second derivative of -l**6/6 + l**5/4 + 2*l. Find y such that s(y) = 0.
0, 1
Let z(v) be the first derivative of v**4/2 + 16*v**3/3 + 7*v**2 + 46. Let z(w) = 0. What is w?
-7, -1, 0
Let w(f) be the third derivative of f**6/1080 - f**3/2 - 2*f**2. Let i(r) be the first derivative of w(r). Factor i(u).
u**2/3
Let l(t) = -t - 5. Let d be l(-7). Factor 0*v**2 + 2*v**3 + 2*v**d + 2*v**2 + 2*v.
2*v*(v + 1)**2
Find m, given that 19/4*m**3 - 54 - 1/4*m**4 + 81*m - 63/2*m**2 = 0.
1, 6
Factor 2/9*u**2 + 2/9*u - 2/9*u**3 - 2/9.
-2*(u - 1)**2*(u + 1)/9
Let h(p) be the third derivative of p**7/280 - p**6/20 + 23*p**5/80 - 7*p**4/8 + 3*p**3/2 + 15*p**2. Suppose h(k) = 0. Calculate k.
1, 2, 3
Let i(y) be the first derivative of -4*y**3/3 - 60*y**2 - 900*y - 37. Factor i(p).
-4*(p + 15)**2
Let 4/5*l**2 - 2/5*l - 2/5 = 0. What is l?
-1/2, 1
Let i be ((-4)/(-30))/((-10)/(-25)). Factor -4/3*j - 4/3 - i*j**2.
-(j + 2)**2/3
Let o(c) = -c**3 + 2*c - 1. Let v = -1 + -1. Let w be o(v). Factor -2*h**4 - h**w + 7 - 7 + 5*h**3.
-2*h**3*(h - 2)
Let v(k) be the first derivative of -k**2 + 0*k + 1/3*k**3 + 1. Determine h, given that v(h) = 0.
0, 2
Factor 4*o**2 + 4*o - o**5 + 2*o**4 - 6*o**2 - 3*o.
-o*(o - 1)**3*(o + 1)
Factor -4/7*j**2 - 24/7 - 20/7*j.
-4*(j + 2)*(j + 3)/7
Let t be 262/(-36) - (4 + -6). Let q = t + 11/2. Determine j so that -q*j**2 + 2/3*j**3 - 2/3*j**4 + 0*j + 0 + 2/9*j**5 = 0.
0, 1
Let d(c) = -8*c**2 + 21*c - 13. Let t(w) = 44*w**2 - 116*w + 72. Let a(p) = -28*d(p) - 5*t(p). Factor a(k).
4*(k - 1)**2
Let n(y) be the second derivative of -y**4/16 + 3*y**2/8 - 20*y. Suppose n(m) = 0. Calculate m.
-1, 1
Factor 6*l + 3*l - 6 - 3*l**2 + 0*l.
-3*(l - 2)*(l - 1)
Suppose -2*x + 2*f + 22 = -2*f, 4*x + 5*f = -8. Let -2/7*h**x + 2/7*h - 2/7 + 2/7*h**2 = 0. What is h?
-1, 1
Let k be 38/18*(2 - 0). Let b = k - -5/18. Factor 0 - b*j**2 - j.
-j*(9*j + 2)/2
Let p(l) be the first derivative of -1/4*l**2 - 1 + 0*l**3 - 1/12*l**6 + 0*l + 1/4*l**4 + 0*l**5. Factor p(o).
-o*(o - 1)**2*(o + 1)**2/2
Let s(c) be the third derivative of c**6/360 - c**5/60 + c**4/24 - c**3/18 - 2*c**2. Determine q so that s(q) = 0.
1
Let a = 53/123 + -4/41. What is h in -a*h**4 + 0 + 4/3*h**3 + 0*h - 4/3*h**2 = 0?
0, 2
Find g such that -5*g**2 + 3 + 7 + 0*g**2 + 5*g = 0.
-1, 2
Let m(c) be the second derivative of c**4/8 - 3*c**3/2 - 21*c**2/4 - 18*c. Let m(z) = 0. What is z?
-1, 7
Suppose 0*s + 3*g = -5*s - 15, 12 = -4*s - 4*g. Let l be 2/(-20) - s/6. Factor 4/5*b + 2/5 + l*b**2.
2*(b + 1)**2/5
Let c = 100/9 - 94/9. Factor 0*y - 2/3*y**4 + 0 + c*y**2 + 0*y**3.
-2*y**2*(y - 1)*(y + 1)/3
Let l be 2 - 10/12*(-357)/28. Let s(q) be the first derivative of -19/4*q**2 - l*q**4 - 65/6*q**3 - q - 73/10*q**5 - 5/3*q**6 - 1. Let s(d) = 0. What is d?
-1, -2/5, -1/4
Let o(t) = t + 2*t - 1 - 6*t. Let d be o(-1). Determine h so that 4*h - 3*h**d + 4*h**2 + 5*h**2 - 6*h**4 + 4*h**4 = 0.
-1, 0, 2
Let q(k) = -k + 1. Let d(p) = 5*p**2 - 15*p. Let f(u) = -d(u) + 10*q(u). Factor f(r).
-5*(r - 2)*(r + 1)
Let u(q) be the first derivative of -q**6/36 + q**4/24 + 1. Factor u(x).
-x**3*(x - 1)*(x + 1)/6
Let m(p) = -p**3 - 12*p**2 + 13*p - 14. Let o be m(-13). Let j be (-64)/o - (-14 - -18). Factor 10/7*l - 2/7*l**3 + 2/7*l**4 - j - 6/7*l**2.
2*(l - 1)**3*(l + 2)/7
Determine r, given that -5/8*r + 1/8*r**2 + 0 = 0.
0, 5
Suppose -4*q + 7*q = -45. Let o be 17/5 - (-6)/q. Factor 2 + i - 2*i**o - 1 + i**3 - i**2.
-(i - 1)*(i + 1)**2
Suppose 0*x = 11*x. Let -2/7 + x*v + 2/7*v**2 = 0. What is v?
-1, 1
Let u(v) be the third derivative of -v**5/450 - v**4/60 - 2*v**3/45 + 5*v**2. Factor u(n).
-2*(n + 1)*(n + 2)/15
Let t(b) be the third derivative of b**6/180 - b**5/90 + 6*b**2. Find x such that t(x) = 0.
0, 1
Let c(a) be the second derivative of -9*a**5/4 + 37*a**4/12 + 2*a**3 - 2*a**2 - 4*a. Factor c(x).
-(x - 1)*(5*x + 2)*(9*x - 2)
Let l(m) = m**3 + m**2 - m - 1. Let d = -9 + 10. Let v(b) = -2*b**4 + 5*b**3 + b**2 - 5*b + 1. Let x(p) = d*v(p) - l(p). Factor x(f).
-2*(f - 1)**3*(f + 1)
Let h be 6*(3 - (-1)/(-3)). Factor -h*d**3 + 3 - 3 + 19*d**3.
3*d**3
Factor -54 - 3/2*u**2 - 18*u.
-3*(u + 6)**2/2
Let l(h) be the second derivative of -h**3/6 - 3*h**2 - 8*h. Let a be l(-6). Factor -6/5*o**3 + a*o - 2/5*o**4 - 4/5*o**2 + 0.
-2*o**2*(o + 1)*(o + 2)/5
Let n(i) = i + 2*i + 1 - 4*i - 3. Let k be n(-4). Find u such that -2/5*u**k + 0 + 2/5*u = 0.
0, 1
Let c(m) be the second derivative of -m**5/140 - m**4/28 - m**3/14 - m**2/14 + 4*m. Factor c(d).
-(d + 1)**3/7
Let g(t) be the second derivative of 1/54*t**4 - 1/27*t**3 + 0 - 1/135*t**6 + 0*t**2 - 2*t + 1/90*t**5. Solve g(z) = 0 for z.
-1, 0, 1
Let p(y) = y**3 - 4*y + 2*y + 3*y**2 + 4*y. Let c be p(-2). Factor -2/3*n + c + 1/3*n**2.
n*(n - 2)/3
Suppose 2*i**4 + 61 - 2*i - 33 - 2*i**5 - 4*i**2 - 26 + 4*i**3 = 0. What is i?
-1, 1
Let r(s) be the first derivative of -s**6/24 + s**4/2 - 2*s**2 + 50. Solve r(a) = 0.
-2, 0, 2
Let -2/3*i**3 - 16/9*i**2 - 14/9*i - 4/9 = 0. Calculate i.
-1, -2/3
Let z(x) be the first derivative of 0*x**2 - 1/15*x**3 - 7 + 0*x. Suppose z(r) = 0. What is r?
0
Factor 5*g**3 - 4*g**3 + g**2 - 7*g + 5*g - 1 + g.
(g - 1)*(g + 1)**2
Factor -2/9*r**2 + 2/9*r + 0.
-2*r*(r - 1)/9
Let b = -171/7 - -3263/133. Let y = 13/57 + b. Factor 0 + 1/3*k**2 + y*k.
k*(k + 1)/3
Let b(c) be the first derivative of 1/3*c**2 - 1/6*c**3 - 1/6*c**4 + 1 + 2/3*c - 1/30*c**5. Factor b(u).
-(u - 1)*(u + 1)*(u + 2)**2/6
Let a(m) be the second derivative of 0*m**2 - 1/18*m**4 + 2/27*m**3 - 2*m + 0 + 1/135*m**6 + 0*m**5. Let a(n) = 0. Calculate n.
-2, 0, 1
Let o(c) = -2*c**2 + 6*c + 8. Let p(h) be the first derivative of 3*h**3 - 12*h**2 - 33*h - 1. Let r(q) = 21*o(q) + 5*p(q). Suppose r(y) = 0. Calculate y.
-1
Let r(t) be the third derivative of -2/15*t**5 + 1/35*t**7 + 0*t**4 + 1/84*t**8 - 1/30*t**6 - 2*t**2 + 0 + 0*t + 1/3*t**3. Find w, given that r(w) = 0.
-1, 1/2, 1
Let a(k) be the third derivative of k**8/30240 - k**7/2520 + k**6/540 + k**5/30 - 7*k**2. Let q(j) be the third derivative of a(j). Solve q(n) = 0.
1, 2
Let q(n) = n**2 - n + 3. Let t(i) = 2*i - 2. Let v(a) = -2*q(a) - 3*t(a). Factor v(c).
-2*c*(c + 2)
Factor 0*y + 0*y**4 + 0*y**2 + 5/6*y**5 + 0 - 10/3*y**3.
5*y**3*(y - 2)*(y + 2)/6
Let n(y) be the first derivative of 0*y - 7 - 1/10*y**4 + 2/25*y**5 + 0*y**2 + 0*y**3. Factor n(r).
2*r**3*(r - 1)/5
Let z(v) be the third derivative of 0 + 5*v**2 - 2/75*v**5 + 0*v + 0*v**3 - 1/60*v**4. Factor z(j).
-2*j*(4*j + 1)/5
Factor 2/3*w**2 - 8/9*w**3 + 0 + 2/9*w.
-2*w*(w - 1)*(4*w + 1)/9
Suppose 5*r = -4 + 14. Factor 3*u**2 - u**2 + u**r - 2*u**2.
u**2
Suppose 2*v - 16 = v. Factor -v*x**4 - 83*x**3 + 79*x**3 - 7*x**5 - 5*x**5.
-4*x**3*(x + 1)*(3*x + 1)
Suppose 0*y + 26 = 2*y. Let p = -11 + y. Find v such that -1/5*v**p + 0*v + 1/5 = 0.
-1, 1
Let m(k) be the first derivative of k**3/4 - 3*k**2/8 - 7. Let m(d) = 0. Calculate d.
0, 1
Let t(z) be the third derivative of -z**8/20160 - z**7/1680 - z**6/360 + z**5/20 - 3*z**2. Let w(x) be the third derivative of t(x). Factor w(n).
-(n + 1)*(n + 2)
Factor -1/4*x**2 + 0 + 1/4*x**5 + 0*x - 1/4*x**3 + 1/4*x**4.
x**2*(x - 1)*(x + 1)**2/4
Let -8/3 - 28/3*v - 1/3*v**5 - 25/3*v**3 - 8/3*v**4 - 38/3*v**2 = 0. Calculate v.
-2, -1
Let p = -1 - -1. Factor 2*u + 0*u + p*u**2 - 3*u + u**2.
u*(u - 1)
Let p(g) be the first derivative of g**9/3024 - g**7/420 + g**5/120 + 2*g**3/3 - 2. Let c(d) be the third derivative of p(d). Suppose c(r) = 0. Calculate r.
-1, 0, 1
Let l(y) be the second derivative of -y**4/36 - y**3/9 - y**2/6 + 8*y. Determine o, given that l(o) = 0.
-1
Let o(a) be the second derivative of -3*a**6/100 + 3*a**5/200 + 23*a**4/120 + 13*a**3/60 + a**2/10 - a. Find b, given that o(b) = 0.
-1, -1/3, 2
Let a = -25 + 227/9. Solve 0*z + 0*z**2 - 2/9*z**5 + a*z**3 + 0*z**4 + 0 = 0 for z.
-1, 0, 1
Let k(r) = r - 6. Let x be k(10). Suppose 3*n - 2*n - x*l = -3, 3*n + 2*l - 19 = 0. Factor 10*d**3 + 4*d**2 + 0*d**5 + 8*d**4 + d**n + d**5.
2*d**2*(d + 1)**2*(d + 2)
Let q be (-2)/10 + 66/30. Let y(a) = -2*a**2 + 3*a - 5. Let x(t) = t**2 - t + 2. Let s(c) = q*y(c) + 5*x(c). Find z, given that s(z) = 0.
-1, 0
Suppose -2*c - 7 = -7*c - 4*x, 2*x + 13 = 3*c. Factor -21 - 2*a**4 + 4*a**2 - 2*a**c + 21.
-2*a**2*(a - 1)*(a + 2)
Let i(g) be the third derivative of -g*