et s(k) be the second derivative of 0 + 1/3*k**4 + 0*k**2 + 1/6*k**3 - c*k + 3/20*k**5. Factor s(w).
w*(w + 1)*(3*w + 1)
Let x(q) be the second derivative of -2*q**7/21 + 4*q**5/5 - 2*q**4/3 - 2*q**3 + 4*q**2 - 7*q. Let x(z) = 0. What is z?
-2, -1, 1
Factor -2*d + 2 + d**2 + 0 - 7 - 2*d.
(d - 5)*(d + 1)
Let t(a) be the first derivative of 2*a**5/5 - a**4 + 2*a**2 - 2*a - 3. Factor t(s).
2*(s - 1)**3*(s + 1)
Let v be ((-2)/12)/(15/(-2)). Let h(s) be the second derivative of -v*s**6 + 0*s**2 + 0*s**3 + 2*s - 1/10*s**5 + 0 - 1/9*s**4. Solve h(k) = 0 for k.
-2, -1, 0
Factor -31*g**3 - 30*g**3 - 4 + 3*g**2 + 62*g**3.
(g - 1)*(g + 2)**2
Suppose p = -3 + 5. Factor -3*m**p + 2 + 4 - 1 - 2.
-3*(m - 1)*(m + 1)
Determine m, given that 1/2*m**3 - 4*m**2 + 0 + 8*m = 0.
0, 4
Let r + 4*r**3 - 13*r - 2*r - 2*r = 0. What is r?
-2, 0, 2
Let g = -235/4 - -59. Suppose -4*u - 16 = -2*f, -1 = 5*f + 2*u + 7. Suppose 1/4*y**2 - 1/4*y**5 + f*y - g*y**4 + 0 + 1/4*y**3 = 0. What is y?
-1, 0, 1
Factor -2 + 6*k**2 + 1 + 380*k + 7 - 395*k.
3*(k - 2)*(2*k - 1)
What is o in 10/3*o**2 + 0*o + 10/3*o**3 + 0 + 5/6*o**4 = 0?
-2, 0
Let d(r) be the second derivative of r**7/49 + r**6/15 + 3*r**5/70 - r**4/14 - 2*r**3/21 - 17*r. Find l, given that d(l) = 0.
-1, 0, 2/3
Let q(k) = 394*k**2 - 180*k + 20. Let r(z) = -79*z**2 + 36*z - 4. Let v(b) = -6*q(b) - 33*r(b). Factor v(l).
3*(9*l - 2)**2
Factor -x**4 - 2*x**4 + x**4 + 11*x**3 - 9*x**3.
-2*x**3*(x - 1)
Let d be (-44)/(-12) + (-8)/12. Let z(r) be the first derivative of 0*r - 2/35*r**5 - 8/7*r**2 - 3/7*r**4 + d - 8/7*r**3. Factor z(c).
-2*c*(c + 2)**3/7
Let n(b) be the first derivative of 0*b + 0*b**2 + 1 + 2/15*b**3. Factor n(i).
2*i**2/5
Let o(s) = -s**3 - s**2. Let a(n) be the second derivative of -n**5/10 - n**4/12 + n**3/6 + 2*n. Let i(z) = 2*a(z) - 3*o(z). Find t such that i(t) = 0.
-1, 0, 2
Let u(d) be the second derivative of -7*d**6/30 - 9*d**5/20 + 5*d**4/12 + 3*d**3/2 + d**2 - 3*d. Solve u(x) = 0 for x.
-1, -2/7, 1
Let s(a) be the third derivative of 1/504*a**8 + 1/90*a**5 + 1/60*a**6 + 3*a**2 + 0*a**4 + 1/105*a**7 + 0*a + 0 + 0*a**3. Solve s(p) = 0 for p.
-1, 0
Let r(y) = 12*y + 146. Let w be r(-12). Let n be ((-2)/10)/((-6)/10). Let n*o - 1/6 - 1/6*o**w = 0. Calculate o.
1
Let w(y) be the first derivative of -5*y**6/12 + 5*y**5/2 - 45*y**4/8 + 35*y**3/6 - 5*y**2/2 + 8. Factor w(p).
-5*p*(p - 2)*(p - 1)**3/2
Let f(n) = 4*n**2 + 24*n + 12. Let j(x) = 3*x**2 + 16*x + 8. Let a(q) = 5*f(q) - 8*j(q). Factor a(r).
-4*(r + 1)**2
Let n(o) be the first derivative of o**9/4536 + o**8/1260 - o**6/270 - o**5/180 - 2*o**3/3 + 1. Let l(t) be the third derivative of n(t). What is i in l(i) = 0?
-1, 0, 1
Let q(o) be the third derivative of 0 - 1/16*o**4 + 0*o**3 + 2*o**2 + 1/20*o**5 + 0*o - 1/80*o**6. Factor q(m).
-3*m*(m - 1)**2/2
Let i(v) be the second derivative of -v**6/60 + v**4/12 - v**2/4 + 17*v. Factor i(a).
-(a - 1)**2*(a + 1)**2/2
Let b be (-365)/60 - -2*1. Let w = b + 19/4. Factor -w*r**3 + 8/3*r**4 - 4/3*r**2 + 0*r + 0 + 2*r**5.
2*r**2*(r + 1)**2*(3*r - 2)/3
Let u(g) = -g + 4. Let w be u(-4). Let s be 7/4 + 2/w. Suppose -1/2*q**3 + 1/2 - 7/4*q + s*q**2 + 1/4*q**5 - 1/2*q**4 = 0. Calculate q.
-2, 1
Let m(j) be the first derivative of -2/9*j + 2 - 1/18*j**4 + 2/27*j**3 + 1/9*j**2. Factor m(w).
-2*(w - 1)**2*(w + 1)/9
Let f = -5 - -8. Find i such that -f*i**3 + 2*i**3 + i**2 + 8*i + 3*i**3 - 9*i**2 = 0.
0, 2
Find o, given that 0 - 2/5*o**3 - 2/5*o + 4/5*o**2 = 0.
0, 1
Let w = 79 - 11. Suppose 0 = 2*z + j - 50, 0*j - 4 = j. Factor z*y**2 + w*y**3 - 4*y - 47*y**3 + 10*y.
3*y*(y + 1)*(7*y + 2)
Find d such that 582 + 3*d - 3*d**2 - 582 = 0.
0, 1
Factor -15*g - 15*g**2 - 13*g - 26*g + 13 + 11.
-3*(g + 4)*(5*g - 2)
Suppose -4*k - 5*b - 5 = 0, 4*b = 2*b - 2. Suppose 0*g + 0 + 4/7*g**3 - 4/7*g**4 + k*g**2 = 0. Calculate g.
0, 1
Let a(k) be the second derivative of 1/50*k**5 + 0 + 0*k**3 + 0*k**2 + 1/30*k**4 - k. Factor a(v).
2*v**2*(v + 1)/5
Let y(v) be the first derivative of 16/25*v**5 + 2/5*v**4 + 17/10*v**2 - 2/5*v - 13/5*v**3 + 2. Factor y(z).
(z - 1)*(z + 2)*(4*z - 1)**2/5
Let q(l) be the third derivative of l**6/24 - 5*l**4/2 + 40*l**3/3 + 15*l**2. Find u such that q(u) = 0.
-4, 2
Let f = -80 + 562/7. Let u = f + 3/14. Determine s so that -1/4*s**5 - 1/4 - 1/4*s + u*s**2 - 1/4*s**4 + 1/2*s**3 = 0.
-1, 1
Let p be -1 - (1 - (-25)/1). Let q be -2 + (0 - p/12). Solve 1/2*b - 1/4*b**2 - q = 0 for b.
1
Suppose -3*j - 5*y - 13 = 0, 0 = j + y + 2*y + 11. Let x = -5 + 9. Factor -4*q + 2 - 2*q**4 + 4*q**3 + q**j - q**x.
-2*(q - 1)**3*(q + 1)
Let m(r) be the second derivative of r**6/240 + 3*r**5/160 + r**4/48 - 11*r. Suppose m(l) = 0. What is l?
-2, -1, 0
Let m = 498/5 - 99. Solve 3/5*i**2 + 0*i - m = 0.
-1, 1
Suppose -3*x = -r - 10, r + 24 = 4*x - 3*r. Factor -n**3 + 13*n**2 - 12*n**x + 0*n**3.
-n**2*(n - 1)
Let j(n) be the second derivative of n**9/15120 + n**8/4480 - n**6/1440 - n**4/6 - n. Let b(v) be the third derivative of j(v). Let b(a) = 0. Calculate a.
-1, 0, 1/2
Let n be 14/10*11/(-462)*-12. Suppose -2/5*b**3 + 0 + 2/5*b**2 - n*b**4 + 2/5*b = 0. What is b?
-1, 0, 1
Let j(t) be the second derivative of 0*t**3 + 0 - 2*t + 1/20*t**5 + 1/15*t**6 - 1/42*t**7 + 0*t**2 - 1/6*t**4. Solve j(x) = 0.
-1, 0, 1, 2
Let a be 4/(-30) + 726/45. Let x be (-42)/(-12)*a/28. What is j in -2/3*j**x + 2/3*j**5 + 2/3*j**4 + 0*j + 0 - 2/3*j**3 = 0?
-1, 0, 1
Let c(m) be the third derivative of 0*m + 1/735*m**7 + 0 - 1/42*m**4 - 1/21*m**3 + m**2 + 0*m**5 + 1/210*m**6. Factor c(k).
2*(k - 1)*(k + 1)**3/7
Let q = 25 + -25. Let l be (-46)/18 + q + 3. What is h in l*h**2 - 2/9*h + 0 - 2/9*h**3 = 0?
0, 1
Let c(t) be the first derivative of -1/4*t**4 + 2*t + 5/2*t**2 + t**3 - 2 - 1/5*t**5. Solve c(b) = 0 for b.
-1, 2
Let g be (-84)/(-56) - 3/4. Factor -g*c**2 + 3/4*c**3 - 1/4*c**4 + 0 + 1/4*c.
-c*(c - 1)**3/4
Let a be (-1 - (25/(-6) - -3))/5. Let o(p) be the second derivative of 2*p + 1/6*p**4 + 0*p**5 + 0 + 0*p**3 - 1/2*p**2 - a*p**6. Factor o(l).
-(l - 1)**2*(l + 1)**2
Let y(p) be the third derivative of 0*p**4 - 1/112*p**8 + 0*p + 0 + 0*p**3 - 1/10*p**6 + 2/35*p**7 - 4*p**2 + 0*p**5. Factor y(s).
-3*s**3*(s - 2)**2
Let d(j) = -j**5 - j**4 + j**2 - j. Let n(c) = 4*c**5 - 20*c**3 - 8*c. Let u(b) = 12*d(b) - n(b). Solve u(o) = 0 for o.
-1, 0, 1/4, 1
Determine u, given that -3/2*u**3 + 0 + 0*u - 3/4*u**4 - 3/4*u**2 = 0.
-1, 0
Let h = 15 + -10. Factor v**4 - 2*v**h - 5*v**4 - 44*v + 12 + 6*v**5 + 56*v**2 - 24*v**3.
4*(v - 1)**4*(v + 3)
Let i(j) = -j**2 - 4*j + 2. Let l be i(-4). Determine f, given that -f - 2*f**2 + l*f**5 + 2*f**4 - f**5 - 3*f + 3*f = 0.
-1, 0, 1
Let r(c) = -c - 7. Let f be r(-9). Let o be (-12)/(-5) - 1*f. Determine b so that 2*b**3 - 2/5*b + 4/5*b**4 - o + 6/5*b**2 = 0.
-1, 1/2
Determine r, given that 0*r + 0 - 4/9*r**3 - 2/9*r**4 + 0*r**2 = 0.
-2, 0
Let -6*i**2 - 3/2 + 6*i = 0. What is i?
1/2
Suppose 5*x = -0*x + 20. Suppose -x*v = v - 10. Find c such that c**3 - 1/2*c + 0 + 0*c**v + 0*c**4 - 1/2*c**5 = 0.
-1, 0, 1
Let j(x) be the second derivative of x**7/21 - 2*x**6/15 + 3*x. Factor j(a).
2*a**4*(a - 2)
Suppose -12 + 1 - 6*j - 2*j**3 - 6*j**2 + 9 = 0. What is j?
-1
Factor -312*y**2 - 34*y**4 - 8*y**5 + 0*y**5 - 53*y - 19*y - 70*y**4 - 386*y**3.
-2*y*(y + 6)**2*(2*y + 1)**2
Let r = -1 - -1. Suppose j + j = r. Solve 1/2*d**2 + j*d + 0 + 2*d**3 = 0.
-1/4, 0
Let i = -370 - -373. Factor -4*d**2 - 8/3*d - 2/3*d**4 - 2/3 - 8/3*d**i.
-2*(d + 1)**4/3
Solve -4/3*x - 14/9 + 2/9*x**2 = 0 for x.
-1, 7
Let o(s) be the third derivative of s**6/180 + 2*s**5/45 + 5*s**4/36 + 2*s**3/9 + 2*s**2. Factor o(t).
2*(t + 1)**2*(t + 2)/3
Let m(t) be the second derivative of t**4/78 - t**3/13 + 2*t**2/13 + 9*t. Find w such that m(w) = 0.
1, 2
Let w(r) be the first derivative of -r**6/45 - r**5/30 + 2*r + 2. Let b(s) be the first derivative of w(s). Factor b(q).
-2*q**3*(q + 1)/3
Let u be (-20)/(-30) + (-5)/3 + 1. Let g be (5/45)/((-2)/(-6)). Factor 1/3 + u*y - g*y**2.
-(y - 1)*(y + 1)/3
Let h be 8/(-6)*(-15)/(-10). Let k be (-32)/3*h/8. Factor k*l**2 + 0 + 2/3*l + 8/3*l**3.
2*l*(2*l + 1)**2/3
Let r(v) be the third derivative of 1/300*v**5 - 1/600*v**6 + 1/120*v**4 + 0*v - 4*v**2 - 1/30*v**3 + 0. Factor r(i).
-(i - 1)**2*(i + 1)/5
Let a(z) be the first derivativ