-6). Determine l, given that 4/11 + 6/11*l - j*l**2 = 0.
-2/5, 1
Let h be -3 - 6*(-63)/120. Let b(a) be the third derivative of h*a**5 + 0*a**4 + 0 + 0*a - 1/40*a**6 - 2*a**3 - 3*a**2. Let b(q) = 0. What is q?
-1, 2
Let n(q) be the second derivative of -q**5/110 + q**4/22 - 2*q**3/33 - 2*q. Factor n(z).
-2*z*(z - 2)*(z - 1)/11
Suppose -5*g + 15 = -8*g, 25 = 2*p - 5*g. Factor -1/6*r**3 + p + 0*r + 1/6*r**2.
-r**2*(r - 1)/6
Let b be 2/5 + 58/5. Factor 9*p**5 + 8*p**2 - 18*p**4 + 0*p**5 + b*p**3 - 4*p**5.
p**2*(p - 2)**2*(5*p + 2)
Let s be 2/10 + (-168)/(-60). Let q(v) be the second derivative of 0*v**2 + 0 - 1/12*v**4 + 0*v**s + v - 1/40*v**5. Determine z, given that q(z) = 0.
-2, 0
Let t(z) be the first derivative of -z**8/120 - z**7/63 - z**6/135 - 4*z**3/3 + 3. Let x(f) be the third derivative of t(f). Factor x(i).
-2*i**2*(3*i + 2)*(7*i + 2)/3
Suppose -g - 3 + 5 = 0. Let j be (-25)/(-6) + 1/(-6). Factor 3*r + r - r**g - 8 + j.
-(r - 2)**2
Let u(w) = 2*w - 3. Let r be u(2). Let t be r/(-5) + (-24)/(-45). Factor -t*f**2 - f - 2/3.
-(f + 1)*(f + 2)/3
Determine p, given that -1 + 14*p**2 + 5 - 6*p**2 + 10*p + 2*p**3 = 0.
-2, -1
Let q(v) = 103*v**3 - 168*v**2 + 73*v - 3. Let i(z) = -51*z**3 + 84*z**2 - 37*z + 1. Let p(y) = 5*i(y) + 3*q(y). Let p(t) = 0. Calculate t.
2/9, 1/3, 1
Let l be -5*10/15*3/(-2). Let x(m) be the second derivative of 1/90*m**6 + 0 + 0*m**2 - 2*m - 1/36*m**4 + 0*m**l + 0*m**3. Solve x(h) = 0.
-1, 0, 1
Let f(q) be the third derivative of -q**8/672 + q**7/210 - q**5/60 + q**4/48 + 13*q**2. Suppose f(x) = 0. What is x?
-1, 0, 1
Let i(a) = a**2 + a + 6. Let h be i(0). Let t be ((-4)/h)/(2/(-9)). Factor z**2 - 4*z + 0*z**2 + 0*z + t*z.
z*(z - 1)
Let r = 96/115 - 10/23. Let d be 3/(-5) - 4/((-40)/6). Let d*p - r*p**2 + 0 = 0. What is p?
0
Let k = -323 - -977/3. Factor 4*o**2 - 2/3*o - 6*o**3 + 0 + k*o**4.
2*o*(o - 1)**2*(4*o - 1)/3
Let h(t) = 10*t**4 - 12*t**3 - 48*t**2 + 68*t - 24. Let s(d) = 12*d**4 - 12*d**3 - 48*d**2 + 68*d - 24. Let r(k) = -2*h(k) + 3*s(k). Let r(x) = 0. What is x?
-2, 3/4, 1
Let i be 16/56 - (-8)/21. Let h be 1 - 2/((-6)/(-1)). Factor 0*b**2 + 1/3 - h*b**3 + i*b - 1/3*b**4.
-(b - 1)*(b + 1)**3/3
Let j be 2/3*(-180)/(-16). Suppose 0 - 3*i - 9/2*i**2 + j*i**3 = 0. What is i?
-2/5, 0, 1
Factor 2*z**3 - 3*z - z**3 + z**3 + z.
2*z*(z - 1)*(z + 1)
Let t(m) be the third derivative of m**6/60 - m**5/12 + m**4/6 - m**3/6 + 6*m**2. What is s in t(s) = 0?
1/2, 1
Suppose 6 = -l + 3*l. Suppose -11*c + 10*c + 2 = 0. Factor -2 + 2*q**2 - q**2 + 2*q + q**c + q**3 - l*q**3.
-2*(q - 1)**2*(q + 1)
Let f(a) be the second derivative of a**4/54 - 2*a**3/27 + a**2/9 + 16*a - 2. Factor f(q).
2*(q - 1)**2/9
Suppose -5 = r, -13 = 3*x - 5*r - 50. Determine k so that x*k**3 - 2*k + 3*k - 5*k**3 = 0.
-1, 0, 1
Let v = 10 + -8. Suppose 0 = v*f - 3*w, -f - w = 2*f. Factor 2/7*c**2 - 2/7*c + 2/7*c**3 + f - 2/7*c**4.
-2*c*(c - 1)**2*(c + 1)/7
Let u(w) be the third derivative of w**8/2520 + 2*w**7/525 + 7*w**6/450 + 8*w**5/225 + w**4/20 + 2*w**3/45 + 11*w**2. Determine g, given that u(g) = 0.
-2, -1
Let r(d) be the third derivative of -1/900*d**6 + 1/6*d**3 + 0 + 1/30*d**4 + 0*d + 1/300*d**5 - 2*d**2. Let y(l) be the first derivative of r(l). Factor y(g).
-2*(g - 2)*(g + 1)/5
Let x be (-2)/(-10) - 12/(-40). Determine r so that -1/2*r + 1/2*r**3 - x*r**2 + 1/2 = 0.
-1, 1
Suppose -z - 4*s = -3*s - 3, 0 = -2*z - 5*s + 6. Factor 0 + 0*x + 3/5*x**2 + 3/5*x**z.
3*x**2*(x + 1)/5
Let g = -19 + 26. Let z(i) be the second derivative of 0*i**2 + 0*i**4 - 2/105*i**6 + 0*i**3 - 1/70*i**5 - 2*i + 0 - 1/147*i**g. Factor z(a).
-2*a**3*(a + 1)**2/7
Let l(q) be the first derivative of -q**6/2 + 6*q**5/5 - 3*q**4/4 - 4. Let l(i) = 0. What is i?
0, 1
Suppose 0 = 2*t - 6 + 4, -5*g + 4*t = -36. Determine i, given that -8*i**4 + 5*i**5 - 4*i**2 + 6*i**4 + g*i**3 - 15*i**4 + 8*i**3 = 0.
0, 2/5, 1, 2
Let d(g) = -2*g + 13. Let v be d(-10). Factor 6*s - v*s**4 + 15*s**3 + 9*s**5 + 30*s**3 + 10*s**2 - 37*s**2.
3*s*(s - 1)**3*(3*s - 2)
Let q(z) be the first derivative of 2*z**5/55 - 2*z**4/11 + 10*z**3/33 - 2*z**2/11 - 23. Solve q(k) = 0 for k.
0, 1, 2
Solve -9*f**3 + 6*f + 3*f**2 - 3*f**4 + 4*f**5 - 3*f**5 + 2*f**5 = 0.
-1, 0, 1, 2
Let s(n) = n**2 + n + 1. Let d(x) be the first derivative of -14*x**3/3 - 11*x**2 - 2*x + 8. Let b(a) = -d(a) + 6*s(a). Determine l so that b(l) = 0.
-1, -2/5
Suppose 2*u - 2*t - 20 = -3*u, u = -t - 3. Let o(h) be the first derivative of -h**2 - u - 2/5*h**5 + 0*h - 2*h**3 - 3/2*h**4. Solve o(k) = 0 for k.
-1, 0
Let v(j) = -j + 1. Let i(c) = 2*c**2 - 5*c - 1. Let a(p) = -i(p) + 3*v(p). Find t, given that a(t) = 0.
-1, 2
Find o such that -2/3*o - 8/3*o**2 - 2/3*o**5 - 4*o**3 + 0 - 8/3*o**4 = 0.
-1, 0
Let l(j) = -2*j**5 - 8*j**4 - 2*j**3 - 6*j**2. Let f(q) = q**4 + q**3 + q**2. Let w(n) = -12*f(n) - 2*l(n). Factor w(d).
4*d**3*(d - 1)*(d + 2)
Let o(g) be the second derivative of 1/6*g**4 - g**3 - 5*g + 2*g**2 + 0. Factor o(v).
2*(v - 2)*(v - 1)
Let p be (-130)/15 + (-4)/(-6). Let q = p + 8. Factor -4/7*j**3 + 0 + 2/7*j**4 + 2/7*j**2 + q*j.
2*j**2*(j - 1)**2/7
Let z(p) be the first derivative of 3*p**5/20 - 3*p**4/16 - 3*p**3/4 + 3*p**2/8 + 3*p/2 - 3. Suppose z(c) = 0. What is c?
-1, 1, 2
Let m(q) be the third derivative of q**7/420 + 34*q**2. Solve m(w) = 0 for w.
0
Suppose 0*u - 5*u = 10. Let g(y) = -4*y**2 + 6*y - 2. Let m(l) be the second derivative of l**4/12 - l**2/2 - 5*l. Let r(s) = u*m(s) - g(s). Factor r(t).
2*(t - 2)*(t - 1)
Let p = -17 + 19. Find m, given that 0 + m**p - 1/3*m = 0.
0, 1/3
Suppose -20*u - 4*u**2 + 8 + 11 + 16 - 11 = 0. Calculate u.
-6, 1
Let k be 4/(4/18*3). Suppose -16 - 2 = -6*x. Factor 2*v - k*v**x + 1/2 + 9/2*v**4 - v**2.
(v - 1)**2*(3*v + 1)**2/2
Suppose -330 = -51*p - 4*p. Let p*n**2 - 12*n + 63*n**3 + 0 - 135/2*n**4 = 0. Calculate n.
-2/5, 0, 2/3
Factor 0*m**3 + 2/7*m + 0 + 4/7*m**4 - 2/7*m**5 - 4/7*m**2.
-2*m*(m - 1)**3*(m + 1)/7
Let w(q) = 4*q**2 - 13*q + 12. Let y be w(2). Factor 12/7*o**y + 0*o - 36/7*o**5 + 12*o**4 + 68/7*o**3 + 0.
-4*o**2*(o - 3)*(3*o + 1)**2/7
Suppose 3*c + 6 = 4*c. Suppose 3*w = 2*m + 12, -3*w - 4*m + 0*m - c = 0. Suppose -3/2*b + 3/2*b**3 - 1/2 + 1/2*b**w = 0. What is b?
-1, -1/3, 1
Let x(w) be the first derivative of -1/8*w**2 + 1/16*w**4 - 1/4*w - 2 + 1/12*w**3. Factor x(d).
(d - 1)*(d + 1)**2/4
Let m(n) be the second derivative of n**7/14 + 2*n**6/5 + 3*n**5/5 - n**4/2 - 5*n**3/2 - 3*n**2 + 6*n. Factor m(c).
3*(c - 1)*(c + 1)**3*(c + 2)
Let x(i) be the third derivative of 1/105*i**7 + 0 - 1/504*i**8 - 1/90*i**6 + 1/12*i**4 - 1/9*i**3 + 0*i - 4*i**2 - 1/45*i**5. Factor x(t).
-2*(t - 1)**4*(t + 1)/3
Suppose -5*x = -17 + 2. Suppose z + 3*z**2 + x*z**2 + 4*z - 3*z = 0. Calculate z.
-1/3, 0
Let h(n) be the second derivative of 0 + 0*n**3 + n + 1/105*n**6 - 1/70*n**5 + 0*n**2 + 0*n**4. Factor h(v).
2*v**3*(v - 1)/7
Let q(g) be the third derivative of g**6/60 - 8*g**5/105 + 11*g**4/84 - 2*g**3/21 - 5*g**2. Factor q(j).
2*(j - 1)**2*(7*j - 2)/7
Let f(p) be the second derivative of -p**5/90 - p**4/27 - p**3/27 - 10*p. What is r in f(r) = 0?
-1, 0
Suppose 4*z**2 - 2 + 2 = 0. What is z?
0
Let f = 376 - 373. Factor -3/2*d**f + 9/4*d**2 + 0*d + 1/4*d**4 + 0.
d**2*(d - 3)**2/4
Suppose 11 - 3 = 4*w. Factor 8/9 + w*n**2 - 8/3*n.
2*(3*n - 2)**2/9
Let q(r) be the first derivative of -6*r**5/55 + 3*r**4/11 + 14. Suppose q(m) = 0. Calculate m.
0, 2
Let x(q) be the second derivative of 1/15*q**6 - q**2 - 1/5*q**5 + 0 + 0*q**4 + 2/3*q**3 - 5*q. Factor x(m).
2*(m - 1)**3*(m + 1)
Let f be (-4)/(4/(-8)*2). Let n(u) be the second derivative of -u + 1/21*u**7 + 13/42*u**f + 27/70*u**5 + 23/105*u**6 + 0*u**2 + 0 + 2/21*u**3. Factor n(v).
2*v*(v + 1)**3*(7*v + 2)/7
Suppose 0 = 2*j - 17 + 7. Factor -30*o - 42*o**2 - 48*o**3 + 1 - 27*o**4 - 4 - 6*o**j + 12*o.
-3*(o + 1)**4*(2*o + 1)
Let j(c) be the first derivative of -1/8*c**4 + 1/4*c**2 - 1/20*c**5 + 1/4*c + 0*c**3 - 1. Factor j(s).
-(s - 1)*(s + 1)**3/4
Let u = -14/3 + 59/12. Factor 1/4*h**4 - 1/4*h**2 - 1/4*h**5 + 0*h + u*h**3 + 0.
-h**2*(h - 1)**2*(h + 1)/4
Factor b**4 + 0*b**3 + 3*b + b**3 - 3*b**2 - 4*b**3 + 2*b**4.
3*b*(b - 1)**2*(b + 1)
Let u(a) be the second derivative of -a**4/54 + 4*a**3/27 - 4*a**2/9 + 36*a. Factor u(v).
-2*(v - 2)**2/9
Let s(b)