o**3 + 27*o**2 + 24*o - 41. Let u(a) = -24*j(a) - 5*r(a). Factor u(s).
4*(s - 3)**2*(s - 1)*(s + 1)
Let u be (-28)/(-3)*6/(-4). Let g = u - -43/3. Factor s + g*s**2 - s**3 - 1/3.
-(s - 1)*(s + 1)*(3*s - 1)/3
Suppose -3*q = -p - 5, 3*p = q - 2*p + 17. Let j be q/(-4) + 9/12. Factor j - 27/2*g**3 + 2*g - 6*g**2 + 81/2*g**5 + 27*g**4.
g*(3*g - 1)**2*(3*g + 2)**2/2
Let l(v) be the first derivative of -v**8/504 + v**7/105 - v**6/90 + 4*v**2 + 6. Let n(p) be the second derivative of l(p). Suppose n(a) = 0. What is a?
0, 1, 2
Let y(d) = d**2 + 3*d - 7. Let x be y(-5). Factor 2/3*g**x + 0*g + g**4 + 0 - 1/3*g**2.
g**2*(g + 1)*(3*g - 1)/3
Let m(b) be the third derivative of b**6/1080 + b**5/360 + b**3/6 + 4*b**2. Let d(g) be the first derivative of m(g). Suppose d(p) = 0. What is p?
-1, 0
Let q(h) be the first derivative of -2/15*h**5 + 0*h**2 - 2/9*h**3 - 1/3*h**4 - 5 + 0*h. Determine p so that q(p) = 0.
-1, 0
Determine q so that 4/7*q**2 - 20/7*q + 16/7 = 0.
1, 4
Find h such that -2/3*h**5 + 2/3*h**4 - 2 - 10/3*h + 4/3*h**2 + 4*h**3 = 0.
-1, 1, 3
Let c = 1/1600 - -129/49600. Let w = c - -1233/2170. Determine b, given that 0 - 6*b**3 + 26/7*b**2 - w*b = 0.
0, 2/7, 1/3
Let d = -9/10 - -7/5. Solve -r**2 + 1/4 + d*r**3 + 3/4*r**4 - 1/2*r**5 + 0*r = 0.
-1, -1/2, 1
Let d(y) be the first derivative of 4*y**5/25 - y**4/5 - 4*y**3/15 + 2*y**2/5 + 8. Factor d(i).
4*i*(i - 1)**2*(i + 1)/5
Factor 4*w**2 + 3*w**3 - w**3 - w + 3*w.
2*w*(w + 1)**2
Let m(x) = 3*x - 6. Let q be m(4). Let f be q - (2 - -1) - -1. Determine b so that -1/4*b**f + 1/4*b**3 + 1/4*b**2 + 0 - 1/4*b = 0.
-1, 0, 1
Let d be 0/1*(-7)/21. Factor k**3 - 1/3*k**4 + d + 1/3*k - k**2.
-k*(k - 1)**3/3
Let u(o) be the first derivative of -9/5*o**5 - 9/4*o**4 + 0*o - 1/2*o**6 - o**3 - 5 + 0*o**2. Suppose u(v) = 0. What is v?
-1, 0
Let d(f) be the third derivative of -f**5/80 + 3*f**4/32 - f**2. Determine o, given that d(o) = 0.
0, 3
Let r(i) be the second derivative of -i**8/480 + 3*i**7/560 + i**6/480 - i**5/120 - i**4/6 - 4*i. Let j(o) be the third derivative of r(o). Factor j(g).
-(g - 1)*(4*g - 1)*(7*g + 2)/2
Let o(l) be the first derivative of -4/11*l**4 - 4 - 6/55*l**5 - 4/11*l**3 + 0*l**2 + 2/11*l. Let o(m) = 0. What is m?
-1, 1/3
Suppose -5*x - 3*b - 33 = 6, 2*b = -2*x - 18. Let l = x + 8. Suppose 3/4*c**3 + 0 + 3/4*c**l - 3/2*c = 0. What is c?
-2, 0, 1
Let u(n) be the first derivative of -n**5/80 + n**4/24 + n**3/24 - n**2/4 + 3*n + 6. Let z(o) be the first derivative of u(o). Find t, given that z(t) = 0.
-1, 1, 2
Let x(y) be the second derivative of 3*y + 0 + 0*y**2 + 1/9*y**3 + 11/10*y**5 + 16/63*y**7 + 5/9*y**4 + 8/9*y**6. Determine l so that x(l) = 0.
-1, -1/4, 0
Let x(d) be the second derivative of -d**4/3 + 2*d**3/3 - 7*d. What is a in x(a) = 0?
0, 1
Let n be 33/70 - (-10)/(-25). Let l(v) be the first derivative of 0*v**2 + 1 + 2/21*v**3 + 0*v + n*v**4. Factor l(a).
2*a**2*(a + 1)/7
Let s(o) = -10*o + 9. Let k be s(5). Let g = k + 289/7. Find i such that g*i + 4/7*i**2 + 2/7*i**3 + 0 = 0.
-1, 0
Let n(j) be the first derivative of -2*j - 1 - 21/2*j**3 - 15/2*j**2 - 49/16*j**4. Solve n(m) = 0 for m.
-2, -2/7
Suppose -24*f**4 + 8 + 20*f + 12*f - 16*f**3 + 2*f + 34*f**2 = 0. Calculate f.
-1, -1/2, 4/3
Let y(g) be the first derivative of -4/3*g + 6 - 1/9*g**3 - 5/6*g**2. Factor y(k).
-(k + 1)*(k + 4)/3
Let c = 199 + -511. Let j = c - -1566/5. Suppose -4/5*n**2 - 2/5 + 2/5*n**5 - 6/5*n + j*n**4 + 4/5*n**3 = 0. What is n?
-1, 1
Let l(s) = -s**3 - s**2. Let m be l(0). Factor -8*f - 21*f**2 + m*f - 27*f**4 + 5*f - 26*f**3 - 19*f**3.
-3*f*(f + 1)*(3*f + 1)**2
Let x(j) be the second derivative of -j**6/150 + j**5/50 - j**4/60 + 2*j. Factor x(w).
-w**2*(w - 1)**2/5
Let m(w) be the second derivative of -w**7/1260 - w**6/180 - w**5/60 - 3*w**4/4 + 3*w. Let y(t) be the third derivative of m(t). Factor y(k).
-2*(k + 1)**2
Let n(s) be the second derivative of -s**6/6 + s**5 - 5*s**4/2 + 10*s**3/3 - 5*s**2/2 + 6*s. Determine z, given that n(z) = 0.
1
Suppose 84*k = 81*k. Solve k + 1/3*a**2 + 1/3*a = 0.
-1, 0
Let v(d) be the second derivative of -d**6/420 + d**2/2 - 2*d. Let w(p) be the first derivative of v(p). Determine y, given that w(y) = 0.
0
Let y be 5/(-5) - (-6)/3. Let v be y*130/(-35) - -4. What is z in 4/7*z + v*z**4 - 2/7*z**2 + 0 - 4/7*z**3 = 0?
-1, 0, 1, 2
Suppose 30 = 5*o - 10. Factor -t**4 + 14*t**2 + 0*t**4 - 8 + 7*t**4 - o*t + 20*t**3.
2*(t + 1)**2*(t + 2)*(3*t - 2)
Factor 6 + 24*w**3 - 12*w**2 + 3*w - 7*w**3 - 12*w**2 - 2*w**3.
3*(w - 1)**2*(5*w + 2)
Let o(x) be the third derivative of x**8/84 - 4*x**7/105 - x**6/30 + 2*x**5/15 + 13*x**2. Solve o(d) = 0 for d.
-1, 0, 1, 2
Let i(p) be the second derivative of -1/2*p**2 - 5/48*p**4 - 3*p - 1/3*p**3 - 1/80*p**5 + 0. Solve i(o) = 0.
-2, -1
Factor 2*s**4 + 0 + 0*s + 2/3*s**5 + 0*s**3 - 8/3*s**2.
2*s**2*(s - 1)*(s + 2)**2/3
Let x be 5/(20/68)*-2. Let s = 36 + x. Determine p, given that 2/3*p**s - 4/3*p + 2/3 = 0.
1
Let s(r) be the second derivative of 5*r**7/42 + 4*r**6/3 + 11*r**5/2 + 35*r**4/3 + 85*r**3/6 + 10*r**2 + 11*r - 4. Solve s(c) = 0.
-4, -1
Let v(y) be the first derivative of 2*y**5/25 + 3*y**4/10 - 2*y**3/15 - 3*y**2/5 + 14. Factor v(j).
2*j*(j - 1)*(j + 1)*(j + 3)/5
Let u = 1 - -3. Let p(y) be the first derivative of 0*y**2 + 1/5*y**u - 6/25*y**5 + 3 + 2/15*y**3 + 0*y. Factor p(w).
-2*w**2*(w - 1)*(3*w + 1)/5
Let o(x) be the second derivative of -x**6/240 - 3*x**5/160 + x**4/32 + 11*x**3/48 + 3*x**2/8 + 5*x. Let o(v) = 0. What is v?
-3, -1, 2
Let m(j) be the first derivative of -j**5/50 + j**4/10 - j**3/5 + j**2/5 - 3*j + 4. Let r(a) be the first derivative of m(a). Solve r(d) = 0.
1
Let h(f) be the first derivative of f**6/15 + 5*f + 5. Let t(v) be the first derivative of h(v). Solve t(g) = 0 for g.
0
Let n be (-6)/16*((-52)/12 + 3). Determine o so that n*o**2 + 0 + 1/2*o = 0.
-1, 0
Let k(x) be the first derivative of x**6/120 + x**5/16 + x**4/8 + 4*x**3/3 + 3. Let p(g) be the third derivative of k(g). Determine v, given that p(v) = 0.
-2, -1/2
Let p = -11 + 15. Determine o so that -4*o - 8*o**2 + p*o**5 + 31*o**3 + 8*o**4 - 31*o**3 = 0.
-1, 0, 1
Let 1/6*q + 0 - 2/3*q**2 + 1/6*q**5 + q**3 - 2/3*q**4 = 0. Calculate q.
0, 1
Let q(a) = -a**3 + 2*a**2 - 4*a + 4. Let f(d) = -2*d**3 + 7*d**2 - 11*d + 11. Let r(o) = 4*f(o) - 11*q(o). Find z, given that r(z) = 0.
-2, 0
Let h(d) be the second derivative of d**7/42 + 7*d**6/30 + 19*d**5/20 + 25*d**4/12 + 8*d**3/3 + 2*d**2 + 6*d. Solve h(x) = 0 for x.
-2, -1
Let o = -201/2 - -103. Let m = 33/10 - o. Let -2/5*p**2 + 14/5*p**3 - m + 6/5*p**4 - 14/5*p = 0. Calculate p.
-2, -1, -1/3, 1
Let j = 1 + -1. Suppose -8 = -4*c - j*c. Find s such that -c + s**2 + 6*s**3 - 2*s + 2 = 0.
-2/3, 0, 1/2
Let n(k) be the third derivative of -k**7/420 + k**6/80 - k**5/40 + k**4/48 + 5*k**2. Solve n(h) = 0.
0, 1
Let d(o) = -2*o**5 + 4*o**4 + 3*o**3 - o**2 - 7*o - 3. Let v(a) = -a**5 + a**2 - a - 1. Let n(z) = -d(z) + 3*v(z). What is j in n(j) = 0?
-2, -1, 0, 1
Let q be 19/3 - (9 + (-26)/3). Solve 2 - x**3 + 9/2*x**2 - q*x = 0 for x.
1/2, 2
Let r(n) be the second derivative of n**6/20 + 3*n**5/40 - 3*n**4/8 - n**3/4 + 3*n**2/2 + 8*n. Suppose r(y) = 0. What is y?
-2, -1, 1
Let t(r) be the third derivative of -r**6/24 + 23*r**5/12 - 25*r**4 - 120*r**3 - 24*r**2. Factor t(z).
-5*(z - 12)**2*(z + 1)
Let v(l) = -l**5 + l**4 + l**3 - l**2 + l + 1. Let r(h) = -38*h**4 + 8*h**3 + 38*h**2 - 22*h - 14. Let w(n) = -2*r(n) - 28*v(n). Find q such that w(q) = 0.
-2, -1, 0, 2/7, 1
Determine g so that 0*g**4 - 2*g**4 + 34*g**2 - g**4 - 31*g**2 = 0.
-1, 0, 1
Let j(s) = 3*s - 1. Let c be j(1). Factor -4/5*h - 2/5 - 2/5*h**c.
-2*(h + 1)**2/5
Let l(q) be the second derivative of q**5/4 - 5*q**3/2 + 5*q**2 - 46*q. Factor l(w).
5*(w - 1)**2*(w + 2)
Factor 21 - 6*d - 12 + 2*d**3 - 13.
2*(d - 2)*(d + 1)**2
Let t(g) be the second derivative of -1/8*g**3 + 0 - g**2 - g - 3/80*g**5 - 1/160*g**6 - 3/32*g**4. Let k(p) be the first derivative of t(p). Solve k(r) = 0.
-1
Factor -2/13*w**2 + 8/13*w - 8/13.
-2*(w - 2)**2/13
Let v(f) = -f**3 - 7*f**2 - 2*f. Let u(x) be the first derivative of 3*x**4/4 + 13*x**3/3 + 3*x**2/2 - 3. Let k(p) = 4*u(p) + 7*v(p). Factor k(y).
y*(y + 1)*(5*y - 2)
Let w(u) be the second derivative of -u**8/30240 + u**6/