et k(v) be the third derivative of v**5/3 + 4*v**4/3 - 8*v**3/3 + v**2. Determine p, given that k(p) = 0.
-2, 2/5
Let q(g) be the first derivative of -g**4 - 8*g**3 - 18*g**2 - 16*g + 14. Let q(f) = 0. What is f?
-4, -1
Let i = -14 - -20. Suppose 2*c + 6*c**3 + i*c**2 + 0*c**4 - 2*c + 2*c + 2*c**4 = 0. Calculate c.
-1, 0
Find w such that 0*w**2 + 34*w**4 - 18*w**4 - 2*w**2 - 10*w**4 + 4*w**3 = 0.
-1, 0, 1/3
Let c(j) = 2 - 2*j**2 + j**3 + 0 - 4*j**2 + 3*j**2 - 4*j. Let q be c(4). Factor -4/7*z**5 + 0*z**3 + 0*z + 6/7*z**4 - 2/7*z**q + 0.
-2*z**2*(z - 1)**2*(2*z + 1)/7
Let u(f) = f**2 + 2. Let y be u(-2). Suppose 2*m + 19 = y*m - 3*g, g = -5*m. Factor b**2 + 1 - m.
b**2
Let r(t) be the second derivative of 0*t**5 + 2*t + 0*t**3 + 0*t**2 - 1/75*t**6 + 1/30*t**4 + 0. Factor r(z).
-2*z**2*(z - 1)*(z + 1)/5
Let b(x) be the first derivative of -x**6/3 - 4*x**5/5 + 3*x**4/2 - 52. Factor b(p).
-2*p**3*(p - 1)*(p + 3)
Factor 0 - 3/10*w**4 + 0*w - 3/10*w**3 - 1/10*w**2 - 1/10*w**5.
-w**2*(w + 1)**3/10
Let l be (-14)/(-5) - (-1)/5. Let -s**l + 2*s**3 - 9*s + 6*s**2 + s**3 - s - 2*s**4 + 4 = 0. What is s?
-2, 1
Suppose -4*p = 3*w - 19 + 6, 2*w + 6 = p. Determine c, given that -12/7*c**3 + 12/7 - 9/7*c**2 + 12/7*c - 3/7*c**p = 0.
-2, -1, 1
Let c(h) be the first derivative of h**6/18 + h**5/15 - h**4/6 - 2*h**3/9 + h**2/6 + h/3 - 6. Factor c(l).
(l - 1)**2*(l + 1)**3/3
Let b be 6/(-10)*46/(-69). Let z(x) be the first derivative of 2/3*x**3 + 1/3*x**6 + 1 - 1/2*x**4 - b*x**5 + 0*x + 0*x**2. Factor z(t).
2*t**2*(t - 1)**2*(t + 1)
Let a(h) be the first derivative of -2*h + 1 + 3/8*h**4 + 0*h**2 + 7/6*h**3. Factor a(y).
(y + 1)*(y + 2)*(3*y - 2)/2
Let m(u) be the first derivative of 1/15*u**5 + 4 - 2/3*u + 1/4*u**4 + 1/9*u**3 - 1/2*u**2. Factor m(d).
(d - 1)*(d + 1)**2*(d + 2)/3
Let p = 25 - 3. Suppose 5*l + p = 3*q, q + l - 10 = -2*q. Let 6*f**5 - 3*f + 0 + 3/2*f**q - 33/2*f**2 - 18*f**3 = 0. Calculate f.
-1, -1/4, 0, 2
Let k(o) be the first derivative of -o**5/10 + o**4/2 - o**3 + o**2 + o + 3. Let n(u) be the first derivative of k(u). Determine f, given that n(f) = 0.
1
Let w(n) = -n**2 - 8*n + 7. Let s be w(-8). Suppose s*x**4 - 3*x**4 + 8*x - 16*x**4 + 16*x**2 + 3*x**3 - 11*x**3 - 4 = 0. Calculate x.
-1, 1/3, 1
Let g be (-126)/84*2/(-12). Determine p so that -1/4*p**3 + 1/2*p**2 + 0*p + 0 - 1/2*p**4 + g*p**5 = 0.
-1, 0, 1, 2
Let z(h) be the third derivative of -h**5/15 + h**4/2 + 8*h**3/3 + 8*h**2. Factor z(f).
-4*(f - 4)*(f + 1)
Suppose 0 = d - 3*d. Find l such that 7 + 2*l - 9 + d*l - 2*l**3 + 2*l**2 = 0.
-1, 1
Let 0 - 49/4*h**4 + 2*h + h**2 - 19/2*h**3 - 15/4*h**5 = 0. What is h?
-2, -1, -2/3, 0, 2/5
Let t(x) be the third derivative of x**5/12 - 5*x**4/6 + 10*x**3/3 - 2*x**2 - 4*x. Factor t(v).
5*(v - 2)**2
Factor -4/3*x - 2 + 2/3*x**2.
2*(x - 3)*(x + 1)/3
Let s be 42/(-16)*(-18)/21. Let g(w) be the first derivative of -3*w + 1/2*w**3 - s*w**2 + 3/10*w**5 + 9/8*w**4 + 3. Suppose g(d) = 0. What is d?
-2, -1, 1
Let l = -27/40 - -7/8. Factor -l - 3/5*f**2 + 4/5*f.
-(f - 1)*(3*f - 1)/5
Let h be 2*(1/(-1))/(-1). Suppose h*b - 8 = -2*b. Factor 5*x + 2*x**2 + b*x - 4 - 5*x.
2*(x - 1)*(x + 2)
Let y(i) = -5*i**2 - 19*i + 11. Let x(g) = 2*g**2 + 9*g - 6. Let u(s) = 7*x(s) + 3*y(s). Find a, given that u(a) = 0.
3
Suppose 14 = -y - y. Let s be y/(-6) + (-1)/2. Let -s + 2/3*k**2 + 0*k = 0. What is k?
-1, 1
Let k be 84/(-455)*46/3. Let p = k + 42/13. Factor 2/5*n**3 + 4/5*n**2 + 0 + p*n.
2*n*(n + 1)**2/5
Let s = 14 - 11. Suppose -u - s = -2*u. Factor 2/7 + 2/7*h**5 + 10/7*h**4 + 10/7*h + 20/7*h**2 + 20/7*h**u.
2*(h + 1)**5/7
Suppose 0 = -58*m + 57*m. Let q(o) be the third derivative of 0*o**6 - 1/210*o**7 + 0*o**5 + m + 0*o**4 + 0*o - 2*o**2 + 0*o**3. Factor q(f).
-f**4
Let t(w) = w**3 - 3*w**2 + 2*w - 4. Let q be t(3). Suppose -5 = -g - q. Solve 2/5*d**4 + 0*d - 4/5*d**2 + 0*d**g + 2/5 = 0 for d.
-1, 1
Suppose -2*r + 218 = 2*h, 0*r = 4*h - 2*r - 412. Let a be 4/(-14) - (-51)/h. Factor -a*f**4 + 0*f**2 + 0 + 0*f + 1/5*f**3.
-f**3*(f - 1)/5
Let t(v) = -16*v**3 + 10*v**2 + 2*v + 4. Let r(b) = -b**3 + b**2. Let a(s) = 28*r(s) - 2*t(s). Factor a(n).
4*(n - 1)*(n + 1)*(n + 2)
Factor 42 + 45*r + 8 + 1978*r**2 - 1983*r**2.
-5*(r - 10)*(r + 1)
Let s = 2 + -4. Let g = -6 - s. Let b(u) = -7*u**3 - 2*u. Let n(h) = 3*h**3 + h. Let v(j) = g*b(j) - 9*n(j). What is z in v(z) = 0?
-1, 0, 1
Let r be 8/10 + (-1)/(-5). Suppose -2*u = r - 9. Factor 0 + 0*t + 0*t**2 + 1/4*t**u - 1/4*t**3.
t**3*(t - 1)/4
Let i be (-3)/(2 - (-1)/(-2)*6). Let q(g) be the second derivative of -3/8*g**5 + 2*g + 0 + 3/8*g**2 - 5/8*g**i - 1/56*g**7 + 1/8*g**6 + 5/8*g**4. Factor q(y).
-3*(y - 1)**5/4
Suppose 3*a**5 - 4*a - 6*a**3 + 7*a - 40*a**2 + 40*a**2 = 0. What is a?
-1, 0, 1
Let j(a) = a. Let h(v) = -8*v**2 + 17*v + 1. Let x(w) = -h(w) + 3*j(w). Let r(d) = -1. Let k(p) = 3*r(p) + x(p). Suppose k(n) = 0. What is n?
-1/4, 2
Let h(n) be the first derivative of 5*n**3/3 - 5*n**2/2 - 24. Suppose h(t) = 0. What is t?
0, 1
Let p(l) be the second derivative of l**4/3 - 8*l**3/3 + 8*l**2 + 7*l. Find t such that p(t) = 0.
2
Let -4 - 521*t**4 - 144*t - 200*t**2 + 501*t**4 - 28 - 108*t**3 = 0. Calculate t.
-2, -1, -2/5
Let s(a) = -13*a**2 + 4*a - 6. Let n(y) = y**2 - y + 1. Let g be (1/2)/((-1)/(-2)). Let h(b) = g*s(b) + 6*n(b). Factor h(c).
-c*(7*c + 2)
Suppose -18/5 + 2*y**2 + 2/5*y**3 + 6/5*y = 0. What is y?
-3, 1
Let g(m) = -m**3 - 2*m**2 - 3*m - 3. Let d be g(-2). Factor 8*l**4 + 0*l**5 + l**2 + l**5 - 5*l**4 + 3*l**d.
l**2*(l + 1)**3
Factor 70*w**2 + 0*w**4 - 72*w**2 - 3*w**3 + 2*w**4.
w**2*(w - 2)*(2*w + 1)
Let p(g) be the first derivative of -2 - 4*g**2 + 2/3*g**3 + 8*g. Factor p(c).
2*(c - 2)**2
Suppose 32*h**2 - 100*h**5 - 24*h**3 + 293 - 4*h - 160*h**4 - 293 = 0. Calculate h.
-1, 0, 1/5
Suppose 0 = u - 0*u. Suppose u*a + a = -2*n - 4, 5*n + 3*a = -12. Solve -1/2*y**3 + 1/2*y - 1/2*y**2 + n + 1/2*y**4 = 0 for y.
-1, 0, 1
Factor -4*u + 12*u**3 + 0*u - 21*u**3 + 13*u**3.
4*u*(u - 1)*(u + 1)
Let d be 84/10 - 10/25. Suppose g = 5*z - 14, 2*g = -3*z + z + d. Suppose 0 + 2*i**z - 3/2*i**2 - 1/2*i = 0. Calculate i.
-1/4, 0, 1
Let o(m) = -m**2 - m + 1. Suppose 28 = 4*g + 5*r, -6 = -g - 0*r - r. Let w(j) = 5 + j + 3*j**g - 8 + 3*j. Let q(b) = 4*o(b) + w(b). Suppose q(s) = 0. What is s?
-1, 1
Factor -20*y**3 - y**4 - 6*y + y**5 + 9*y**2 + 4*y**2 + 13*y**3.
y*(y - 2)*(y - 1)**2*(y + 3)
Suppose -5*z + 68*j + 18 = 70*j, -4*z = 3*j - 20. Factor 6/5 - 6/5*b**z + 2/5*b**3 - 2/5*b.
2*(b - 3)*(b - 1)*(b + 1)/5
Let k(l) be the third derivative of 0*l + 0*l**3 - 1/60*l**6 - 2*l**2 + 1/12*l**4 + 0*l**5 + 0. Factor k(i).
-2*i*(i - 1)*(i + 1)
Let s(b) = -b**2 - 2*b - 2. Let i be s(-2). Let q be i/((-4)/(-3)) - -2. Factor -a**2 - q*a - 1/2*a**3 + 0.
-a*(a + 1)**2/2
Let p(b) = b**3 - 8*b**2 + 8*b - 2. Let c be p(7). Let y(v) be the third derivative of 0 + 1/15*v**3 + 0*v**4 + 0*v - 1/150*v**c + 3*v**2. Factor y(n).
-2*(n - 1)*(n + 1)/5
Let d(b) = -5*b**3 - 4*b**2 + 5*b + 4. Let k(y) = -11*y**3 - 8*y**2 + 11*y + 8. Let f(w) = -9*d(w) + 4*k(w). What is l in f(l) = 0?
-4, -1, 1
Let a be 0/(-2) + (2 - 70/49). Factor -a - 8/7*q**2 - 10/7*q - 2/7*q**3.
-2*(q + 1)**2*(q + 2)/7
Suppose 2*v + 7 = -8*d + 3*d, -5*v = 5*d - 5. Suppose 12 = 3*l + v*a, -2*l + 8 + 0 = a. Factor b - l*b**2 + 0*b + b**3 + 6*b**2.
b*(b + 1)**2
Let i(r) be the first derivative of 1 - 1/3*r**3 + 1/4*r**4 + 1/5*r**5 + 0*r - 1/2*r**2. Factor i(a).
a*(a - 1)*(a + 1)**2
Let u(f) be the third derivative of 0*f**3 + 7/120*f**5 + 3/140*f**7 + 1/48*f**4 + 3*f**2 + 0*f + 1/16*f**6 + 0. Factor u(o).
o*(o + 1)*(3*o + 1)**2/2
Solve 2/3*f**5 + 0*f - 2/3*f**2 - 2*f**4 + 2*f**3 + 0 = 0.
0, 1
Determine v, given that 0*v**2 + 0*v + 1/3*v**3 + 0 - 1/3*v**5 + 0*v**4 = 0.
-1, 0, 1
What is s in 4/7*s - 4/7*s**2 + 0 = 0?
0, 1
Let t(j) be the second derivative of -j**6/30 + 3*j**5/20 + 7*j**4/12 - 5*j**3/2 - 9*j**2 - 28*j. Factor t(r).
-(r - 3)**2*(r + 1)*(r + 2)
Let w(m) be the third derivative of m**8/112 - m**7/70 - 3*m**6/40 + m**5/20 + m**4/4 - 3*m**2. Factor w(q).
3*q*(q - 2)*(q - 1)*(q + 1)**2
Suppose -25 - 21*i + 4*i**2 - 9 - i**2 + 10 = 0. What is i?
-1, 8
Let l(p) be the third derivative of p**8/20160 - p**6/2160 - 5*p**4/24 - 5*p**2. Let f(v) be the second derivative of l(v). F