Let r(p) be the second derivative of x(p). Factor r(u).
-2*(u + 1)**2
Determine c so that -8*c**2 - 8/3*c - 6*c**3 + 0 = 0.
-2/3, 0
Factor 0 - 1/10*a**2 + 0*a.
-a**2/10
Let g(i) = -4*i**4 - 20*i**3 - 4*i**2 + 12*i + 8. Let v(o) = -o**3. Let b(x) = -g(x) + 8*v(x). Determine n, given that b(n) = 0.
-2, -1, 1
Let h(t) be the first derivative of -t**4/3 + 4*t**3/3 - 4*t**2/3 - 13. Suppose h(d) = 0. What is d?
0, 1, 2
Let w(q) be the third derivative of q**6/720 - q**5/10 + 3*q**4 - 48*q**3 + 11*q**2. Let w(d) = 0. What is d?
12
Let x(a) = 9*a**5 + 9*a**4 + 55*a**3 + 64*a**2 + 39*a - 7. Let u(s) = -4*s**5 - 5*s**4 - 27*s**3 - 32*s**2 - 19*s + 3. Let v(b) = 7*u(b) + 3*x(b). Factor v(q).
-q*(q + 2)**4
Let a = -144 - -4321/30. Let b(d) be the third derivative of a*d**5 + 0*d + 0 + 1/3*d**4 + 2*d**2 + 4/3*d**3. What is c in b(c) = 0?
-2
Suppose 0*w - 8 = -2*w. Factor -238 + 4*d**3 + 4*d**w - 4*d + 238 - 4*d**2.
4*d*(d - 1)*(d + 1)**2
Solve 1/2*y**5 + 6*y**4 + 30*y**2 + 23*y**3 + 0 + 25/2*y = 0 for y.
-5, -1, 0
Let q(u) = 6*u**5 + 13*u**3 + 9*u**2 + 5. Let n(b) = -b**5 + b**4 - b**3 - b**2 - 1. Let j(w) = 5*n(w) + q(w). Suppose j(d) = 0. What is d?
-2, -1, 0
Let h(v) be the first derivative of -v**6/6 - 7*v**5/5 - 7*v**4/2 - 2*v**3/3 + 15*v**2/2 + 9*v + 31. Suppose h(r) = 0. What is r?
-3, -1, 1
Factor 3*i**3 - 14*i**4 + 0*i**3 + 17*i**4.
3*i**3*(i + 1)
Let s(j) = -5*j**2 - 4*j + 1. Let c(h) = 4*h**2 + 3*h - 1. Let r(d) = -6*c(d) - 5*s(d). Factor r(p).
(p + 1)**2
Find y, given that 3*y**5 + 91*y**3 - 13*y**3 - 39*y**3 - 6*y**2 - 18*y**4 - 30*y**2 + 12*y = 0.
0, 1, 2
Factor 2*x**2 + 6*x - x**2 - 5*x**2.
-2*x*(2*x - 3)
Let m(j) be the first derivative of -j**6/8 - 9*j**5/20 - 3*j**4/8 + j**3/2 + 9*j**2/8 + 3*j/4 - 7. Factor m(k).
-3*(k - 1)*(k + 1)**4/4
Suppose -m + 0*m = -4. Let u be ((-2)/m - -2)*2. Determine s, given that -4*s**2 + 2*s**2 + 6*s**4 + u*s + s**2 - 5*s**2 - 3*s**5 = 0.
-1, 0, 1
Let b(x) = 12*x**3 - 92*x**2 + 324*x - 324. Let s(p) = -4*p**3 + 31*p**2 - 108*p + 108. Let m(n) = -5*b(n) - 16*s(n). Solve m(t) = 0 for t.
3
Determine d, given that -24*d + 4 + 8*d**2 + 13*d**2 + 86*d**3 - 37*d**3 = 0.
-1, 2/7
Let b(c) be the third derivative of 1/392*c**8 + 0*c**3 + 0 + 0*c**4 - 1/105*c**5 - 1/420*c**6 + 0*c + 4/735*c**7 + 4*c**2. Determine h, given that b(h) = 0.
-1, 0, 2/3
Let p(s) be the second derivative of -4/3*s**2 + 0 - 1/18*s**4 + 6*s + 4/9*s**3. Suppose p(z) = 0. Calculate z.
2
Let o(h) be the third derivative of -1/132*h**4 + 0*h**3 + 0*h + 2*h**2 + 1/660*h**6 + 0 + 0*h**5. Factor o(g).
2*g*(g - 1)*(g + 1)/11
Let b(c) be the second derivative of c**9/30240 - c**8/6720 + c**7/5040 - c**4/4 + 4*c. Let q(v) be the third derivative of b(v). Solve q(f) = 0 for f.
0, 1
Let x(j) = 10*j**3 - 30*j**2 + 7*j + 33. Let l(t) = -5*t**3 + 15*t**2 - 4*t - 16. Let i(m) = 7*l(m) + 4*x(m). Find o, given that i(o) = 0.
-1, 2
Suppose 0 = -4*s - z + 117, -4*s + 132 = -5*z + z. Let g = 35 - s. Let 22/3*l**4 + 11*l**3 + 20/3*l**2 + 0 + 4/3*l + 5/3*l**g = 0. Calculate l.
-2, -1, -2/5, 0
What is p in 0*p - 12/5*p**2 - 4/5*p**3 + 16/5 = 0?
-2, 1
Factor -36/5*k**2 + 12/5*k**4 + 3/5*k**5 + 0 + 27/5*k - 6/5*k**3.
3*k*(k - 1)**2*(k + 3)**2/5
Let m(f) be the first derivative of f**4/2 - 16*f**3/15 - 4*f**2/5 - 5. Find n such that m(n) = 0.
-2/5, 0, 2
Let g be (-119)/(-85) + (-2 - -1). Let u(s) be the first derivative of 0*s**3 - 1/6*s**6 + 0*s - 1/4*s**4 + g*s**5 + 0*s**2 - 3. Solve u(h) = 0.
0, 1
Let c(g) = -g**2 + g + 1. Let v(q) = -5*q**2 + 3*q + 8. Let d = 7 - 4. Suppose d = -3*a - 0. Let f(n) = a*v(n) + 6*c(n). Determine m so that f(m) = 0.
1, 2
Factor j**3 + 3*j - 6*j**2 + 3 + 3*j**4 + 3*j**5 - 10*j**3 + 3*j**3.
3*(j - 1)**2*(j + 1)**3
Let t be (-8)/(-36) - 212/(-18). Let b be (12/(-3))/((-10)/t). Factor b*g + 16/5 + 2/5*g**3 + 12/5*g**2.
2*(g + 2)**3/5
Suppose -451 = 7*h - 465. Factor -6/5*w**3 + 22/5*w**h - 8/5 - 16/5*w.
-2*(w - 2)**2*(3*w + 1)/5
Let l(b) be the first derivative of 1 + 1/8*b**4 + 0*b + 0*b**2 - 2/5*b**5 - 1/4*b**6 + 1/3*b**3. Factor l(q).
-q**2*(q + 1)**2*(3*q - 2)/2
Factor -4 - 8*x**2 + 16*x**3 + 4*x + 0*x + 12*x**4 - 11*x - 9*x.
4*(x - 1)*(x + 1)**2*(3*x + 1)
Let c(r) be the third derivative of -r**10/60480 + r**8/6720 - r**6/1440 + r**4/24 + 5*r**2. Let a(l) be the second derivative of c(l). Factor a(b).
-b*(b - 1)**2*(b + 1)**2/2
Suppose -5*x + 5 = t - 8, -x - t + 5 = 0. What is k in -7*k**2 + 8*k**x + 4 - 4*k + 0 = 0?
2
Let j(b) = 31*b**5 - 17*b**4 - 32*b**3 + 21*b**2 + 5. Let w(x) = 78*x**5 - 42*x**4 - 80*x**3 + 52*x**2 + 12. Let i(s) = -12*j(s) + 5*w(s). Factor i(a).
2*a**2*(a + 1)*(3*a - 2)**2
Suppose 4*k + 22 = 5*u, 13 = 2*u - 6*k + 3*k. Determine t so that 0*t - 2/7*t**4 + 0 + 2/7*t**u - 2/7*t**5 + 2/7*t**3 = 0.
-1, 0, 1
Let k = 11971423/35236 - -2/8809. Let i = k + -337. Factor -i*b**3 - 1/4*b - 1/4 + b**4 + 9/4*b**2.
(b - 1)**3*(4*b + 1)/4
Find w, given that 40*w - 28 - 95*w - 2*w**2 + 25*w = 0.
-14, -1
Suppose 5*w = 32 + 28. Suppose 3*q + q = w. Factor -8/3*f - 4*f**2 - 8/3*f**q - 2/3 - 2/3*f**4.
-2*(f + 1)**4/3
Find c such that 6 - 9*c**2 + 4*c**2 + 7*c**2 - 8*c = 0.
1, 3
Let o(g) be the first derivative of 0*g - 3 - 1/9*g**3 - 1/6*g**2. Solve o(q) = 0 for q.
-1, 0
Let y = -39 + 41. Let s(c) be the second derivative of 1/90*c**6 - 1/126*c**7 + c + 0*c**5 + 0*c**y + 0*c**4 + 0 + 0*c**3. Suppose s(g) = 0. Calculate g.
0, 1
Let x(t) = -t**2 - 5*t + 3. Let n = 20 + -17. Let d(v) = -v**2 - 6*v + 4. Let j(g) = n*d(g) - 4*x(g). Let j(y) = 0. What is y?
-2, 0
Let u = -42 - -42. Let l(z) be the third derivative of 0*z**4 - z**2 + 0*z**3 + 0 - 1/336*z**8 - 1/300*z**6 + 1/150*z**7 + 0*z + u*z**5. Solve l(t) = 0.
0, 2/5, 1
Find d, given that -2/5*d + 0 + 0*d**2 + 2/5*d**3 = 0.
-1, 0, 1
Suppose 0 = 4*l - 5*z - 35 - 2, 3*l - 4 = -z. What is a in 0 + 8/5*a - 243*a**4 + 594/5*a**l + 729/5*a**5 - 116/5*a**2 = 0?
0, 2/9, 1
Determine l so that -2/7 - 2*l**4 - 4/7*l + 8/7*l**5 + 16/7*l**2 - 4/7*l**3 = 0.
-1, -1/4, 1
Suppose 3 = -3*a + 4*a. Solve 0*j**a + 2 - 2*j**3 + 4*j**2 - 2 - 2*j = 0 for j.
0, 1
Suppose 2*h + 10 = -10. Let p be 4/10 - 16/h. Factor p + 6*l - 2*l**2 - 2 - 4.
-2*(l - 2)*(l - 1)
Let b(q) be the first derivative of -q**5/20 - q**4/6 - q**3/6 - 3*q**2/2 + 3. Let a(n) be the second derivative of b(n). Let a(r) = 0. What is r?
-1, -1/3
Factor 1/2*h**4 + 0 - h + h**3 - 1/2*h**2.
h*(h - 1)*(h + 1)*(h + 2)/2
Factor 114 + p**2 + 2*p**2 - 102 + 3*p**5 + 24*p - 15*p**3 - 3*p**4.
3*(p - 2)**2*(p + 1)**3
Suppose 0 = -h + l, l = -4*h + 3*l + 10. Factor -5*q - 3*q**h + q**3 + 5*q**3 + 0*q + 2*q.
-3*q*(q - 1)**2*(q + 1)**2
Let j(f) be the first derivative of -f**4 - 8*f**3/3 - 2*f**2 - 13. What is k in j(k) = 0?
-1, 0
Let p(y) = 5*y**4 - 12*y**3 + 26*y**2 - 24*y + 9. Let s(c) = -14*c**4 + 35*c**3 - 77*c**2 + 72*c - 27. Let i(t) = 11*p(t) + 4*s(t). Factor i(h).
-(h - 3)**2*(h - 1)**2
Let m(p) be the first derivative of p**6/60 + p**5/50 - 3*p**4/40 - p**3/6 - p**2/10 - 12. Determine w so that m(w) = 0.
-1, 0, 2
Let z(k) be the third derivative of 0*k - k**2 + 0*k**4 + 0 - 1/60*k**5 - 1/120*k**6 + 0*k**3. Solve z(v) = 0 for v.
-1, 0
Let o(h) be the second derivative of 0 + 0*h**2 - h - 1/6*h**4 + 0*h**3 + 1/10*h**5. Suppose o(j) = 0. What is j?
0, 1
Let o be 1*1/(17 - 5). Let a(c) be the first derivative of -1/8*c**4 - 1/3*c**3 + o*c**6 - 1 + 0*c + 0*c**2 + 1/5*c**5. Factor a(g).
g**2*(g - 1)*(g + 1)*(g + 2)/2
Let b(w) be the second derivative of -1/30*w**6 + 0*w**3 + 1/84*w**7 + 0*w**4 + 1/40*w**5 + 0 + 4*w + 0*w**2. Factor b(y).
y**3*(y - 1)**2/2
Let z(g) be the third derivative of g**5/3 + g**4/3 - 8*g**2. Suppose z(f) = 0. What is f?
-2/5, 0
Let c be (50/60)/(5/4). Let 4/9 + 10/9*p**3 + 2/9*p**2 - 10/9*p - c*p**4 = 0. What is p?
-1, 2/3, 1
Let h(c) be the second derivative of -c + 1/105*c**7 - 1/50*c**5 - 1/30*c**4 + 0*c**2 + 1/75*c**6 + 0*c**3 + 0. Solve h(j) = 0.
-1, 0, 1
Factor -1/5*x**2 + 1/5*x + 2/5.
-(x - 2)*(x + 1)/5
Let f be (-15)/18*2/1*-3. Let q(t) be the third derivative of 1/42*t**4 + 1/30*t**f + 2*t**2 + 0*t**3 + 0*t + 0. Factor q(u).
2*u*(7*u + 2)/7
Let a(f) = -f**3 - 3*f**2 - 6*f - 1. Let k be 6*((-3)/(-6) - 0). Let p(b) = -b. Let g(w) = k*p(w) - a(w). Solve g(j) = 0 for j.
-1
Let q = 9 - 3. Let f = q - 6. Find t, given that 