n that b(r) = 0.
-1, 0
Factor 4/3*i**2 + 8*i + 12.
4*(i + 3)**2/3
Let x be (-4 - -1)/(3/(-15)). Factor 3*q**3 - 15*q - 3*q**4 - 3*q**4 + 3*q**5 + x*q.
3*q**3*(q - 1)**2
Let u(r) be the second derivative of 0*r**2 + 0 + 1/2*r**3 + 4*r + 1/8*r**4. Factor u(o).
3*o*(o + 2)/2
Let z(a) be the second derivative of a**7/3360 + a**4/6 + 2*a. Let u(r) be the third derivative of z(r). Factor u(t).
3*t**2/4
Let o be 3 - (-12)/9*-6. Let n be (-4)/6*30/o. Factor -3*c**4 - 2*c**4 + 4*c**3 - 2*c**2 + c**n + 2*c**4.
-2*c**2*(c - 1)**2
Let 0*p - 2/15*p**4 - 2/5*p**2 + 0 - 8/15*p**3 = 0. What is p?
-3, -1, 0
Let z = -30 - -53. Factor -3*w**4 - 23 - w**2 + z + 4*w**3.
-w**2*(w - 1)*(3*w - 1)
Let s(n) be the third derivative of n**10/151200 - n**5/60 + 2*n**2. Let f(r) be the third derivative of s(r). Let f(u) = 0. Calculate u.
0
Factor 2/3*m**2 - 1/3*m + m**3 + 0.
m*(m + 1)*(3*m - 1)/3
Let g(u) be the second derivative of 0 - 5*u - 3/40*u**5 + 3/2*u**2 + 1/4*u**3 - 3/8*u**4 + 1/20*u**6. Factor g(r).
3*(r - 2)*(r - 1)*(r + 1)**2/2
Let t be 1 + -6 + 1 + (-50 - -54). Let u(a) be the first derivative of -1/3*a**2 + 1/6*a**4 + 2 + t*a**3 + 1/3*a - 1/15*a**5. Determine l, given that u(l) = 0.
-1, 1
Let l be 1 + (-2)/(0 + -2). Suppose l*z = -3*z + 25. Let -2*y**3 - 4*y**3 + 2*y**2 - 4*y**z - y + 3*y**5 + 4*y**4 + 2*y**2 = 0. Calculate y.
0, 1
Let p(z) be the third derivative of -6*z**2 + z**3 + 0 - 7/8*z**4 + 0*z - 1/5*z**5. Determine j, given that p(j) = 0.
-2, 1/4
Let q = -2 + 12. Suppose -4*h + q = h. Factor 0*a**4 + a**3 - a**4 - a**2 + 3*a**h.
-a**2*(a - 2)*(a + 1)
Let b be 361/90 - (22/2 + -7). Let o(h) be the third derivative of -1/36*h**4 - 2/9*h**3 + 0*h + b*h**5 + 0 + 2*h**2. Let o(s) = 0. What is s?
-1, 2
Let z(f) be the third derivative of -2*f**2 + 0*f - 1/8*f**4 - 1/20*f**5 + 0*f**3 + 0. Factor z(b).
-3*b*(b + 1)
Let k(w) be the first derivative of w**3/5 + 9*w**2/10 + 6*w/5 + 57. Factor k(t).
3*(t + 1)*(t + 2)/5
Suppose -3*h + 10*h = -42. Let a be (18/156)/(h/(-8)). Factor 0 - a*u**2 + 0*u.
-2*u**2/13
Let m(x) be the second derivative of x**7/4200 + x**6/3600 - x**4/2 - x. Let c(b) be the third derivative of m(b). Determine a so that c(a) = 0.
-1/3, 0
Let o be (-2)/6 + (-7)/(-3). Suppose 5*a - w - 19 = 0, 4*a - a = -3*w + 15. Factor 6*u + 0*u**2 - a - u**o - u**2.
-2*(u - 2)*(u - 1)
Let a(h) be the first derivative of 2*h**5/55 + 13*h**4/22 + 70*h**3/33 - 49*h**2/11 + 28. Find y, given that a(y) = 0.
-7, 0, 1
Factor 12*d**3 - 7*d**3 - d**3 + 3*d - 7*d**2.
d*(d - 1)*(4*d - 3)
Let h(b) be the third derivative of -b**8/17920 - b**7/6720 + b**4/6 - 5*b**2. Let x(c) be the second derivative of h(c). What is q in x(q) = 0?
-1, 0
Let o be 4 + (-28)/16 - 2. Let q be 45/84 - 2/7. Factor -q*s**2 + 0*s + o.
-(s - 1)*(s + 1)/4
Let q be 10/3 + 16/72*3. What is p in 0 + 2/3*p - 2/3*p**3 + 7/3*p**2 - 7/3*p**q = 0?
-1, -2/7, 0, 1
Let c(a) = -a - 11. Let u be c(-5). Let y(d) = -d**3 + d**2 - d. Let x(z) = 4*z**3 - 8*z**2 + 6*z. Let l(n) = u*y(n) - x(n). Factor l(t).
2*t**2*(t + 1)
Let i be (-15)/20 - (2 + (-177)/60). Determine j, given that i*j**2 + 0*j + 0 + 1/5*j**3 = 0.
-1, 0
Suppose 3*b = -3*g - 6, 5*b - 4*g - 1 - 25 = 0. Let -3*s**2 + s + b*s - s + 4*s**2 = 0. What is s?
-2, 0
Let s = -683 + 685. Find x, given that 10/7*x**3 - 10/7*x + 2/7*x**s - 2/7 = 0.
-1, -1/5, 1
Let x = -6 - -10. Factor 10*o**3 + 13*o**4 + 4*o**2 - 3*o**x - 2*o**4 + 2*o**5.
2*o**2*(o + 1)**2*(o + 2)
Let n(t) be the second derivative of -3/4*t**3 + 6*t - 1/2*t**2 - 1/10*t**6 + 0 - 7/20*t**5 - 2/3*t**4 - 1/84*t**7. Find q, given that n(q) = 0.
-2, -1
Suppose 0 + 2 = -2*j. Let a(q) = 8*q**3 + 10*q**2 - 8*q - 10. Let c(n) = -n**3 - n**2 + n + 1. Let k(f) = j*a(f) - 6*c(f). Solve k(b) = 0 for b.
-2, -1, 1
Find p, given that 0*p + p**3 + 4*p - 142*p**2 + 2*p**3 + 155*p**2 = 0.
-4, -1/3, 0
Let p(v) = 5*v**4 - 16*v**3 - 21*v**2 + 36*v - 12. Let s(a) = -5*a**4 + 17*a**3 + 21*a**2 - 35*a + 12. Let r(l) = 5*p(l) + 4*s(l). Determine n so that r(n) = 0.
-2, 2/5, 1, 3
Let x(i) be the third derivative of 0*i + 0 + 5*i**2 + 1/4*i**4 + 1/20*i**5 - 3/2*i**3. Factor x(z).
3*(z - 1)*(z + 3)
Let u = -245/6 + 41. Let o(v) be the first derivative of -1/4*v - 1/24*v**6 + u*v**3 - 1/20*v**5 + 1/8*v**4 + 3 - 1/8*v**2. Factor o(f).
-(f - 1)**2*(f + 1)**3/4
Let k be (0 - 1/(-9))*882/196. Factor w + k + 1/2*w**2.
(w + 1)**2/2
Let s be ((-26)/91)/(26/(-14)). Determine p, given that -2/13*p**5 - 2/13*p**4 + s*p**3 + 0 + 2/13*p**2 + 0*p = 0.
-1, 0, 1
Let k be ((-2)/4)/(1*(-2 + 1)). Let x be ((-3)/(-8))/((-9)/(-6)). Suppose -k*d + 1/4*d**2 + x = 0. What is d?
1
Let j be (-1 - -19)/(-3) + 2. Let s be (-1)/j - (-4)/112. Factor 0*z**2 - 6/7*z + s*z**3 + 4/7.
2*(z - 1)**2*(z + 2)/7
Suppose 3 = 3*v - 2*v. Factor 0 + 0*h + 0*h**2 + 0*h**4 + 2/5*h**v - 2/5*h**5.
-2*h**3*(h - 1)*(h + 1)/5
Let t(c) be the first derivative of c**3/8 + 11*c**2/16 + 3*c/4 - 4. Let t(s) = 0. What is s?
-3, -2/3
Determine k, given that 0 - 6/5*k**3 - 8/5*k + 2/5*k**5 + 4/5*k**4 - 16/5*k**2 = 0.
-2, -1, 0, 2
Let f = 7 - 5. Suppose -g - 1 = m, -3*m + 1 = -f*g + 4. Factor 1/3*u**3 - 1/3*u**5 + g + 1/3*u**4 + 0*u - 1/3*u**2.
-u**2*(u - 1)**2*(u + 1)/3
Let r(b) = 7*b**4 - 8*b**3 + 7*b**2 - 3*b + 2. Let l(x) = -11*x**4 + 12*x**3 - 10*x**2 + 4*x - 3. Let i(m) = -5*l(m) - 8*r(m). Solve i(q) = 0 for q.
1
Let q(r) = -4*r - 10. Let b be q(-4). Let w be 9*2/b*1. Find s, given that -1/4*s + 1/4*s**w - 1/4 + 1/4*s**2 = 0.
-1, 1
Let d(s) = 21*s**3 + 64*s**2 + 13*s - 13. Let y(t) = -10*t**3 - 32*t**2 - 6*t + 6. Let k(c) = 6*d(c) + 13*y(c). Find l, given that k(l) = 0.
-8, 0
Let h(w) be the first derivative of w**6/30 - 8*w**5/25 + 11*w**4/10 - 8*w**3/5 + 9*w**2/10 + 5. Factor h(d).
d*(d - 3)**2*(d - 1)**2/5
Let d(t) be the second derivative of t**4/12 + t**3/2 - t**2/2 + 3*t. Let x be d(-4). Find v, given that -2*v + 4*v**4 + v**2 + 2*v + v**5 - v**4 + 3*v**x = 0.
-1, 0
Let d(g) be the second derivative of 5*g**4/16 + g**3 + 9*g**2/8 - 3*g. Factor d(v).
3*(v + 1)*(5*v + 3)/4
Let s(u) = -u**5 + u**3. Let i(w) = 90*w**5 + 210*w**4 + 117*w**3 + 24*w**2. Let g(l) = -i(l) - 15*s(l). Factor g(m).
-3*m**2*(m + 2)*(5*m + 2)**2
Suppose 3*b + 16 = -2. Let z be b/14 - 17/(-7). Factor 1/5*i**4 - 1/5*i**z - 1/5*i + 0 + 1/5*i**3.
i*(i - 1)*(i + 1)**2/5
Let b(i) = i**2 + 3*i - 2. Let t be b(-3). Let w(h) = h**2 - 2*h - 2. Let l(o) = o**2 - 2*o - 3. Let g(f) = t*l(f) + 3*w(f). Determine q, given that g(q) = 0.
0, 2
Let x = -319039/9867 - -2/3289. Let q = x - -33. Determine f so that -q*f**4 + 0*f + 2/3*f**5 + 0 + 2/3*f**2 - 2/3*f**3 = 0.
-1, 0, 1
Let j(b) be the second derivative of b**8/168 - 4*b**7/105 + b**6/12 - b**5/15 + 5*b**2/2 - b. Let u(z) be the first derivative of j(z). Factor u(h).
2*h**2*(h - 2)*(h - 1)**2
Let c(m) be the first derivative of -7/4*m**3 + 0*m + 6 + 1/8*m**6 + 3/4*m**2 - 3/4*m**5 + 27/16*m**4. Factor c(d).
3*d*(d - 2)*(d - 1)**3/4
Determine k so that -1/5*k**3 + 0*k + 0 + 0*k**2 = 0.
0
Factor -22*y**3 - 21*y**3 + 39*y**3 + 4*y**2.
-4*y**2*(y - 1)
Factor 0*c - 2/3*c**3 + 2/3*c**2 + 0.
-2*c**2*(c - 1)/3
Let x(g) = -5*g**3 - 5*g**2 - 12*g - 4. Let y(d) = 3*d**3 + 3*d**2 + 8*d + 3. Let f(q) = 5*x(q) + 8*y(q). Suppose f(c) = 0. What is c?
-2, -1, 2
Let r = -20 - -27. Let g(t) be the second derivative of -3/80*t**5 + 0 - 1/168*t**r + 1/48*t**4 + 1/40*t**6 + 0*t**3 - t + 0*t**2. Factor g(d).
-d**2*(d - 1)**3/4
Let u(m) be the first derivative of -3*m**5/35 - 3*m**4/7 - m**3/7 + 9*m**2/7 - 26. Factor u(s).
-3*s*(s - 1)*(s + 2)*(s + 3)/7
Let z(d) = -10*d**2 - 145*d - 135. Let b(a) = -a**2 - 16*a - 15. Let p(u) = -55*b(u) + 6*z(u). Factor p(s).
-5*(s - 3)*(s + 1)
Let q(c) be the second derivative of -3*c + 0 + 1/2*c**2 + 1/12*c**4 - 1/3*c**3. Factor q(o).
(o - 1)**2
Let f be 2/2*1/4. Let o = 46 - 46. Factor o*k - 1/4*k**2 + f.
-(k - 1)*(k + 1)/4
Let f(u) = 9*u**2 - 5*u - 15. Let z(k) = -1. Let x(g) = 5*g**2 - 3*g - 7. Let j(r) = x(r) + z(r). Let c(w) = -6*f(w) + 11*j(w). Determine p so that c(p) = 0.
1, 2
Suppose -2*w - 2*x = x - 21, -2*w + 5*x - 3 = 0. Factor -w*l**3 + 2*l**4 - 5*l**4 + 4*l**2 - 7*l**2.
-3*l**2*(l + 1)**2
Let b(k) be the third derivative of -k**5/12 + 25*k**4/12 - 125*k**3/6 - 2*k**2 + 9*k. Factor b(g).
-5*(g - 5)**2
Let b(u) be the second derivativ