0*l + 1/6*l**4. Solve r(v) = 0.
0, 1
Let q = 88 + -88. Factor 2/3*h - 2/3*h**3 + q + 0*h**2.
-2*h*(h - 1)*(h + 1)/3
Let t(g) = 3*g**2 + 63*g - 33. Let q(d) = d**2 + 16*d - 8. Suppose -2*b + 28 = -2. Let i(x) = b*q(x) - 4*t(x). Factor i(r).
3*(r - 2)**2
Let y(n) be the third derivative of 5*n**8/504 + 8*n**7/315 + n**6/180 - n**5/45 - 5*n**2. Suppose y(k) = 0. What is k?
-1, 0, 2/5
Let q(y) be the third derivative of -y**7/350 + 3*y**6/200 - 3*y**5/100 + y**4/40 + 6*y**2. Factor q(m).
-3*m*(m - 1)**3/5
Let a(j) be the second derivative of 8*j**2 + 2/15*j**6 + 0 - 2*j - j**4 - 2/5*j**5 + 8/3*j**3. Suppose a(k) = 0. Calculate k.
-1, 2
Let l(o) = 3*o. Let w be l(1). Let d = -19 - -77/4. What is x in -d - 1/4*x**w - 3/4*x - 3/4*x**2 = 0?
-1
Suppose 0 = 4*y - 9*y + 40. Let v(s) = s - 5. Let x be v(y). Factor -x*o**2 - 3*o**2 + 5*o**2 + o**3.
o**2*(o - 1)
Let j(y) = -4*y**3 - 6*y**2 + 2*y + 2. Let q(x) = -5*x**3 - 7*x**2 + 3*x + 3. Let k(l) = 6*j(l) - 4*q(l). Factor k(o).
-4*o**2*(o + 2)
Let p be (-1)/6 - 10956/(-27). Let d = -809/2 + p. Factor -2/9 + 4/3*b - d*b**2.
-2*(b - 1)*(5*b - 1)/9
Let y(h) be the first derivative of 1/5*h**5 + 0*h + 0*h**2 + 0*h**3 + 2 + 1/4*h**4. Factor y(c).
c**3*(c + 1)
Suppose 4/9*t**3 - 2/9*t**4 + 0 - 4/9*t + 2/9*t**2 = 0. Calculate t.
-1, 0, 1, 2
Let t(m) be the third derivative of m**5/40 - m**4/4 + 3*m**3/4 + 18*m**2. Let t(x) = 0. Calculate x.
1, 3
Factor 0*f**3 + 11*f**2 + 256 + 192*f + 4*f**3 + 37*f**2.
4*(f + 4)**3
Let v(k) = -k**2 - k - 1. Let q(y) = 5*y**2 + y + 4. Let m(h) = 16*h**2 + 2*h + 13. Let l(n) = 6*m(n) - 21*q(n). Let g(p) = 3*l(p) - 24*v(p). Factor g(t).
-3*(t - 1)*(t + 2)
Let z(d) be the third derivative of d**6/300 + 2*d**5/15 + 37*d**4/60 + 6*d**3/5 - 41*d**2. Suppose z(u) = 0. What is u?
-18, -1
Let i be (-64)/120*(-9)/4. Factor 2/5*w**3 + 6/5*w - i*w**2 - 2/5.
2*(w - 1)**3/5
Let o(y) be the second derivative of -y**5/50 + y**3/5 + 2*y**2/5 + 4*y. What is t in o(t) = 0?
-1, 2
Let p be (-6)/(-21) - (-24)/14. Factor 4*k**2 + 3*k**2 - 7*k**p - 2 - 2*k**2 - 4*k.
-2*(k + 1)**2
Let w = 1 - -1. Factor 2*g**2 + 0*g**2 - 2*g - w - 2.
2*(g - 2)*(g + 1)
Suppose 2*m - 11 = 5*f, -m - 4*m = -2*f - 17. Suppose -v - 4*w - m = -2, -5*w - 2 = v. Factor 2/3*d**v + 0 + 2/3*d - 4/3*d**2.
2*d*(d - 1)**2/3
Let c(j) = -6*j**2 + 8*j - 18. Let o(x) = -13*x**2 + 15*x - 36. Let n(p) = 9*c(p) - 4*o(p). Suppose n(h) = 0. Calculate h.
3
Factor -5*i - 5*i**5 - 5*i**2 + 5 + 3*i**4 + 2*i**4 + 4*i**2 - 9*i**2 + 10*i**3.
-5*(i - 1)**3*(i + 1)**2
Let w(q) be the second derivative of -q**6/120 + 7*q**5/80 + q**4/6 - 46*q. Factor w(y).
-y**2*(y - 8)*(y + 1)/4
Factor 2/7*l**3 + 0 - 2/7*l**2 - 4/7*l.
2*l*(l - 2)*(l + 1)/7
Let f(g) be the first derivative of -g**5/20 + g**4/16 + g**3/12 - g**2/8 - 15. Factor f(p).
-p*(p - 1)**2*(p + 1)/4
Solve 1/3*b**3 + 2/3 + 1/3*b**4 - 1/3*b - b**2 = 0.
-2, -1, 1
Let w(s) = -s + 9. Let x(t) = t**2 + 7*t + 12. Let f be x(-6). Let i be w(f). Suppose -72/5*p - 252/5*p**i - 8/5 - 98/5*p**4 - 218/5*p**2 = 0. What is p?
-1, -2/7
Suppose -69 + 81 = 4*h. Let m(v) be the second derivative of 1/24*v**4 + 0 + 3*v + v**2 - 1/3*v**h. Determine d so that m(d) = 0.
2
Let y(a) be the second derivative of a**7/1400 - a**6/600 - a**5/200 + a**4/40 - a**3/6 + 2*a. Let f(m) be the second derivative of y(m). Factor f(d).
3*(d - 1)**2*(d + 1)/5
Let u(i) be the second derivative of i**6/150 + i**5/25 + i**4/30 - 2*i**3/15 - 3*i**2/10 + 4*i. Solve u(r) = 0 for r.
-3, -1, 1
Let a(b) be the second derivative of b**5/50 + b**4/30 + 14*b. Factor a(k).
2*k**2*(k + 1)/5
Factor -7 + 3 + 3*a + 5*a - 4*a**2 + 0*a**2.
-4*(a - 1)**2
Let l(o) = -2*o**3 - o**2 + 1. Let i be l(-1). Let j(a) be the second derivative of 0 - 2/9*a**i + 1/27*a**3 + 1/54*a**4 + a. Factor j(k).
2*(k - 1)*(k + 2)/9
Let x(d) be the first derivative of -d**8/6720 - d**7/840 - d**6/288 - d**5/240 - d**3 - 1. Let j(p) be the third derivative of x(p). Factor j(u).
-u*(u + 1)**2*(u + 2)/4
Let r(h) be the first derivative of h**4/22 + 4*h**3/33 + h**2/11 - 6. Find z such that r(z) = 0.
-1, 0
Factor -2/5*h**2 + 0 - 1/5*h**3 - 1/5*h.
-h*(h + 1)**2/5
Let f(x) = -23*x**3 - 11*x**2 + 18*x + 6. Let r(u) = 12*u**3 + 6*u**2 - 9*u - 3. Let t(d) = -3*f(d) - 5*r(d). Factor t(z).
3*(z - 1)*(z + 1)*(3*z + 1)
Let o = -8 + 10. Let q be (o/(-27))/(11/(-33)). Factor 2/9 + 0*y - q*y**2.
-2*(y - 1)*(y + 1)/9
Let f = 4 - -3. Solve f*a**3 + 2*a**3 - a**4 - 8*a**3 = 0 for a.
0, 1
Let q = -31 - -33. Let u be ((-4)/(-6))/(q/1). Factor 7/6*v**2 + 1/3*v - u*v**3 - 7/6*v**4 + 0.
-v*(v - 1)*(v + 1)*(7*v + 2)/6
Let y(s) be the first derivative of s**6/21 + 4*s**5/35 + s**4/14 - 6. Factor y(l).
2*l**3*(l + 1)**2/7
Let k(n) = 2*n**3 + 12*n**2 - n - 1. Let a be k(-6). Let -1/2*v**3 + 0*v**2 + 1/2*v**a + 0 + 0*v**4 + 0*v = 0. What is v?
-1, 0, 1
Let w(n) be the third derivative of n**5/270 - n**4/54 + n**3/27 + 3*n**2. Factor w(v).
2*(v - 1)**2/9
Factor 3/4 + 1/4*o**2 + o.
(o + 1)*(o + 3)/4
Let b(u) be the third derivative of u**6/780 - u**5/130 + u**4/78 - 26*u**2. Factor b(d).
2*d*(d - 2)*(d - 1)/13
Suppose 0 = -4*o + z + 7, -o + 7 = 2*o + z. Find n, given that 0*n**o + 2*n**3 - 3*n**2 + 3*n**2 + 2*n**2 = 0.
-1, 0
Let l(k) = 3*k**3 + 3*k**2 - 6*k - 9. Let s(p) = p + 5. Let j be s(4). Let f(g) = -g**2 - 7 + g**3 + 3 - 3*g + 3*g**2. Let u(o) = j*f(o) - 4*l(o). Factor u(z).
-3*z*(z - 1)**2
Let r(x) be the first derivative of -8/9*x**3 - 4/3*x + 4/5*x**5 - 2*x**2 + 2/9*x**6 - 1 + 2/3*x**4. Factor r(z).
4*(z - 1)*(z + 1)**4/3
Let z be (45/(-4))/(-5)*8. Suppose -4*x = -x - z. What is h in -x*h + 2*h**2 - 2 + 6*h = 0?
-1, 1
Factor -h + 6/5 - 1/5*h**2.
-(h - 1)*(h + 6)/5
Let b be (0 - 3) + 3/3. Let a be (2/6)/(b/(-12)). Factor 1/2 + t**a - 1/4*t**3 - 5/4*t.
-(t - 2)*(t - 1)**2/4
Let a be 2/((5 - 8) + 7). Find o, given that 2*o**3 + 3*o**2 + 1/2 + a*o**4 + 2*o = 0.
-1
Let k(v) be the third derivative of v**5/300 + 6*v**2. Let k(w) = 0. Calculate w.
0
Let w = -54/23 + 670/207. Factor 4/3*n**2 + 8/9*n + 2/9 + 2/9*n**4 + w*n**3.
2*(n + 1)**4/9
Let -2*t**3 + 3/2*t**2 + 0*t + 3/4*t**4 - 1/4 = 0. Calculate t.
-1/3, 1
Factor -2 - 10*r**3 - 6*r**3 - 48*r**2 - 17*r + 8*r**2.
-(r + 2)*(4*r + 1)**2
What is l in -5*l**2 + 17*l**2 - 4*l**4 - 2*l - l - 5*l = 0?
-2, 0, 1
Let n(c) be the third derivative of 7/180*c**5 + 0*c + 1/1008*c**8 - 3*c**2 + 1/40*c**6 + 1/36*c**4 + 1/126*c**7 + 0*c**3 + 0. Factor n(k).
k*(k + 1)**3*(k + 2)/3
Suppose -1 + v - 1/4*v**4 - 1/2*v**3 + 3/4*v**2 = 0. Calculate v.
-2, 1
Let j(g) = g**2 + 1. Let x(t) = 3*t**2 - 10*t + 5. Let p(i) = -5*j(i) + x(i). Factor p(u).
-2*u*(u + 5)
Suppose 2*l + 0 = 4. Suppose x - 15 = -l*x. Let x*c**3 + c**2 - 2*c**2 - c**2 + 2*c**3 = 0. What is c?
0, 2/7
Let y(j) be the second derivative of -5*j**4/12 + 5*j**3 - 45*j**2/2 - 35*j. Solve y(u) = 0 for u.
3
Let b(z) be the first derivative of -2/5*z**5 + 0*z**4 + 0*z - 1 + 1/6*z**6 + 2/3*z**3 - 1/2*z**2. Find f, given that b(f) = 0.
-1, 0, 1
Let v(t) be the second derivative of -t**4/78 + 8*t**3/13 - 144*t**2/13 - 38*t. Factor v(m).
-2*(m - 12)**2/13
Let w(v) be the third derivative of 0 + 0*v**3 - 1/120*v**6 + 0*v + 1/336*v**8 + 0*v**5 + 0*v**7 + 0*v**4 - v**2. Find f, given that w(f) = 0.
-1, 0, 1
Let a(r) be the first derivative of r**3/3 - r**2 + r + 43. Determine j so that a(j) = 0.
1
Let z(i) be the second derivative of -i**5/5 + i**4/3 + 6*i**3 - 18*i**2 + 36*i. Find r such that z(r) = 0.
-3, 1, 3
Let x(k) be the first derivative of -k**6/30 - k**5/20 + k**4/12 + k**3/6 - 3*k - 1. Let m(s) be the first derivative of x(s). Factor m(n).
-n*(n - 1)*(n + 1)**2
Let y(p) be the third derivative of -p**6/720 - p**5/120 + p**3/2 + 9*p**2. Let x(b) be the first derivative of y(b). Factor x(u).
-u*(u + 2)/2
Suppose 0*x + 0 + 1/2*x**2 = 0. What is x?
0
Let w(a) = 5*a**4 - 2*a**3 + 15*a**2 + a. Let g(i) = 2*i**4 - i**3 + 7*i**2 + i. Let k(x) = -7*g(x) + 3*w(x). Factor k(n).
n*(n - 2)*(n + 1)*(n + 2)
Factor -16*c - 15*c**2 - 3 + 11*c**2 - 9.
-4*(c + 1)*(c + 3)
Let j(t) be the second derivative of -t**4/36 + t**2/6 - 4*t. Factor j(f).
-(f - 1)*(f + 1)/3
Suppose 3*b = 5*b - 14. Let v be b/(-2)*8/(-70). Suppose 0 - 2/5*s**5 - v*s**2 + 2/5*s**4 + 0*s + 2/5*s**3 = 0. What is s?
-1, 0, 1
Let x(g) = -g**3 + 8*g**2 - 8*g + 7. Let