2
Factor -2 - 10/3*w**3 + 14/3*w**2 + 2/3*w.
-2*(w - 1)**2*(5*w + 3)/3
Let q = -1 - 3. Let j(p) = 13*p**4 - 8*p**3 - 5*p**2 - 9*p. Let w(o) = 3*o**4 - 2*o**3 - o**2 - 2*o. Let c(s) = q*j(s) + 18*w(s). Factor c(z).
2*z**2*(z - 1)**2
Let m(j) be the second derivative of j**5/90 - 11*j**4/9 + 484*j**3/9 - 10648*j**2/9 - 14*j + 2. Let m(y) = 0. What is y?
22
Let l(t) = 4*t**4 + 16*t**3 - 8*t**2 + 12. Let b(k) = k**3 + k**2 - k + 1. Let a(y) = 12*b(y) - l(y). Determine d so that a(d) = 0.
-3, 0, 1
Suppose 6*i**2 - 13 - 12 - 21*i - 11 - 9*i**2 = 0. What is i?
-4, -3
Let h be (-18)/(-12)*(-8)/(-54). Let d(q) = -q**2 - 3*q + 4. Let l be d(-4). Let 2/9*c - 2/9*c**2 + l + 2/9*c**4 - h*c**3 = 0. Calculate c.
-1, 0, 1
Let v(r) = -2*r**3 + r**2 + r. Let w be v(-1). Let i(b) be the second derivative of -1/6*b**3 + w*b + 1/36*b**4 + 0 + 1/3*b**2. Factor i(m).
(m - 2)*(m - 1)/3
Let u(n) = 6*n**3 - 20*n**2 + 2*n. Suppose 4*h + 16 = -0*h. Let d(o) = -6*o**3 + 21*o**2 - o + 1. Let i(s) = h*d(s) - 5*u(s). Determine v, given that i(v) = 0.
-1/3, 1, 2
Let s(j) be the third derivative of j**8/168 - j**6/60 - 2*j**2. Factor s(u).
2*u**3*(u - 1)*(u + 1)
Suppose -33*w**2 + 2*w**3 - 137 - 20*w**3 - 3*w**4 - 18*w + 137 = 0. Calculate w.
-3, -2, -1, 0
Let i(v) be the second derivative of -v**8/7560 + v**7/1890 - v**5/270 + v**4/108 + v**3/6 - 3*v. Let f(c) be the second derivative of i(c). Factor f(b).
-2*(b - 1)**3*(b + 1)/9
Let d(t) be the first derivative of 0*t**4 - 6/5*t**5 - 1/3*t**6 + 4 + 0*t**2 + 0*t + 8/3*t**3. Determine r so that d(r) = 0.
-2, 0, 1
Let d(m) = -m**5 - 8*m**4 - 5*m**3 - 2*m**2 + 2. Let i(h) = -4*h**5 - 41*h**4 - 26*h**3 - 11*h**2 + 11. Let r(k) = 11*d(k) - 2*i(k). Factor r(z).
-3*z**3*(z + 1)**2
Let t be (-13)/28 - (-36)/48. Let k = 1087/1260 + -1/180. Factor -6/7*c - t*c**3 - k*c**2 - 2/7.
-2*(c + 1)**3/7
Let h = -5394/19 - -284. Factor 0*z**2 - h - 4/19*z + 2/19*z**4 + 4/19*z**3.
2*(z - 1)*(z + 1)**3/19
Factor -24*o**3 - 18*o + 3 + 3 + 10*o**2 - 9 + 35*o**2.
-3*(o - 1)**2*(8*o + 1)
Factor -4/5 + 18/5*z + 22/5*z**3 - 6/5*z**4 - 6*z**2.
-2*(z - 1)**3*(3*z - 2)/5
Let a be (-1)/(-2)*((-12)/4 - -3). Factor a + 2/9*q**5 + 0*q**2 - 4/9*q**3 + 2/9*q + 0*q**4.
2*q*(q - 1)**2*(q + 1)**2/9
Suppose -10 = 4*n - 9*r + 4*r, -r = -4*n - 2. Let i(o) be the first derivative of 1/7*o**2 + 1/14*o**4 + n*o - 4/21*o**3 + 1. Factor i(l).
2*l*(l - 1)**2/7
Suppose 0 = -h + 2*h. Let q be (-2 - -1)*(0 - h). Factor 0*u + 1/3*u**4 + 0 + q*u**3 + 0*u**2.
u**4/3
Let z = -16 - -21. Factor -8*k**3 + 4*k**5 + k**5 + 3*k + k - k**z.
4*k*(k - 1)**2*(k + 1)**2
Find t such that 2/13*t**4 + 0 + 2/13*t**3 + 0*t - 2/13*t**2 - 2/13*t**5 = 0.
-1, 0, 1
Suppose 4*i - 2*k = -2, -3*i - 19 + 5 = -4*k. Let u be (4/(-25))/((-4)/10). Factor -3/5*g - u - 1/5*g**i.
-(g + 1)*(g + 2)/5
Factor -2/5*o - 6/5*o**2 + 2/5*o**4 + 2/5*o**3 + 4/5.
2*(o - 1)**2*(o + 1)*(o + 2)/5
Let c(k) be the second derivative of k**4/4 - 3*k**2/2 + 14*k. Factor c(n).
3*(n - 1)*(n + 1)
Let t = 125 