**2 + 4*q. Let s(k) = -11*h(k) - 4*o(k). Factor s(z).
5*z**2*(z - 1)*(5*z + 2)
Let p(f) = -4*f - 2. Let n be p(-3). Suppose 92*m = 83*m + 36. Determine q so that 0 + 2*q + 12*q**2 + 4 + n*q + m*q**3 = 0.
-1
Let d = -5348 + 106987/20. Let b(p) be the second derivative of 0*p**4 + 0 + d*p**5 - 3*p**2 - 7/2*p**3 + p. Solve b(j) = 0 for j.
-2/3, -1/3, 1
Let a(s) be the third derivative of -s**6/30 + 14*s**5/5 + 29*s**4/2 + 88*s**3/3 - 291*s**2 + 1. Factor a(z).
-4*(z - 44)*(z + 1)**2
Let t(w) = 5*w**2 + 26*w - 19. Let x(r) = 5*r**2 + 25*r - 20. Let s(d) = -5*t(d) + 6*x(d). Factor s(v).
5*(v - 1)*(v + 5)
Solve 15/2*h**3 + 41/2*h - 1/4*h**4 - 27/4 - 21*h**2 = 0 for h.
1, 27
Let a(u) be the first derivative of 3/5*u**5 + 2*u**3 + 23 - 9/4*u**4 + 0*u + 0*u**2. Factor a(c).
3*c**2*(c - 2)*(c - 1)
Let z(t) be the third derivative of t**9/3780 - t**8/420 + t**7/210 + 13*t**4/12 - 24*t**2. Let m(x) be the second derivative of z(x). Factor m(o).
4*o**2*(o - 3)*(o - 1)
Let i(t) be the third derivative of -t**5/240 + 13*t**4/24 - 169*t**3/6 + 26*t**2 + 1. Suppose i(y) = 0. What is y?
26
Let l(d) be the second derivative of -d**7/84 - d**6/12 - d**5/4 - 5*d**4/12 - 5*d**3/12 - d**2/4 - 59*d. Suppose l(t) = 0. Calculate t.
-1
Let o(g) be the first derivative of -g**3/5 - 51*g**2/5 + 456*g/5 + 112. Factor o(b).
-3*(b - 4)*(b + 38)/5
Let i(v) be the third derivative of v**6/24 - 5*v**5/12 + 5*v**4/12 + 5*v**3/3 - 14*v**2. Let t(y) = -y**2 + y. Let x(h) = -i(h) + 25*t(h). Factor x(n).
-5*(n - 1)**2*(n + 2)
Let o(v) = v**3 - 5*v**2 - 5*v - 3. Let j be o(6). Suppose j*n = -22*n + 75. Factor -1/6*g - 1/2*g**n - 1/2*g**2 + 0 - 1/6*g**4.
-g*(g + 1)**3/6
Let m(f) be the first derivative of 0*f - 8/5*f**5 + 0*f**2 + 0*f**3 - 3/2*f**4 - 27 - 1/3*f**6. Let m(n) = 0. What is n?
-3, -1, 0
Let u(z) be the first derivative of 15/2*z**2 - 27 - z**3 + 0*z. Factor u(l).
-3*l*(l - 5)
Let j(g) = g**3 - 11*g**2 + 10*g + 2. Let c be j(10). Suppose -12 - 3 = -5*o. Factor -u**o + c*u - 191 + u**2 + 191.
-u*(u - 2)*(u + 1)
Let r(v) be the first derivative of 0*v**3 + 4 + 1/420*v**6 + 3*v**2 + 1/84*v**4 + 0*v - 1/105*v**5. Let t(d) be the second derivative of r(d). Factor t(h).
2*h*(h - 1)**2/7
Let g(o) = o**3 + 7*o**2 + o + 10. Let u be (-2)/(4*(-1)/(-14)). Let d be g(u). Suppose 2*l**2 + 8/3 + 4*l + 1/3*l**d = 0. Calculate l.
-2
Let t(h) be the first derivative of -h**6/57 + 34*h**5/95 - 79*h**4/38 + 94*h**3/57 + 80*h**2/19 - 128*h/19 + 76. Let t(i) = 0. What is i?
-1, 1, 8
Let y(a) = a + 11. Let s be y(-7). Factor 4*r**4 + 4*r**3 + 2*r**2 + 2 - 8*r**s + 0*r**2 + 5*r - 8*r**3 - r**5.
-(r - 1)*(r + 1)**3*(r + 2)
Suppose 0 = -x - 11 - 1. Let l be (-48)/(-14) - x/(-4). Solve 15/7*u**3 + 6/7*u**4 - l*u - 3/7 + 9/7*u**2 = 0.
-1, 1/2
Determine f, given that -10/3*f**4 + 29/3*f**3 + 1/3*f**5 - 20/3*f**2 + 0 + 0*f = 0.
0, 1, 4, 5
Let p = 4347 + -2086559/480. Let v(c) be the third derivative of -1/12*c**4 + 0 + 1/6*c**3 + 0*c - 4*c**2 - p*c**6 + 1/48*c**5. Factor v(z).
-(z - 2)**2*(z - 1)/4
Let d be 20/160*(-112)/(-63). Factor d*r**2 + 2/9*r**3 - 2/9*r**4 + 0 - 2/9*r.
-2*r*(r - 1)**2*(r + 1)/9
Factor -2/5*f - 18/5*f**3 - 8/5 + 28/5*f**2.
-2*(f - 1)**2*(9*f + 4)/5
Factor 98*y + 20*y**2 + 82*y - 98*y + 126*y + 80.
4*(y + 10)*(5*y + 2)
Let h be 3/1 - 6/(-1). Let c(j) = 17*j**4 - 9*j**3 - 7*j**2 + 9*j + 8. Let a(f) = 4*f**4 - 2*f**3 - 2*f**2 + 2*f + 2. Let i(v) = h*a(v) - 2*c(v). Factor i(k).
2*(k - 1)**2*(k + 1)**2
Let h(t) be the first derivative of -t**8/105 - 3*t**7/70 - t**6/45 - t**3 + 5. Let i(v) be the third derivative of h(v). Solve i(m) = 0.
-2, -1/4, 0
Let v(z) be the second derivative of 0 - 10*z**2 + 10/3*z**3 - 5/12*z**4 - 16*z. Factor v(d).
-5*(d - 2)**2
Let i be (25/10)/((-2)/(-4)). Suppose -8 = -3*y + 2*n + 9, i*y + 5*n + 5 = 0. Factor 3*r**3 + 6*r**2 + 8*r + 2*r**2 + r**y + 4*r**2.
4*r*(r + 1)*(r + 2)
Suppose -2*r + 4 = -2. Suppose 0 = -r*u - 0 + 12. Solve m + 19*m**2 - u + 17*m**4 - 34*m**3 - 2*m**4 + 3*m = 0 for m.
-2/5, 2/3, 1
Let p be ((-3)/(-9))/((-2)/(-12)). Let a be (-20)/15*(-3)/2. Determine y so that -4 + 6*y**2 - 2*y - 112*y**3 + 114*y**3 - p*y**a = 0.
-2, -1, 1
Let w(o) = 11*o**3 - 139*o**2 + 149*o - 27. Let b(n) = n**3 - 3*n**2 - n + 1. Let q(t) = 6*b(t) - 2*w(t). What is s in q(s) = 0?
1/4, 1, 15
Let h(r) be the first derivative of 7/18*r**4 + 0*r**2 + 0*r + 4/27*r**3 - 12 + 2/15*r**5. Factor h(b).
2*b**2*(b + 2)*(3*b + 1)/9
Let z(f) = 60*f**2 + 2099*f - 35. Let k be z(-35). Find r, given that -18/7*r + 2/7*r**2 + k = 0.
0, 9
Let 91/4*i - 43/2 - 5/4*i**2 = 0. Calculate i.
1, 86/5
Let f(l) = -l**3 + l**2 - 80*l - 100. Let v(a) = a**3 - a**2. Let b(o) = f(o) + 6*v(o). Suppose b(g) = 0. Calculate g.
-2, 5
Let j(i) be the first derivative of i**8/5880 - i**7/980 + i**5/105 - 4*i**3/3 + 12. Let n(v) be the third derivative of j(v). Suppose n(m) = 0. What is m?
-1, 0, 2
Let u(b) be the first derivative of 8*b**4/5 - 16*b**3/15 - 7*b**2/5 - 2*b/5 + 230. Determine x, given that u(x) = 0.
-1/4, 1
Let r be -3*(-8)/12*2. Let z(t) = 0 - 5 - 9*t - 5*t**2 - 2*t**2. Let u(j) = -6*j**2 - 8*j - 4. Let o(p) = r*z(p) - 5*u(p). Suppose o(y) = 0. Calculate y.
-2, 0
Let v(c) = c**3 - 12*c**2 - 23*c + 132. Let u be v(13). Factor 0 + 4/17*o + 2/17*o**4 + 0*o**3 - 6/17*o**u.
2*o*(o - 1)**2*(o + 2)/17
Let m be 1/7 - (-843)/(-21). Let n be (168/35)/((-18)/m). Factor 2/3*u**5 - 50/3*u**2 + 38/3*u**3 + n*u - 8/3 - 14/3*u**4.
2*(u - 2)**2*(u - 1)**3/3
Let u(h) = 15*h**3 + 45*h**2 - 65*h - 5. Let x(k) = 8*k**3 + 22*k**2 - 33*k - 3. Let i(w) = -3*u(w) + 5*x(w). Find l such that i(l) = 0.
-6, 0, 1
Suppose -34*i + 55*i = -47*i. Solve 2/11*s**2 + i*s + 0 = 0.
0
Let 2/21*a**5 + 4/7*a**4 + 8/21*a + 8/7*a**2 + 0 + 26/21*a**3 = 0. What is a?
-2, -1, 0
Factor 7*k**2 + 6*k - 5*k**2 + 24*k + 80 - 2*k**2 - 5*k**2.
-5*(k - 8)*(k + 2)
Let o(g) be the first derivative of -1/3*g**2 + 3 + 1/6*g**4 + 0*g - 2/15*g**5 + 2/9*g**3. Factor o(a).
-2*a*(a - 1)**2*(a + 1)/3
Determine g so that 0*g**4 - 925*g + 4*g**3 - 2940*g**2 + 966*g**3 + 5*g**4 - 985 + 3875*g = 0.
-197, 1
Let y(d) = -6*d**5 + 25*d**4 + 91*d**3 + 73*d**2 - 13. Let f(t) = t**5 - 4*t**4 - 15*t**3 - 12*t**2 + 2. Let n(l) = 39*f(l) + 6*y(l). Solve n(u) = 0.
-2, -1, 0, 5
Suppose -13*a = -0*a + 104. Let r = 58/7 + a. Factor 0 - r*f - 2/7*f**2.
-2*f*(f + 1)/7
Let f(m) be the third derivative of 0*m**3 - 1/28*m**4 + 1/420*m**6 + 0*m - 1/105*m**5 + 0 - 19*m**2. Factor f(g).
2*g*(g - 3)*(g + 1)/7
Let t(f) be the first derivative of -3*f**4/5 - 3*f**3/5 + 3*f**2/10 - 26. Factor t(u).
-3*u*(u + 1)*(4*u - 1)/5
Factor 4/3*n - 4/3*n**3 - 1/3*n**2 + 1/3*n**4 + 0.
n*(n - 4)*(n - 1)*(n + 1)/3
Factor -1/4*j**5 + 4*j**3 + 0 + 0*j - 5*j**2 - 1/4*j**4.
-j**2*(j - 2)**2*(j + 5)/4
Let d(x) be the second derivative of -x**8/1680 + x**6/360 + 5*x**3/6 - 8*x. Let t(w) be the second derivative of d(w). Solve t(g) = 0.
-1, 0, 1
Let o(j) be the second derivative of 5*j + 1/20*j**5 + 5/12*j**4 + 0*j**2 - 1 + 1/2*j**3 - 1/30*j**6. Factor o(q).
-q*(q - 3)*(q + 1)**2
Suppose -3*r + r + 4 = 0. Suppose -h + r + 0 = 0. Let 16 - 16*s - 11*s**2 - 11*s**h - 8*s**3 - 6*s**2 = 0. Calculate s.
-2, 1/2
What is x in 891/2*x**2 - 543/2*x + 36 + 24*x**4 + 252*x**3 = 0?
-8, -3, 1/4
Let c(a) be the third derivative of -a**8/90720 - a**7/22680 + a**6/1620 - 11*a**5/60 + 4*a**2. Let x(i) be the third derivative of c(i). Factor x(j).
-2*(j - 1)*(j + 2)/9
Let j(a) = -26*a**2 - 3512*a - 267. Let l be j(-135). Factor -6/5*t + 1/5*t**l - 3/5*t**2 + 8/5.
(t - 4)*(t - 1)*(t + 2)/5
Solve -24*f**3 + 619 + 652 + 670 - 2085 - 4*f**4 + 108*f**2 - 16*f = 0 for f.
-9, -1, 2
Let g(j) be the first derivative of 4*j**3/15 + 2*j**2/5 - 38. Factor g(c).
4*c*(c + 1)/5
Let q(k) be the third derivative of k**11/332640 + k**10/18900 + k**9/5040 - k**5/15 - k**3/2 + 40*k**2. Let f(z) be the third derivative of q(z). Factor f(h).
h**3*(h + 2)*(h + 6)
Let v = 961 - 961. Factor -3/7*y**3 + 0 + 0*y**4 + v*y**2 + 3/7*y**5 + 0*y.
3*y**3*(y - 1)*(y + 1)/7
Let d(g) = -3*g**3 + 12*g**2 - 10*g - 5. Let u(w) = 2*w**3 - 5*w**2 + 6*w + 3. Let s(c) = 3*d(c) + 5*u(c). Solve s(n) = 0 for n.
-11, 0
Let y(d) be the first derivative of -d**5/90 + d**4/36 + 2*d**3/3 + 11*d**2/2 + 19. Let s(i) be the second derivative of y(i). Factor s(v).
-2