z) = z**3 - 8*z**2 - 7*z + 2. Let b(n) = -34*l(n) + 6*t(n). Determine y so that b(y) = 0.
-1, -1/2
Find t such that 1/3*t - 1/3*t**3 + 2/3 - 2/3*t**2 = 0.
-2, -1, 1
Let j(t) be the second derivative of -5*t**4/12 - 5*t**3/2 - 5*t**2 - 8*t. Factor j(x).
-5*(x + 1)*(x + 2)
Let l(z) be the second derivative of 0 - 1/4*z**3 - 1/16*z**4 - 3/8*z**2 - 2*z. Factor l(s).
-3*(s + 1)**2/4
Let l(t) be the first derivative of -9*t**7/56 - 3*t**6/40 + 3*t**5/16 - t**4/16 - 3*t - 6. Let s(f) be the first derivative of l(f). Factor s(u).
-3*u**2*(u + 1)*(3*u - 1)**2/4
Let v(w) be the first derivative of -w**4/14 + 10*w**3/21 - 8*w**2/7 + 8*w/7 + 2. Factor v(k).
-2*(k - 2)**2*(k - 1)/7
Let c be (-4 - -3)*(-5)/((-15)/(-6)). Let -26/9*d**c - 32/9*d - 2/3*d**3 - 8/9 = 0. Calculate d.
-2, -1/3
Let y(x) be the third derivative of x**7/60 - x**6/48 - 3*x**5/40 + 5*x**4/48 + x**3/6 + 6*x**2. Factor y(o).
(o - 1)**2*(o + 1)*(7*o + 2)/2
Determine j so that -2/3*j**4 + 2/3*j**2 + 0 - 4/3*j - 2/3*j**5 + 2*j**3 = 0.
-2, -1, 0, 1
Let z = 2/23 - -28/207. Let 2/3*q**2 + 0 - z*q + 8/9*q**3 = 0. What is q?
-1, 0, 1/4
Let i(v) be the third derivative of -v**5/80 + 5*v**4/16 - 4*v**2 - 3. Factor i(l).
-3*l*(l - 10)/4
Let l(t) be the first derivative of t**7/84 - t**6/30 + t**4/12 - t**3/12 + 4*t + 1. Let v(a) be the first derivative of l(a). Determine u, given that v(u) = 0.
-1, 0, 1
Let t(o) = -20*o**2 - 26*o + 14. Let r(n) = -11 + 4*n**2 + 14 - 6 + 5*n. Let u(g) = -14*r(g) - 3*t(g). Factor u(x).
4*x*(x + 2)
Let o be (-2)/(-3*(-6)/(-81)). Let s be 3*(-2)/(-18)*o. Factor -2*i**3 + 2 - i**4 + s*i**2 + 7*i + i**3 - 2*i.
-(i - 2)*(i + 1)**3
Let m(t) be the second derivative of -t**6/6 + 3*t**5/4 - 5*t**4/6 + 20*t. Determine b so that m(b) = 0.
0, 1, 2
Let r(a) = a**3 - 2*a**2 - 4*a - 4. Let w be r(4). Let u be 2/(-14) + w/84. Factor -1/2*t**2 + u*t + 1/2.
-(t - 1)*(t + 1)/2
Let w(p) be the second derivative of 1/140*p**5 + 0*p**3 + 0 + p + 0*p**2 - 1/42*p**4. Factor w(l).
l**2*(l - 2)/7
Let t(k) be the second derivative of -3*k**5/100 + k. Find x such that t(x) = 0.
0
Let a be ((-2)/2)/(8/(-32)*2). Let -2/11*k**5 + 0*k**a - 4/11*k**4 + 0 + 0*k - 2/11*k**3 = 0. What is k?
-1, 0
Let r(w) be the third derivative of -w**7/210 + w**6/40 - w**5/30 - 35*w**2. Solve r(f) = 0.
0, 1, 2
Let d(s) be the third derivative of s**5/120 + 5*s**2. Factor d(i).
i**2/2
Suppose -4*p = -0*p - 56. Let q be 36/p - (3 - 1). What is d in -6/7*d**2 + q*d + 2/7 - 8/7*d**3 + 8/7*d**4 = 0?
-1/2, 1
Let o(a) = -a**5 + a**4 - a**3 - a - 1. Let f(j) = -8*j**4 - 14*j**3 - 13*j**2 - 3*j + 1. Let d(l) = 2*f(l) + 2*o(l). Solve d(c) = 0 for c.
-4, -1, 0
Factor -32/3 - 2/3*g**2 + 16/3*g.
-2*(g - 4)**2/3
Let t(x) = 2*x - 8. Let n be t(6). Let h be 212/7 - n/14. Factor -h*p**4 + 7*p + 18*p**5 - 3*p - 11*p**3 + 12*p**2 + 7*p**5.
p*(p - 1)**2*(5*p + 2)**2
Find d, given that 6 - 2*d + 2*d**3 - 12*d**2 + 6 - 7 + 7 = 0.
-1, 1, 6
Let a = 2835/4 - 524707/740. Let b = 18/37 - a. Solve 2*z + 14/5*z**2 - b = 0.
-1, 2/7
Let i = 109 + -101. Let o(b) be the third derivative of 1/12*b**4 + 0*b**6 + 0 + 2*b**2 + 0*b**3 + 1/15*b**5 + 0*b - 2/105*b**7 - 1/168*b**i. Factor o(l).
-2*l*(l - 1)*(l + 1)**3
Let r(q) be the third derivative of 0 + 4/525*q**7 + 4/15*q**3 - q**2 + 1/24*q**6 + 19/150*q**5 + 0*q + 7/30*q**4 + 1/1680*q**8. Factor r(j).
(j + 1)**2*(j + 2)**3/5
Factor k**2 - 9*k**3 - 10*k**2 - 2*k - k - 3*k**4 + 0*k.
-3*k*(k + 1)**3
Determine o, given that -2*o + 5*o**2 + 19*o + 1 + 5 = 0.
-3, -2/5
Let z(h) = -7*h**5 + 9*h**4 + 5*h**3 + 5*h + 5. Let c(v) = 6*v**5 - 10*v**4 - 4*v**3 - 4*v - 4. Let p(x) = 5*c(x) + 4*z(x). Suppose p(k) = 0. What is k?
0, 7
Suppose 4*d + 957 = 965. Suppose 0 + 0*t**d + 1/2*t**3 + 0*t + 1/2*t**5 - t**4 = 0. What is t?
0, 1
Let i(k) = k**2 - 4*k - 2. Let d be i(5). Suppose -d*t - v = t - 12, -4*v + 16 = 0. Find a, given that 2/3*a - 2/3*a**t + 0 = 0.
0, 1
Let t(p) = 18*p - 88. Let i be t(5). Factor 1/2 - 1/2*f**i - 1/2*f + 1/2*f**3.
(f - 1)**2*(f + 1)/2
Let w(q) be the second derivative of -q**5/5 + 3*q + 7. Factor w(b).
-4*b**3
Suppose 0 - 1/2*n - 1/4*n**2 = 0. Calculate n.
-2, 0
Let 47*o**3 - 113*o**4 - 11*o**3 - 29*o**2 + 60*o**5 + 2*o**4 + 50*o**2 - 6*o = 0. What is o?
-2/5, 0, 1/4, 1
Let s be 2/7 + (-4)/14. Let y = s + 0. Factor y*k**2 + k**2 + k**2 + 2*k - 2 - 2*k**3.
-2*(k - 1)**2*(k + 1)
Suppose 0*q + 4*q = 16. Factor 54*o**4 + 4*o**2 - 15*o**5 - 10*o**2 - 27*o**3 - 90*o**q.
-3*o**2*(o + 1)**2*(5*o + 2)
Suppose -q - g + 4 = 0, 0*q - 3*q = g - 8. Determine r, given that 7*r**q + 0*r - r - r**3 - 5*r**2 = 0.
0, 1
Factor 128*k - 45*k**3 - 60 + 35*k + 0*k**3 - 75*k**2 - 3*k.
-5*(k + 3)*(3*k - 2)**2
Let v(i) be the third derivative of 5*i**8/336 + i**7/70 - i**6/60 + i**2. Factor v(r).
r**3*(r + 1)*(5*r - 2)
Let g(q) be the second derivative of -q**7/357 - q**6/255 + q**5/85 + q**4/51 - q**3/51 - q**2/17 + 4*q. Let g(r) = 0. What is r?
-1, 1
Let i(s) be the second derivative of -s**7/420 - 2*s**2 - s. Let w(d) be the first derivative of i(d). Let w(r) = 0. What is r?
0
Let g(p) = 3*p**2 - 24*p + 3. Let d(u) = -u**2 + 6*u - 1. Let o(s) = 9*d(s) + 2*g(s). Factor o(f).
-3*(f - 1)**2
Let g(r) be the second derivative of r**5/4 + 25*r**4/12 + 20*r**3/3 + 10*r**2 + 10*r. Factor g(f).
5*(f + 1)*(f + 2)**2
Let g = 127/348 + 3/58. Let q(v) be the second derivative of -1/4*v**2 + 0 - 2*v - 3/8*v**4 - 7/40*v**5 - g*v**3 - 1/30*v**6. Suppose q(m) = 0. What is m?
-1, -1/2
Let h = 0 + 0. Let o = 2 + h. Factor -1/4*s - 1/4*s**o + 1/4 + 1/4*s**3.
(s - 1)**2*(s + 1)/4
Let a(t) be the second derivative of -5*t**4/12 + 10*t**3/3 - 10*t**2 + 5*t. Factor a(s).
-5*(s - 2)**2
Let y(m) be the second derivative of -11*m**7/84 - 31*m**6/60 - 27*m**5/40 - 5*m**4/24 + m**3/6 + 3*m. Factor y(q).
-q*(q + 1)**3*(11*q - 2)/2
Let c(s) = -4*s**3 + 8*s**2 - 4*s - 24. Let k(p) = p**3 + p**2 + p. Let j(o) = c(o) + 8*k(o). Factor j(a).
4*(a - 1)*(a + 2)*(a + 3)
Let u(v) = -3*v**3 + 18*v**2 + 59*v + 54. Let j(y) = -4*y**3 + 27*y**2 + 88*y + 81. Let k(m) = 5*j(m) - 7*u(m). Factor k(i).
(i + 3)**3
Let s(t) = -6*t**2 - 49*t - 67. Let q(y) = y**2 - y. Let b(c) = -9*c - 11. Let k(l) = -b(l) + q(l). Let n(o) = 39*k(o) + 6*s(o). Factor n(r).
3*(r + 3)**2
Let w = 4 - -1. Let c be 5/(-1)*(-2)/w. Solve 1/2*r**2 + c - 2*r = 0 for r.
2
Let f(l) = l**3 + l. Let j(t) = -8*t**3 + 4*t**2 + 20*t. Let v(y) = 4*f(y) + j(y). Factor v(h).
-4*h*(h - 3)*(h + 2)
Let b(u) be the first derivative of 2*u**3/9 - 2*u**2 + 10*u/3 + 20. Let b(r) = 0. What is r?
1, 5
Let f(x) be the first derivative of x**3/21 + x**2/7 - 19. Determine s so that f(s) = 0.
-2, 0
Let o(f) be the second derivative of f**6/2 + f**5/2 - 5*f**4/4 - 5*f**3/3 + 5*f. Let o(x) = 0. Calculate x.
-1, -2/3, 0, 1
Suppose 3*o - 3*s - 2 = -5*s, 0 = 5*o + 2*s - 10. Let c**4 + 2*c**2 - 4*c**5 - 2*c**5 - 6*c**4 - o*c + 3*c**4 + 10*c**3 = 0. Calculate c.
-1, 0, 2/3, 1
Let t be (2/(-120))/(8/(-16)). Let o(y) be the third derivative of 0 + 1/3*y**3 - 3*y**2 + 1/6*y**4 + 0*y + t*y**5. Factor o(v).
2*(v + 1)**2
Let q(z) be the second derivative of -5*z**7/42 + z**5/2 - 5*z**3/6 + 8*z. Solve q(j) = 0 for j.
-1, 0, 1
Factor 49*b**3 + 4*b**5 - b**5 - 6*b**2 + 12*b + 6*b**4 - 61*b**3 - 3*b.
3*b*(b - 1)**2*(b + 1)*(b + 3)
Let w(p) be the second derivative of -5*p**7/42 - 2*p**6/3 - 3*p**5/4 + 5*p**4/3 + 10*p**3/3 + p. Determine t, given that w(t) = 0.
-2, -1, 0, 1
Let g(h) be the second derivative of -h**6/60 + h**5/10 - 5*h**4/24 + h**3/6 + 5*h. Let g(i) = 0. What is i?
0, 1, 2
Let r(k) be the first derivative of -k**5 + 15*k**4/4 - 10*k**3/3 - 56. Factor r(s).
-5*s**2*(s - 2)*(s - 1)
Let r(f) be the first derivative of -f**6/30 - 6*f**5/25 - 9*f**4/20 - 4*f**3/15 - 10. Determine h so that r(h) = 0.
-4, -1, 0
Suppose 0 = n - 2 - 0. Factor -2*g + g**n - g**2 - 2*g**2.
-2*g*(g + 1)
Let t = -1 + 4. Suppose 0*a - t*a = -12. Factor -2*j**3 + 9*j**3 + 7*j**a + 9*j**3 + 2*j + 11*j**2 + 0*j**2.
j*(j + 1)**2*(7*j + 2)
Factor -12*f**4 - 3/2*f + 6*f**5 + 15/2*f**2 + 3/2*f**3 - 3/2.
3*(f - 1)**3*(2*f + 1)**2/2
Let a(g) be the third derivative of g**7/630 + g**6/60 + 2*g**5/45 - g**4/12 - g**3/2 - 20*g**2. Suppose a(v) = 0. Calculate v.
-3, -1, 1
Determine x, given that 6/7 + 27/7*x + 3*x**2 = 0.
-1, -2/7
Let d(o) be the first d