 + 4. Let x(v) = -2*a(v) + i(v). Factor x(s).
2*s*(s - 24)*(s - 1)*(5*s - 3)
Let s(j) be the third derivative of -j**5/15 + j**4/2 + 510*j**2. Factor s(l).
-4*l*(l - 3)
Let u be ((-15)/3)/((-25)/6). Let m(k) be the first derivative of -99/2*k**2 + 5 + 27*k + u*k**5 - 45/4*k**4 + 37*k**3. Find c, given that m(c) = 0.
1/2, 1, 3
Suppose 9*o**2 - 210*o + 4*o**2 + 9*o**2 - 21*o**2 + 8595 + 2430 = 0. Calculate o.
105
Let x(b) be the first derivative of 28*b**3 - 33*b**2/2 + 3*b + 17. Factor x(a).
3*(4*a - 1)*(7*a - 1)
Let f(c) be the first derivative of 3*c**5/40 - c**3/4 - 30*c - 22. Let s(j) be the first derivative of f(j). Determine m, given that s(m) = 0.
-1, 0, 1
Let d(s) be the second derivative of s**4/72 + s**3/18 - 2*s**2/3 - 26*s - 2. Factor d(h).
(h - 2)*(h + 4)/6
Let p(r) be the second derivative of -r**4/8 - 29*r**3/2 + 177*r**2/4 - 4*r. Factor p(n).
-3*(n - 1)*(n + 59)/2
Suppose 0 = -4*d - 5*a + 8*a + 3, -3*a + 24 = 5*d. Suppose 2*u + d*l = -0*u + 4, -2*l - 8 = -4*u. Factor 4*v - u - 2*v + 1 + 0*v - v**2.
-(v - 1)**2
Suppose -s = -w - 5*s + 30, 120 = 3*w + 2*s. Let g be (w/10 - 1)/((-22)/(-55)). Suppose -52/5*m**2 + 16/5 - g*m - 14/5*m**3 = 0. What is m?
-2, 2/7
Let y(k) = -k + 2. Let r be y(0). Suppose -2*j + 13 = 3*u, -1 = j - 3. Solve -d**r - d**2 + 3*d**5 + 0*d**2 - 6*d**3 + 2*d**4 + u*d**5 = 0 for d.
-1, -1/3, 0, 1
Let t = 101/36 - 23/9. Let p(a) be the second derivative of 0*a**3 + 0 + 3/2*a**2 - t*a**4 - 7*a. Factor p(m).
-3*(m - 1)*(m + 1)
Let x(f) be the first derivative of -4*f + 0*f**4 + 0*f**3 + 1/20*f**5 + 0*f**2 - 1/30*f**6 + 2. Let o(y) be the first derivative of x(y). Factor o(h).
-h**3*(h - 1)
Let k be ((-198)/132)/((-4)/((-32)/(-9))). Factor 0 - 2*t**3 - 4/3*t**4 - k*t**2 - 1/3*t - 1/3*t**5.
-t*(t + 1)**4/3
Suppose -128/5*n + 0 + 32/5*n**2 - 2/5*n**3 = 0. What is n?
0, 8
Let m be (5 + (1155/14)/(-15))*0. Factor 1/2*s**2 + m + s.
s*(s + 2)/2
Let s(q) = q + 6. Let z be s(-3). Suppose g + 3*a + 4 - 12 = 0, z*g - 2*a - 2 = 0. Let 0*c**2 - 13 - 3*c**2 + 17 - c**4 + g*c + 2*c - 4*c**3 = 0. Calculate c.
-2, -1, 1
Let l(f) = -f + 16. Let d be l(13). Factor 3*b**2 + 3*b - b**d - 2*b**3 - 12 - 2*b + 11*b.
-3*(b - 2)*(b - 1)*(b + 2)
Let v(l) = 2*l**4 + 11*l**3 + 31*l**2 + 31*l + 15. Let a(t) = -2*t**4 - 12*t**3 - 32*t**2 - 32*t - 14. Let w(c) = -6*a(c) - 4*v(c). Find b such that w(b) = 0.
-3, -2, -1
Let u = 18370 + -238668/13. Solve -50/13*v**4 - u*v**2 + 24/13 + 32/13*v - 200/13*v**3 = 0.
-3, -1, -2/5, 2/5
Let t = 40162 + -80323/2. Factor 0 - 1/4*a**4 + 0*a**3 + t*a + 3/4*a**2.
-a*(a - 2)*(a + 1)**2/4
Let h(g) = -3*g**3 + g**2 - 2*g - 2. Let k be h(-1). Let z(r) = 3*r**2 + r - 10. Let f(s) = -3*s**2 - 2*s + 8. Let b(l) = k*z(l) + 5*f(l). Factor b(p).
-3*p*(p + 2)
Let m(a) be the second derivative of -a**7/672 + a**6/144 - a**5/96 - 7*a**3/2 - 10*a. Let l(i) be the second derivative of m(i). What is x in l(x) = 0?
0, 1
Suppose 10/7*m**3 - 26/7*m - 4/7*m**2 - 12/7 = 0. Calculate m.
-1, -3/5, 2
Let v = 32 + -27. Suppose 0*f + f = 4. Factor -5 + 24*h**3 + v + 4*h**5 + 16*h**4 - 12*h**2 + f*h + 28*h**2.
4*h*(h + 1)**4
Suppose -s + 3 + 1 = 0. Suppose -s*a + 30 = 6. Find f, given that 6*f - 4*f**2 + f**5 - 4*f**4 - 5*f + 0*f + a*f**3 = 0.
0, 1
Let z(s) be the third derivative of s**7/1365 - s**6/130 + 4*s**5/195 + s**4/26 - 3*s**3/13 + 72*s**2 + s. Let z(u) = 0. What is u?
-1, 1, 3
Factor 2*y**2 - 11*y**4 - y**5 + 2*y**3 - y + 14*y**4 - y**2 - 7*y**2 + 3.
-(y - 3)*(y - 1)**2*(y + 1)**2
Let p(x) be the first derivative of x**6/15 + 12*x**5/25 + 4*x**4/5 - 4*x**3/5 - 9*x**2/5 - 134. Solve p(n) = 0 for n.
-3, -1, 0, 1
Let u(p) be the second derivative of -p**4/84 + p**3/7 - 4*p**2/7 + 35*p - 1. Suppose u(h) = 0. Calculate h.
2, 4
Let y(l) = -5*l + 40. Let u be y(7). Factor 2*p**4 + 3*p**5 - 10*p**5 + 11*p**u - 6*p**3.
2*p**3*(p - 1)*(2*p + 3)
Let j = 7784 + -7781. Factor 4/5*p**4 - 16/5*p + 0 + 0*p**2 + 12/5*p**j.
4*p*(p - 1)*(p + 2)**2/5
Let d(m) be the first derivative of 1/90*m**5 - 1/360*m**6 + 5 + 1/72*m**4 - 3/2*m**2 - 1/9*m**3 + 0*m. Let k(h) be the second derivative of d(h). Factor k(l).
-(l - 2)*(l - 1)*(l + 1)/3
Let y(p) be the third derivative of p**7/42 - 7*p**6/24 - 3*p**2 - 1. Factor y(q).
5*q**3*(q - 7)
Let d be (72/810)/((-2)/(-36)). Suppose -d*u + 0 - 2/5*u**3 - 8/5*u**2 = 0. Calculate u.
-2, 0
Let j(r) be the third derivative of 5*r**8/336 + r**7/42 - r**6/8 - r**5/12 + 5*r**4/12 + 82*r**2. Factor j(x).
5*x*(x - 1)**2*(x + 1)*(x + 2)
Suppose 98 = 6*n + 68. Let u(t) be the second derivative of 0*t**2 + 1/75*t**6 - 2/15*t**3 - 1/18*t**4 + 11*t + 0 + 4/75*t**n. Determine q, given that u(q) = 0.
-3, -2/3, 0, 1
Let o = 34/9 - 28/9. Let h be (1 - 1/2)*(-16)/(-12). Factor 0 + 13/6*u**3 - h*u**2 - 5/6*u**4 - o*u.
-u*(u - 2)*(u - 1)*(5*u + 2)/6
Let v(m) be the first derivative of 0*m**2 - 4 - 3/4*m**4 - 2*m**3 + 0*m. Find k such that v(k) = 0.
-2, 0
Let d(a) = -3*a**4 - 24*a**3 - 18*a**2 - 24*a - 3. Let u(y) = y - 5 + 1 + 4. Let n be u(1). Let s(b) = -b**3 - b. Let o(p) = n*d(p) - 12*s(p). Factor o(f).
-3*(f + 1)**4
Let j(p) be the second derivative of -p**4/57 + p**3/57 + p**2/19 - 2*p + 98. What is i in j(i) = 0?
-1/2, 1
Let l(k) be the third derivative of 8*k**7/245 - 5*k**6/7 - 103*k**5/140 - 13*k**4/56 - 60*k**2 - 2. Find p such that l(p) = 0.
-1/4, 0, 13
Let t(x) = -9*x**2 - 206*x + 400. Let a(u) = 26*u**2 + 614*u - 1200. Let b(o) = -4*a(o) - 11*t(o). Solve b(q) = 0 for q.
-40, 2
Suppose 0 = -3*v + 12 - 3. Suppose 4*l + 2*u = 44, 0 + 33 = 5*l - v*u. Find g such that -3*g + l*g**2 - 3 + 6*g**3 - 3*g**5 - g**4 - 3*g**2 - 2*g**4 = 0.
-1, 1
Factor 0*s**2 - 6*s**2 + 7*s**5 - s**3 - 12*s**4 - 4*s**3 + 20*s**4.
s**2*(s + 1)**2*(7*s - 6)
Let j(c) = 3*c**2 - 41*c + 28. Let l be j(13). Factor 2/7*w**l + 50/7 + 20/7*w.
2*(w + 5)**2/7
Let s(n) = 98*n + 688. Let t be s(-7). Determine y so that 2/3 + 1/6*y**t + 2/3*y = 0.
-2
Suppose 0 = 2*i - f - 367, 382 = -i + 3*i + 2*f. Let d be (-6)/(-8) - i/(-24). Factor -8*m - 2*m**3 - d*m**2 - 3/2.
-(m + 1)*(m + 3)*(4*m + 1)/2
Let j(a) be the first derivative of 3*a**4/4 - 5*a**3/3 + 2*a**2 - 9. Let q(t) = -3*t**3 + 6*t**2 - 3*t. Let v(h) = -3*j(h) - 4*q(h). Factor v(c).
3*c**2*(c - 3)
Let m be 4*((-4)/(-2))/8. Let k be (-3)/m - (-8)/2. Find z, given that 2*z**3 - 21*z - k + 15*z - 1 + 6 = 0.
-2, 1
Let z(t) be the third derivative of 1/1680*t**7 + 0*t**5 - 1/2688*t**8 + 0 + 0*t**3 + 0*t + 9*t**2 + 0*t**6 + 0*t**4. Factor z(s).
-s**4*(s - 1)/8
Let l(x) be the first derivative of -1/2*x**4 + 0*x + 4/5*x**5 + 0*x**3 - 5 + 0*x**2 - 1/3*x**6. Factor l(z).
-2*z**3*(z - 1)**2
Let f be ((-1)/2)/((-7)/42). Let l(u) be the first derivative of 1/6*u**3 - f + 1/20*u**5 + 0*u**2 + 0*u + 3/16*u**4. Factor l(r).
r**2*(r + 1)*(r + 2)/4
Factor 20/9*g + 16/9*g**2 - 4/9*g**3 + 0.
-4*g*(g - 5)*(g + 1)/9
Let r(f) be the third derivative of f**8/5040 + f**7/420 + f**6/90 + 23*f**5/60 + f**3/6 - 40*f**2 - f. Let s(c) be the third derivative of r(c). Factor s(k).
4*(k + 1)*(k + 2)
Let r(c) = 2*c**2 - 196*c + 3122. Let i be r(78). Solve 0 + 4/9*u**i - 2/9*u - 2/9*u**3 = 0.
0, 1
Let o(i) = -3*i**3 - i**2. Let f(g) = -3*g**4 + 29*g**3 + 46*g**2 - 96*g - 36. Let c(r) = f(r) + 5*o(r). Find a such that c(a) = 0.
-3, -1/3, 2, 6
Let q(z) be the first derivative of -1/2*z**2 - 5 + 0*z + 7/10*z**5 + 1/2*z**3 + 3/2*z**4. Suppose q(r) = 0. What is r?
-1, 0, 2/7
Suppose -u - 24 = -5*u. Suppose -3*o - 4*l = -2*o - 3, 2*o = l + u. What is z in -12*z**2 - 8*z**3 - 6 + 15*z - 3*z**3 - z**o + 6*z = 0?
-2, 1/2
Let h(z) be the first derivative of -3 + 2/27*z**3 + 8/9*z - 5/9*z**2. Factor h(c).
2*(c - 4)*(c - 1)/9
Suppose 3*z - 59 = -47, 3*d - 3*z + 12 = 0. Determine m so that -3/7*m**5 - 15/7*m**4 - 27/7*m**3 - 6/7*m - 3*m**2 + d = 0.
-2, -1, 0
Suppose 4/7*z**2 - 8/7*z + 0 = 0. What is z?
0, 2
Let w(y) = -y - 5. Let r be w(-8). Suppose -r*f = -l - 10, 2*f - 5*l + 2*l + 5 = 0. Solve -78 - 2*v**4 + v**f + 4*v**2 - 4*v + 8*v**3 + 76 - 5*v**5 = 0.
-1, -1/2, 1
Let v(l) = -l**3 - 3*l**2 + 3*l - 8. Let d be v(-8). Let w be d/(-270)*(-5)/2. Factor 10/3*c + 2/3*c**3 - w*c**2 - 4/3.
2*(c - 2)*(c - 1)**2/3
Let n(k) = -k**2 - 5*k + 11. Let w be n(-6). Let l(z) = -z**2 + 65*z + 223. Let m(i) = i**2 - 43*i - 149. Let x(v) = w*l(v) + 7*m(v). Factor 