*2 + 2/3*j.
-j*(j - 2)/3
Let d(x) = x**3 + x**2 + x + 1. Let c(f) = 4*f**3 + 7*f**2 + 4*f + 5. Let o(k) = c(k) - 5*d(k). Factor o(u).
-u*(u - 1)**2
Suppose 4*a = 9 - 1. Factor 2*n**3 - 3*n**3 + n**3 - a*n - 2*n**3 - 4*n**2.
-2*n*(n + 1)**2
Determine w so that 34/5*w**3 - 4/5 - 2*w**4 - 42/5*w**2 + 22/5*w = 0.
2/5, 1
Suppose 5*m = 22 - 7. Factor -1/2 - 3/2*q - 3/2*q**2 - 1/2*q**m.
-(q + 1)**3/2
Let 0 + 0*j**2 + 6*j - 3/2*j**3 = 0. Calculate j.
-2, 0, 2
Suppose 13 + 33 = 2*y. Let o = 23 - y. Suppose o - 1/3*l**3 - 2/3*l**2 + 0*l = 0. What is l?
-2, 0
Let i be (-19)/(-7) + (-8)/(-28). Suppose n + 4 = 3*n. Factor -2*m + 3*m**2 - m**n + 2*m**i - m - 2 + m.
2*(m - 1)*(m + 1)**2
Let k be (-18)/(-15) + (-266)/455. Factor k*g**4 + 8/13*g**3 - 4/13*g - 6/13*g**2 + 2/13.
2*(g + 1)**2*(2*g - 1)**2/13
Let s(q) = q**3 - 6*q**2 + 9*q. Let c(v) = -v**3 + v**2 + v. Let g(j) = -4*c(j) + s(j). Solve g(d) = 0.
0, 1
Suppose -22*s = -10*s. Let o(a) be the third derivative of 0*a**3 + 0*a + 1/175*a**7 + 1/150*a**5 + 0*a**4 + 1/840*a**8 + s - 3*a**2 + 1/100*a**6. Factor o(z).
2*z**2*(z + 1)**3/5
Factor 0*p**2 + 0 + 3/5*p**4 + 1/5*p**5 + 0*p + 2/5*p**3.
p**3*(p + 1)*(p + 2)/5
Let z be 1*5 + (25 - 24). Let c(b) be the second derivative of 0*b**5 + 0 + 1/9*b**4 - 1/3*b**2 - 1/45*b**z + 0*b**3 - 2*b. Factor c(p).
-2*(p - 1)**2*(p + 1)**2/3
Let z be (-2 - -4)*1/(-2). Let b = 6 + z. Factor 19*x**2 - 9*x - 16*x**3 + 0 + b*x**2 + 1.
-(x - 1)*(4*x - 1)**2
Let n be (-1)/(2 + -1) - -2. Let u(m) be the first derivative of 5/3*m**3 - 2/3*m**6 - 8/5*m**5 + 1/2*m**2 - m - 1/4*m**4 - n. Factor u(h).
-(h + 1)**3*(2*h - 1)**2
Factor -1/5*n**2 + 0 - 1/5*n.
-n*(n + 1)/5
Let v(q) be the third derivative of q**6/120 - q**5/20 + q**4/8 - q**3/6 + 2*q**2. Suppose v(c) = 0. Calculate c.
1
Let l(x) be the third derivative of x**8/28 - 4*x**7/15 + 11*x**6/15 - 4*x**5/5 - x**4/6 + 4*x**3/3 + 8*x**2. Factor l(m).
4*(m - 2)*(m - 1)**3*(3*m + 1)
Let r be (0 - -4) + 9 + -10. Determine f, given that -2 + 3*f**r - 2*f**3 - 2*f**3 + f + 2*f**2 = 0.
-1, 1, 2
Let h(c) be the third derivative of -c**8/2352 + c**7/490 - c**6/840 - c**5/140 + c**4/84 + 5*c**2. Determine i, given that h(i) = 0.
-1, 0, 1, 2
Determine f, given that -2 + 5*f**2 + 3 - 6*f**2 = 0.
-1, 1
Let i be (-3)/(-36)*52 + -4. Suppose -i*k**3 + 1/3*k**2 + 0 + 1/3*k**5 - 1/3*k**4 + 0*k = 0. What is k?
-1, 0, 1
Suppose -8 = 2*i - 4*i. Let 4*w**4 - 2*w**5 + w**2 + w**5 + w**3 - i*w**3 - w**4 = 0. Calculate w.
0, 1
Let b(r) = -2*r**5 + 4*r**4 + 2*r**3 + 4*r + 4. Let h(v) = v**5 - 3*v**4 - v**3 - 3*v - 3. Let s = 5 + -9. Let n(t) = s*h(t) - 3*b(t). Factor n(c).
2*c**3*(c - 1)*(c + 1)
Factor -13 - 38 - 1820*u**2 + 3 + 676*u**3 - 608*u.
4*(u - 3)*(13*u + 2)**2
Factor 4/3*j - 1/3*j**2 - 1.
-(j - 3)*(j - 1)/3
Solve -36/11*v**2 - 2/11*v**4 - 14/11*v**3 - 16/11 - 40/11*v = 0 for v.
-2, -1
Let t(y) be the first derivative of -9*y**4/16 - 5*y**3/2 - 9*y**2/8 - 11. Find v such that t(v) = 0.
-3, -1/3, 0
Let l(m) be the second derivative of m**5/10 - 7*m**4/6 + 16*m**3/3 - 12*m**2 - 35*m. Factor l(b).
2*(b - 3)*(b - 2)**2
Let x(s) = 12*s**5 - 51*s**4 + 60*s**3 - 36*s**2 + s - 7. Let q(k) = 6*k**5 - 26*k**4 + 30*k**3 - 18*k**2 - 4. Let l(j) = 7*q(j) - 4*x(j). Factor l(a).
-2*a*(a - 1)**3*(3*a - 2)
Let r(b) be the first derivative of b**3/6 - 3*b**2/2 + 9*b/2 - 3. Find a, given that r(a) = 0.
3
Let d(y) = -11*y**2 - 4*y - 5. Let z(h) = h**2 - h. Let x(w) = -d(w) - 6*z(w). Factor x(c).
5*(c + 1)**2
Factor 0 - 30/7*r**2 - 2/7*r**4 + 18/7*r + 2*r**3.
-2*r*(r - 3)**2*(r - 1)/7
Let j = -216 + 411/2. Let p = -39/4 - j. Determine r so that p*r**2 + 0*r - 3/4 = 0.
-1, 1
Let c(w) be the first derivative of 5*w**4/4 + 20*w**3/3 + 25*w**2/2 + 10*w - 1. Factor c(h).
5*(h + 1)**2*(h + 2)
Let p(b) be the second derivative of -b**4/36 - b**3/9 - b**2/6 + b. Factor p(g).
-(g + 1)**2/3
Determine l, given that 7/3*l + 5/6*l**2 - 1/2 = 0.
-3, 1/5
Suppose -4 = w - 6. Factor 27*r + 81*r**3 + 81*r**w - 5 + 2 + 6.
3*(3*r + 1)**3
Let q**3 + 11*q**2 + 9*q + 3*q**3 + 11*q - 8 - 27*q**2 = 0. What is q?
1, 2
Suppose 5*b - 3*b = 4*i - 12, 2*i = 5*b + 22. Let a(c) be the first derivative of 0*c**3 + 0*c - 1/6*c**4 + 0*c**2 - 2/15*c**5 - 1/36*c**6 + i. Factor a(q).
-q**3*(q + 2)**2/6
Let z(q) be the first derivative of -q**4/60 + 2*q**3/15 - 2*q**2/5 - 2*q - 1. Let i(v) be the first derivative of z(v). Factor i(k).
-(k - 2)**2/5
Let x be ((-9)/(-6))/(12/16). Determine u so that 3*u - 71*u**x - 3*u**3 + 71*u**2 = 0.
-1, 0, 1
Suppose -k + 3*k = 0. Determine o so that k - 2/3*o**2 + 1/3*o = 0.
0, 1/2
Let j = 23 + -17. Let h = -11/2 + j. Factor 0 + i - h*i**2.
-i*(i - 2)/2
Factor 966*w**5 - w**2 - 3*w**4 - 967*w**5 + 0*w**4 - 3*w**3.
-w**2*(w + 1)**3
Let s(v) be the third derivative of 0*v + 0*v**4 - 8*v**2 - 1/2*v**3 + 0 + 1/20*v**5. Factor s(g).
3*(g - 1)*(g + 1)
What is m in 95*m**2 + 3*m**4 - 205*m**2 + 101*m**2 - 6*m = 0?
-1, 0, 2
Let v(z) be the third derivative of -z**6/24 + z**5/6 + 5*z**4/24 - 5*z**3/3 + 4*z**2. What is y in v(y) = 0?
-1, 1, 2
Let x = 1489/5 + -297. Factor 12/5*s**3 - x*s**4 - 1/5 - 13/5*s**2 + 6/5*s.
-(s - 1)**2*(2*s - 1)**2/5
Let a(t) = 3*t**5 + 14*t**4 + 14*t**3 + 8*t**2 + 5*t - 5. Let q(b) = b**4 + b**3 + b**2 + b - 1. Let v(u) = a(u) - 5*q(u). Let v(y) = 0. What is y?
-1, 0
Factor 9*h - 9*h - 4*h**2 + 4*h.
-4*h*(h - 1)
Suppose 3*x = 5*x - 24. Suppose 3*h - x = -2*u - 2*u, h = 0. Let -5/3*v**4 + 2/3 - 3*v**2 + 13/3*v**u - 1/3*v = 0. Calculate v.
-2/5, 1
Suppose -4*o - 12 = -5*g, -35 = -4*o - 5*g - 7. Let j(f) be the first derivative of 2/3*f**3 + 1 + 0*f - 2*f**o. Factor j(w).
2*w*(w - 2)
Let a = -199 + 199. Factor 0*t**2 + 0*t**3 + 1/5*t**4 + a*t + 0.
t**4/5
Let g = 5 + -5. Let h(n) = -n**2 + 3. Let i be h(g). Find r, given that -2/3*r + 0 - 2/3*r**2 + 2/3*r**i + 2/3*r**4 = 0.
-1, 0, 1
Let w(n) be the first derivative of 0*n - 2/3*n**3 + 1/2*n**4 + 4/5*n**5 + 0*n**2 - 6. Factor w(g).
2*g**2*(g + 1)*(2*g - 1)
Let n be 18/6*(16/(-6))/(-4). Let p(y) be the third derivative of -4*y**n - 2/3*y**3 - 1/12*y**4 + 1/30*y**5 + 0*y + 0. Factor p(z).
2*(z - 2)*(z + 1)
Let i(r) be the third derivative of 1/420*r**6 - 1/42*r**4 + 1/210*r**5 + 4*r**2 + 0*r + 0*r**3 + 0. Solve i(u) = 0 for u.
-2, 0, 1
Let f(z) be the second derivative of -z**4/6 + z**3/3 - z + 12. Factor f(l).
-2*l*(l - 1)
Let m be (-88)/(-672) - 4/(-14). Let n = 1/3 + m. Determine p so that n*p + 1/4 + 1/2*p**2 - 3/4*p**4 - 1/4*p**5 - 1/2*p**3 = 0.
-1, 1
Let r(i) be the third derivative of -i**5/120 + i**4/16 - i**3/6 + 17*i**2. Factor r(s).
-(s - 2)*(s - 1)/2
Let b(q) be the first derivative of q**3/3 - 2*q**2 + 34. Factor b(a).
a*(a - 4)
Factor 81/4*m**4 - 40*m + 4 - 90*m**3 + 118*m**2.
(m - 2)**2*(9*m - 2)**2/4
Let k be -2*(-50)/(-16)*4. Let l be (-45)/k - (2 - 1). Let -2/5*x**2 - 2/5 + l*x = 0. Calculate x.
1
Let z(b) be the third derivative of -b**8/10080 + b**4/12 - 2*b**2. Let a(o) be the second derivative of z(o). Let a(t) = 0. What is t?
0
Let z(w) = 2*w**2 - 7*w - 1. Let l be z(5). Let m be (7/l)/((-3)/(-2)). Factor -m*o**2 - o - 2/3.
-(o + 1)*(o + 2)/3
Let h be (-9)/15 + 36/(-15). Let r be -6 - -2 - 13/h. Solve r*i**3 - 1/3*i - 2/3*i**2 + 2/3 = 0.
-1, 1, 2
Let b(f) be the third derivative of -2*f**7/105 - f**6/30 + f**5/15 + f**4/6 + 14*f**2. Factor b(a).
-4*a*(a - 1)*(a + 1)**2
Factor -8*j**3 - 21*j**4 - 27*j**2 + 51*j**3 - 18*j**4 + 6*j**5 + 29*j**3.
3*j**2*(j - 3)**2*(2*j - 1)
Let b(a) be the third derivative of -5/3*a**6 + 2*a**2 - 4/3*a**3 + 0 + 0*a + 11/6*a**5 + 1/3*a**4. Determine p so that b(p) = 0.
-1/4, 2/5
Let r = 0 - -2. Let q = 5 - r. Factor -2 - 14*t + 3*t**3 - 15*t**2 - 15*t**2 - 21*t**q.
-2*(t + 1)*(3*t + 1)**2
Let s(c) = -c**3 - 6*c**2 - 2*c - 8. Let a = 7 - 13. Let y be s(a). Determine o, given that -y*o**3 - 4 + 6*o**3 + 10*o**2 - 2*o - 6*o**4 + 0 = 0.
-1, -2/3, 1
Factor 3*q**5 - 142*q - 24 - 20*q**2 + 87*q**3 + 0*q**5 + 232*q - 109*q**2 - 27*q**4.
3*(q - 4)*(q - 2)*(q - 1)**3
Let h(u) be the second derivative of 1/3*u**3 - 1/63*u**7 - 1/15*u**6 - 3*u + 0 + 1/3*u**2 - 1/15*u**5 + 1/9*u**4. Factor h(g).
-2*(g - 1)*(g + 1)**4/3
Let p(m) be the first derivative of -2*m**5/25 + m**4/10 + 2*m**3/5 - m**2/5 - 4*m/5 + 15. Let p(q) = 0. Calculate q.
-1, 1, 2
Let z be 2/4 + 1 - 1. Le