-4*l + 3. Factor -9*b**2 + 17*b**3 - 46*b - 2*b**l + 10*b - 12.
3*(b - 2)*(b + 1)*(5*b + 2)
Let g(j) = -j**2 + 3*j + 5 - 8*j - 5. Let s be g(-5). Factor 2/7*i**5 + s*i + 0 + 0*i**3 + 0*i**2 + 2/7*i**4.
2*i**4*(i + 1)/7
Suppose 3*h + 5*k = 6, -1 = -2*h - 2*k + 3. Factor -15*q**4 - q**5 - q**5 - 4*q**2 + 19*q**4 + h*q.
-2*q*(q - 1)**3*(q + 1)
Suppose 0 = -3*w + 18 + 3. Let q(f) be the third derivative of -1/210*f**6 + 0*f**3 + 0*f + 0 - 1/735*f**w - 4*f**2 - 1/210*f**5 + 0*f**4. Factor q(d).
-2*d**2*(d + 1)**2/7
Let j(z) be the second derivative of z**6/45 - 2*z**5/15 + z**4/6 + 4*z**3/9 - 4*z**2/3 - 4*z. Find t such that j(t) = 0.
-1, 1, 2
Let g(w) be the third derivative of w**5/80 + w**4/16 - 3*w**3/8 - 9*w**2. Factor g(t).
3*(t - 1)*(t + 3)/4
Let k(b) be the first derivative of b**6/8 + 9*b**5/20 + 3*b**4/8 - b**3/2 - 9*b**2/8 - 3*b/4 + 9. Factor k(n).
3*(n - 1)*(n + 1)**4/4
Let j(t) be the first derivative of -t**4/8 - 7*t**3/6 - 15*t**2/4 - 9*t/2 + 1. Factor j(k).
-(k + 1)*(k + 3)**2/2
Let g(t) be the first derivative of t**4/26 + 4*t**3/39 - 3*t**2/13 + 29. Suppose g(h) = 0. Calculate h.
-3, 0, 1
Factor -71*u**3 + 21*u**3 - 99*u**2 - 16 - 88*u - 41*u**2 + 0*u**2.
-2*(u + 2)*(5*u + 2)**2
Let w(v) be the first derivative of v**7/1680 + v**6/240 - v**5/240 - v**4/16 - 5*v**3/3 + 4. Let l(s) be the third derivative of w(s). Factor l(f).
(f - 1)*(f + 1)*(f + 3)/2
Let v(f) be the first derivative of f**7/2520 + f**6/216 + f**5/45 + f**4/18 + f**3/3 + 3. Let j(u) be the third derivative of v(u). Factor j(i).
(i + 1)*(i + 2)**2/3
Let r(w) be the first derivative of w**5/10 + w**4/8 - w**3/3 + 16. Factor r(s).
s**2*(s - 1)*(s + 2)/2
Let y(f) be the first derivative of 3/20*f**4 + 1 + 0*f + 0*f**2 - 1/5*f**3. Solve y(c) = 0.
0, 1
Suppose 4*p = -1 + 9. Let t(b) = b**2 + 2*b - 3. Let h be t(p). Let r**3 + 2*r - 5*r**3 + 2*r**5 + 0*r**h = 0. Calculate r.
-1, 0, 1
Let k(m) be the first derivative of m**6/2 - 3*m**4/2 + 3*m**2/2 - 3. What is o in k(o) = 0?
-1, 0, 1
Let l(q) = 4*q**3 - 2*q**2 + 3*q + 5. Suppose -3*m + 30 = -g + 8, m + 36 = -4*g. Let i(v) = -v**3 - 1. Let d(u) = g*i(u) - 2*l(u). Solve d(s) = 0 for s.
-3, 0, 1
Let w(r) be the second derivative of r**4/3 - 2*r**3/3 + 3*r. Factor w(f).
4*f*(f - 1)
Determine j, given that -8/3*j**2 - 32/9 + 16/3*j + 4/9*j**3 = 0.
2
Let y(o) = 5*o + 4 - 4*o - 3 + 1. Let k be y(-2). Factor k*v + 2/9 - 2/9*v**2.
-2*(v - 1)*(v + 1)/9
Let r = 2458/2163 - -2/309. Factor -8/7 - r*l - 2/7*l**2.
-2*(l + 2)**2/7
Let z(d) be the first derivative of -2*d**3/51 + 3*d**2/17 - 4*d/17 + 6. Let z(s) = 0. What is s?
1, 2
Let v be (-1 + 1 - 3/(-6))*6. Factor 0 - 3/5*a**2 - 6/5*a + 3/5*a**v.
3*a*(a - 2)*(a + 1)/5
Let w = -53 + 53. Let v(o) be the second derivative of 2*o + 0 - 1/50*o**5 + 0*o**3 + w*o**4 + 0*o**2. Factor v(d).
-2*d**3/5
Let o(q) be the second derivative of q**4/6 - 4*q**3/3 + 3*q**2 + q. Determine z, given that o(z) = 0.
1, 3
Let k = 3 - 0. Find w, given that -1 + 0 + 2*w**2 - k + 0 - 2*w = 0.
-1, 2
Let v(l) be the second derivative of -1/2*l**4 + 0 + 5*l - 1/3*l**3 - 1/15*l**6 - 3/10*l**5 + 0*l**2. Factor v(o).
-2*o*(o + 1)**3
Suppose -4*q = w - 18, 0 = w - 4*q + 3 - 5. Let c = -8 + w. Let 2/3*s + 1/3 + 1/3*s**c = 0. Calculate s.
-1
Let z(r) be the third derivative of r**6/300 - r**5/30 + 2*r**4/15 - 4*r**3/15 + 10*r**2. Factor z(x).
2*(x - 2)**2*(x - 1)/5
Let k(q) be the second derivative of q**6/180 - q**5/40 + q**4/72 + q**3/12 - q**2/6 + 15*q. Let k(l) = 0. What is l?
-1, 1, 2
Let r(v) = 2*v - 12. Let i be r(6). Suppose d = -i + 2. Factor 1/4*y**d + 0*y - 1/4*y**4 - 1/4*y**5 + 0 + 1/4*y**3.
-y**2*(y - 1)*(y + 1)**2/4
Suppose -2*s = -s - 2. Let i be (-44)/(-33) - 8/12. Let 2/3*g**5 + i*g**3 - 4/3*g + s*g**4 - 2*g**2 + 0 = 0. Calculate g.
-2, -1, 0, 1
Let p(d) = -d**3 - 12*d**2 - 12*d - 7. Let c be p(-11). Determine a, given that -3*a**2 + 8*a + 1 - c*a - 3 + a**2 = 0.
1
Let g = 16 - 14. Let n(j) be the second derivative of 0*j**g - 1/10*j**5 + 1/7*j**6 + 0*j**3 + 0 + 2*j - 3/49*j**7 + 1/42*j**4. Let n(r) = 0. What is r?
0, 1/3, 1
Let m(w) be the second derivative of w**6/120 + w**5/16 + w**4/6 + w**3/6 - 20*w. Factor m(f).
f*(f + 1)*(f + 2)**2/4
Let m(x) be the third derivative of -x**9/11340 + x**8/10080 + x**4/12 - 3*x**2. Let h(k) be the second derivative of m(k). Factor h(p).
-2*p**3*(2*p - 1)/3
Let t = -6587 + 32832/5. Let i = t + 21. Determine r, given that -2/5*r + 4/5*r**3 + 2/5*r**4 - 4/5*r**2 + 2/5 - i*r**5 = 0.
-1, 1
Let h be ((-1)/3)/(15/(-9)). Let w = 6/5 + h. Factor 2/5*u - 9/5*u**2 + w*u**3 + 0.
u*(u - 1)*(7*u - 2)/5
Let k(r) = 2*r + 17. Let l be k(-6). Let z(q) be the first derivative of -2/21*q**3 + 0*q - 1/7*q**2 + 3 + 1/14*q**4 + 2/35*q**l. What is d in z(d) = 0?
-1, 0, 1
Factor 0 - 2/5*u + 1/5*u**2.
u*(u - 2)/5
Suppose -2*n + 2 = -0*n - s, 0 = 4*n - 4*s - 8. Let o(t) be the third derivative of n*t + 0 + 1/12*t**3 + 1/120*t**5 - 2*t**2 + 1/24*t**4. Factor o(a).
(a + 1)**2/2
Let k(y) = -y**3 - 9*y**2 - 11*y - 19. Let t be k(-8). Let j(w) be the second derivative of -2*w - 1/30*w**4 + 1/50*w**t + 0 + 0*w**2 + 0*w**3. Factor j(a).
2*a**2*(a - 1)/5
Let h(x) be the second derivative of -5*x**4/12 - 25*x**3/3 - 125*x**2/2 - 2*x. Factor h(n).
-5*(n + 5)**2
Let p = 13 - 16. Let l(k) = k**2 + 3*k. Let n be l(p). What is j in 0*j**4 + 2/3*j - 4/3*j**3 + n*j**2 + 0 + 2/3*j**5 = 0?
-1, 0, 1
Factor 0*j**3 + 3*j**3 - j**2 - 5*j**2 + 27*j - 24*j.
3*j*(j - 1)**2
Let g(v) be the third derivative of v**7/1260 - v**5/360 - 16*v**2. Determine z so that g(z) = 0.
-1, 0, 1
Suppose -i = -3*i + 110. Let d be 12/i - 10/(-55). Factor 0*r**3 - d*r**4 + 2/5*r**2 + 0 + 0*r.
-2*r**2*(r - 1)*(r + 1)/5
Let g(h) be the first derivative of 4*h**5/5 + 3*h**4/4 - h**3/3 + 4. Factor g(i).
i**2*(i + 1)*(4*i - 1)
Let x(j) be the first derivative of 2*j**3/3 - 2*j**2 + 2*j + 14. Solve x(n) = 0.
1
Suppose -8*q + 6*q = 12. Let p(o) = -o**3 - 6*o**2 - 2*o - 8. Let k be p(q). Determine i, given that 3 - 2 - 2*i**2 + i**k + 0*i**2 = 0.
-1, 1
Let s = 55 + -52. Factor -2/7*b**5 + 6/7*b**4 - 4/7*b**2 - 4/7*b**s + 6/7*b - 2/7.
-2*(b - 1)**4*(b + 1)/7
Let y be -5*(12/(-15))/1. Factor -6*b**2 - b**y - 1 + 6*b**3 + 4*b + b**3 - 3*b**3.
-(b - 1)**4
Let r = 52/189 - -62/27. Let 10/7*g**3 + 4/7*g + 0 - r*g**2 + 18/7*g**4 - 2*g**5 = 0. Calculate g.
-1, 0, 2/7, 1
Let u(z) be the second derivative of -z**5/5 + z**4/3 + 4*z**3 - 20*z. Factor u(q).
-4*q*(q - 3)*(q + 2)
Let f(x) be the second derivative of -3*x + 0*x**4 - 1/90*x**5 + 0*x**3 + 0*x**2 + 0. Factor f(c).
-2*c**3/9
Let v(t) be the third derivative of -t**7/735 + t**5/70 + t**4/42 - 27*t**2. Factor v(u).
-2*u*(u - 2)*(u + 1)**2/7
Solve -7 + 24 - 35*f**3 + 13 - 139*f**2 + 9*f**2 - 65*f = 0 for f.
-3, -1, 2/7
Factor 0 - 2/7*d**2 - 2/7*d.
-2*d*(d + 1)/7
Let k(z) = -8*z**3 - 12*z**2 + 12*z - 16. Let t(j) = j**3 + j**2 + j + 1. Let b(u) = -k(u) - 6*t(u). Solve b(a) = 0.
-5, 1
Let y(k) = -4*k**3 + 1. Let w be y(-1). Let m = -3 + w. Factor -2*q**3 + 2 - 2*q**m + 3*q**4 + 2*q**5 - 1 - 2*q**2.
(q - 1)*(q + 1)**3*(2*q - 1)
Suppose 18/7*s**3 + 2/7*s**4 - 48/7 + 36/7*s**2 - 8/7*s = 0. Calculate s.
-6, -2, 1
Suppose g = -4*g - 25. Let q(y) = y**4 - y**2 - y - 1. Let s(a) = -6*a**4 + a**3 + 6*a**2 + 4*a + 5. Let u(l) = g*q(l) - s(l). Factor u(d).
d*(d - 1)**2*(d + 1)
Let h(o) be the second derivative of o**5/3 + 8*o**4/9 - 8*o**3/9 + 11*o. Let h(y) = 0. What is y?
-2, 0, 2/5
Let o(s) = -37*s**3 + 78*s**2 - 31*s - 24. Let y(h) = -19*h**3 + 39*h**2 - 16*h - 12. Let p(x) = 4*o(x) - 7*y(x). Let p(u) = 0. Calculate u.
-2/5, 1, 2
Let w be (-3 + 32/12)*-33. Factor -36*o**2 - 2*o + 9 - 15*o - w.
-(4*o + 1)*(9*o + 2)
Let x(n) be the first derivative of -1/4*n**4 + 1/5*n**5 + 1/2*n**2 + 0*n - 1/3*n**3 - 3. Determine f, given that x(f) = 0.
-1, 0, 1
Suppose -16*u + 11*u - 13*u = 0. Factor 0*r - 1/2*r**2 + 5/4*r**3 + u.
r**2*(5*r - 2)/4
Factor 2/9*f**4 + 0 - 2/9*f**5 - 2/9*f**2 + 0*f + 2/9*f**3.
-2*f**2*(f - 1)**2*(f + 1)/9
Let a(v) be the second derivative of v**8/8960 + v**7/1680 + v**4/6 - 2*v. Let c(m) be the third derivative of a(m). Factor c(i).
3*i**2*(i + 2)/4
What is u in 2/3*u**3 + 2/3*u + 0 + 4/3*u**2 = 0?
-1, 0
Let o(g) be the third derivative of -g**10/15120 + g**9/3780 - g**8/3360 + 5*g**4/24 + 