 2*b(c) + 45*y(c). Determine u, given that g(u) = 0.
-1, 2
Suppose 0 = 4*m + 3*h - 7, 0*h = -h - 3. Solve -m*r**2 + 4 + r**2 + 2*r**2 + 4*r + 2*r**2 = 0.
-2
Let a(n) = -7*n**4 + 10*n**3 - 6*n - 1. Let b(v) = 8*v**4 - 11*v**3 + 6*v + 2. Let j(t) = 5*a(t) + 4*b(t). Solve j(x) = 0 for x.
-1, 1
Let y(g) be the second derivative of g**7/84 + 2*g**6/15 + 9*g**5/20 + 2*g**4/3 + 5*g**3/12 - 28*g. Factor y(m).
m*(m + 1)**3*(m + 5)/2
Let n(g) be the third derivative of g**8/672 - g**6/240 - 5*g**2. Factor n(t).
t**3*(t - 1)*(t + 1)/2
Let k(b) be the second derivative of b**9/15120 - b**7/1400 + b**6/900 + b**3 - 6*b. Let j(w) be the second derivative of k(w). Solve j(h) = 0 for h.
-2, 0, 1
Factor -2/9*g**3 + 4/9*g**2 + 2/9*g - 4/9.
-2*(g - 2)*(g - 1)*(g + 1)/9
Factor -4/9*r**2 + 4/9*r**4 + 0 + 0*r**3 + 2/9*r - 2/9*r**5.
-2*r*(r - 1)**3*(r + 1)/9
Suppose 3*m - 9 = 0, -6*m = 5*r - 4*m - 46. Suppose -5*x = -4*a + r, x = -3*a - a + 8. Let 0*b + 1/3*b**3 + x*b**2 + 1/3*b**4 + 0 = 0. Calculate b.
-1, 0
Solve 8/9 - 4/9*s**2 - 4/9*s = 0 for s.
-2, 1
Suppose 3/2*b**5 + 3/2*b**4 + 0 - 9/2*b**3 - 3/2*b**2 + 3*b = 0. What is b?
-2, -1, 0, 1
Let k(i) be the second derivative of 0 + 1/30*i**4 + 1/75*i**6 + 0*i**3 - 2*i + 1/25*i**5 + 0*i**2. Factor k(g).
2*g**2*(g + 1)**2/5
Let w(h) = 24*h**4 - 114*h**3 + 180*h**2 - 105*h + 15. Let c(x) = 25*x**4 - 115*x**3 + 181*x**2 - 105*x + 14. Let n(r) = -3*c(r) + 4*w(r). Factor n(z).
3*(z - 3)*(z - 1)**2*(7*z - 2)
Let x(y) be the first derivative of -2/15*y**3 + 4 + 2/5*y + 0*y**2. Find g such that x(g) = 0.
-1, 1
Let x be 2/(2 - 24/14). Let t = 3 + x. Factor -4*y**3 + 2*y**4 + 4*y + 0*y**4 - 12*y**4 + t*y**2.
-2*y*(y - 1)*(y + 1)*(5*y + 2)
Suppose 0 = r + 2*r - 15. Let b(z) be the third derivative of z**2 - 1/15*z**4 - 3/100*z**6 + 0*z + 0*z**3 + 2/25*z**r + 0. Factor b(l).
-2*l*(3*l - 2)**2/5
Let k(u) be the third derivative of -u**7/1260 + u**6/240 + u**5/360 - u**4/48 - 43*u**2. Factor k(h).
-h*(h - 3)*(h - 1)*(h + 1)/6
Let z be 6*(4/(-6))/(-2). Let j(s) be the second derivative of -5/36*s**4 - z*s + 1/18*s**6 - 1/30*s**5 + 1/9*s**3 + 0*s**2 + 0. Suppose j(v) = 0. What is v?
-1, 0, 2/5, 1
Let d(c) be the first derivative of c**5 - 5*c**3/3 - 9. Factor d(m).
5*m**2*(m - 1)*(m + 1)
Let s(x) be the second derivative of 3*x**5/20 - 2*x**3 + 45*x. Suppose s(b) = 0. Calculate b.
-2, 0, 2
Factor 0*b**4 + 6 - 4*b**3 - 6 + 4*b**4.
4*b**3*(b - 1)
Let b(i) be the third derivative of i**10/105840 - i**8/11760 + i**6/2520 - i**4/8 + 2*i**2. Let n(r) be the second derivative of b(r). Let n(g) = 0. What is g?
-1, 0, 1
Suppose 3*a - z + 20 = 3*z, -5*a - 4*z + 20 = 0. Let d = -24 + 28. Find m such that a*m - m**3 + 1/2*m**d + 1/2*m**2 + 0 = 0.
0, 1
Let b(l) = l**2 - 7*l + 1. Suppose -d - 3*d = 8. Let k = -4 - d. Let c(x) = x**2 - 6*x + 2. Let g(q) = k*b(q) + 3*c(q). Let g(f) = 0. What is f?
2
Let w(t) be the second derivative of t**4/6 - 2*t**3/3 - 17*t. Determine i so that w(i) = 0.
0, 2
Factor -1/3*q + 1/3*q**2 + 0.
q*(q - 1)/3
Let z = -1/326 - -1799/1956. Let w(g) be the first derivative of 3/2*g**2 + 5/4*g**5 + 3 - z*g**3 + g - 15/8*g**4. Factor w(p).
(p - 1)**2*(5*p + 2)**2/4
Suppose -i = -3*i. Factor i - 4/3*k**2 + 0*k + 2/3*k**3.
2*k**2*(k - 2)/3
Let u(w) be the second derivative of -1/9*w**3 + 2/3*w**2 + 0 + 2*w - 1/18*w**4. Factor u(b).
-2*(b - 1)*(b + 2)/3
Let x be (-2)/((-6)/(-2) - 11). Find k such that -1/4 + 1/4*k**5 + 1/2*k**2 - 1/2*k**3 - 1/4*k**4 + x*k = 0.
-1, 1
Factor 1/3*b**5 + b**3 + 0*b + 0 + b**4 + 1/3*b**2.
b**2*(b + 1)**3/3
Let a(v) be the third derivative of v**8/420 - v**7/120 + v**6/180 + v**5/120 + v**3/6 - 2*v**2. Let b(q) be the first derivative of a(q). Factor b(r).
r*(r - 1)**2*(4*r + 1)
Let y(l) be the first derivative of l**8/280 + l**7/105 - l**6/90 - l**5/15 - l**4/12 - 11*l**3/3 - 10. Let w(z) be the third derivative of y(z). Factor w(v).
2*(v - 1)*(v + 1)**2*(3*v + 1)
Let q(v) = -v**4 - v**2. Let r(y) = 9*y**3 + 6*y**2 - 9*y. Let h(d) = -3*q(d) - r(d). Factor h(c).
3*c*(c - 3)*(c - 1)*(c + 1)
Let x(q) = -9*q**2 + 35*q - 105. Let n(y) = 8*y**2 - 36*y + 104. Let l(g) = -5*n(g) - 4*x(g). Factor l(p).
-4*(p - 5)**2
Let h(n) be the second derivative of n**9/504 - n**8/105 + n**7/60 - n**6/90 + 3*n**3/2 + 6*n. Let g(r) be the second derivative of h(r). What is u in g(u) = 0?
0, 2/3, 1
Let c = 128/399 + -2/57. Determine z so that -c*z**5 + 0*z**2 + 0 - 4/7*z**3 + 6/7*z**4 + 0*z = 0.
0, 1, 2
Let o(f) be the third derivative of -f**5/140 + 3*f**2. Suppose o(q) = 0. What is q?
0
Let c be 15/10 - 41/138. Let m = c + 3/23. What is i in -m*i**2 + 5/3*i - 2/3 + 1/3*i**3 = 0?
1, 2
Let q(n) = 6*n**4 + 5*n**3 + 25*n**2 + 15*n - 11. Let x(m) = m**4 + m**3 + 5*m**2 + 3*m - 2. Let r(d) = -2*q(d) + 11*x(d). Determine l so that r(l) = 0.
-1, 0, 3
Factor 2*r**3 + 0*r**3 + 3*r**2 + 0*r**3 + r**3 - 12*r - 12.
3*(r - 2)*(r + 1)*(r + 2)
Let d(t) be the first derivative of t**3/9 + 2*t**2/3 - 5*t/3 - 32. Factor d(x).
(x - 1)*(x + 5)/3
Let l(u) = u**2 + 3*u + 2. Let t be l(0). Determine n so that -1/2*n**3 - 3/4*n**4 + 3/4*n**t + 1/2*n + 0 = 0.
-1, -2/3, 0, 1
Let m(z) be the first derivative of z**5/60 - z**4/24 - z**3/3 - 7*z**2/12 - 5*z/12 - 24. Solve m(a) = 0.
-1, 5
Factor -2/5 + 8*s**2 - 11/5*s.
(5*s - 2)*(8*s + 1)/5
Solve 5/3*v**2 - 2/3*v + 0 - v**3 = 0.
0, 2/3, 1
Let l(c) be the first derivative of -5*c**6/3 - 11*c**5/3 - 5*c**4/6 + 25*c**3/9 + 5*c**2/3 + 15. Determine d so that l(d) = 0.
-1, -1/2, 0, 2/3
Let -2/3*w**2 - 24 + 8*w = 0. What is w?
6
Let y(w) be the first derivative of 1/9*w**3 - 1 + 0*w**2 + 0*w. Factor y(v).
v**2/3
Let y be (-468)/(-30) + 2/10*-2. Factor 16/5 + 16/5*p**4 - 56/5*p - 2/5*p**5 - 10*p**3 + y*p**2.
-2*(p - 2)**3*(p - 1)**2/5
Let r(o) be the first derivative of o**3/9 - o**2/6 - 2*o/3 - 67. Factor r(c).
(c - 2)*(c + 1)/3
Suppose 4*w - 18 = w. Let b(c) be the second derivative of 0*c**3 - c + 0*c**2 + 2/7*c**5 + 1/5*c**w + 2/21*c**4 + 0. Let b(r) = 0. Calculate r.
-2/3, -2/7, 0
Let j = -269 - -6457/24. Let i(a) be the third derivative of 0*a + 2*a**2 - 1/3*a**3 + j*a**4 - 1/120*a**6 + 0 + 1/30*a**5. Suppose i(q) = 0. What is q?
-1, 1, 2
Let v(l) be the first derivative of -1 + 0*l**2 + 2/45*l**5 + 0*l**3 + 0*l + 1/18*l**4. Let v(b) = 0. What is b?
-1, 0
Let l(r) be the third derivative of -1/84*r**4 + 1/210*r**5 + 2*r**2 + 0 + 0*r**3 + 0*r. Factor l(j).
2*j*(j - 1)/7
Let f(x) be the first derivative of x**6/5 + x**5/50 - x**4/40 + 8. Factor f(c).
c**3*(3*c + 1)*(4*c - 1)/10
Let q(k) = 4*k - 10. Let c be q(6). Solve -9*m**5 - 6*m - 39*m**4 + c*m**3 - 33*m**2 - 20*m**3 - 51*m**3 = 0 for m.
-2, -1, -1/3, 0
Let h(s) = 164*s**4 - 92*s**3 - 134*s**2 + 104*s - 14. Let a(p) = -p**4 + p**3 + p**2 - 1. Let t(m) = -4*a(m) - 2*h(m). What is f in t(f) = 0?
-1, 2/9, 2/3
Let j(t) be the third derivative of -t**5/60 - 7*t**4/120 - t**3/15 - 27*t**2. Solve j(s) = 0.
-1, -2/5
Let j(n) be the third derivative of 2*n**7/105 - n**6/30 - n**5/15 + n**4/6 + 19*n**2. Find f, given that j(f) = 0.
-1, 0, 1
Let -12*c**2 - 3*c**4 + 2*c + 9*c**3 + 0*c + 9*c**4 - 14*c - 3*c**5 = 0. What is c?
-1, 0, 2
Suppose 4*f + 7 - 3 = 0. Let j be f/2*(3 - 3). Factor -1/2*i**2 + j*i + 0.
-i**2/2
Let o(i) be the third derivative of -i**9/1512 - i**8/280 - i**7/140 - i**6/180 - 2*i**3/3 + 3*i**2. Let n(l) be the first derivative of o(l). Factor n(g).
-2*g**2*(g + 1)**3
Suppose 0 = 6*w + 4*w - 20. Factor 3/2*o**4 + 0 - 3/2*o**w - 3/2*o + 3/2*o**3.
3*o*(o - 1)*(o + 1)**2/2
Let u(x) be the third derivative of 15*x**5/2 - 5*x**4 + 4*x**3/3 - 14*x**2. Factor u(p).
2*(15*p - 2)**2
Let 0 - 1/6*f + 1/3*f**2 - 1/6*f**3 = 0. What is f?
0, 1
Let n(d) be the second derivative of 2/3*d**4 + 0 + 10*d - 4*d**2 - 1/5*d**5 + 2/3*d**3. Determine j so that n(j) = 0.
-1, 1, 2
Let b = -98/23 - -340/69. Let 2/3*l**2 + 0 - b*l = 0. What is l?
0, 1
Let m be 1/(-3 - (-14)/4). Factor -2*w - 10*w**2 + 21*w**m - 13*w**2.
-2*w*(w + 1)
Let a be (-1)/(-1) - (3 - 6). Factor 2*o**3 + 5*o - a*o - 2*o**3 - o**2 + o**4 - o**3.
o*(o - 1)**2*(o + 1)
Let u(m) = m**2 - 8*m + 3. Let q be u(9). Let z be (-2)/8 + 99/q. Suppose 8/3*n**3 - 8/3 + z*n + 10*n**2 = 0. What is n?
-2, 1/4
Let -8*w**3 + 3*w**4 + 4*w**2 + 3*w**4 + 0*w**2 - 2*w**4 = 0. What is w?
0, 1
Determine r so that 1/4*r