 116. Let i be l(29). Suppose 0*k + 0 - 2/5*k**4 + 4/5*k**3 + i*k**2 = 0. Calculate k.
0, 2
Let y = 1578/7 - 4717/21. Let t = 8/7 - y. Find u such that -4/3 - t*u**2 - 4/3*u = 0.
-2
Let g(w) be the third derivative of -w**5/15 + 7*w**2. Factor g(y).
-4*y**2
Let g = 18/503 - 5416/123235. Let w = 20/49 + g. Find h such that w*h - 4/5*h**4 + 0 + 0*h**3 + 4/5*h**2 - 2/5*h**5 = 0.
-1, 0, 1
Suppose 4*w - w + 9 = 0. Let y(t) = 8*t**2 + 8*t + 4. Let l(p) = -p**3 + 9*p**2 + 9*p + 5. Let v(s) = w*y(s) + 2*l(s). Factor v(f).
-2*(f + 1)**3
Factor 4*k**5 - 8*k**2 + 3*k**5 + 2*k + 5*k**4 - 9*k**3 + 3*k**2.
k*(k - 1)*(k + 1)**2*(7*k - 2)
Let w(h) be the second derivative of -h**7/98 - 3*h**6/70 - 3*h**5/70 + h**4/14 + 3*h**3/14 + 3*h**2/14 - 5*h. Solve w(j) = 0 for j.
-1, 1
Let v(q) be the second derivative of -1/24*q**4 + 1/4*q**3 - 1/2*q**2 + 3*q + 0. Let v(b) = 0. Calculate b.
1, 2
Let t(q) be the second derivative of -q**4/4 + q**3/6 - 5*q. Factor t(p).
-p*(3*p - 1)
Let t(z) = -7*z + 42. Let m be t(6). Let k(x) be the second derivative of 0 + 0*x**3 - 1/25*x**5 - 1/75*x**6 + m*x**2 + x - 1/30*x**4. Factor k(q).
-2*q**2*(q + 1)**2/5
Let l(s) be the third derivative of s**8/112 - s**6/40 + 5*s**2. Factor l(c).
3*c**3*(c - 1)*(c + 1)
Suppose p = 2*p + 95. Let q = 477/5 + p. Factor q*x**3 + 0*x**2 + 0 + 0*x.
2*x**3/5
Let p(m) be the second derivative of -3*m + 0 + 1/21*m**3 - 1/7*m**2 + 1/42*m**4 - 1/70*m**5. Suppose p(f) = 0. Calculate f.
-1, 1
Suppose 0 = 2*a - 13 - 7. Let s be (-5)/a + (-10)/(-12). Let s*r - 1/3*r**2 + 0 = 0. Calculate r.
0, 1
Let u(h) be the first derivative of -h**4/24 - h**3/6 - h**2/4 + h + 3. Let k(d) be the first derivative of u(d). Factor k(z).
-(z + 1)**2/2
Suppose 0*o + 0 + 2/21*o**2 + 0*o**3 - 2/21*o**4 = 0. Calculate o.
-1, 0, 1
Factor 7/3*k**2 - 3*k**3 + 2/3*k + 0.
-k*(k - 1)*(9*k + 2)/3
Let x = 21 - 19. Suppose 64*i + 0*i**x + 4 - 60*i + i**2 = 0. Calculate i.
-2
Suppose -14*f = -19*f. Factor 0*a + 2/9*a**2 - 4/9*a**3 + 2/9*a**4 + f.
2*a**2*(a - 1)**2/9
Let n(b) be the third derivative of -4*b**2 + 0 + 1/150*b**5 + 0*b + 1/15*b**3 - 1/30*b**4. Factor n(i).
2*(i - 1)**2/5
Let k(h) be the third derivative of h**5/12 - 5*h**4/2 + 30*h**3 + 2*h**2 + 2*h. Factor k(l).
5*(l - 6)**2
Let y(u) be the third derivative of -u**8/10080 + u**7/420 - u**6/40 + 3*u**5/20 + u**4/4 - 4*u**2. Let i(j) be the second derivative of y(j). Factor i(n).
-2*(n - 3)**3/3
Factor 1/2*v**2 + 1/4*v**3 - 1/2 - 1/4*v.
(v - 1)*(v + 1)*(v + 2)/4
Let u(m) be the third derivative of -1/945*m**7 + 0*m - 1/270*m**6 - m**2 - 1/270*m**5 + 0*m**4 + 0 + 0*m**3. What is w in u(w) = 0?
-1, 0
Let p(q) be the first derivative of -5 - 1/9*q**3 - 1/6*q**2 + 2/3*q. Let p(b) = 0. What is b?
-2, 1
Let f(v) be the first derivative of 4*v**2 - v - 4/3*v**3 - 2 + 1/6*v**4. Let x(t) be the first derivative of f(t). Factor x(y).
2*(y - 2)**2
Suppose -3*d - 2*p = -19, -2*d - 3*p + 30 = 3*d. Let r = d - 1. Factor -2/5*u + 2/5*u**3 - 2/5*u**r + 2/5.
2*(u - 1)**2*(u + 1)/5
Let d(z) = 2*z + 2. Let s be d(0). Factor 0*m - 2/3 + 2/3*m**s.
2*(m - 1)*(m + 1)/3
Factor -8*t - 8/3 - 4*t**3 - 2/3*t**4 - 26/3*t**2.
-2*(t + 1)**2*(t + 2)**2/3
Let j(u) = -u**3 + 7*u**2 - u + 10. Let h be j(7). Let -2 + 20*x - 3 + 2 + 3*x**h - 14*x**2 - 5 = 0. What is x?
2/3, 2
Suppose 2*c = -81 + 85. Factor 6/5*b**c + 0*b + 3/5*b**5 + 0 + 0*b**4 - 9/5*b**3.
3*b**2*(b - 1)**2*(b + 2)/5
Let o(q) be the second derivative of q**7/14 + 3*q**6/2 + 9*q**5/2 - 95*q**4/2 + 225*q**3/2 - 243*q**2/2 + 35*q. Let o(n) = 0. Calculate n.
-9, 1
Let q(f) be the second derivative of -f**7/84 - 11*f**6/180 - f**5/20 + f**4/6 + 2*f**3/9 + 15*f. Determine c, given that q(c) = 0.
-2, -2/3, 0, 1
Let q(u) be the second derivative of u**4/78 + u**3/39 + 3*u. Factor q(g).
2*g*(g + 1)/13
Let z(m) = -m**5 - m**3 + m. Let p(v) = -6*v**5 - 2*v**3 + 2*v**2 + 5*v. Let w(i) = -3*p(i) + 15*z(i). Factor w(a).
3*a**2*(a - 2)*(a + 1)**2
Let h be 8/14 - 36/112. Factor -u - 1 - h*u**2.
-(u + 2)**2/4
Factor -6*s**3 - 3*s**2 - 64 + 8*s**3 - 4*s**3 - 17*s**2 - 64*s.
-2*(s + 2)*(s + 4)**2
Let f = -15 - -18. Factor -2*a + 1 + 0 - 3*a**f - a**4 + 5*a**3.
-(a - 1)**3*(a + 1)
Let k(d) be the third derivative of -d**8/120960 - d**7/15120 - d**6/4320 + 2*d**5/15 - 2*d**2. Let o(a) be the third derivative of k(a). Factor o(m).
-(m + 1)**2/6
Let s be 2/(-9) + 145/45. Suppose 5*b - s*i - 22 = 0, b - 3*i - 8 = 6. Factor -j**b - j**3 + j - 2*j**4 + 2*j**4 + j**4.
j*(j - 1)**2*(j + 1)
Let w(r) be the first derivative of -r**4/2 + 2*r**3 - 2*r**2 + 11. Suppose w(q) = 0. What is q?
0, 1, 2
Let k(p) be the third derivative of 16/15*p**3 - 1/150*p**6 + 2/25*p**5 - 2/5*p**4 + 0*p - 4*p**2 + 0. Determine m, given that k(m) = 0.
2
Let i = 434 - 431. What is j in 0*j - 1/3*j**i + 2/3*j**2 + 0 = 0?
0, 2
Let u(j) be the third derivative of j**6/10 - j**5/15 - j**4/2 + 2*j**3/3 - 3*j**2. Find k, given that u(k) = 0.
-1, 1/3, 1
Suppose 0 = 5*c - 5*w + 6*w - 12, -4*w = -4*c + 24. Solve 0 + 1/6*n**4 + 0*n + 1/2*n**c + 0*n**2 = 0 for n.
-3, 0
Let v(l) = -l + 3*l**3 - 3 + 2*l**3 + 5*l**2 - 4*l**3. Let a be v(-5). Factor -4*u**a + 2*u**2 + 2*u + 4*u**2.
2*u*(u + 1)
Suppose 2*v + 14 = 18. Suppose 5*o = v + 8. Solve 3/5*s - 2/5 - 1/5*s**o = 0 for s.
1, 2
Let f(i) be the first derivative of -25*i**3/3 - 105*i**2 - 80*i + 4. Factor f(n).
-5*(n + 8)*(5*n + 2)
Let r(l) be the second derivative of 2*l**3 - 6*l**2 + 0 - l - 1/4*l**4. Factor r(v).
-3*(v - 2)**2
Suppose -z - 2*y = -3, 5*z = -y + 4*y + 15. Find t such that -t + 0*t**3 + 2*t**2 + 3*t**3 - t**z - 3*t**3 = 0.
0, 1
Let z(r) be the third derivative of r**7/5040 - r**5/240 + r**4/12 + 2*r**2. Let f(i) be the second derivative of z(i). Factor f(d).
(d - 1)*(d + 1)/2
Let r be ((-3)/(-7))/(8/(-574)). Let m = r + 31. Determine h, given that -m*h**3 - h**2 - 1/2 - 5/4*h = 0.
-2, -1
Let i(k) = -4*k**2 + 7*k - 1. Let d be (6 + -9)*1*-1. Let y(t) = 5*t**2 - 8*t. Let q(s) = d*y(s) + 4*i(s). Suppose q(a) = 0. What is a?
2
Let k = 94 + -753/8. Let u = 5/8 + k. Find m, given that 1/2*m**4 + u*m**2 + m**3 + 0 + 0*m = 0.
-1, 0
Let u(f) = 4*f**3 - f**2. Suppose 0 = c - 0*c - 1. Let z be u(c). Solve -3*g**3 + g + 2*g**z + g + g**2 = 0.
-1, 0, 2
Let x = -21 - -15. Let z = 8 + x. Determine k so that 14*k**z - 2 + 2 - 4*k = 0.
0, 2/7
Let x = 48/119 - 2/17. Let 0 - 5/7*v**2 - 4/7*v**3 - x*v - 1/7*v**4 = 0. Calculate v.
-2, -1, 0
Let d(v) be the third derivative of -v**7/840 + v**6/480 + v**5/80 - v**4/96 - v**3/12 - 5*v**2. Determine w so that d(w) = 0.
-1, 1, 2
Let d(q) be the first derivative of q**6/120 + q**2 - 2. Let x(s) be the second derivative of d(s). Find b, given that x(b) = 0.
0
Suppose -2*u + 9 = z, -5*u = -3*z - 8 + 2. Determine n so that 0 - 4/3*n**u + 2/9*n**2 + 4/9*n = 0.
-1/2, 0, 2/3
Let h(g) be the first derivative of -g**6/720 - g**5/240 + g**4/24 + 2*g**3/3 + 4. Let z(n) be the third derivative of h(n). Find r such that z(r) = 0.
-2, 1
Let y(h) be the first derivative of -3*h**4/4 - 2*h**3 + 3*h**2/2 + 6*h + 5. Factor y(v).
-3*(v - 1)*(v + 1)*(v + 2)
Suppose -4*x - 2*y = 12, -5*y - 10 = x - 8*y. Let s(c) = 4*c**2 - 3*c + 17. Let i(z) = -z**2 + z - 4. Let o(g) = x*s(g) - 18*i(g). Let o(b) = 0. Calculate b.
1, 2
Let w(u) be the second derivative of -u**5/30 - u**4/18 + 2*u**3/9 - 11*u. Solve w(z) = 0.
-2, 0, 1
Let p(n) be the second derivative of -n**6/30 + n**5/10 + 7*n**4/12 - 10*n**3/3 + 6*n**2 - 22*n. Solve p(y) = 0.
-3, 1, 2
Let l(i) be the first derivative of -i**6/72 + 2*i**5/45 - i**4/72 - i**3/9 + 4*i**2 - 4. Let m(o) be the second derivative of l(o). Factor m(f).
-(f - 1)**2*(5*f + 2)/3
Let a(p) be the second derivative of p**4/48 - p**3/8 + p**2/4 + 4*p. Let a(z) = 0. Calculate z.
1, 2
Suppose -9 = -m - 2*m. Let u = 4 - m. Factor -u + 3*f + 2 - f**2 - 7*f + 4*f**3.
(f - 1)*(f + 1)*(4*f - 1)
Let l(a) be the first derivative of -1 + 25/6*a**4 + 16/15*a**5 - 4/3*a**2 - 7/3*a**6 - 16/9*a**3 + 0*a. Let l(u) = 0. Calculate u.
-1, -2/7, 0, 2/3, 1
Let v(i) be the third derivative of i**8/90720 - i**7/3780 + i**6/360 + i**5/60 + 4*i**2. Let z(u) be the third derivative of v(u). Let z(y) = 0. What is y?
3
Let s(h) = -h**2 - h + 1. Let g(m) = m**2 - 9*m - 3. Let c(y) = 2*g(y) + 6*s(y). Determine i, given that c(i) = 0.
-6, 0
Let c(