10 = 5*a. Suppose a*t + 4*j - 13 = 3*j, 5*t - 5*j + 5 = 0. Factor -1/4*s**t - 3/4*s - 1/2.
-(s + 1)*(s + 2)/4
Let g(l) be the second derivative of -5*l**4/12 + 5*l**3/2 - 2*l - 40. What is y in g(y) = 0?
0, 3
Let x(f) be the second derivative of 0*f**4 + 0 - f**2 - 1/300*f**5 + 1/30*f**3 - f. Let c(m) be the first derivative of x(m). Let c(n) = 0. Calculate n.
-1, 1
Let w = 13 + -9. Suppose -6*b + b + m + 10 = 0, 4*b = w*m - 8. Factor 2*k**3 - k**3 + k - 1 - 4*k + b.
(k - 1)**2*(k + 2)
Let w be -2*(-72)/(-45) - -4. Factor -w - 4/5*a**2 - 8/5*a.
-4*(a + 1)**2/5
Let z(p) be the first derivative of 0*p + 0*p**2 + 1/7*p**4 - 1/7*p**6 + 0*p**3 - 2/35*p**5 + 3. Factor z(t).
-2*t**3*(t + 1)*(3*t - 2)/7
Let w(o) be the second derivative of 1/20*o**5 + 0*o**4 + o - 1/10*o**6 + 0*o**3 + 0*o**2 + 0 - 2/21*o**7. Factor w(v).
-v**3*(v + 1)*(4*v - 1)
Factor -3 + 4 - 3 + 8*n - 5*n**2 + 6.
-(n - 2)*(5*n + 2)
Let t(k) be the first derivative of -k**5/30 + k**4/24 + k**3/18 - k**2/12 - 1. What is n in t(n) = 0?
-1, 0, 1
Suppose -4*o + 3*g = -o - 3, -4*o = 5*g - 13. Factor -1/3*l + 2/3*l**4 + 0*l**o + l**3 + 0.
l*(l + 1)**2*(2*l - 1)/3
Let m = 5 - 2. Let c = 15 - 10. Factor 3*x - 6*x**m + 4*x**5 - x**c - x**2 + x**2.
3*x*(x - 1)**2*(x + 1)**2
Let p(z) = -z + 18. Let j be p(13). Let d(l) be the second derivative of 4/3*l**3 + 4*l**2 + 0 + 1/2*l**j - 2*l - 13/6*l**4. Suppose d(h) = 0. Calculate h.
-2/5, 1, 2
Let a(q) = -q**4 - 3*q**3 - 3*q**2 + 3*q + 4. Let r(m) = -m**4 - 3*m**3 - 3*m**2 + 2*m + 3. Let u(h) = 3*a(h) - 4*r(h). Determine n so that u(n) = 0.
-1, 0
Let x(y) be the third derivative of -y**5/20 + y**4/4 + y**2. Let x(n) = 0. What is n?
0, 2
Let s(u) be the first derivative of 1/4*u + 5 + 1/8*u**2 - 1/12*u**3 - 1/16*u**4. Factor s(v).
-(v - 1)*(v + 1)**2/4
Factor 4*d**2 + 2 - 2*d**3 - 2 - 2*d.
-2*d*(d - 1)**2
Let s(o) be the third derivative of o**8/1344 - o**7/840 + 6*o**2. Factor s(t).
t**4*(t - 1)/4
Let w(d) be the second derivative of 2/15*d**6 - 23/40*d**5 - 3*d - 7/24*d**4 - 1/4*d**2 + 0 + 7/12*d**3 + 4/21*d**7. Solve w(y) = 0.
-1, 1/4, 1
Let j(g) be the first derivative of g**8/168 - 2*g**7/105 - g**6/60 + g**5/15 - g**2/2 - 2. Let y(z) be the second derivative of j(z). What is x in y(x) = 0?
-1, 0, 1, 2
Let j = 7 + -7. Let f(w) be the third derivative of j*w**4 + 0 + 1/270*w**5 + w**2 + 0*w - 1/27*w**3. Find t, given that f(t) = 0.
-1, 1
Let k(z) be the second derivative of 1/30*z**4 + 0*z**2 - 1/15*z**3 + 0 + 3*z. Factor k(a).
2*a*(a - 1)/5
Let y be 33/(-18) + 2/(-3) + 3. Factor 0 + 1/4*a**3 + 1/4*a - y*a**2.
a*(a - 1)**2/4
Let o(p) = -4*p**2 - 3*p + 7. Let j(c) = -c**2 - 3*c**2 - 4*c + 2*c**2 + 4 + 2*c. Let a(h) = 7*j(h) - 4*o(h). Suppose a(z) = 0. Calculate z.
0, 1
Let h(i) be the second derivative of -i**5/270 + i**3/27 + i**2/2 + 2*i. Let m(f) be the first derivative of h(f). Factor m(r).
-2*(r - 1)*(r + 1)/9
Let l(h) be the second derivative of h**4/3 - 8*h**3 + 22*h**2 - 4*h. Suppose l(z) = 0. Calculate z.
1, 11
Suppose 4*z - 5*t - 2 = -5, -3 = -4*z + 3*t. Factor -5/8*b**2 + 3/8*b**z + 0 + 1/4*b.
b*(b - 1)*(3*b - 2)/8
Let i(j) = 2*j**3 - 6*j**2 + 6*j + 2. Let f(b) = 4*b**3 - 12*b**2 + 13*b + 5. Let t(x) = -2*f(x) + 5*i(x). Factor t(a).
2*a*(a - 2)*(a - 1)
Let c(x) be the third derivative of x**6/960 + 2*x**3/3 - 6*x**2. Let k(r) be the first derivative of c(r). Solve k(d) = 0.
0
Let s(w) be the second derivative of -2*w**7/21 + 6*w**5/5 + 8*w**4/3 + 2*w**3 + w. Solve s(r) = 0 for r.
-1, 0, 3
Let p(b) be the first derivative of b**5/10 + 5*b**4/8 - b**3/6 - 5*b**2/4 - 45. Factor p(o).
o*(o - 1)*(o + 1)*(o + 5)/2
Suppose 4*w - 35 = -2*m - 9, m = 3*w - 7. Let 0*g**w - 2/7*g**3 + 0*g**2 + 1/7*g + 1/7*g**5 + 0 = 0. Calculate g.
-1, 0, 1
Let w(y) be the third derivative of 0*y**4 + 8/3*y**3 + 0*y - 1/15*y**5 - 8*y**2 + 0. Factor w(f).
-4*(f - 2)*(f + 2)
Let n(w) = -w**3 + w**2 + 2*w + 1. Let v be n(-1). Let l = v + 0. Factor -19/4*u**2 + l + 2*u + 7/4*u**3.
(u - 2)*(u - 1)*(7*u + 2)/4
Let k(w) be the third derivative of -1/168*w**8 + 0*w**5 + 1/105*w**7 + 0*w**3 + 0 + 0*w**4 - 4*w**2 + 0*w**6 + 0*w. Factor k(q).
-2*q**4*(q - 1)
Let o(j) be the first derivative of 7*j**5/50 + j**4/15 - j - 1. Let u(l) be the first derivative of o(l). Determine v, given that u(v) = 0.
-2/7, 0
Let i(q) = -q - 2. Let y be i(-5). Let r(g) = g**3 - 3*g**2 + 1. Let t be r(y). Factor -32*f**2 + t - 38*f**3 - 18*f**4 - 4*f**4 - 3 - 13*f - 5*f**5.
-(f + 1)**4*(5*f + 2)
Let r(k) = -k**3 + k + 1. Suppose -3*f - 5 = 4. Let y(q) = q**4 - 6*q**3 + 15*q**2 - 10*q - 1. Let i(m) = f*y(m) - 3*r(m). Suppose i(b) = 0. What is b?
0, 1, 3
Determine a so that -29*a + 8*a**2 - 32*a**2 - 12*a**3 + 9*a - 4*a**4 + 2*a**4 - 6 = 0.
-3, -1
Let z(i) be the first derivative of -3 + 1/24*i**3 + 0*i + 1/80*i**5 - i**2 + 1/24*i**4. Let b(n) be the second derivative of z(n). Suppose b(d) = 0. What is d?
-1, -1/3
Let x(z) be the third derivative of 0*z + 2*z**3 + 2/3*z**4 + 1/15*z**5 + 5*z**2 + 0. Factor x(f).
4*(f + 1)*(f + 3)
Let n(x) be the second derivative of x**6/40 - 9*x**5/80 + x**4/16 + 3*x**3/8 - 3*x**2/4 - 5*x. Factor n(i).
3*(i - 2)*(i - 1)**2*(i + 1)/4
Let c(a) be the second derivative of 0 - 4*a + 1/54*a**4 + 2/9*a**2 - 1/9*a**3. Factor c(w).
2*(w - 2)*(w - 1)/9
Let n(p) be the second derivative of p**4/6 + 2*p**3 + 9*p**2 - p - 2. Factor n(o).
2*(o + 3)**2
Let s be 2 + 12/(-2) + -1. Let a = s + 7. Factor 5/3*f**4 - 16/3*f**3 + 0*f + 0 + 25/3*f**5 + 4/3*f**a.
f**2*(f + 1)*(5*f - 2)**2/3
Let i be 4/(-6)*(124/(-14) + 8). Factor -6/7*l**2 + 2/7*l**4 - 2/7*l**3 + 2/7*l + i.
2*(l - 2)*(l - 1)*(l + 1)**2/7
Factor -3/7*w + 0 - 1/7*w**2.
-w*(w + 3)/7
Let -5/4*u**3 - 1/8 - 1/8*u**4 + 1/4*u**2 + 5/8*u + 5/8*u**5 = 0. Calculate u.
-1, 1/5, 1
Let h(n) be the third derivative of -1/360*n**6 - 1/60*n**5 - 1/2*n**3 + 3*n**2 + 0 - 1/24*n**4 + 0*n. Let l(x) be the first derivative of h(x). Factor l(d).
-(d + 1)**2
Let g(j) be the second derivative of -j**7/21 + 7*j**6/30 - j**5/10 - 11*j**4/12 + 2*j**3/3 + 2*j**2 - 20*j. Determine o so that g(o) = 0.
-1, -1/2, 1, 2
Let w(o) be the third derivative of -4/9*o**3 + 0*o - 5/18*o**4 - 1/630*o**7 - 4*o**2 - 7/360*o**6 - 1/10*o**5 + 0. Determine p, given that w(p) = 0.
-2, -1
Let -2*m**3 + 4*m**2 + m**2 - 3*m + m**2 - m**3 = 0. Calculate m.
0, 1
Let f(v) be the second derivative of -v**5/80 - v**4/24 + v**3/24 + v**2/4 - 17*v. Factor f(g).
-(g - 1)*(g + 1)*(g + 2)/4
Let a = -4 - -8. Suppose a = -z + 3*z. Let 6*x**z + 2*x**3 - 5*x**3 + 0*x**3 - 3*x**4 = 0. Calculate x.
-2, 0, 1
Factor -4 + 4*b**4 + 0 + 4 + 2*b + 8*b**2 + 10*b**3.
2*b*(b + 1)**2*(2*b + 1)
Suppose -15 = -5*x + 3*c, 2*x - 3*x = -5*c - 3. Suppose -10 = -x*h - 5*w + 4, 0 = h - 3*w. What is z in h - 3/2*z - 3/2*z**2 = 0?
-2, 1
Find y, given that 7*y**2 - y**2 - 18*y**3 + 16*y**3 - 4*y = 0.
0, 1, 2
Let f = 383 - 380. Let -2/9*d**f - 8/3*d**2 - 32/3*d - 128/9 = 0. What is d?
-4
Let g(x) be the first derivative of 2*x**5/5 + x**4/2 - 2*x**3/3 - x**2 + 9. Determine p so that g(p) = 0.
-1, 0, 1
Let i(o) = 16 - 14*o**2 - 12*o - 10*o**2 + 22*o**2 - o**3. Let u(r) = -r**2 + 1. Let t(p) = 3*i(p) - 24*u(p). Solve t(m) = 0 for m.
2
Suppose 0 = -2*z, 0*r + 2*z = -3*r + 9. Suppose 0 + 2/9*w**2 + 2/9*w**r + 0*w = 0. Calculate w.
-1, 0
Let x(c) be the second derivative of c**7/3360 + c**6/1440 - c**5/480 - c**4/96 - c**3/3 + c. Let z(o) be the second derivative of x(o). Factor z(h).
(h - 1)*(h + 1)**2/4
Let g(y) be the third derivative of y**6/1260 - y**5/140 + 2*y**3/3 - 9*y**2. Let z(m) be the first derivative of g(m). Factor z(k).
2*k*(k - 3)/7
Let u(s) = -2*s**3 - 12*s**2 + 8*s + 8. Let h(k) = -9*k**3 - 59*k**2 + 39*k + 40. Let f(p) = -2*h(p) + 11*u(p). Factor f(v).
-2*(v - 1)*(v + 4)*(2*v + 1)
Let b(s) = s**3 - 7*s**2 + 6*s. Let t be b(6). Let h = 2 + t. Factor y**4 - 2*y**2 - 6*y**3 - 2*y**h - 3*y**4 + 0*y**2.
-2*y**2*(y + 1)*(y + 2)
Let m(c) = -2*c - 2. Let d be m(3). Let t = -6 - d. Factor 0 - t - 10*u + 8*u**2 + 4.
2*(u - 1)*(4*u - 1)
Suppose -6*v = -2*v - 8. Let a(l) be the second derivative of l + 0 - 1/6*l**3 + l**v - 1/12*l**4. Let a(k) = 0. What is k?
-2, 1
Let h be (-2)/(1 + 1) - -3. Factor 2*g**4 - 3*g + 0*g + 5*g - 4*g**2 + 2*g**4 - h*g**5.
-2*g*(g - 1)**3*(g + 1)
Let v(q) be the third deriva