*r(k). Determine o so that s(o) = 0.
2, 6
Let q(o) be the first derivative of -8/3*o**2 + 5/4*o**4 + 1/18*o**6 + 8/9*o**3 + 1 + 0*o - 8/15*o**5. Factor q(v).
v*(v - 4)**2*(v - 1)*(v + 1)/3
Factor 0*b**3 + 0*b**4 + 0*b**2 + 0*b + 0 + 1/3*b**5.
b**5/3
Let a be (1*(-1)/3)/((-57)/1026). Factor 3/2*n**4 + 6 - 3*n**3 + a*n - 9/2*n**2.
3*(n - 2)**2*(n + 1)**2/2
Let u(q) be the third derivative of -q**8/504 - q**7/63 - 2*q**6/45 - 2*q**5/45 + 471*q**2. Determine y, given that u(y) = 0.
-2, -1, 0
Let q(x) = -x**2 + 14*x + 6. Let f(p) = -p + 2. Let a(w) = -6*f(w) - 2*q(w). Find c such that a(c) = 0.
-1, 12
Let u(q) be the third derivative of q**5/20 + 6*q**4 - 49*q**3/2 + 40*q**2. Factor u(j).
3*(j - 1)*(j + 49)
Let w(l) = -12*l**2 + 9*l - 6. Let u(x) = 11*x**2 + 2*x + x - 13*x + 5. Let y(m) = 3*u(m) + 2*w(m). Determine k, given that y(k) = 0.
1/3, 1
Let c = -2/241 + 265/2892. Let l(r) be the first derivative of 1/4*r**2 + 3 + 0*r - c*r**3. Let l(b) = 0. Calculate b.
0, 2
Let y be (-77)/(-35)*(-3)/(-18). Let m(z) be the second derivative of 2/5*z**2 + 0 + 1/3*z**3 - y*z**4 + 15*z + 2/25*z**5. Factor m(f).
2*(f - 2)*(f - 1)*(4*f + 1)/5
Let x(g) = 12*g**2 + 24*g - 111. Let j(r) = -r**2 + r - 1. Let a(f) = 15*j(f) + x(f). Factor a(u).
-3*(u - 7)*(u - 6)
Let r(s) be the first derivative of 2*s**4 - 26*s**3/3 + 4*s**2 + 24*s + 47. What is c in r(c) = 0?
-3/4, 2
Let t(b) = 7*b**5 + 60*b**4 - 132*b**3 + 71*b**2 - 3*b - 6. Let f(m) = -m**5 - m**2 + m + 2. Let y(i) = 3*f(i) + t(i). Factor y(s).
4*s**2*(s - 1)**2*(s + 17)
Let v(j) = 7*j**2 - 3*j + 2. Let k be v(2). Factor -19*o - k*o**2 - 3*o**5 + 0*o**5 + 0*o**4 - 14*o**4 - 2 - 26*o**3 + 8*o.
-(o + 1)**4*(3*o + 2)
Suppose -27*d + 25*d + 4 = 0. Let m(l) be the first derivative of -d - 3/4*l + 1/2*l**2 - 1/12*l**3. Factor m(b).
-(b - 3)*(b - 1)/4
Suppose -4*k - 2*h - 3 = h, 0 = 3*k + 3*h + 3. Factor k + 8/17*j - 2/17*j**2.
-2*j*(j - 4)/17
Let q(u) be the first derivative of -7/48*u**4 - 1/4*u**3 - 1/24*u**5 + 0*u - 3*u**2 - 4 - 1/240*u**6. Let z(m) be the second derivative of q(m). Factor z(h).
-(h + 1)**2*(h + 3)/2
Let k(r) be the second derivative of r**5/80 - r**4/4 + 3*r**3/2 - 3*r - 33. Find n, given that k(n) = 0.
0, 6
Suppose -6*j - 30 = -0*j. Let w be 4 - 3 - (j + 2). What is l in 1/4*l**3 + 0*l**2 + 0 + 1/4*l**w + 0*l = 0?
-1, 0
Let r(g) = -g**2 - 4*g + 535. Let m(v) = -6*v**2 - 21*v + 2943. Let d(p) = -5*m(p) + 27*r(p). Solve d(s) = 0 for s.
-9, 10
Let n(c) be the third derivative of c**6/660 - 17*c**5/330 + 31*c**4/132 - 5*c**3/11 + 2*c**2 - 4. Factor n(p).
2*(p - 15)*(p - 1)**2/11
Let j = -926/9 + 3707/36. Let p(n) be the first derivative of j*n**3 + 1/8*n**2 + 6 + 0*n. Factor p(u).
u*(u + 1)/4
Let r be 43/(-7 + 12/3). Let t = r - -15. Suppose -4/9 - 2/9*s**2 + t*s = 0. What is s?
1, 2
Suppose -805 = -118*i + 123*i. Let a = 1129/7 + i. Determine u so that 2/7*u**2 + 0 + a*u**5 - 2/7*u**3 + 0*u - 2/7*u**4 = 0.
-1, 0, 1
Suppose -2*y - 2 = 4*f - f, -4*y = -5*f - 18. Let u be (-8 - -8)*(-1)/(-2) - f. Determine t, given that -2/11*t + 6/11*t**3 + 0 - 4/11*t**u = 0.
-1/3, 0, 1
Factor -4800 - 720*w - 3/5*w**3 - 36*w**2.
-3*(w + 20)**3/5
Let q = 25118/45969 - 4/4179. Find b such that -126/11*b + 108/11 + 48/11*b**2 - q*b**3 = 0.
2, 3
Let l(y) be the first derivative of y**4/26 - 6*y**3/13 + 24*y**2/13 - 32*y/13 - 132. Factor l(t).
2*(t - 4)**2*(t - 1)/13
Let v = -70 + 70. Factor c**2 + v*c**3 + 2*c**2 - 2*c**3 - c**3.
-3*c**2*(c - 1)
Let x(v) = -5*v**2 - 214*v + 4. Let j(p) = 5*p**2 + 215*p - 5. Let n(f) = 4*j(f) + 5*x(f). Factor n(m).
-5*m*(m + 42)
Suppose 0 = 2*i - b - 2*b - 33, 135 = 5*i + 3*b. Suppose 72 = 10*n + 8*n. Factor 11 - i*k + 7*k**3 + 0*k**2 + 1 + 9*k**2 - k**3 - 3*k**n.
-3*(k - 2)*(k - 1)**2*(k + 2)
Let y(i) = -4*i - 1. Let f(t) = 5*t**2 - 149*t - 6. Let h(r) = f(r) - 6*y(r). Factor h(k).
5*k*(k - 25)
Let f(o) be the first derivative of o**4/12 + 4*o**3/3 + 6*o**2 - 17. Factor f(t).
t*(t + 6)**2/3
Let q be (-78)/(-19) - (-82)/(-779). Let o be (-52)/16 - -3 - -3. Let -7/2*i**2 - o*i**3 + 0 - 5/8*i**q - i = 0. What is i?
-2, -2/5, 0
Let g(q) = q**3 - 9*q**2 + 9*q. Let s be g(8). Let r be 25/20 + (-2)/s. Factor 2*v**2 + v**5 - 3*v - v**3 - 3*v**4 + 3*v**3 + r + 0*v**2.
(v - 1)**4*(v + 1)
Let p(t) = 17 + 3*t - 2*t**2 - 3*t + 23*t**3 + 31*t**2. Let m(b) = -8*b**3 - 10*b**2 - 6. Let q(r) = -17*m(r) - 6*p(r). Factor q(j).
-2*j**2*(j + 2)
Let w be 18*6/(-12) - -4. Let j be (3 + -9)/(-6) + (-1)/w. Suppose 4/5*b**4 + 2/5*b - 4/5*b**2 - 8/5*b**3 + 0 + j*b**5 = 0. Calculate b.
-1, 0, 1/3, 1
Let z(j) = 12*j**4 - 20*j**3 + 5*j**2 + 3*j + 6. Let m(h) = -11*h**4 + 20*h**3 - 5*h**2 - 4*h - 8. Let x(o) = -3*m(o) - 4*z(o). Factor x(u).
-5*u**2*(u - 1)*(3*u - 1)
Let i = -1696 - -1698. Factor -8/9*f - 2/3*f**i + 0 + 2/9*f**3.
2*f*(f - 4)*(f + 1)/9
Let q = -16 - -18. Factor -q*a**5 - 6 + 32*a - 20*a**3 + 6*a**5 - 4*a**4 + 4*a**2 + 22.
4*(a - 2)**2*(a + 1)**3
Let i(l) = -2*l**2 - 9*l - 1. Let h(g) = -11*g**2 - 52*g - 7. Let k(z) = 6*h(z) - 34*i(z). Factor k(n).
2*(n - 4)*(n + 1)
Let l(x) be the third derivative of -x**5/105 + 4*x**4/21 - 32*x**3/21 - 153*x**2. Suppose l(w) = 0. Calculate w.
4
Let u(w) be the third derivative of -w**5/60 + w**4/9 - 5*w**3/18 + 238*w**2 - 1. Let u(v) = 0. What is v?
1, 5/3
Let y(n) be the second derivative of 93*n**5/10 - 20*n**4/3 + n**3 - 439*n. Factor y(v).
2*v*(3*v - 1)*(31*v - 3)
Let q(d) be the first derivative of -108*d**5/5 + 105*d**4/4 + 37*d**3 - 105*d**2/2 - 3*d - 309. Suppose q(o) = 0. Calculate o.
-1, -1/36, 1
Let j(v) = -v**3 + 1. Let d be j(-1). Solve 34*c**2 - 20 - 12*c + 20*c**3 - 8*c + 5*c**4 - 19*c**d = 0 for c.
-2, -1, 1
Let d(l) be the first derivative of -7*l**4 - 92*l**3/3 - 40*l**2 - 16*l - 22. Factor d(k).
-4*(k + 1)*(k + 2)*(7*k + 2)
Determine u so that 20 - u**4 - 11*u**3 + 12*u + 39*u**2 - 112*u**2 + 9*u**3 - 10*u**3 + 54*u**2 = 0.
-10, -2, -1, 1
Let g(u) be the second derivative of -u**4/4 + 156*u**3 - 36504*u**2 + 509*u. Determine v so that g(v) = 0.
156
Let a = 68/9 + -304/45. Suppose 2/5*h**2 + 6/5*h + a = 0. Calculate h.
-2, -1
Solve j**4 + 51*j**2 - 5*j**5 - 18*j**3 - 34*j**4 - 18*j**3 + 4*j**5 + 60*j - 36 - 5*j**5 = 0.
-3, -2, 1/2, 1
Let n(r) be the second derivative of r**7/56 + r**6/120 - 3*r**5/20 - r**4/12 - 682*r. Let n(q) = 0. Calculate q.
-2, -1/3, 0, 2
Let q(i) = i**2 + 4*i - 5. Let z(d) = -5*d**2 - 15*d + 20. Let m = -22 + 28. Let o(c) = m*z(c) + 25*q(c). Factor o(a).
-5*(a - 1)**2
Let j(a) be the second derivative of 21/10*a**5 + 3/2*a**2 - 22*a - 3/2*a**4 - 1/2*a**3 + 0 - 11/10*a**6 + 3/14*a**7. Factor j(s).
3*(s - 1)**4*(3*s + 1)
Let u(y) = -y**3 + y. Let g(d) = 17*d**2 - 2*d**2 - 11*d**3 + d - d + 56*d. Let r(a) = g(a) - 6*u(a). What is z in r(z) = 0?
-2, 0, 5
Let p = -707/2 + 354. Let j(r) be the first derivative of 8 + 0*r + 2/3*r**3 - p*r**2 - 1/4*r**4. Factor j(a).
-a*(a - 1)**2
Suppose 57 - 22 = 7*s. What is p in 0*p**4 + 0*p - 1/3*p**s + 0*p**2 + 1/3*p**3 + 0 = 0?
-1, 0, 1
Let o = -29 - -32. Factor 6*x**2 - 2*x - 76*x**3 + 75*x**o - 7*x.
-x*(x - 3)**2
Let h(a) be the first derivative of -a**3/12 + a**2 + 5*a + 442. Let h(d) = 0. Calculate d.
-2, 10
Let 44/7*g**2 + 0 - 4/7*g**3 - 40/7*g = 0. Calculate g.
0, 1, 10
Determine f so that 6/17 - 2/17*f**2 - 4/17*f**4 - 14/17*f + 14/17*f**3 = 0.
-1, 1/2, 1, 3
Let p be (-30)/18 - 51/(-9). Let h(s) be the second derivative of 0 + 2*s + 0*s**p + 1/80*s**5 - 1/24*s**3 + 0*s**2. Factor h(c).
c*(c - 1)*(c + 1)/4
Let y be -1 + (6/(-21) - (-322)/98). Factor -1/6*u - 1/3 + 1/6*u**y.
(u - 2)*(u + 1)/6
Let i(m) be the second derivative of m**4/24 - 5*m**3/3 + 9*m**2 - m - 44. Factor i(t).
(t - 18)*(t - 2)/2
Let i = 44992/91 - 6394/13. Let 3/7*d**4 + 15/7*d**2 - 3*d**3 - i + 3*d = 0. Calculate d.
-1, 1, 6
Let y(m) = -5*m - 5*m + 11*m + 1 - 2*m - m**2. Let s be 3/(-2)*2 + 1. Let d(p) = 4*p**2 + 5*p - 2. Let z(x) = s*d(x) - 6*y(x). Solve z(h) = 0.
-1
Let j(c) be the first derivative of -c**9/13608 - c**8/2520 - c**7/1260 - c**6/1620 + 8*c**3/3 - 1. Let g(s) be the third derivative of j(s). Factor g(p).
-2*p**2*(p + 1)**3/9
Let s = -33 + 36. Let p(o) be the first derivative of 0*o - 1/6*o**2 + 1/9*o**3 + s. Factor p(h).
h*(h - 1)/3
Let z = 0 + -6. Let g be z/(-12)*(-4)/(-9). Factor 2/3*q + g*q**2 + 4/