 be the third derivative of i**7/630 + i**6/90 + i**5/36 + i**4/36 + 4*i**2. Factor c(a).
a*(a + 1)**2*(a + 2)/3
Let 2/3 - 2*f - 8/3*f**2 = 0. Calculate f.
-1, 1/4
Let y(o) be the third derivative of -o**6/600 - o**5/150 + o**4/120 + o**3/15 - 16*o**2. Factor y(j).
-(j - 1)*(j + 1)*(j + 2)/5
Let z(c) = c**3 - 7*c**2 - c + 10. Let y be z(7). Factor 0*u**y - u**3 - 5*u**3 + 2*u**3 + 2*u**2 + 2*u**4.
2*u**2*(u - 1)**2
Let u be (6/(-4))/((-9)/(-48)). Let o = u + 2. Let q(b) = 3*b**3 + 3*b**2 - 6*b. Let x(a) = -8*a**3 - 10*a**2 + 17*a. Let z(n) = o*x(n) - 17*q(n). Factor z(v).
-3*v**2*(v - 3)
Let j(a) be the first derivative of -a**3/21 - 5*a**2/14 - 11. Determine g so that j(g) = 0.
-5, 0
Let g(r) be the first derivative of 2*r**2 + 9 + 0*r + 4/3*r**3. Factor g(y).
4*y*(y + 1)
Let z(f) = 9*f**3 + 12*f**2 + 3*f + 3. Let o(i) = 1. Let j(h) = -3*o(h) + z(h). Find k, given that j(k) = 0.
-1, -1/3, 0
Suppose -4*h = -2*o + 3*o - 14, -h - 2*o = -7. Factor 0*a**2 + 2/5*a**4 + 0 + 0*a + 0*a**h.
2*a**4/5
Find u, given that 0 + 1/3*u**2 + 0*u + 1/3*u**3 = 0.
-1, 0
Let v(p) be the third derivative of -p**7/1575 + p**5/450 - 2*p**2. Suppose v(i) = 0. What is i?
-1, 0, 1
Let j(b) be the first derivative of -1 + 192/55*b**5 + 2/11*b + 9/11*b**2 - 73/22*b**4 + 2/11*b**3 - 12/11*b**6. Factor j(x).
-2*(x - 1)**3*(6*x + 1)**2/11
Let x(o) = 8*o - 126. Let c be x(16). Factor 0 + 1/3*v - 1/6*v**c.
-v*(v - 2)/6
Let v(i) = 11*i**4 - 21*i**3 + 11*i**2 + 15*i - 4. Let d(l) = 65*l**4 - 125*l**3 + 65*l**2 + 90*l - 25. Let k(s) = 6*d(s) - 35*v(s). Let k(w) = 0. What is w?
-1, 1, 2
Let g(f) = 6*f**3 + 4*f**2 - 14*f. Let p be 3/(-2)*40/(-12). Let z(w) = 6*w**3 + 3*w**2 - 15*w + 1. Let j(k) = p*g(k) - 4*z(k). What is t in j(t) = 0?
-2, -1/3, 1
Let l(q) be the first derivative of -4/25*q**5 + 1/5*q**4 + 0*q + 4 + 0*q**2 + 8/15*q**3. Factor l(a).
-4*a**2*(a - 2)*(a + 1)/5
Let a be (-1)/3*(-1)/12. Let v(p) be the second derivative of 0*p**2 + a*p**4 + 0 + 1/18*p**3 + 3*p. Factor v(y).
y*(y + 1)/3
Let x(l) be the third derivative of l**8/504 - l**7/105 - l**6/180 + l**5/30 + 19*l**2. Find k, given that x(k) = 0.
-1, 0, 1, 3
Let c = -4639/7 - -663. Factor 0 - c*u**2 - 2/7*u**3 + 2/7*u + 2/7*u**4.
2*u*(u - 1)**2*(u + 1)/7
Let s(w) be the first derivative of w**5/10 - 3*w**3/2 + w**2 + 6*w + 20. Determine m so that s(m) = 0.
-3, -1, 2
Let f = -47/161 - -33/23. Solve 4/7*u**4 + 0 + f*u**2 + 30/7*u**3 - 10/7*u**5 - 8/7*u = 0.
-1, 0, 2/5, 2
Let d(p) be the third derivative of -25*p**6/8 - 15*p**5/4 - 15*p**4/8 - p**3/2 + 9*p**2. Let d(z) = 0. Calculate z.
-1/5
Factor 2/7*x**4 + 0*x + 0 + 2/7*x**3 + 0*x**2.
2*x**3*(x + 1)/7
Let c(z) be the first derivative of -z**7/4200 + z**6/600 - z**5/200 + z**4/120 + z**3 + 2. Let j(k) be the third derivative of c(k). Factor j(s).
-(s - 1)**3/5
Let g be 19/((-399)/6) + 2/7. Let d(k) be the first derivative of -2/3*k**3 - k**4 - 2 - 2/5*k**5 + 0*k**2 + g*k. Find l, given that d(l) = 0.
-1, 0
Factor 3/7*a**5 - 9/7*a**4 + 0 - 3/7*a**2 + 0*a + 9/7*a**3.
3*a**2*(a - 1)**3/7
Let o(y) be the second derivative of y**7/147 - 2*y**6/15 + 38*y**5/35 - 100*y**4/21 + 256*y**3/21 - 128*y**2/7 - 60*y. Factor o(c).
2*(c - 4)**2*(c - 2)**3/7
Let o(q) be the second derivative of q**6/1800 - q**5/100 + 3*q**4/40 - q**3 + 7*q. Let w(p) be the second derivative of o(p). What is i in w(i) = 0?
3
Suppose 0*n**2 + 0 + 1/3*n**5 + 0*n + 0*n**3 + 1/3*n**4 = 0. Calculate n.
-1, 0
Suppose -r - 3*y + 7 = r, -4*r - 4*y + 12 = 0. Let n(m) be the first derivative of -r*m**2 + 2*m + 2/3*m**3 + 1. Factor n(f).
2*(f - 1)**2
Let d = -5 - -3. Let h(o) = 8*o**4 + 9*o**3 - 9*o**2 - 9*o. Let z(q) = -2*q**4 - 2*q**3 + 2*q**2 + 2*q. Let b(u) = d*h(u) - 9*z(u). Factor b(s).
2*s**4
Let w(m) be the first derivative of -4*m**3/9 - m**2/2 + m/3 + 7. Factor w(f).
-(f + 1)*(4*f - 1)/3
Let r(c) = 4*c**2 + 4*c - 5. Let j be r(1). Factor 0*l**2 - 2/3*l**4 + 1/3*l**5 + 0 + 0*l + 1/3*l**j.
l**3*(l - 1)**2/3
Suppose 6*x - 3*o - 102 = 3*x, -x + 24 = 4*o. Find w, given that 293*w**5 + 16 - 452*w**3 - 118*w**5 + x*w - 176*w**2 - 47*w**4 - 38*w**4 = 0.
-1, -2/5, 2/7, 2
Factor 8/9*l**3 + 0*l + 7/9*l**4 - 16/9*l**2 + 0 + 1/9*l**5.
l**2*(l - 1)*(l + 4)**2/9
Let h(q) be the first derivative of 1/14*q**4 + 1/7*q**2 + 0*q + 4/21*q**3 + 2. Factor h(v).
2*v*(v + 1)**2/7
Suppose 0 = 4*p + 4*t - 64, 0 = 5*p - 5*t - 11 - 89. Let y = -53/3 + p. Factor y*u**4 + 0*u**3 + 0*u**2 + 0*u + 1/6*u**5 + 0.
u**4*(u + 2)/6
Suppose -2 = w - 2*w. Let a be 4/6 + w/3. Factor -a - 2/3*p + 2/3*p**3 + 4/3*p**2.
2*(p - 1)*(p + 1)*(p + 2)/3
Suppose -2*x**3 - 16*x + x**3 + 12*x - 4*x**2 = 0. Calculate x.
-2, 0
Let h = -161 + 105. Let l be h/(-90) + 4/(-10). Find s such that -l*s - 2/9*s**5 + 4/9*s**3 + 2/9 + 2/9*s**4 - 4/9*s**2 = 0.
-1, 1
Suppose z - 28 = -3*z. Let w(b) be the third derivative of 0 + 0*b**5 - 1/300*b**6 - 2*b**2 + 0*b + 0*b**3 - 1/280*b**8 - 4/525*b**z + 0*b**4. Factor w(d).
-2*d**3*(d + 1)*(3*d + 1)/5
Solve 25*h**3 - 58*h**3 + 17*h**3 - 2*h**4 + 20*h**3 - 2*h**5 = 0.
-2, 0, 1
Let w(j) be the second derivative of j**6/84 - 4*j**5/105 + j**4/84 + 2*j**3/21 - 3*j**2/2 + 7*j. Let n(b) be the first derivative of w(b). Factor n(t).
2*(t - 1)**2*(5*t + 2)/7
Let d(n) be the first derivative of -1/22*n**4 + 1/11*n**2 + 0*n - 2/33*n**3 + 1 + 2/55*n**5. Factor d(a).
2*a*(a - 1)**2*(a + 1)/11
Suppose 3*r - 7 - 5 = 0. Let d be (-116)/(-14) + r/(-14). Solve -7*l**3 - d*l**2 - 7*l + 4*l**5 - 9*l - 2*l**5 + 10*l**4 + 19*l**3 = 0 for l.
-2, 0, 1
Suppose 1 + 3 = a. Let c = 12 - a. Determine v so that 0*v**2 - 7*v + c*v - v**2 = 0.
0, 1
Let v(q) = 3*q + 45. Let y be v(-14). Let b(k) be the first derivative of 1/5*k - 1/5*k**2 + 1/15*k**y - 1. Suppose b(i) = 0. What is i?
1
Let f = -6047/146832 - -17/368. Let o = f - -2789/798. Factor -u - o*u**2 + 0.
-u*(7*u + 2)/2
Let b = 16 + -31/2. Suppose 3/4*r**2 + 0*r**3 + 0 - 1/4*r**4 + b*r = 0. Calculate r.
-1, 0, 2
Factor -3/4*d - 3/4*d**2 + 3/2.
-3*(d - 1)*(d + 2)/4
Let s(q) be the third derivative of q**8/80640 - q**7/6720 + q**6/1440 - q**5/30 - 3*q**2. Let i(f) be the third derivative of s(f). Solve i(n) = 0 for n.
1, 2
Factor 21*s + 2*s**5 - 10*s - 11*s - 10*s**4 + 12*s**3.
2*s**3*(s - 3)*(s - 2)
Let x be (-20)/(-64)*(-2)/(-5). Let v(k) be the first derivative of -x*k**2 + 1 + 0*k**3 + 1/16*k**4 + 0*k. Determine m so that v(m) = 0.
-1, 0, 1
Suppose -w = -3*w + 5*s + 21, -2*s = -4*w + 18. Solve k + 2*k**3 - 2*k**2 - w*k**3 - k = 0.
-2, 0
Let j(h) be the first derivative of 1/16*h**4 + 3 + 1/12*h**3 - 1/8*h**2 - 1/4*h. Factor j(i).
(i - 1)*(i + 1)**2/4
Factor -6*u**4 - 3*u + 6*u**2 - 29 + 29 + 3*u**5.
3*u*(u - 1)**3*(u + 1)
Suppose 0 = -5*z + 7 + 13. Let x(s) be the third derivative of 1/7*s**z - s**2 - 3/70*s**5 + 0*s - 4/21*s**3 + 0. Factor x(j).
-2*(3*j - 2)**2/7
Let g(o) be the first derivative of 5*o**3/3 + 5*o**2 - 15*o - 8. Factor g(l).
5*(l - 1)*(l + 3)
Let w(n) be the first derivative of -2*n - 1 - 1/3*n**3 - 3/2*n**2. Let a(f) = f**2 + 4*f + 3. Let h(s) = -4*a(s) - 6*w(s). Solve h(z) = 0 for z.
-1, 0
Factor -4*o + 62*o**3 - 14*o**3 - 2*o**2 - 32*o**3 - 10*o**4.
-2*o*(o - 1)**2*(5*o + 2)
Let q(v) = -v**3 - v**2. Let h(z) = 6*z**3 + 36*z**2 + 72*z - 108. Let t(w) = -h(w) - 3*q(w). Let t(d) = 0. What is d?
-6, 1
Suppose -5*h + 15 = v, h + 3*h + 2 = 2*v. Let b be h/4 + 0 + 0. Determine l so that -b*l + 1/4*l**2 + 0 = 0.
0, 2
Let a = -3 - -7. Suppose a*z - 6 = 2. Factor -z*i**4 + 3*i**4 - 2*i**2 - 2*i**4 - i**5 + 3*i**4 + i.
-i*(i - 1)**3*(i + 1)
Let c(w) be the third derivative of 3*w**7/385 - w**6/55 + 2*w**5/165 + 2*w**2. Let c(l) = 0. What is l?
0, 2/3
Let o = 12151/30 + -405. Let g(v) be the second derivative of -2*v + o*v**5 + 0*v**2 + 0 + 0*v**4 - 1/9*v**3. What is m in g(m) = 0?
-1, 0, 1
What is z in 0*z + 1/3*z**5 + 0 - z**4 - 1/3*z**2 + z**3 = 0?
0, 1
Let m(g) = 25*g**3 - g**2. Let q be m(1). Let s be q/63 + (-8)/(-28). Factor 2/3*i**2 + 0 - s*i.
2*i*(i - 1)/3
Find b such that -2/11*b**2 + 4/11*b - 2/11 = 0.
1
Let o(s) be the third derivative of 1/15*s**5 + 1/12*s**4 + 0*s + 1/60*s**6 - 2*s**2 + 0*s**3 + 0. Factor o(p).
2*p*(p + 1)**2
Let w = -8 + 8. Suppose w = p + p. Factor 1/4*z**4 + 0*z**2 + 0*z - 1/4*z**3 + p.
z**3*(z - 1)/4
Suppose -4*c = f + 1, -2*f - 2 = -4*f - 4*c. Let g