3
Let f(w) be the third derivative of -w**8/6720 - w**7/3360 + w**6/1440 + w**5/480 - w**3/2 + 3*w**2. Let v(i) be the first derivative of f(i). Factor v(u).
-u*(u - 1)*(u + 1)**2/4
Let o = -5/242 - -3907/1694. Factor -1/7*n**2 + 8/7*n - o.
-(n - 4)**2/7
Let 0*g + 0*g**2 + 0*g**3 - 1/3*g**4 + 0 = 0. Calculate g.
0
Let c(x) be the first derivative of x**6/5 + 36*x**5/25 + 39*x**4/10 + 24*x**3/5 + 12*x**2/5 + 48. Determine n, given that c(n) = 0.
-2, -1, 0
Let d(s) be the third derivative of s**8/1512 + s**7/945 - s**6/270 - 4*s**2. Factor d(o).
2*o**3*(o - 1)*(o + 2)/9
Let t be (-3 + 5)*(-5 - 0). Let k be (t/(-4))/((-1)/(-2)). Factor -2*p**2 - 4 + 1 + k.
-2*(p - 1)*(p + 1)
Let q = -6 - -8. Let i = 5 - q. Suppose 0*g - 2/3*g**2 + 2/3*g**i + 0 = 0. What is g?
0, 1
Solve -2/3 + 2/3*c**2 + c = 0 for c.
-2, 1/2
Let s be (-1 + (-10)/(-8))/((-261)/(-232)). Suppose 4/9*i + 0 + s*i**2 = 0. What is i?
-2, 0
Let 1/4*j**2 - 5/4*j + 1 = 0. Calculate j.
1, 4
Let o be (-30)/(-9)*(-5 + 2)/(-9). Suppose -o*z**2 + 14/9*z - 4/9 = 0. Calculate z.
2/5, 1
Let z(f) be the second derivative of -2/27*f**3 - 1/54*f**4 - 5*f + 0 - 1/9*f**2. Factor z(p).
-2*(p + 1)**2/9
Let h(i) be the first derivative of -4 + 0*i**3 + 0*i**5 + 0*i + 1/16*i**4 + 0*i**2 - 1/24*i**6. Let h(n) = 0. Calculate n.
-1, 0, 1
Suppose m + 3*h = 15, 6*m + 8 = 2*m + 5*h. Factor -15*u + m*u**2 - 9*u**3 + 0 - 24*u**2 - 3.
-3*(u + 1)**2*(3*u + 1)
Factor 24/5*x**4 + 18/5*x**3 + 4/5*x**2 + 2*x**5 + 0 + 0*x.
2*x**2*(x + 1)**2*(5*x + 2)/5
Let g(u) = -u**4 + 2*u**3 + 2*u**2 + 2. Suppose -4*f - 7 - 1 = 0. Let q(x) = x**4 - x**2 - 1. Let a(p) = f*q(p) - g(p). Factor a(t).
-t**3*(t + 2)
Let s = 2712 - 3824. Let f be 2/5 - s/20. Factor -3*j - f + 56 + 3*j**2.
3*j*(j - 1)
Let h(t) be the second derivative of -t**4/78 - 7*t**3/39 - 28*t. Factor h(s).
-2*s*(s + 7)/13
Factor -a + 402*a**2 + 0*a**3 + 4 + a**3 - 406*a**2.
(a - 4)*(a - 1)*(a + 1)
Suppose 0 = -m - 2*m + 12. Suppose -79*a**5 - 3*a + 60*a**m + 63*a**3 + 2*a + 13*a - 60*a**2 + 4*a**5 = 0. What is a?
-1, 0, 2/5, 1
Let i(v) be the first derivative of -v**3/15 - v**2/10 + 33. Factor i(r).
-r*(r + 1)/5
Let l(m) be the third derivative of m**8/6720 - m**7/1680 - m**6/120 + m**5/30 + 9*m**2. Let h(w) be the third derivative of l(w). Solve h(b) = 0.
-1, 2
Let x(m) be the third derivative of m**11/388080 - m**10/264600 - m**5/30 + 2*m**2. Let j(y) be the third derivative of x(y). Suppose j(w) = 0. What is w?
0, 2/3
Let t(d) = -d**4 - d**3 + d. Suppose 3*r + 65 = 20. Let m be r/9 + (-2)/6. Let z(s) = -3*s**4 + 2*s. Let o(n) = m*z(n) + 4*t(n). Factor o(f).
2*f**3*(f - 2)
Let y(w) = -3*w - 8. Let k be y(-5). Let j = 15/2 - k. Let -n**2 + n**4 + 0 - 1/2*n**5 + j*n + 0*n**3 = 0. Calculate n.
-1, 0, 1
Let p(n) = 5*n**3 - 22*n**2 + 33*n - 8. Let r(u) = u. Let z(j) = p(j) - 5*r(j). Determine c so that z(c) = 0.
2/5, 2
Let y be (-2)/10*(-6)/12*4. Factor -y + 1/5*l**2 - 1/5*l.
(l - 2)*(l + 1)/5
Let s(y) be the first derivative of 1/14*y**4 - 9 - 1/21*y**6 + 0*y + 0*y**3 + 0*y**5 + 0*y**2. Find d, given that s(d) = 0.
-1, 0, 1
Let m be (57/(-1824))/((-1)/4) - 0. Factor -m*c**2 + 0 + 1/8*c.
-c*(c - 1)/8
Suppose 2*k = 6*k. Suppose -1/3*b**3 - 1/3*b**2 + 0 + k*b = 0. Calculate b.
-1, 0
Let v(k) be the first derivative of 0*k**2 + 1/21*k**3 + 0*k - 2 + 1/28*k**4. Factor v(c).
c**2*(c + 1)/7
Let y(l) be the first derivative of l**6/18 - l**5/15 - l**4/12 + l**3/9 + 1. Suppose y(t) = 0. What is t?
-1, 0, 1
Factor -4/7*o**2 + 0 - 4/7*o**3 + 0*o.
-4*o**2*(o + 1)/7
Let p(i) be the third derivative of i**6/1260 + i**5/105 + i**4/28 + i**3/3 + 2*i**2. Let r(d) be the first derivative of p(d). Factor r(l).
2*(l + 1)*(l + 3)/7
Let g(p) = 2*p**3 - 3*p**2 - 3*p - 1. Let j(m) = -2*m**3 + 2*m**2 + 4*m + 2. Let a(r) = 2*g(r) + 3*j(r). Factor a(z).
-2*(z - 2)*(z + 1)**2
Let q(o) = o**3 + o**2 - 2*o. Let h be 1 - (3/(-1) + 2). Let z(c) = 3*c**3 + 3*c**2 - 7*c. Let w(k) = h*z(k) - 7*q(k). Factor w(a).
-a**2*(a + 1)
Let v(u) = -14*u - 1. Let n be v(-1). Let p = n - 8. Factor -p*z**2 - z - z - 2*z**2.
-z*(7*z + 2)
Factor 8/3*v + 2*v**2 + 2/3.
2*(v + 1)*(3*v + 1)/3
Suppose 5 - 13 = -2*y. Determine j, given that 10*j**4 + 7*j**4 - 3*j**2 - 20*j**y + 6*j**3 = 0.
0, 1
Let a(y) be the second derivative of -y**8/168 - y**7/105 - y**2/2 - 5*y. Let n(r) be the first derivative of a(r). Suppose n(x) = 0. What is x?
-1, 0
Let c(q) be the second derivative of -q**5/80 + q**4/12 - 5*q**3/24 + q**2/4 + 5*q. Factor c(w).
-(w - 2)*(w - 1)**2/4
Let z(m) be the second derivative of m**10/30240 + m**9/10080 + m**8/13440 + m**4/4 + m. Let s(g) be the third derivative of z(g). Factor s(w).
w**3*(w + 1)*(2*w + 1)/2
Let a(q) be the first derivative of q**6/2 - 3*q**4 + 2*q**3 + 9*q**2/2 - 6*q + 2. Suppose a(j) = 0. What is j?
-2, -1, 1
Suppose 5*w - 3*w - u - 13 = 0, 2*w - 3*u = 23. Find r, given that 2*r + 2*r**w + 2*r**5 - r**3 - 2*r - r**3 - 2*r**2 = 0.
-1, 0, 1
Let h(g) = 3*g**3 + 0*g**3 + 3 - 3*g**2 - 3*g**2 + 3*g**4. Let w(u) = 3*u**4 + 3*u**3 - 5*u**2 - u + 2. Let p(y) = 2*h(y) - 3*w(y). Solve p(j) = 0.
-1, 0, 1
Let u be 85/25 - 2/5. Suppose 3*m + u*o = 2*m - 6, -o = m. Let 0*n**m - 1/2*n**4 + 0*n + 1/2*n**2 + 0 = 0. Calculate n.
-1, 0, 1
Suppose 3*s + 10 = 5*s. Let n be (36/s)/(3/2). What is m in 2/5*m**4 - 12/5*m**3 + 26/5*m**2 + 8/5 - n*m = 0?
1, 2
Factor 3/2 - 3/4*t - 3/2*t**2 + 3/4*t**3.
3*(t - 2)*(t - 1)*(t + 1)/4
Let f(z) be the second derivative of z**5/5 + z**4/3 + 27*z. Solve f(x) = 0 for x.
-1, 0
Factor 21*u**2 - 27*u**3 + 2*u + 15*u**4 - 3*u**5 - 6*u + 0*u**5 - 2*u.
-3*u*(u - 2)*(u - 1)**3
Let i(h) be the second derivative of -h**5/100 + h**4/5 - 3*h**3/2 + 5*h**2 - 2*h - 19. Factor i(p).
-(p - 5)**2*(p - 2)/5
Let k = -2 - -6. Let j(r) be the first derivative of 4/3*r**3 + 3*r**2 - k - 4*r. Factor j(f).
2*(f + 2)*(2*f - 1)
Let p(f) be the third derivative of -f**6/80 - f**5/20 - f**4/16 - 10*f**2. Factor p(b).
-3*b*(b + 1)**2/2
Let f(y) = -9*y**4 + 19*y**2 - 14*y - 4. Let i(x) = x**4 - x**2 + x + 1. Let d(q) = f(q) + 4*i(q). Factor d(m).
-5*m*(m - 1)**2*(m + 2)
Suppose -5*h - 20 = 0, 5*m - 5*h + h + 24 = 0. Let s be m/16*4/(-3). Let 0 + 5/3*d**2 - s*d = 0. Calculate d.
0, 2/5
Let k(j) be the second derivative of 3*j**5/80 - j**4/16 - j**3/2 + 3*j**2/2 + 44*j. Solve k(s) = 0 for s.
-2, 1, 2
Let m(h) be the second derivative of 2*h**4/27 + 7*h**3/9 + 5*h**2/9 + h + 7. Factor m(b).
2*(b + 5)*(4*b + 1)/9
Let c = -25 + 25. Let r be 8/28 - 4/14. What is w in 0 + 1/5*w**2 + r*w**3 + c*w - 1/5*w**4 = 0?
-1, 0, 1
Let m(w) be the first derivative of -w**3/6 - w**2/4 + 26. Let m(o) = 0. Calculate o.
-1, 0
Factor 5/2*q + 3/2*q**2 - 1.
(q + 2)*(3*q - 1)/2
Let p(b) be the second derivative of b**4/21 - 4*b**3/7 + 18*b**2/7 - 18*b. Suppose p(c) = 0. What is c?
3
Suppose 7*f - 8 = 3*f. What is l in 1/2*l**5 + 1/2*l - 2*l**f - 2*l**4 + 3*l**3 + 0 = 0?
0, 1
Let p(f) be the third derivative of f**8/1680 + f**7/525 - f**5/150 - f**4/120 - 18*f**2. Solve p(s) = 0 for s.
-1, 0, 1
Let x be (-2)/4 - 372/(-720). Let z(j) be the third derivative of j**2 + 0*j**4 + 0*j - x*j**6 + 0 - 1/30*j**5 + 0*j**3. Factor z(i).
-2*i**2*(i + 1)
Let v(u) be the first derivative of -u**6/42 + u**4/7 + 2*u**3/21 - 3*u**2/14 - 2*u/7 + 14. Find i, given that v(i) = 0.
-1, 1, 2
Let l(q) be the first derivative of -q - 1/36*q**4 + 1/18*q**3 - 4 + 1/6*q**2 - 1/60*q**5. Let h(w) be the first derivative of l(w). Solve h(d) = 0 for d.
-1, 1
Suppose -12/7 + 12/7*f**2 + 3/7*f - 3/7*f**3 = 0. What is f?
-1, 1, 4
Let w = 6/19 - -20/57. Determine r, given that -8/3 - w*r**2 + 8/3*r = 0.
2
Let h(t) = 2*t - 7. Let f be h(5). Let x be (2/(-10))/(f/(-10)). Determine j, given that 0 - 2*j**3 + 4/3*j**2 + 0*j + x*j**4 = 0.
0, 1, 2
Let r(i) be the first derivative of i**4/24 + i**3/12 - i**2/2 + 3*i + 1. Let d(k) be the first derivative of r(k). Solve d(s) = 0.
-2, 1
Let u(t) be the second derivative of -t**7/42 - t**6/45 + t**5/20 + t**4/18 + 5*t. Determine d so that u(d) = 0.
-1, -2/3, 0, 1
Let m(x) = -x**2 - 2*x - 6. Let u be m(4). Let i be (-1)/(-2) + (-9)/u. Factor 2/5*s**4 + 0 - i*s + 4/5*s**3 - 2/5*s**2.
2*s*(s - 1)*(s + 1)*(s + 2)/5
Let o(z) be the first derivative of -z**9/12096 - z**8/3360 + z**6/720 + z**5/480 - z**3 + 1. Let w(h) be the third de