third derivative of -a**6/200 + a**5/100 - a**4/120 - a**3/3 - 2*a**2. Let b(l) be the first derivative of j(l). What is u in b(u) = 0?
1/3
Let b(i) be the first derivative of -3*i**2/2 - 9*i - 4. Let y be b(-4). Factor -1/2*l**4 + 1/2*l**2 + 1/2*l + 0 - 1/2*l**y.
-l*(l - 1)*(l + 1)**2/2
Let u(l) be the third derivative of l**8/840 - 4*l**7/525 - l**6/100 + 3*l**5/25 - 6*l**2. Factor u(k).
2*k**2*(k - 3)**2*(k + 2)/5
Suppose 4*i - 6 = i. Let l(b) be the second derivative of -2*b**3 + 3*b + 0 - 1/6*b**4 - 9*b**i. Let l(o) = 0. Calculate o.
-3
Let j be 4/(-42)*-6 + (-18)/63. Factor 0 - j*q**2 - 2/7*q.
-2*q*(q + 1)/7
Let q(j) = 2*j**3 + 14*j**2 + 3. Let y be q(-7). Factor -4/9*b**2 + 2/9*b + 0 + 2/9*b**y.
2*b*(b - 1)**2/9
Let q = 9/19 - -107/95. What is d in -2/5*d**2 - q + 8/5*d = 0?
2
Let a(q) be the second derivative of q**7/3360 + q**6/240 + q**5/40 - q**4/6 - 2*q. Let m(y) be the third derivative of a(y). Find k, given that m(k) = 0.
-2
Let t(r) be the first derivative of -r**6/2 + 3*r**5/4 + 21*r**4/16 - r**3/2 + 2. Determine x, given that t(x) = 0.
-1, 0, 1/4, 2
Let r(d) = -d**4 + d**3. Let p(u) = u**2 - u**3 - 4*u**3 + 4*u**4 + u - u**3. Let m(v) = 3*p(v) + 15*r(v). Find o, given that m(o) = 0.
-1, 0, 1
Let s(r) be the first derivative of 1/3*r**3 + r + 2 - r**2. Factor s(z).
(z - 1)**2
Let t(r) be the second derivative of -r**7/441 - 20*r. Solve t(y) = 0.
0
Let b(y) = y - 4. Let t be b(6). Suppose -18 - t = -5*x. Factor -7*f + 6*f + 5*f**2 - x*f**2.
f*(f - 1)
Let f be (-7)/(14/4) - -26. Let p be 16/56 - f/(-14). What is c in 2/3*c**4 + 2*c**2 + p*c**3 + 2/3*c + 0 = 0?
-1, 0
Let z(o) = -o**3 - 13*o**2 - 13*o - 18. Let w be z(-12). Let q be (w/(-32))/(1/4). Suppose -3*d**2 + 1/2 - q*d - 7/4*d**3 = 0. What is d?
-1, 2/7
Let o = 1224 + -1224. Find t, given that 2/7*t + 6/7*t**2 + o = 0.
-1/3, 0
Let k(g) be the second derivative of -2/3*g**3 + 3/20*g**5 - 1/42*g**7 - g + 1/3*g**4 - 1/15*g**6 + 0*g**2 + 0. Factor k(z).
-z*(z - 1)**2*(z + 2)**2
Suppose 0 = -5*l + 1 + 29. Factor -8*i - 2 + 0 - 2*i**3 + 2*i - l*i**2.
-2*(i + 1)**3
Let b(o) be the first derivative of -o**6/600 - o**5/200 + o**3 + 3. Let c(y) be the third derivative of b(y). Determine a so that c(a) = 0.
-1, 0
Let r be 8*((-2)/4 - -1). Let s = -26 - -31. What is y in -2/5*y**s + 0*y**2 + 0 + 0*y**r + 4/5*y**3 - 2/5*y = 0?
-1, 0, 1
Let c(d) = -d**2 + 7*d - 2. Let s be c(6). Factor s*t**2 - 8/3*t + 2/3*t**4 + 2/3 - 8/3*t**3.
2*(t - 1)**4/3
Let o(u) be the first derivative of -3*u**4/4 - 27*u**3 - 729*u**2/2 - 2187*u + 2. Factor o(p).
-3*(p + 9)**3
Let l = -15 + 14. Let v = l + 3. Solve 0 + 0*f + 2/7*f**3 + 0*f**v = 0 for f.
0
Let w = 8 + -6. Factor -2*g + 2 + 2*g**3 + 0*g**3 - 2*g**w + 4*g**2 - 4*g**2.
2*(g - 1)**2*(g + 1)
Suppose w + 6 = 4*w. Let f(l) be the first derivative of 0*l - 1/3*l**3 - 1/2*l**2 - w. Let f(s) = 0. What is s?
-1, 0
Let z(w) = -10*w**2 + 2*w + 1. Suppose 3*u = -51 + 9. Let x(b) = -3*b**2 + b. Let r(s) = u*x(s) + 4*z(s). Factor r(c).
2*(c - 2)*(c - 1)
Let h = 74/3 + -139/6. Let 0*x**2 + h*x + 1 - 1/2*x**3 = 0. What is x?
-1, 2
Let r(i) = -i**3 - 21*i**2 + 22*i. Let l be r(-22). Factor l - 2/5*v**2 + 6/5*v**3 - 4/5*v.
2*v*(v - 1)*(3*v + 2)/5
Let k be (2/(-1) - -2)/((-1)/1). Let a(i) be the second derivative of 0*i**2 + 0 + 1/10*i**5 + k*i**4 + 0*i**3 + 3*i. Factor a(l).
2*l**3
Let u = 22 + -18. Suppose 3*k - 10 = 5*z, -5 + 3 = -2*z. Factor 2*c**2 + c - u*c**3 - 2*c**4 + 4*c**2 + 3*c**k - 4*c**2.
c*(c - 1)**2*(c + 1)*(3*c + 1)
Let m = 5/9 + -2/9. Factor -m*v + 2/3 - 1/3*v**2.
-(v - 1)*(v + 2)/3
Let m(g) = g**2. Let u(y) = -21*y**2 + 6*y - 3. Let v(z) = 12*m(z) + u(z). Let f(l) = l**2 - l + 1. Let o(d) = 6*f(d) + v(d). Factor o(c).
-3*(c - 1)*(c + 1)
Let n(x) be the third derivative of 0 + 0*x**3 + 1/60*x**5 - 1/48*x**4 + 5*x**2 + 0*x - 1/240*x**6. Solve n(t) = 0 for t.
0, 1
Let u(t) be the second derivative of t**6/60 - 42*t. Find w, given that u(w) = 0.
0
Let q(j) be the third derivative of j**6/360 + j**5/60 + j**4/24 + j**3/18 + 13*j**2. Suppose q(t) = 0. Calculate t.
-1
Let p(i) be the second derivative of i**5/60 - i**4/6 - 27*i. Factor p(b).
b**2*(b - 6)/3
Let d(k) be the second derivative of k**7/630 - k**6/360 - k**5/60 - k**4/4 - 3*k. Let f(h) be the third derivative of d(h). Factor f(o).
2*(o - 1)*(2*o + 1)
Let s be 7 - 5 - 20/15. Find v such that s*v**2 - 2*v + 4/3 = 0.
1, 2
Let -4/3*n**3 + 0 + 1/6*n + 3/4*n**4 + 5/12*n**2 = 0. Calculate n.
-2/9, 0, 1
Let j(k) = -13*k**4 + 9*k**3 + 6*k**2 + k - 3. Let c(a) = 12*a**4 - 9*a**3 - 5*a**2 + 2. Let n(l) = -3*c(l) - 2*j(l). Find h, given that n(h) = 0.
-1/2, 0, 2/5, 1
Let k = -12/25 + 399/50. Let p = -7 + k. Solve -p*s + 1/2*s**2 + 0 = 0.
0, 1
Let d = -623/11 + 57. Let q(j) be the first derivative of 2 + 10/33*j**3 + d*j**2 + 1/11*j**4 + 2/11*j. Find p, given that q(p) = 0.
-1, -1/2
Let k(o) = -6*o**3 + 3*o**2 - 6*o + 9. Let t(x) = 3*x**3 - 2*x**2 + 3*x - 4. Let n be (-4)/6 - (-174)/18. Let h(y) = n*t(y) + 4*k(y). Let h(d) = 0. Calculate d.
0, 1
Suppose 13 = -2*g + 19. Let s(z) = -z**2 - 3*z. Let l be s(-3). Solve -16/3*u**2 + 25/3*u**4 - 5/3*u**g - 4/3*u + l = 0 for u.
-2/5, 0, 1
Let g = 7 + 3. Determine n, given that -n**5 - 2*n**2 + 6*n**3 + 3*n**4 - g*n**3 + 3*n - 1 + 2*n**3 = 0.
-1, 1
Let i(q) be the second derivative of 1/30*q**3 + 1/60*q**4 + 0 - 1/5*q**2 + 3*q. Factor i(n).
(n - 1)*(n + 2)/5
Let t(n) = 27*n**5 + 15*n**4 - 12*n**3 - 15*n**2. Let o(p) = -7*p**5 - 4*p**4 + 3*p**3 + 4*p**2. Let h(x) = 15*o(x) + 4*t(x). Factor h(i).
3*i**3*(i - 1)*(i + 1)
Let q(p) be the first derivative of -2*p**6/15 + 8*p**5/25 - p**4/5 + 7. Find u such that q(u) = 0.
0, 1
Let r(z) = z**2 - z + 2. Let h(l) = l**2 - 2*l + 2. Let s(m) = -4*h(m) + 5*r(m). Factor s(o).
(o + 1)*(o + 2)
Let l(c) be the third derivative of -c**5/360 - c**4/144 + c**3/6 + 51*c**2. Determine j, given that l(j) = 0.
-3, 2
Let r(g) be the second derivative of g**6/30 - g**5/20 - 6*g. Factor r(t).
t**3*(t - 1)
Let z(j) be the third derivative of j**6/60 + 3*j**5/5 + 27*j**4/4 - 9*j**2. Determine x, given that z(x) = 0.
-9, 0
Let k(x) be the first derivative of 1/2*x**6 + 2 + 0*x - 6/5*x**5 + 0*x**3 + 0*x**2 + 3/4*x**4. Factor k(w).
3*w**3*(w - 1)**2
Let g be (1/(-118))/((-13)/26). Let o = g + 111/413. Factor -4/7*b**2 + 2/7*b**4 + 2/7 + 4/7*b**3 - 2/7*b - o*b**5.
-2*(b - 1)**3*(b + 1)**2/7
Factor -7*h**4 - 37*h**3 - 2*h**4 + 12*h**3 + 4*h**4.
-5*h**3*(h + 5)
Let a(h) = -h + 3*h**2 + 4*h**2 - 3*h**2 - h**3 - 2. Let v(x) = 3*x**2 - 3. Let s(j) = 3*a(j) - 2*v(j). Factor s(z).
-3*z*(z - 1)**2
Find b, given that -2*b + 6*b**2 + 0 - 5/2*b**3 = 0.
0, 2/5, 2
Let u be (-1*(-1)/6)/((-19)/(-38)). Let r(y) be the second derivative of 0*y**2 - 2*y + 1/6*y**4 + 0 - u*y**3. Find z, given that r(z) = 0.
0, 1
Let s(l) = -l**3 + l**2 + 6*l - 6. Let c(q) = q**2 - q. Let h(u) = 15*c(u) + 3*s(u). Let h(z) = 0. What is z?
-1, 1, 6
Let f(m) be the third derivative of m**8/3528 + 8*m**7/735 + 16*m**6/105 + 256*m**5/315 + 34*m**2. Find s, given that f(s) = 0.
-8, 0
Let i = -13/21 - -193/210. Let l(u) be the second derivative of -1/15*u**6 + 0 + i*u**5 + 1/3*u**3 - 1/2*u**4 + 0*u**2 - 2*u. Let l(t) = 0. Calculate t.
0, 1
Let o(x) = x**2 + x. Let u(v) = -3*v**2 - 12*v. Let p(w) = -6*o(w) - u(w). Find i, given that p(i) = 0.
0, 2
Let b(p) be the third derivative of p**6/120 + p**5/15 - p**4/4 - p**3/2 - 3*p**2. Let x be b(-5). Factor -c**x + c - 1/4.
-(2*c - 1)**2/4
Let w(k) = k**2 - k - 2. Let i(y) = -6*y**2 + 3*y + 10. Let d(t) = 3*i(t) + 15*w(t). Find n such that d(n) = 0.
-2, 0
Let r(s) be the first derivative of -2*s**3/21 + 2*s**2/7 - 2*s/7 - 1. Solve r(k) = 0 for k.
1
Suppose 4*z - 7 = 5. Let i(f) be the first derivative of 2/9*f**z + 0*f - 1 - 1/6*f**2 - 1/12*f**4. Factor i(g).
-g*(g - 1)**2/3
Let r be (9/(-72))/(5/(-10)). Suppose -r*a + 0 + 1/4*a**3 + 0*a**2 = 0. Calculate a.
-1, 0, 1
Suppose 112*y - 104*y = 0. Let k = -1 - -1. Suppose 1/2*r**4 + 1/6*r**2 + k*r + 1/2*r**3 + 1/6*r**5 + y = 0. What is r?
-1, 0
Suppose 3*w - 20 = -20. Determine f so that 0 - 1/3*f**2 + 1/3*f**3 + w*f = 0.
0, 1
Let o = -3 - -4. Let x(z) = 5*z. Let l be x(o). Determine d, given that -3*d**2 + 1 - 3 + l*d**2 = 0.
-1, 1
Let j = -22 + 13. Let u = j - -9. Factor -2/3*b**4 + 0*b + u*b**3 +