j) be the second derivative of 0*j**2 - 3*j + 1/9*j**3 + 0 + 1/18*j**4. Factor f(b).
2*b*(b + 1)/3
Suppose 0 = 8*j - 2*j - j. Let s(u) be the second derivative of 0*u**3 + 0*u**2 + j - 1/24*u**4 + 3*u. Factor s(g).
-g**2/2
Let r(t) be the third derivative of 1/270*t**5 - 2/27*t**3 + 0*t - 1/108*t**4 + 0 + t**2. Determine h, given that r(h) = 0.
-1, 2
Let s(h) = 4*h + 16. Let t be s(-4). Let q(k) be the second derivative of t - 2*k - 1/12*k**4 - 1/3*k**3 - 1/2*k**2. Factor q(w).
-(w + 1)**2
Suppose 14*j**3 - 3*j**5 - 18*j**3 + 6*j**4 - 6*j**2 + 7*j**3 = 0. What is j?
-1, 0, 1, 2
Determine l so that 5/2 - 1/4*l**2 - 9/4*l = 0.
-10, 1
Factor -40*x**4 + 41*x**4 - 4*x**2 + 0*x**2.
x**2*(x - 2)*(x + 2)
Let c(f) = -3*f**3 + f. Let k be c(-1). Solve 0*z**3 + 0 + 4/3*z**k + 2/3*z**5 - 2/3*z - 4/3*z**4 = 0 for z.
-1, 0, 1
Let k(c) be the third derivative of c**10/15120 + c**9/3780 - c**7/630 - c**6/360 + c**4/24 - c**2. Let n(f) be the second derivative of k(f). Factor n(d).
2*d*(d - 1)*(d + 1)**3
Let p = 4/1491 - -257/89460. Let v(a) be the third derivative of p*a**6 + 0*a + 0*a**5 - 1/315*a**7 + a**2 + 0 + 0*a**3 + 0*a**4. Find l such that v(l) = 0.
0, 1
Suppose -2*v + 2 + 2 = -f, 2*f = -3*v + 13. Find p such that -6*p**v - 9*p**2 - 6*p + 9*p**3 - 6*p**3 = 0.
-2, -1, 0
Let d = 622/21 + -88/3. Solve -6/7*w**2 - 6/7*w - 2/7 - d*w**3 = 0 for w.
-1
Let l(c) be the first derivative of -4 - 2/11*c**3 - 1/22*c**4 + 0*c - 2/11*c**2. Factor l(o).
-2*o*(o + 1)*(o + 2)/11
Suppose 10 = -i - 4*v, 4*v + 27 = 2*i + 11. Let w be (-48)/(-20) + i/(-5). Factor 2/3 + 2/3*q**w + 4/3*q.
2*(q + 1)**2/3
Let x(n) = -4*n**2 - 20*n - 20. Let p(o) = 4*o**2 + 20*o + 21. Let d(h) = 4*p(h) + 5*x(h). Factor d(l).
-4*(l + 1)*(l + 4)
Let l(w) be the second derivative of w**7/840 - w**5/120 + w**3/3 - 3*w. Let a(r) be the second derivative of l(r). Solve a(c) = 0.
-1, 0, 1
Let a(i) be the third derivative of -i**5/30 + i**4/4 + 4*i**3/3 + 8*i**2. Factor a(z).
-2*(z - 4)*(z + 1)
Let j = -8/767 + 82093/2301. Let v = -35 + j. Determine k so that 0*k + 0 + 2/3*k**2 - v*k**3 = 0.
0, 1
Let c be 66/(-154)*(-5)/3. Factor c*o**3 - 2/7 - 12/7*o**2 + 9/7*o.
(o - 1)**2*(5*o - 2)/7
Suppose 0 = -6*r + 4*r + 6. Let n be (9/(-2))/((-6)/8). Factor 2*h**3 - 4*h**5 + h**4 + n*h**5 + r*h**4.
2*h**3*(h + 1)**2
Suppose -4*j + 16 = -2*r, j - 6*r + 2*r = 18. Suppose n**4 + 4/3*n**5 - 1/3*n**3 + 0*n**j + 0 + 0*n = 0. Calculate n.
-1, 0, 1/4
Let i(y) be the first derivative of 4*y**3/3 - 4*y**2 + 4*y + 11. Solve i(q) = 0.
1
Let b be (-2)/6 - 4/(-12). Let -1/3*s + b - 1/3*s**2 = 0. What is s?
-1, 0
Let b(m) = 2*m**2. Let w(h) = h - 4. Let t be w(3). Let q be b(t). Factor 1/4*a**3 + a**q - 1/4*a - a**4 + 0.
-a*(a - 1)*(a + 1)*(4*a - 1)/4
Let m = -1909 + 1145401/600. Let k(u) be the third derivative of u**2 + m*u**6 - 1/60*u**4 + 0 - 1/300*u**5 + 0*u**3 + 0*u. Factor k(h).
h*(h - 2)*(h + 1)/5
Let b(o) = -o + 10. Let a be b(-7). Determine i, given that 12*i**2 - a + 1 + 8*i + 8*i = 0.
-2, 2/3
Let r(m) = -2*m**4 + 4*m**2 + 2. Let x(l) = 6*l**4 - l**3 - 12*l**2 - 7. Let n(t) = 7*r(t) + 2*x(t). Find q, given that n(q) = 0.
-2, 0, 1
Let p(l) be the first derivative of l**5/180 - l**4/36 + l**3/18 + 3*l**2/2 - 4. Let f(u) be the second derivative of p(u). Factor f(z).
(z - 1)**2/3
Let k(p) be the third derivative of -p**5/120 - p**4/16 - p**3/6 - 6*p**2. Solve k(y) = 0 for y.
-2, -1
Let b(j) be the first derivative of j**4/2 + 4*j**3/3 + 2. Solve b(s) = 0 for s.
-2, 0
Let t(y) be the first derivative of y**7/735 + y**6/210 - y**5/210 - y**4/42 - 5*y**2/2 - 4. Let q(s) be the second derivative of t(s). Factor q(j).
2*j*(j - 1)*(j + 1)*(j + 2)/7
Factor -4 + 3*u**2 + 1 - u**2 - 8*u - 5 + 2*u**3.
2*(u - 2)*(u + 1)*(u + 2)
Let l(r) = -3*r**2 - 4*r + 1. Let b = 3 + -5. Let p(x) = -4*x**2 - 5*x + 2. Let q(u) = b*p(u) + 3*l(u). Suppose q(w) = 0. What is w?
-1
Let n(s) be the first derivative of 4/3*s + 1/3*s**2 - 2/9*s**3 + 2. Let n(j) = 0. What is j?
-1, 2
Let k(i) = -i**2 + i + 3. Let z be k(0). Factor 6*a**2 + a**3 + 5*a**z - a**3 - 2*a**3.
3*a**2*(a + 2)
Let g = -28 + 30. Let u(m) be the second derivative of 0*m**g - 1/3*m**3 + 1/10*m**5 - m + 0*m**4 + 0. Factor u(a).
2*a*(a - 1)*(a + 1)
Let p(r) = r + 1. Let u(o) = 22 + 22*o + 3*o**2 - 5*o**2 + 2. Let m(w) = -44*p(w) + 2*u(w). Find a, given that m(a) = 0.
-1, 1
Suppose 0 = 2*l + 4*y - 6, 4*l + 5*y - 3*y = 12. Let q(o) be the first derivative of 0*o**2 + 1/3*o + 3 - 1/9*o**l. Determine r so that q(r) = 0.
-1, 1
Suppose -2*q = -q - 1. Let c be (0/(q + -4))/3. Determine y so that c + y**2 - 5/2*y**4 - 3/2*y**3 + 0*y = 0.
-1, 0, 2/5
Let l = 44 + -34. Factor -4 - 3*c**2 - 9/2*c**3 + l*c.
-(c + 2)*(3*c - 2)**2/2
Let t = -172/3 - -58. Factor -2/9 - 2/9*q**3 - t*q - 2/3*q**2.
-2*(q + 1)**3/9
Let g(r) = -r**2 + 11*r + 2. Let h be g(11). Let u = 1 + h. Let -u*n**2 - 3*n + 2*n**2 + 2*n = 0. What is n?
-1, 0
Let a(i) be the first derivative of -i**3/5 + 3*i**2/5 - 3*i/5 - 25. Factor a(k).
-3*(k - 1)**2/5
Let a(q) be the first derivative of -2*q**6/15 - 4*q**5/25 + 2*q**4/5 + 8*q**3/15 - 2*q**2/5 - 4*q/5 - 3. Determine r so that a(r) = 0.
-1, 1
Suppose 0 = -5*r - 7*v + 11*v, 0 = -4*r + 2*v. Factor 1/5*x**2 + r + 2/5*x - 1/5*x**3.
-x*(x - 2)*(x + 1)/5
Factor -3*s + 2*s**4 + 7/2*s**3 - 5/2*s**2 + 0.
s*(s - 1)*(s + 2)*(4*s + 3)/2
Let b(k) be the third derivative of 2*k**5/105 - k**4/28 - k**3/21 - k**2. What is s in b(s) = 0?
-1/4, 1
Let p(n) = 3*n**2 - 11*n - 10. Let w(a) = 14*a**2 - 43*a - 39. Let h(i) = 18*p(i) - 4*w(i). Factor h(q).
-2*(q + 1)*(q + 12)
Let n(h) = 2*h**2 - 3*h. Let t be n(2). What is i in -5*i**2 + i**3 - 2*i**4 + 3*i**3 + 3*i**t = 0?
0, 1
Factor 75/4*x**2 + 12*x**4 + 42*x**3 + 9/4*x + 0.
3*x*(x + 3)*(4*x + 1)**2/4
Let v(x) be the third derivative of -x**8/784 - x**7/490 + x**6/280 + x**5/140 + 2*x**2. Factor v(s).
-3*s**2*(s - 1)*(s + 1)**2/7
Find h such that -6 + 6*h**4 + 3*h**3 - 5*h - 3*h**4 - 10*h - 9*h**2 = 0.
-1, 2
Let p(a) be the second derivative of -a**5/70 + a**4/42 + 4*a**3/21 - 4*a**2/7 + 8*a. Let p(l) = 0. Calculate l.
-2, 1, 2
Let w(v) be the second derivative of -v**5/200 - v**4/60 + v**3/60 + v**2/10 - 24*v. Find n, given that w(n) = 0.
-2, -1, 1
Let j be 5 - 8/60*27. Determine x so that 1/5*x**5 - 1/5*x**3 + j*x**2 - 4/5 + 0*x - 3/5*x**4 = 0.
-1, 1, 2
Let k(x) = -2 + 0*x + 0 - x. Let t be k(-5). Factor -t*d + 2*d**5 + 3*d - 2*d**3.
2*d**3*(d - 1)*(d + 1)
Let v(x) be the first derivative of 2*x**4/3 + 2*x**3/5 + x**2/15 + 3. Factor v(y).
2*y*(4*y + 1)*(5*y + 1)/15
Suppose 5*l = 3*n + 2*l - 12, -4*n - 4*l = 0. Let d(i) be the first derivative of 0*i + 1/12*i**4 + 0*i**3 + 0*i**n - 3. Suppose d(o) = 0. What is o?
0
Let f(z) = -3*z - 1. Let r(s) = s**3 + 2*s**2 - 3*s - 1. Let u be r(-3). Let p be f(u). Factor 2*t**2 + 6*t - 4*t**2 - 4 - t**2 + t**p.
-2*(t - 2)*(t - 1)
Let a(g) = 3*g**4 - 55*g**3 + 305*g**2 + 5*g - 5. Let i(k) = -3*k**4 + 54*k**3 - 306*k**2 - 6*k + 6. Let z(w) = 6*a(w) + 5*i(w). Solve z(r) = 0.
0, 10
Let t(h) be the second derivative of h**7/21 - 2*h**6/15 + h**4/3 - h**3/3 - 9*h. Factor t(a).
2*a*(a - 1)**3*(a + 1)
Let i(m) = 2*m**2 + 3*m + 1. Let z be i(-2). Factor 2*s**4 + 0*s**3 + 2*s**2 - s**3 - z*s**3.
2*s**2*(s - 1)**2
Suppose -65 = 2*s - 69. Factor -1/4*r**4 + 0 + 3/4*r**3 - 3/4*r**s + 1/4*r.
-r*(r - 1)**3/4
Suppose 4*w - 15 - 9 = 0. Let h(i) be the second derivative of -1/6*i**4 + 0*i**2 + 2*i + 1/10*i**w + 0 + 0*i**3 + 1/20*i**5. Determine x so that h(x) = 0.
-1, 0, 2/3
Let x(g) be the first derivative of g**6/60 + 3*g**5/40 + g**4/24 - g**3/4 - g**2/2 - 3*g + 2. Let a(y) be the first derivative of x(y). Factor a(l).
(l - 1)*(l + 1)**2*(l + 2)/2
Let t = 9 - 7. Let -2*r**t - 9 - 3*r + 3*r + 11 = 0. What is r?
-1, 1
Suppose 1/3 - 1/3*y**2 + 1/3*y**3 - 1/3*y = 0. Calculate y.
-1, 1
Let s be (-32 + 2)*(1 - 0). Let v be 5/s - (-2)/12. Factor 1/3*i + 1/3*i**2 + v.
i*(i + 1)/3
Factor -3*r**2 - 14*r**3 - 10*r**3 - 8*r**3 + 31*r**3.
-r**2*(r + 3)
Let u = 2873/428 + 4/107. Factor -1/4*t**3 + u + 9/4*t**2 - 27/4*t.
-(t - 3)**3/4
Let i(h) = 7*h**3 + 9*h**2 + 9*h + 7. Let o(l) = -15*l**3 - 18*l**2 - 18*l - 15. Let w(s) = 9*i(s) + 4*o(s). Let w(v) = 0. Calculate v.
-1
Factor 66*b**2 - 24*b**2 + 4*b**4 - 20*b**2 - 2*b + 2*b**5 - 26*b**2.
2