ven that n(z) = 0.
-1, 0
Let d(y) be the first derivative of y**2 + 0*y**3 + 0*y - 1/30*y**5 + 3 + 1/12*y**4. Let g(w) be the second derivative of d(w). Factor g(c).
-2*c*(c - 1)
Let z(n) be the second derivative of n**5/10 - n**4/6 - n**3/3 + n**2 + 6*n. Solve z(b) = 0.
-1, 1
Suppose -2*k = -17 - 15. Factor 3*u**2 + 48*u**3 + 32*u**4 - 6*u + 3 + k*u**4 - 12*u + 24*u**3.
3*(u + 1)**2*(4*u - 1)**2
Let y = -1 - 4. Let i(g) = -g**5 - g**3 + g**2 - 1. Let u(f) = -4*f**5 - 2*f**4 - 4*f**3 + 5*f**2 - 5. Let w(s) = y*i(s) + u(s). Factor w(o).
o**3*(o - 1)**2
Suppose -3*t + 8*t = 25. Suppose 0 = t*i + 5, 4*v - 2*i = 3*i + 33. Factor -1 + 2*r**3 - r + 3 + 6*r**2 + v*r.
2*(r + 1)**3
Suppose -35*c + 9*c = 0. Factor 0*u**2 + c - 1/4*u + 1/4*u**3.
u*(u - 1)*(u + 1)/4
Suppose -m = -2*s - 0*m - 137, 0 = 3*m - 15. Let x = 200/3 + s. Factor 0*f**2 - x + 4/3*f - 4/3*f**3 + 2/3*f**4.
2*(f - 1)**3*(f + 1)/3
Factor -8/5*n**3 - 6/5*n**2 - 4/5 + 18/5*n.
-2*(n - 1)*(n + 2)*(4*n - 1)/5
Let u be ((-2)/7)/((-1)/7). Let s(w) be the first derivative of -2 + 2/3*w**3 + 4*w - 3*w**u. Factor s(o).
2*(o - 2)*(o - 1)
Suppose 13*z - 15*z = -2. Factor z + 4*j + 7/4*j**2.
(j + 2)*(7*j + 2)/4
Find k such that -8*k**4 - 2*k**2 + 5*k**4 + 2*k**2 - 6*k**3 = 0.
-2, 0
Let j = 5 - 2. Factor -11*i**4 + i**3 + 2*i**2 + 3*i**4 + 5*i**j.
-2*i**2*(i - 1)*(4*i + 1)
Let d(l) be the third derivative of 1/156*l**4 - 1/390*l**5 - 1/390*l**6 + 0*l + 0*l**3 - 3*l**2 + 0. Let d(r) = 0. What is r?
-1, 0, 1/2
Let g = -8 - -13. Let x be 10/14*8/g. Solve -2/7*h**2 - x + 8/7*h = 0.
2
Let a be 10/(-4)*(-1)/75. Let p(f) be the third derivative of -a*f**4 + 0 - 1/150*f**5 + 0*f - 1/15*f**3 + f**2. Determine s, given that p(s) = 0.
-1
Let c be (-9)/(-10) - (-11)/(-22). Let i be 1/(-10)*-4*1. Suppose i*p**3 + 0 + 4/5*p**2 + c*p = 0. What is p?
-1, 0
Factor 3/2 - 3/2*w**2 - 3/2*w**3 + 3/2*w.
-3*(w - 1)*(w + 1)**2/2
Let r(c) be the second derivative of c**5/30 - 5*c**4/36 + 2*c**3/9 - c**2/6 - 4*c + 6. Solve r(s) = 0.
1/2, 1
Let -1/3*l**2 - 49/3 + 14/3*l = 0. What is l?
7
Suppose 5*k - 3*k = 0. Suppose -3*y + 4*y = k. Solve -2/3 + y*c + 4*c**3 + 14/3*c**2 = 0 for c.
-1, -1/2, 1/3
Let a(n) be the third derivative of -1/90*n**5 + 0*n**3 + 0*n + 1/72*n**4 + 0 + 1/360*n**6 - 3*n**2. Factor a(s).
s*(s - 1)**2/3
Suppose -4*y + 6*y - 2 = 0. Suppose -4*h = -11 - y. Factor 9 - 9 + h*g**3 - 2*g - g**3.
2*g*(g - 1)*(g + 1)
Factor 2/5*o**2 - 2/5*o + 0.
2*o*(o - 1)/5
Let h(u) be the third derivative of u**5/80 + u**4/8 - 5*u**3/8 - 41*u**2. Determine n so that h(n) = 0.
-5, 1
Let h be 4 + ((-35)/(-21))/(4/(-6)). Factor -1/2*r**3 + 3/2*r**2 - h*r + 1/2.
-(r - 1)**3/2
Let r = -6246 + 24803/4. Let h = r + 46. Determine a, given that 1/2 + h*a - 1/4*a**3 + 0*a**2 = 0.
-1, 2
Let l = 2/453 + 443/2265. Let 0 + 1/5*c + l*c**2 = 0. Calculate c.
-1, 0
Let j = -23 - -26. Suppose -12 = -j*a - 6. Factor 2/3*g**4 - 2/3*g**a + 0 - 2/3*g**3 + 2/3*g.
2*g*(g - 1)**2*(g + 1)/3
Let s(y) = -y**3 - 6*y**2 + 4. Let b be s(-6). Let f(r) be the third derivative of 0*r**3 - r**2 + 1/240*r**5 + 0 + 0*r + 1/96*r**b. Factor f(v).
v*(v + 1)/4
Let h = -22 - -45/2. Let q = -10/3 - -23/6. Determine a, given that h + a + q*a**2 = 0.
-1
Let q(n) be the first derivative of 2*n**7/105 - n**6/10 + n**5/5 - n**4/6 - n**2/2 - 2. Let o(a) be the second derivative of q(a). Factor o(c).
4*c*(c - 1)**3
Let x be 1/(-3) - (-40)/48. Suppose x*s**2 - 1/2*s + 0 = 0. Calculate s.
0, 1
Let v = -9 - -13. Suppose -3*x + v*c = -0*c - 8, -2*x = -3*c - 6. Find r, given that 2/3*r**2 + x + 0*r = 0.
0
Factor 9/5*v + 3/5*v**3 - 3/5 - 9/5*v**2.
3*(v - 1)**3/5
Let h(f) = -f + 10*f**2 - 5 + 0 - f. Let d(m) = -11*m**2 + 3*m + 6. Let n(u) = 6*d(u) + 7*h(u). Factor n(a).
(2*a + 1)**2
Factor -16 - 16*z + 5*z**3 + 7*z**2 - 3*z**2 + 3*z**3 - 4*z**3.
4*(z - 2)*(z + 1)*(z + 2)
Suppose 5*l - 95 = 4*y, -3*l + 64 = 2*y - 3*y. Suppose 2*o + 0*o = -4*m - 10, -l = -o + 5*m. Determine n so that -2/5*n + 0*n**2 + 2/5*n**o + 0 = 0.
-1, 0, 1
Let r = 11 + -7. Suppose -r*g + 6 + 2 = 0. Determine y, given that 1/4*y**3 + 3/4*y**g + 3/4*y + 1/4 = 0.
-1
Let y = -1 + 7. Let t = -6 + y. Solve 2/9*m**5 + 0*m + 0*m**3 + t + 2/9*m**4 + 0*m**2 = 0 for m.
-1, 0
Let u(l) be the second derivative of l**4/72 - l**3/12 - 9*l. Factor u(k).
k*(k - 3)/6
Let f(k) = -k**3 + 4*k**2 - k - 4. Let x be f(3). Suppose a = -4*n + 10, n - x = 3*a - 3*n. Factor 3*d**a + 2 + 0*d**2 - 5*d**2.
-2*(d - 1)*(d + 1)
Let l(p) = -4*p**3 - 2*p**2 + 8*p + 10. Let f be l(-1). Determine h so that 4/3*h**f + 4/9*h + 0 - 10/9*h**3 - 2/3*h**2 = 0.
-2/3, 0, 1/2, 1
Let t be -1*(8 + 39/(-3)). Factor -5/2*j**3 - 1/4*j**t + 1/4 - 5/4*j + 5/2*j**2 + 5/4*j**4.
-(j - 1)**5/4
Let x be 6/(-4) + (-65)/(-10). Let r(c) = c**3 - 5*c**2 + c - 3. Let n be r(x). Factor -5/3*u**4 + 5/3*u - 1/3 + 10/3*u**3 - 10/3*u**n + 1/3*u**5.
(u - 1)**5/3
Factor 0*z**4 - 4/3*z**2 + 0 - 2*z**3 + 0*z + 2/3*z**5.
2*z**2*(z - 2)*(z + 1)**2/3
Let s = 6 + -4. What is d in -s*d**2 + 2*d**3 + 159 - 159 = 0?
0, 1
Suppose -10 = 4*i - 9*i + 5*m, -5*i = 5*m - 40. Suppose -i*j = w - 3, j - 4*j - 5*w = -15. Suppose 2/7 + j*v - 2/7*v**2 = 0. What is v?
-1, 1
Let r(f) be the first derivative of -f**6/10 - 3*f**5/10 + f**3 + 3*f**2/2 + 6*f + 1. Let x(h) be the first derivative of r(h). Find p such that x(p) = 0.
-1, 1
Let f = 4 - 2. Factor 0*n + 0*n - n**f.
-n**2
Let j(a) = 6*a**3 - 42*a**2 + 48*a + 96. Let o(k) = 3*k**3 - 21*k**2 + 24*k + 48. Let q(u) = 4*j(u) - 9*o(u). What is g in q(g) = 0?
-1, 4
Let w be (1 + 1)*35/(-14). Let m = w - -8. Factor 2*y**2 - y**m - y**2 - 2*y**2.
-y**2*(y + 1)
Suppose 4*o + 72 = 2*o. Let k = o + 73/2. Factor 0*w**2 + w**3 - k*w**4 - w + 1/2.
-(w - 1)**3*(w + 1)/2
Let p(k) be the first derivative of 7*k**4/12 - 16*k**3/9 + 11*k**2/6 - 2*k/3 - 5. Suppose p(b) = 0. What is b?
2/7, 1
Let k(j) = -j**3 + 6*j**2 + 7*j + 3. Let c be k(7). Let o be c*1 + (-4 - -1). What is a in -1/2*a - 8*a**4 - 12*a**3 + o - 9/2*a**2 = 0?
-1, -1/4, 0
Let o(v) be the first derivative of 3*v**3/5 - 21*v**2/10 + 6*v/5 - 4. Factor o(d).
3*(d - 2)*(3*d - 1)/5
Factor -1 + 6*f + 1 - 3*f**2 + 0*f**2.
-3*f*(f - 2)
Factor -2*z - 2/3*z**2 - 4/3.
-2*(z + 1)*(z + 2)/3
Factor -1 - 4 - 10*t - 3*t**3 + 13*t**3 - 7*t**4 + 12*t**4.
5*(t - 1)*(t + 1)**3
Determine h, given that -h - 3 + 1/4*h**2 = 0.
-2, 6
Suppose 1/4 - 1/2*g**3 - g + 5/4*g**2 = 0. What is g?
1/2, 1
Let m(a) be the first derivative of -1 + 0*a**2 + 0*a + 1/20*a**5 + 1/3*a**3 - 1/45*a**6 + 1/12*a**4. Let c(j) be the third derivative of m(j). Factor c(s).
-2*(s - 1)*(4*s + 1)
Let w = -11 - -19. Let t(h) = h - 6. Let f be t(w). Factor -4*q**2 + 1 + 2*q + 5*q**2 + 0*q**f.
(q + 1)**2
Factor 0*w**2 - 4*w**3 + 26*w**4 - 19*w**4 - 2*w**2 - 9*w**4.
-2*w**2*(w + 1)**2
Let a be (-3)/33 + (-6 - (-893)/143). Solve a*s**3 + 0 - 4/13*s + 2/13*s**2 = 0.
-2, 0, 1
Find i such that -28/9*i**2 - 4/3 + 2/3*i**3 - 46/9*i = 0.
-1, -1/3, 6
Let g(k) be the third derivative of 1/36*k**4 + 0 + 0*k + 1/180*k**6 - 1/45*k**5 - 3*k**2 + 0*k**3. Factor g(c).
2*c*(c - 1)**2/3
Let v = 2 + 0. Suppose -3*k - 3*k + 7*k - 2 + k**v = 0. Calculate k.
-2, 1
Let n(i) be the first derivative of i**6/240 - i**5/60 - i**2 + 3. Let u(h) be the second derivative of n(h). Determine q so that u(q) = 0.
0, 2
Let b(i) = 2*i**2 + 5. Let m(f) be the third derivative of f**5/60 + f**3/3 - 5*f**2. Let g(u) = -6*b(u) + 14*m(u). Suppose g(v) = 0. What is v?
-1, 1
Let w(h) be the first derivative of -3*h**4/4 - h**3/3 + 4*h**2/3 + 4*h/3 + 2. Factor w(b).
-(b - 1)*(3*b + 2)**2/3
Factor -3/8*j**2 + 0*j + 0 + 1/8*j**4 - 1/4*j**3.
j**2*(j - 3)*(j + 1)/8
Let b = -3 - -1. Let i be -1*7*(b + 1). Factor -8*m**2 - 6*m**2 + 4 + 6*m + 10*m**4 - 13*m**3 + i*m**3.
2*(m - 1)**2*(m + 1)*(5*m + 2)
Let j = 10 - 9. Let n = 7 - j. Factor 3*g + 4*g**3 + 2*g**3 - n*g**2 - 3*g**3.
3*g*(g - 1)**2
Factor -2 - 7/2*z - z**2 + 1/2*z**3.
(z - 4)*(z + 1)**2/2
Let b = 2/141 + 131/705. Determine n so that b*n**2 - 3/5*n + 2/5 = 0.
1, 2
Let v(r) be the second derivative of r**7/280 + r**6/40 - r**4/2 - 2*r**3/3 - 2*r. Let k(n) be the second derivative of v(n). Let k(d) = 0. What is d?
-2, 1
Factor -96/11*d - 128/11 + 30/11*d**2 - 2/11*d**3.
-2*(d - 8)**2*(d + 1)/11
Suppose -q = -18 - 1. Suppose -1 - q = 4*b, -l = 4*b + 20. 