t m(s) = 3*s**2 + s - 4. Let k(f) = 5*m(f) + 7*u(f). Factor k(n).
(n - 1)**2
Let a(s) be the second derivative of -s**7/840 + s**6/360 - s**3/2 + s. Let z(g) be the second derivative of a(g). Determine v so that z(v) = 0.
0, 1
Let l(m) = -m**5 - m**3 - m**2 - 1. Let t(o) = -14*o**5 + 75*o**4 + 5*o**3 - 65*o**2 - 24*o + 11. Let k(d) = 22*l(d) + 2*t(d). Determine v, given that k(v) = 0.
-3/5, -2/5, 0, 2
Let x(d) be the second derivative of 0 + 1/30*d**5 - 1/6*d**4 - d**2 - d + 1/3*d**3. Let h(z) be the first derivative of x(z). Factor h(k).
2*(k - 1)**2
Factor -4*l + l**4 + 19*l**3 - 2*l**4 - 15*l**3 - 3*l**2 + 4.
-(l - 2)**2*(l - 1)*(l + 1)
Let f(s) be the third derivative of 0 - s**2 + 0*s**3 + 1/96*s**4 + 0*s + 1/240*s**5. Factor f(b).
b*(b + 1)/4
Let p(k) be the first derivative of -k**6/54 - 7*k**5/45 - k**4/2 - 22*k**3/27 - 13*k**2/18 - k/3 + 5. Solve p(z) = 0 for z.
-3, -1
Suppose -3/4 - 3/4*z**2 - 3/2*z = 0. Calculate z.
-1
Let y = -23 - -28. Let p(a) be the first derivative of 0*a + 0*a**3 - 2/35*a**y - 3 + 0*a**2 - 1/14*a**4. Factor p(x).
-2*x**3*(x + 1)/7
Let o be 6*(1/2 + 0). Suppose -13 + o = -5*f. Factor 0*z + 4*z - f*z**2 + 1 - 3.
-2*(z - 1)**2
Suppose -8*p + 6 = -5*p. Suppose 6/5*t**p + 1/5 - 4/5*t**3 + 1/5*t**4 - 4/5*t = 0. Calculate t.
1
Suppose 81 + 63 = 4*s. Factor 2*v**2 - s*v + 2*v**3 + 36*v.
2*v**2*(v + 1)
Let m(z) be the third derivative of z**7/420 - z**6/60 + z**5/20 - z**4/12 + z**3/12 - 2*z**2 - 7. Factor m(x).
(x - 1)**4/2
Let o = 2249 - 337349/150. Let q(n) be the third derivative of 0 + o*n**5 - 1/20*n**4 + n**2 + 0*n + 2/15*n**3. Let q(d) = 0. What is d?
1, 2
Suppose 0 = 8*k - 6*k. Suppose 2/3*m**4 - 2/9*m**3 - 2/3*m**2 + 2/9*m + k = 0. Calculate m.
-1, 0, 1/3, 1
Let i be (-4)/(-64)*233*4. Let m = -58 + i. Solve 1/4 + 1/4*a - 1/4*a**2 - m*a**3 = 0.
-1, 1
Suppose 0 = -2*r + 6*r - 12. Let o(q) = -q**2 + 3*q - 2. Let p be o(2). Find k such that -14/5*k**5 + 0*k**2 + 0*k + p - 4/5*k**4 + 0*k**r = 0.
-2/7, 0
Let c(b) be the third derivative of -b**11/498960 + b**9/90720 - b**5/10 - b**2. Let y(g) be the third derivative of c(g). Suppose y(m) = 0. What is m?
-1, 0, 1
Determine k, given that -28*k**4 - 99*k**3 + 165 - 64*k + 23*k**3 - 100*k**2 - 181 - 4*k**5 = 0.
-2, -1
Factor 2/15*y**3 + 0 - 2/15*y**2 - 4/15*y.
2*y*(y - 2)*(y + 1)/15
Let g(d) be the third derivative of d**5/270 - d**4/36 + 2*d**3/27 - 5*d**2. Suppose g(f) = 0. What is f?
1, 2
Find r such that -8 - 4*r**4 + 57*r**2 - 2*r**3 + 6*r**3 - 45*r**2 - 4*r = 0.
-1, 1, 2
Let i be 3/2 - 26/52. Let n be -4*i/(-20)*1. Factor 4/5*z + 13/5*z**3 - 12/5*z**2 - 6/5*z**4 + 0 + n*z**5.
z*(z - 2)**2*(z - 1)**2/5
Let o(w) = w**3 + 20*w**2 - w - 20. Let t be o(-20). Solve 1/3*s**2 + 0 + t*s = 0.
0
Find o, given that -4*o + 2*o**5 + 0*o**3 - 77*o**2 + 6*o**4 - 79*o**2 + 2*o**3 + 150*o**2 = 0.
-2, -1, 0, 1
Let y be (-4)/(-3) + 6/9. Let s(n) = 7*n**2 - 3*n. Let q be s(y). Factor 22 + 2*a**2 - q + 2*a**3.
2*a**2*(a + 1)
Let x(l) = 11*l**2 - 6*l. Let b(g) be the third derivative of -7*g**5/60 + g**4/6 - 4*g**2. Let a = 12 - 20. Let p(m) = a*b(m) - 5*x(m). Solve p(n) = 0 for n.
0, 2
Suppose -6*y = -0*y + y. Find d such that 4*d**3 - 8/3*d**2 + 2/3*d - 8/3*d**4 + 2/3*d**5 + y = 0.
0, 1
Let x(g) = g**3 - 4*g**2 + 3*g - 2. Let v(h) = h**3 - 5*h**2 + 4*h - 3. Let j(i) = -2*v(i) + 3*x(i). Solve j(l) = 0 for l.
0, 1
Let n = -29/42 + 6/7. Let k(j) be the second derivative of 0 + n*j**3 - 3/20*j**5 + 1/30*j**6 + 2*j + 0*j**2 + 1/21*j**7 - 1/12*j**4. Factor k(c).
c*(c - 1)*(c + 1)**2*(2*c - 1)
Suppose -5 - 720*a**2 + 360*a**2 + 365*a**2 = 0. Calculate a.
-1, 1
Suppose 12 = -4*u - 4*s + 44, -28 = -3*u - 4*s. Factor 5/4*f + 3/4*f**2 - 1/4*f**u - 1/4*f**3 + 1/2.
-(f - 2)*(f + 1)**3/4
Let u = -31/45 + 8/9. Suppose -4*n = 25 - 9, 5*n + 26 = 3*i. What is l in -u*l**i + 0*l + 1/5*l**3 + 0 = 0?
0, 1
Let z = 49/57 - 10/19. What is g in -z*g**4 + 4/3*g - 4/3 - 2/3*g**3 + g**2 = 0?
-2, 1
Solve -4/5 - 2/5*z + 2/5*z**2 = 0.
-1, 2
Factor -2/9*h**2 + 0 + 0*h.
-2*h**2/9
Let g = 30 - 25. Let o(d) be the third derivative of -1/30*d**g + 0*d + 0*d**4 + 0 - 3*d**2 + 0*d**3. Factor o(w).
-2*w**2
Let b = 5/2 - 7/6. Let c = -1/46 - -95/138. Factor b*r**2 + 0*r + 0 + c*r**3 - 2/3*r**4.
-2*r**2*(r - 2)*(r + 1)/3
Suppose 4*v + 16 = -0*v, 5*v = 2*c - 26. Suppose 3*f - c*b - 9 = 0, 4*f - 5*b - 6 = 7. Factor 0*u - 2/7 + 2/7*u**f.
2*(u - 1)*(u + 1)/7
Factor 22 + 2/11*x**2 + 4*x.
2*(x + 11)**2/11
Determine a, given that 0 + 9/4*a**4 - 6*a**2 + 3/4*a**3 + 3*a = 0.
-2, 0, 2/3, 1
Let d = -44 + 177/4. Let t = -1 + 3. Solve -d*q**4 + 0 + 1/4*q**t - 1/4*q + 1/4*q**3 = 0.
-1, 0, 1
Let u = 671 - 669. Find g such that 2/9*g**4 + 2/9*g + 0 - 2/9*g**u - 2/9*g**3 = 0.
-1, 0, 1
Suppose -2*h - 10 = -2*x, -x = 3*h + 11 - 4. Let i be -1 - (x - (-2 - -8)). Factor -1/4*a**2 + 0 + 1/4*a**i + 0*a.
a**2*(a - 1)/4
Let x(i) = -2*i**3 + 7*i**2 + i. Let s(f) = -3*f**3 + 15*f**2 + 3*f. Suppose 5*h = -5 - 45. Let w(u) = h*x(u) + 4*s(u). Factor w(n).
2*n*(n - 1)*(4*n - 1)
Let r = 18 + -5. Suppose 5*g - 2 = r. Let -2/7*u**5 + 20/7*u**2 - 20/7*u**g + 2/7 + 10/7*u**4 - 10/7*u = 0. Calculate u.
1
Let g(z) be the first derivative of z**5/5 + z**4/4 + 8. Factor g(o).
o**3*(o + 1)
Let q(v) be the first derivative of -v**2 - 3/2*v**4 + 2*v**3 + 6 + 0*v + 2/5*v**5. Factor q(a).
2*a*(a - 1)**3
Let o = 2 - 0. Factor -1/2 + i**3 - 3/2*i + 1/2*i**5 + 3/2*i**4 - i**o.
(i - 1)*(i + 1)**4/2
Let k = 2/123 - -365/246. Factor 0 - 1/2*u**4 + 3/2*u**3 + 1/2*u - k*u**2.
-u*(u - 1)**3/2
Suppose 0 = 4*l - 2*l. Let p = l - -2. Find h, given that -2/3*h**3 + p*h**2 + 2/3 - 2*h = 0.
1
Let k(i) be the second derivative of -i**4/8 - 25*i. Factor k(p).
-3*p**2/2
Let k(q) be the first derivative of 3*q**4/4 - 18*q**3 + 162*q**2 - 648*q - 47. Factor k(p).
3*(p - 6)**3
Factor 54*f**3 + 4*f**4 - 4*f**2 - 98*f**3 + 48*f**3 - 4*f.
4*f*(f - 1)*(f + 1)**2
Let x(b) be the second derivative of 0 - 1/24*b**4 - 4*b - 1/12*b**3 + 0*b**2. Factor x(u).
-u*(u + 1)/2
Let v(r) be the third derivative of -r**6/180 + r**5/25 - r**4/15 + r**3/6 + 2*r**2. Let x(a) be the first derivative of v(a). Factor x(p).
-2*(p - 2)*(5*p - 2)/5
Let n(x) = -x**5 + 5*x**4 - 4*x**3 + 2*x**2 - 2*x - 2. Let a(m) = -5*m**5 + 20*m**4 - 15*m**3 + 9*m**2 - 9*m - 9. Let b(j) = -4*a(j) + 18*n(j). Factor b(i).
2*i**3*(i - 1)*(i + 6)
Let u(f) be the third derivative of 0*f - 1/180*f**6 + 0 + 1/90*f**5 + 5/36*f**4 + 1/3*f**3 + 3*f**2. Solve u(w) = 0 for w.
-1, 3
Let n = -53 + 55. Factor -3/5*d + 1/5 - 1/5*d**3 + 3/5*d**n.
-(d - 1)**3/5
Let x(n) be the first derivative of -7*n**2 - 11/2*n**4 + 4*n - 40/3*n**3 + 3. Let x(o) = 0. What is o?
-1, 2/11
Let n(s) = s**4 + s**3 - 3*s**2 - 3. Let r(o) = 2*o**4 + 2*o**3 - 5*o**2 - 5. Let i = -4 + 7. Let q(v) = i*r(v) - 5*n(v). Determine z so that q(z) = 0.
-1, 0
Suppose 0 = t - 3*t + 12. Suppose t = o + 2*o. Factor 3*v - 3*v - 4*v - 2*v**4 + o + 4*v**3.
-2*(v - 1)**3*(v + 1)
Let v = 38/87 - 370/493. Let k = 412/663 + v. Suppose 2/13 - 2/13*f**4 - 4/13*f + 0*f**2 + k*f**3 = 0. What is f?
-1, 1
Let f(l) = l**2 - l. Let b(u) = -6*u**2 + 5*u. Let n(v) = 2*b(v) + 11*f(v). Factor n(w).
-w*(w + 1)
Let n(i) be the second derivative of i**6/5 + i**5/10 - 5*i**4/6 - i**3/3 + 2*i**2 - 7*i. Let n(u) = 0. What is u?
-1, 2/3, 1
Let t be -3 - (-1)/((-3)/(-27)). Factor 6*i + 16 + t*i + 3*i**2 - i**2 + 2.
2*(i + 3)**2
Let d be 0*(0 + (-4)/(-8)). Suppose -7*y + 14*y = d. Factor 5/2*o**3 + o**2 + 0 + 2*o**4 + 1/2*o**5 + y*o.
o**2*(o + 1)**2*(o + 2)/2
Let t(f) = -7*f**4 + 5*f**3 + 13*f**2 + 3*f - 24. Let g(p) = p**4 - p**3 + p**2 + p. Let r(s) = 5*g(s) + t(s). Factor r(b).
-2*(b - 3)*(b - 1)*(b + 2)**2
Let p(b) = b**3 + 9*b**2 - b - 5. Let z be p(-9). Suppose 3*n - 13 = -5*i, -5*i + i + 4 = -z*n. Factor -2/7 - 4/7*u - 2/7*u**i.
-2*(u + 1)**2/7
Suppose -d + 4*s = 2*s + 5, 2*s + 13 = -5*d. Let z be (d/12)/(55/(-40)). Let z*n**2 + 6/11*n**3 - 4/11*n**4 + 2/11 - 6/11*n = 0. Calculate n.
-1, 1/2, 1
Let v(d) = -7*d - 2. Let l be v(-1). Let n = 14 - 10. Determine k so that 4*k + 2 + 2*k**l + 3*k + 2*k**4 - 5*k - n*k**2 - 4*k**3 = 0.
-1, 1
Let o(s) = s**2 - s. Suppose 0 = z + 1. Let h = 2 + z. Let i(d) = 8*d**2 - 12*d + 4. Let a(g) = h*i(g) - 6*o(g). Factor a(c).
2*(c - 2)*(c - 1)
Let b(t) be the third deriva