d = 74 - 64. Factor 0*w**3 + 13*w**4 - 12*w - 3*w**3 - 12*w**3 - d*w**4 + 24*w**2.
3*w*(w - 2)**2*(w - 1)
Let n(k) be the third derivative of k**6/160 - 89*k**5/80 + 2107*k**4/32 - 5547*k**3/8 + 71*k**2 - k. Find z, given that n(z) = 0.
3, 43
Let p(s) be the second derivative of -1/5*s**5 + 10*s - s**4 + 8*s**2 + 0*s**3 + 0. Suppose p(x) = 0. What is x?
-2, 1
Suppose -z**3 + 0*z**3 - 135 - 51358*z + 31*z**2 + 51255*z = 0. What is z?
-1, 5, 27
Suppose -3*n + 2*c = -5*n, -3*n - 2*c = 0. Let m(g) be the third derivative of 1/600*g**6 + n + 1/600*g**5 + 0*g**3 - 1/240*g**4 + 3*g**2 + 0*g. Factor m(x).
x*(x + 1)*(2*x - 1)/10
Suppose 12*q**2 - 143*q**3 + 16*q + 71*q**3 + 74*q**3 = 0. What is q?
-4, -2, 0
Let y(n) be the first derivative of -24334*n**5/15 - 13754*n**4/3 - 1472*n**3 - 560*n**2/3 - 32*n/3 - 177. Factor y(g).
-2*(g + 2)*(23*g + 2)**3/3
Let s(p) be the first derivative of -9 + 8/27*p**3 - 4/9*p + 2/9*p**2 - 4/45*p**5 - 2/9*p**4 + 2/27*p**6. Factor s(w).
4*(w - 1)**3*(w + 1)**2/9
Let k(f) be the first derivative of -27*f**6 - 216*f**5/5 + 189*f**4/4 - 17*f**3 + 47*f**2/16 - f/4 + 208. Solve k(a) = 0 for a.
-2, 1/6
Let t(h) = 1. Let o(z) = -35*z**3 + 136*z**2 - 99*z + 26. Let l(x) = 5*o(x) - 40*t(x). Factor l(w).
-5*(w - 3)*(5*w - 3)*(7*w - 2)
Let p(m) = -2*m. Let h be p(-2). Suppose 0 = -4*z - h, -3*t - t + 38 = -2*z. Let -5*g + 21*g**3 + 2 - 4*g**4 + g**5 - 8*g**3 + 2*g**2 - t*g**3 = 0. What is g?
-1, 1, 2
Let s(w) be the second derivative of -w**5/10 + 83*w**4/12 + 43*w**3/6 - 21*w**2 + 2*w - 863. Let s(l) = 0. What is l?
-1, 1/2, 42
Let o = 9 - 23. Let j = o - -16. Let 2*c + 0 + 1 + 3*c - j*c**3 + 8*c**2 + 6*c**3 = 0. What is c?
-1, -1/2
Find l such that 20*l**2 + 85*l**4 - 5*l**5 - 5*l**2 + 68*l**3 - 50*l - 100*l**4 - 13*l**3 = 0.
-5, -1, 0, 1, 2
Find t such that -76*t**3 - 59*t**3 - 36*t - 36*t**2 - 44 - 48*t + 139*t**3 = 0.
-1, 11
Factor 6*g + 164*g**2 - 162*g**2 - 39 + 31.
2*(g - 1)*(g + 4)
Let r(s) be the third derivative of s**8/378 - 16*s**7/315 + 41*s**6/540 + 7*s**5/54 - 7*s**4/36 - 11*s**3/27 - 2*s**2 + 31*s. Solve r(g) = 0 for g.
-1/2, 1, 11
Let v(p) = -2*p**2 + 7*p + 5. Let z be v(4). Let l be 6/(-2 + 4) + 1/z. Factor 0*i**2 + 0 - 2/7*i - 2/7*i**5 + 4/7*i**3 + 0*i**l.
-2*i*(i - 1)**2*(i + 1)**2/7
Factor -5/2*h - 3 - 1/2*h**2.
-(h + 2)*(h + 3)/2
Let s be 3*2/12*4. Suppose -4*c - 3*g = -3*c - 11, 3*c = 2*g. Factor 0*x**3 + s*x**5 + 6*x**3 - 4*x**c + 2*x**2 - 6*x**4.
2*x**2*(x - 1)**3
Let z(a) be the third derivative of a**6/40 - 3*a**5/20 + 2*a**3 - a**2 + 40. Factor z(t).
3*(t - 2)**2*(t + 1)
Let r(s) = s**2 - 16*s - 1. Let g be r(7). Let l be (g/(-28) - 2)*7. Solve -32 - 3*w**2 + w**l - 8*w + 24*w = 0.
4
Let m(g) = -g**2 + 5*g + 2. Let h(l) = -l - 1. Let p(r) = -1. Let b(i) = h(i) - p(i). Suppose 3*k + 7 = -5. Let q(y) = k*b(y) - m(y). Factor q(u).
(u - 2)*(u + 1)
Let a(x) = 3*x**2 + 9*x + 3. Let q(c) = 18*c - 2 + 5 + 4 + 6*c**2. Suppose 5 = r - 5*r - 5*u, 0 = 5*r + 4*u - 5. Let j(d) = r*a(d) - 3*q(d). Factor j(b).
-3*(b + 1)*(b + 2)
Suppose 20 + 14 = 17*n. Let l(m) be the third derivative of 0*m**3 + 1/240*m**6 + 2*m**n + 0 + 1/120*m**5 + 0*m**4 + 0*m. Factor l(f).
f**2*(f + 1)/2
Let a = -9427/5 - -1886. Factor 0 + a*n + 6/5*n**2 - 9/5*n**3 + 12/5*n**5 - 12/5*n**4.
3*n*(n - 1)**2*(2*n + 1)**2/5
Let n(j) be the third derivative of 0*j - 1/20*j**5 + 0 + 1/3*j**3 + 1/120*j**6 + 1/210*j**7 - j**2 - 1/24*j**4. Suppose n(a) = 0. What is a?
-2, -1, 1
Let b(i) be the third derivative of -i**7/1050 - i**6/75 - 17*i**5/300 - i**4/12 + 10*i**2 + 4. Factor b(q).
-q*(q + 1)*(q + 2)*(q + 5)/5
Let i(q) be the second derivative of q**7/105 + q**6/75 - 3*q**5/25 - 2*q**4/15 + 8*q**3/15 + 2*q + 2. Solve i(k) = 0 for k.
-2, 0, 1, 2
Let h be ((-715)/5577)/(-2 - 7/(-6)). Factor -h*f**2 + 0*f + 2/13.
-2*(f - 1)*(f + 1)/13
Let l(z) be the second derivative of 12*z**6/5 + 39*z**5/5 + 49*z**4/24 + z**3/6 - 10*z - 5. Solve l(m) = 0.
-2, -1/12, 0
Let m(b) = b**2 - 160*b - 1610. Let s(x) = x**2 - 2. Let n(q) = -m(q) + 5*s(q). Factor n(v).
4*(v + 20)**2
Suppose -4*p + 0*p + 8 = x, -1 = -p. Factor -167*m**3 + 20*m**5 - 10 + 25*m**x - 115*m**2 - 122*m**3 - 65*m + 234*m**3.
5*(m - 2)*(m + 1)**3*(4*m + 1)
Let d(q) be the third derivative of q**8/20160 - q**7/2520 + q**6/720 + 4*q**5/15 - q**2. Let n(a) be the third derivative of d(a). Solve n(o) = 0 for o.
1
Let t be 2/6 - 16/(-6). Suppose 17*o - 12*o - 15 = 0. Solve -3*z**4 - o*z**2 + 3 - t - 6*z**3 = 0.
-1, 0
Factor -12/5*t**2 + 13/10*t**3 + 0 - 2/5*t.
t*(t - 2)*(13*t + 2)/10
Factor 0 + 1/4*r**2 - 11/4*r**3 + 11/4*r - 1/4*r**4.
-r*(r - 1)*(r + 1)*(r + 11)/4
Find i such that -87051*i - 6795 - 5994 + 41668*i - 70249*i - 15*i**3 - 10443 + 2637*i**2 = 0.
-1/5, 88
Let o(x) = x**2 + 5. Let q be o(2). Suppose -25 = -5*y + 5*c, 3*y + 2*c + 3*c + q = 0. Determine w, given that -w**4 + 3/2*w**3 + 1/2*w**y + 1/2 - 3/2*w = 0.
-1, 1/2, 1
Let x(p) be the first derivative of -p**6/120 + p**5/15 - 5*p**4/24 + p**3/3 + 6*p**2 - 25. Let w(d) be the second derivative of x(d). Factor w(r).
-(r - 2)*(r - 1)**2
What is a in -a**2 + 2*a**2 - 3*a**2 - 25 + 22*a - 35 = 0?
5, 6
Determine k so that -2 - 4*k**4 + 5*k + 164*k**3 - 78*k**3 + 12*k**2 - 85*k**3 = 0.
-1, 1/4, 2
Let y(k) be the second derivative of 2/9*k**3 - 1/3*k**2 + 0 + 15*k - 1/18*k**4. Solve y(s) = 0.
1
Let p be ((36/14)/3)/(261/406). Factor -p*a + 0 - 6*a**2.
-2*a*(9*a + 2)/3
Let h = -38686 - -154753/4. Factor -h*o**2 + 9/4*o - 3/4 + 3/4*o**3.
3*(o - 1)**3/4
Suppose -2*u = 3*u - n, -n = 4*u. What is r in -r**2 + u + 3*r - 1 - 8*r + 3*r = 0?
-1
Factor -27/2*y - 3/2*y**2 + 54.
-3*(y - 3)*(y + 12)/2
Suppose -19/4*b**3 + b - 16 + 1/4*b**4 + 12*b**2 = 0. What is b?
-1, 2, 16
Let n be (6 - (41 - 33))*((-18)/4)/3. Factor n*d + 1/4*d**3 - 2 - 3/2*d**2.
(d - 2)**3/4
Let x(r) be the first derivative of r**4/4 - 5*r**3/4 + r**2 + 3*r/4 - 80. Factor x(c).
(c - 3)*(c - 1)*(4*c + 1)/4
Find t such that -2/7*t**4 - 6/7*t**3 + 0 + 18/7*t**2 - 10/7*t = 0.
-5, 0, 1
Let k = 3 - 3. Let c be (-5)/(-1)*(1 + k). Solve c*v**2 - 7*v**2 + 5*v**2 + v**2 = 0.
0
Let g(j) = -j + 10. Let a be ((-27)/(-18))/(6/28). Let z be g(a). Determine m so that -4*m**4 - 31*m**3 - 21*m**z + 64*m**3 - 8*m**2 = 0.
0, 1, 2
Let b(p) be the second derivative of p**6/60 - p**4/4 + 2*p**3/3 + p**2/2 + 2*p. Let i(r) be the first derivative of b(r). Factor i(j).
2*(j - 1)**2*(j + 2)
Suppose 0*x - 5*l - 697 = -2*x, 1059 = 3*x - 3*l. Let z = x + -2488/7. Factor -4/7*n**2 + 2/7*n**5 + 2/7*n**4 + 2/7*n + 2/7 - z*n**3.
2*(n - 1)**2*(n + 1)**3/7
Factor -1 + 3*y**3 - 2*y**3 + 24 - 8*y**2 + 3 - 8 - 11*y.
(y - 9)*(y - 1)*(y + 2)
Let f(x) = 3*x - 7. Let j be f(4). Suppose -6*a = -j*a - 3. Solve -6*w**2 - 9/2*w**a + 15/2*w + 3 = 0.
-2, -1/3, 1
Let p(u) be the first derivative of 27*u**4/4 - 21*u**3 - 51*u**2/2 - 9*u + 111. Find x, given that p(x) = 0.
-1/3, 3
Let l be (-62)/26 - 3/(0 - 1). Let a be (6/(-15))/((-130)/200). Factor 2/13*b**4 - 6/13*b**2 + a + 4/13*b**3 - l*b.
2*(b - 1)**2*(b + 2)**2/13
Let i(z) be the first derivative of 9 + 0*z - 5*z**2 + 3*z**5 + 35/3*z**3 - 10*z**4. Factor i(r).
5*r*(r - 1)**2*(3*r - 2)
Suppose 5*r - 4 = -3*c, 5*r + c - 12 = 2*c. Factor -2 + 6*o - 4*o**2 + 7*o**r + 0 + 5.
3*(o + 1)**2
Let m(c) = -117*c - 1284. Let y be m(-11). Suppose 0*h + 6/7*h**2 + 9/7*h**y + 3/7*h**4 + 0 = 0. Calculate h.
-2, -1, 0
Factor -3/2 + 3/2*t**5 + 3/2*t + 3*t**2 - 3/2*t**4 - 3*t**3.
3*(t - 1)**3*(t + 1)**2/2
Let q(j) be the third derivative of -j**7/840 - j**6/120 + 3*j**5/40 + j**4/6 + 17*j**2. Let i(v) be the second derivative of q(v). Factor i(x).
-3*(x - 1)*(x + 3)
Suppose 4*l = 16*l - 24. Let t(v) be the first derivative of 0*v**4 - 2/21*v**3 + 2/35*v**5 + 0*v**l + 0*v - 2. Determine d so that t(d) = 0.
-1, 0, 1
Let h(x) = -5*x**3 - 22*x**2 - 16*x + 5. Let d be h(-8). Factor -1275*j**2 + 4 + 22*j + 0*j + d*j**2.
2*(j + 2)*(5*j + 1)
Let a be (-3 + -1 + 3)/(5/(-20)). Let -11*w + 7 + a - 9 + 9*w**2 = 0. Calculate w.
2/9, 1
Let q(k) = -4*k**3 - 121*k**2 - 128*k - 121. Let a(f) = -2*f**3 - 60*f**2 - 64*f - 66. Let d(r) = -11*a(r) + 6*q(r). Find n such that d(n) = 0.
-32, -1, 0
Let d(n) = -n**4 + 58*n**3 - 299*n**2 - 62*n + 296. Let s(g) = 9*g**4 - 579*g**3 + 2991*g**2 + 621*g - 2958. Let p(w) = -21*d(w) - 2*s