derivative of 2*y**6/15 + 4*y**5/5 + 5*y**4/3 + 4*y**3/3 - 48*y. Factor p(h).
4*h*(h + 1)**2*(h + 2)
Let a(x) be the third derivative of -13*x**5/105 + x**4/21 + 4*x**2. Let a(q) = 0. What is q?
0, 2/13
Let c(j) be the first derivative of 2 + 1/4*j**2 + 1/12*j**3 + 0*j. Suppose c(r) = 0. What is r?
-2, 0
Factor -6*z**4 - z**5 + 10*z - 3*z + 5*z + 4*z**5 - 9*z**3 + 12*z**2.
3*z*(z - 2)**2*(z + 1)**2
Let m(b) be the second derivative of 3/2*b**5 - 2*b**2 + 0 - 3/10*b**6 + 10/3*b**3 - 37/12*b**4 - b. Factor m(x).
-(x - 1)**2*(3*x - 2)**2
Let r(p) be the second derivative of 16*p**6/15 - 4*p**5/5 - 7*p**4/6 - p**3/3 + 8*p. What is v in r(v) = 0?
-1/4, 0, 1
Let l(k) = 12*k**2. Let o be l(-1). Factor 12*c**3 + 18*c**2 + 7 + 3*c**4 - 1 - 2 - 1 + o*c.
3*(c + 1)**4
Factor -12*j**2 + 5*j - 18 - 2*j**2 + 23*j + 2*j + 2*j**3.
2*(j - 3)**2*(j - 1)
Let p(l) be the second derivative of -l**5/5 - l**4/3 + 9*l. Factor p(b).
-4*b**2*(b + 1)
Let f(v) be the second derivative of -v**6/135 - 2*v**5/45 + v**4/27 + 4*v**3/9 - v**2 - 4*v - 1. What is b in f(b) = 0?
-3, 1
Let q = 25/9 - 1/9. Let c(a) be the first derivative of -q*a**3 + 3*a**2 - a - 1. Find g such that c(g) = 0.
1/4, 1/2
Determine c so that 2/13*c**4 + 0*c - 2/13*c**5 - 2/13*c**2 + 0 + 2/13*c**3 = 0.
-1, 0, 1
Let i(q) = 5*q**3 - 5*q**2 + q. Let u(m) = -m**3 + m**2. Let n(r) = -4*i(r) - 22*u(r). Factor n(y).
2*y*(y - 2)*(y + 1)
Let q = -31 + 21. Let m be 190/150 - (-6)/q. Solve 1/3*x + m - 1/3*x**2 = 0 for x.
-1, 2
Let p(u) be the second derivative of 5*u**7/42 - u**6/3 + u**5/4 + 6*u + 1. Factor p(g).
5*g**3*(g - 1)**2
Let m(i) be the first derivative of i**9/1512 + i**8/210 + i**7/70 + i**6/45 + i**5/60 + 2*i**3/3 - 1. Let j(w) be the third derivative of m(w). Factor j(s).
2*s*(s + 1)**4
Suppose -2 = -2*f - 4*k + 3*k, 4 = -4*f - 4*k. Let t = f + -1. Let 0*w + 2/7*w**t + 0 + 2/7*w**3 = 0. Calculate w.
-1, 0
Let d be 14/(-28) - (-5)/6. Determine u, given that 1/3*u**2 - 1/3*u + d*u**3 - 1/3 = 0.
-1, 1
Let y(m) = 3*m**4 - 10*m**3 + 13*m**2 - 8*m. Let o(k) = 12*k**4 - 39*k**3 + 51*k**2 - 33*k. Let z(a) = 2*o(a) - 9*y(a). Factor z(v).
-3*v*(v - 2)*(v - 1)**2
Solve 0*h**2 + 0 + 1/2*h**3 - 1/2*h = 0 for h.
-1, 0, 1
Suppose c + 4*t - t - 16 = 0, -8 = -2*t. Suppose -2 = -5*h + c*h. Factor -h*i**4 + 0 - 7 - 26*i**2 + 12*i**3 + 24*i - 1.
-2*(i - 2)**2*(i - 1)**2
Let w(n) be the first derivative of n**6/33 - 4*n**5/55 - n**4/11 + 16*n**3/33 - 7*n**2/11 + 4*n/11 - 16. Solve w(d) = 0.
-2, 1
Let f(z) be the second derivative of -z**5/70 + 11*z**4/42 + 4*z**3/7 - z + 3. Find x, given that f(x) = 0.
-1, 0, 12
Factor -15/4*k**3 + 0 - 9/4*k - 3/4*k**4 - 21/4*k**2.
-3*k*(k + 1)**2*(k + 3)/4
Let v(w) = -6*w**3 + 6*w**2 + 2*w - 10. Let x(l) = -7*l**3 + 5*l**2 + l - 11. Let p(u) = -3*v(u) + 2*x(u). Let p(i) = 0. What is i?
-1, 1, 2
Let z(a) be the first derivative of -a**7/1260 + a**6/540 + 2*a**3/3 - 4. Let l(v) be the third derivative of z(v). What is q in l(q) = 0?
0, 1
Let o(n) = -3*n**3 - 9*n**2 - 13*n - 3. Let y(i) = 21*i**3 + 63*i**2 + 90*i + 21. Let a(x) = -27*o(x) - 4*y(x). Find s such that a(s) = 0.
-1
Suppose 4 - 46 = -2*k. Suppose 3*n - 5*o - k = 0, -n - 7 = -0*o + 3*o. Find j, given that 2/3*j**n - 4/3*j + 2/3 = 0.
1
Let h be (0 + -9)/3*-1. Factor -g**4 - 2*g**4 - 13*g**3 + 4*g**h + 12*g.
-3*g*(g - 1)*(g + 2)**2
Let i(f) be the second derivative of f**6/120 - f**5/20 + f**4/8 - f**3/6 - f**2 + 4*f. Let t(v) be the first derivative of i(v). Factor t(l).
(l - 1)**3
Suppose w - 6 = -0. Solve 3*h**2 - 2*h + 15*h**3 - 4*h**4 - 6*h**3 - 12*h**3 + w*h**2 = 0.
-2, 0, 1/4, 1
Let f(i) be the second derivative of i**6/900 - i**5/150 - i**3/3 + 2*i. Let u(o) be the second derivative of f(o). What is y in u(y) = 0?
0, 2
Factor -10 - 2*v - 15*v**2 - 3 - 25*v - v**3.
-(v + 1)**2*(v + 13)
Suppose 0 = -2*g + 3*z + 4, 3*g + z + 6 = 1. Let u(a) = -a**3 + 2*a + 1. Let b be u(g). Determine t so that 1/2*t**2 + 0*t**3 - 1/4*t**4 - 1/4 + b*t = 0.
-1, 1
Suppose -2*n + 3*q = -5, 9*n = 4*n - 3*q + 23. Find h, given that 2/11*h**3 + 0*h - 2/11*h**5 + 0*h**n + 0*h**2 + 0 = 0.
-1, 0, 1
Suppose -8 = -2*g - 0. Let y be g + 7/(14/(-8)). What is d in -6/5*d + 3/5*d**2 + y = 0?
0, 2
Let b = 11372/9 - 1262. Factor -b*k**2 + 4/9 + 10/9*k.
-2*(k - 1)*(7*k + 2)/9
Factor 0*y + y + y**3 + y**2 - 3*y**2.
y*(y - 1)**2
Let b(a) be the third derivative of -a**8/504 - a**7/45 - a**6/12 - 13*a**5/90 - a**4/9 - 5*a**2. Suppose b(z) = 0. Calculate z.
-4, -1, 0
Let l be (45/(-260))/(6/(-4)). Let j = l + 5/13. Suppose 1/4*c**2 + 3/4*c + j = 0. What is c?
-2, -1
Let v(c) be the first derivative of 6*c + 7 - 17*c**3 + 2*c**6 + 9/5*c**5 - 9/2*c**2 - 39/4*c**4. Factor v(o).
3*(o - 2)*(o + 1)**3*(4*o - 1)
Let d(y) be the second derivative of -1/4*y**2 - 1/40*y**5 + 1/24*y**4 + 0 + 1/12*y**3 - 5*y. Suppose d(f) = 0. Calculate f.
-1, 1
What is x in 12*x**2 + 4 + 2*x**3 + 2*x**2 + 15*x + 2*x**3 - x = 0?
-2, -1, -1/2
Let a = -18 - -22. Suppose -3*f**2 - 2*f**5 + 2*f**3 + f**2 + 4*f**a - 2*f**4 = 0. What is f?
-1, 0, 1
Let v(h) be the second derivative of h**5/5 + h**4/3 + 6*h. Factor v(z).
4*z**2*(z + 1)
Let n(p) be the second derivative of p**4/28 - p**3/14 - 3*p**2/7 + p. Let n(h) = 0. Calculate h.
-1, 2
Let a be 9/27*(-12)/(-50). Let b = 21/50 + a. Solve b*o**3 + 1/2 + 3/2*o**2 + 3/2*o = 0 for o.
-1
Let q(r) be the second derivative of -r**6/20 - 9*r**5/20 - 3*r**4/2 - 2*r**3 - 38*r. Factor q(s).
-3*s*(s + 2)**3/2
Suppose y**5 - 14*y**5 + 9*y**5 = 0. What is y?
0
Let u(t) be the third derivative of t**5/150 - t**4/30 - t**3/5 + 8*t**2. Let u(n) = 0. What is n?
-1, 3
Let y be (-16)/(-7) + 6/(-21). Find r such that -2*r**2 + r**2 - 4*r - r**y = 0.
-2, 0
Suppose -3*h + z + 13 = 5*z, -5*h = -3*z - 12. Find p such that -2 - 2*p**h + p**2 + p + 0*p + p + p**2 = 0.
-1, 1
Let t be ((-6)/(-8))/(24/16). Suppose 2*i - 2 - t*i**2 = 0. What is i?
2
Factor -6/7*c - 2/7*c**2 + 20/7.
-2*(c - 2)*(c + 5)/7
Let g(o) be the third derivative of -o**7/385 - o**6/20 - 9*o**5/22 - 81*o**4/44 - 54*o**3/11 - 34*o**2. Factor g(c).
-6*(c + 2)*(c + 3)**3/11
Let k(r) be the first derivative of 1 + 2/21*r**3 + 0*r + 0*r**2. Factor k(l).
2*l**2/7
Let x be (0 - (-40)/12) + 1 - 3. Factor 2/3 + x*p**2 + 5/3*p + 1/3*p**3.
(p + 1)**2*(p + 2)/3
Determine q, given that 2/13*q**3 + 2/13*q**2 - 2/13*q - 2/13 = 0.
-1, 1
Suppose 3*g - 53 = 2*o, 2*g = -2*o + 4*o + 38. Let z be ((-5)/g)/((-2)/12). Find a, given that 0*a**2 - 2*a**2 + 3*a**z = 0.
0
Let k(u) be the second derivative of 2*u + 1/4*u**4 + 1/2*u**2 + 0 - 1/20*u**5 - 1/2*u**3. Factor k(x).
-(x - 1)**3
Let g(h) = -h**2 - 7*h - 3. Let s be g(-6). Suppose 6/7*m**s + 0 - 4/7*m + 10/7*m**2 = 0. What is m?
-2, 0, 1/3
Solve 5*b**4 + 1/3*b**3 - 4*b**2 + 0 - 4/3*b = 0 for b.
-2/3, -2/5, 0, 1
Let g(t) be the third derivative of t**7/4200 - t**6/600 + t**5/200 + t**4/6 - t**2. Let z(v) be the second derivative of g(v). Factor z(j).
3*(j - 1)**2/5
Let o(u) be the third derivative of -u**7/10080 - u**6/480 - 3*u**5/160 - u**4/12 + 3*u**2. Let j(m) be the second derivative of o(m). Factor j(c).
-(c + 3)**2/4
Let f(q) be the third derivative of -q**7/1680 - q**6/480 + q**5/40 - 5*q**4/24 + 4*q**2. Let y(m) be the second derivative of f(m). Solve y(a) = 0 for a.
-2, 1
Factor -1/3*x**4 + 0*x - 4/3*x**3 + 0 - 4/3*x**2.
-x**2*(x + 2)**2/3
Let p(a) = 2*a**2 + 2*a - 21. Let b be p(-4). Factor -4/11 - 10/11*f - 8/11*f**2 - 2/11*f**b.
-2*(f + 1)**2*(f + 2)/11
Determine h so that 2/5*h**2 + 0 - 6/5*h = 0.
0, 3
Factor -2/19*s**2 - 162/19 + 36/19*s.
-2*(s - 9)**2/19
Let g be 0/(-2*-3*(-4)/12). Factor 3/5*j**3 + g + 0*j**2 - 3/5*j.
3*j*(j - 1)*(j + 1)/5
Let f = 130 + -130. Let d(i) be the third derivative of 0*i**4 - 3*i**2 + 0 + f*i + 1/30*i**5 - 1/3*i**3. Suppose d(l) = 0. What is l?
-1, 1
Let m = -207/4 - -52. Suppose m*a**4 - 1/4 + 0*a**2 + 1/2*a**3 - 1/2*a = 0. What is a?
-1, 1
Suppose v + 4 = -2. Let y be (-1)/2*(v + -2). Factor -1/2*p + 0 - 3/2*p**2 - 3/2*p**3 - 1/2*p**y.
-p*(p + 1)**3/2
Let d(f) be the first derivative of -2*f**3/3 - 2*f**2 - 6. Solve d(n) = 0.
-2, 0
Suppose -5*t - 43 = -2*z, 0*z = 4*z + 3*t - 21. Factor 1 - 7*d + z*d - d**2 - 3*d**2 + 5*d**2.
(d + 1)**2
Let j(t) be the first derivative of -t**5/25 + t**4/20 + t**3/15 - t**2/10 - 17. Factor j(o).