) be the first derivative of 4 - 4/3*y**3 - 4/3*y**2 - 2/15*y**5 - 2/3*y**4 - 2/3*y. Find p, given that u(p) = 0.
-1
Let x(c) be the first derivative of c**6/3 - 3*c**5/10 - c**4/8 - 3. Factor x(k).
k**3*(k - 1)*(4*k + 1)/2
Factor -4*d**2 - d**4 - 14*d**3 + 14*d**3 + 5*d**4.
4*d**2*(d - 1)*(d + 1)
Factor 27*n + 1/3*n**3 - 6*n**2 + 0.
n*(n - 9)**2/3
Suppose -2*f - 2/3 - 2*f**2 - 2/3*f**3 = 0. Calculate f.
-1
Let 12*x - 40*x**2 + 21 - 3 + 42*x**2 = 0. What is x?
-3
Suppose 4*h + 3*a = 27, 0 = 5*h + 2*a - 0*a - 25. Factor 3*q**4 + 19*q**2 + 5*q**3 + h*q + 0*q**3 + 4*q**3 - 10*q**2.
3*q*(q + 1)**3
Let x(z) = -z**2 - 10*z - 7. Let w be x(-9). Factor t**2 + 0*t + 2 - 4*t**w + t.
-(t - 1)*(3*t + 2)
Let a = -20 + 45. Let n be (a*3/(-6))/(-2). Factor j + n*j**3 + 0 + 5*j**2.
j*(5*j + 2)**2/4
Let j be (0 + 0)/(2 - 12/4). Solve j + 3/2*v**2 - 3/2*v = 0 for v.
0, 1
Let j(f) be the third derivative of -f**5/60 + f**4/12 - f**3/6 - 2*f**2. Suppose j(z) = 0. Calculate z.
1
Determine h, given that -3*h**3 - 3*h**2 + 0*h**3 + 36*h - h**3 - 29*h**2 = 0.
-9, 0, 1
Let 8 + 34*k + 3*k**2 - 46*k + k**2 = 0. What is k?
1, 2
Suppose -m + 11 = 9. Let x(n) be the first derivative of 2*n + 1 + 2/3*n**3 - 2*n**m. Let x(z) = 0. What is z?
1
Let f(x) = -x**3 + 5*x**2 - 3*x - 2. Let s be f(4). What is l in 0*l + 1/5*l**s + 0 = 0?
0
Suppose 2*a + 37 - 37 = 0. Find z such that 2/5*z**5 - 4/5*z**3 + 2/5*z + 0*z**2 + a + 0*z**4 = 0.
-1, 0, 1
Let t(h) be the first derivative of -h**4/8 - h**3/3 - h**2/4 + 10. Suppose t(v) = 0. What is v?
-1, 0
Let k(j) = -2*j**3 - 7*j**2 + j + 3. Let g(t) = -3*t**3 - 13*t**2 + 3*t + 5. Let y(r) = 3*g(r) - 5*k(r). Factor y(q).
q*(q - 2)**2
Let b(a) = a**5 - a**4 + 1. Let x(l) = 10*l**5 - 32*l**4 + 50*l**3 - 36*l**2 + 8*l + 5. Let f(d) = -5*b(d) + x(d). Factor f(n).
n*(n - 2)**2*(n - 1)*(5*n - 2)
Let q(h) be the third derivative of 7*h**6/270 - 16*h**5/135 + 2*h**4/27 + 13*h**2. Factor q(p).
4*p*(p - 2)*(7*p - 2)/9
Let l(b) be the third derivative of -b**8/112 - b**7/70 + b**6/20 + b**5/10 - b**4/8 - b**3/2 + 10*b**2. Factor l(u).
-3*(u - 1)**2*(u + 1)**3
Let a(x) = 2*x**2 - 2*x. Let d(w) be the first derivative of w**2/2 - w - 2. Let h(b) = a(b) - 4*d(b). Factor h(z).
2*(z - 2)*(z - 1)
Let d = 319/3 + -105. Let u(b) be the first derivative of 2 + 1/4*b**4 + 2*b**2 + 0*b - d*b**3. Factor u(r).
r*(r - 2)**2
Factor f**3 - 27 + 5*f + 17*f - 21*f**2 + 23*f + 2*f**3.
3*(f - 3)**2*(f - 1)
Let d(r) = -r**2 + 5*r. Let h be d(5). Suppose -6*x**3 - 9*x**4 - 3*x + h + 12*x - 3*x**5 + 0*x**5 + 3 + 6*x**2 = 0. Calculate x.
-1, 1
Factor -3/2*v**2 - 9/2 - 6*v.
-3*(v + 1)*(v + 3)/2
Let y(m) be the second derivative of m**7/28 + 3*m**6/10 + 33*m**5/40 + m**4/4 - 3*m**3 - 6*m**2 + 36*m. Suppose y(o) = 0. Calculate o.
-2, -1, 1
Let d(b) = -b**3 - 7*b**2 - 8*b - 6. Let r be d(-6). Factor 4*o**2 + 0*o**2 - o**4 - r*o**2 - o**4 - 4*o**3.
-2*o**2*(o + 1)**2
Determine g, given that 0*g + 0 - 1/3*g**2 + g**5 + 5/3*g**4 + 1/3*g**3 = 0.
-1, 0, 1/3
Let d = -14 + 18. Factor -7*y**d + 5*y**4 - 4*y**3 + 3*y**5 - y**5.
2*y**3*(y - 2)*(y + 1)
Let f be (-4)/(-18) - (-16)/252. Determine i so that 2/7*i + 0 - f*i**3 + 0*i**2 = 0.
-1, 0, 1
Let w(a) be the second derivative of 5*a**7/14 - 5*a**6/3 + 3*a**5 - 5*a**4/2 + 5*a**3/6 + 14*a. Suppose w(q) = 0. Calculate q.
0, 1/3, 1
Let z(f) be the second derivative of f**7/70 + f**6/50 - 3*f**5/100 - f**4/20 - 6*f. Find k such that z(k) = 0.
-1, 0, 1
Let o(d) = -d - 1. Let r be o(-8). Let j be 2 + (-4 - r/(-3)). Solve j*s**3 - 4/3*s**2 + 4/3*s + 0 = 0 for s.
0, 2
Let g be 0 + (3 - 2) + (-4)/(-4). Factor -3/2*w - 3/2*w**g - 1/2 - 1/2*w**3.
-(w + 1)**3/2
Factor 0 + 4/3*z - 4/3*z**2.
-4*z*(z - 1)/3
Let g be 24/132 - 40/(-22). What is a in 2/5*a + 2/5*a**3 - 4/5*a**g + 0 = 0?
0, 1
Let o be 12/81*(-24)/(-16). Determine j so that 2/9*j**3 + 0 - 2/9*j - o*j**2 + 2/9*j**4 = 0.
-1, 0, 1
Let s(g) be the third derivative of g**6/360 - g**5/36 + g**4/18 - 8*g**2. Factor s(y).
y*(y - 4)*(y - 1)/3
Let q(s) be the first derivative of -s**4/18 - 16*s**3/27 - 7*s**2/3 - 4*s - 21. Factor q(m).
-2*(m + 2)*(m + 3)**2/9
Let i be -2 - (-56)/(-63)*-6. Determine n, given that 2/3*n**3 - 8/3 + 16/3*n - i*n**2 = 0.
1, 2
Let p(m) = 3*m**2 - 20*m + 29. Let v(o) = o**2 - o + 1. Let k(j) = p(j) - 2*v(j). Let s(d) = -18*d + 27. Let b(l) = -3*k(l) + 2*s(l). Factor b(t).
-3*(t - 3)**2
Let j(v) be the third derivative of v**5/15 - 2*v**4/3 + 8*v**3/3 - 4*v**2. Factor j(k).
4*(k - 2)**2
Suppose 0 = 4*f + 3*i - 211, 3*f - 3*i - i = 127. Solve 175*o**4 - 5*o**3 - 89*o**3 - f*o**5 + 6*o**3 - 184*o**2 + 112*o - 16 = 0 for o.
-1, 2/7, 2
Let m(a) be the third derivative of a**10/151200 - a**8/20160 + a**5/12 - a**2. Let g(r) be the third derivative of m(r). Find o such that g(o) = 0.
-1, 0, 1
Determine q so that -2*q**4 - 4*q**4 - 14*q**3 - 5*q**4 + 3*q**4 - 4*q**2 + 2*q = 0.
-1, 0, 1/4
Solve -2*u**2 + 69*u - 89*u - 3*u**2 - 3 - 17 = 0.
-2
Let q(t) be the first derivative of t**6/180 - t**4/12 + 2*t**3/3 + 3. Let d(z) be the third derivative of q(z). Determine n, given that d(n) = 0.
-1, 1
Let g(v) be the second derivative of -v**6/10 + 7*v**5/20 - 4*v**4/9 + 2*v**3/9 + 3*v. What is a in g(a) = 0?
0, 2/3, 1
Factor -1/4*w**5 - 3/2*w**3 - 5/4*w**4 + 1/2*w**2 + 3/4 + 7/4*w.
-(w - 1)*(w + 1)**3*(w + 3)/4
Let b(z) be the second derivative of z**4/2 - 5*z**3/2 - 9*z**2/2 + 15*z. Factor b(f).
3*(f - 3)*(2*f + 1)
Let -2*x**4 - x**4 + 0*x**4 + 3*x**2 + x**5 + x**3 + 4*x - 6*x = 0. What is x?
-1, 0, 1, 2
Let l(b) be the third derivative of 0*b**5 + 0*b - 1/360*b**6 + 0 + 1/72*b**4 + 2*b**2 + 0*b**3. Factor l(j).
-j*(j - 1)*(j + 1)/3
Let m(r) be the second derivative of r**7/140 - r**5/40 + 3*r**2/2 + 7*r. Let u(k) be the first derivative of m(k). Factor u(y).
3*y**2*(y - 1)*(y + 1)/2
Solve -624 - 3068*u - 139194*u**4 - 5716*u - 110544*u**3 - 46536*u**2 - 7203*u**5 + 37323*u**4 = 0 for u.
-13, -2/7
Let q(f) be the first derivative of f**4/30 + f**3/15 + 2*f + 3. Let k(x) be the first derivative of q(x). Factor k(n).
2*n*(n + 1)/5
Suppose 5 = c + 2. Factor 12 + 3*s**2 - 12 + c*s.
3*s*(s + 1)
Determine x, given that 0*x - 1/4*x**4 + 0*x**3 + 1/2*x**2 - 1/4 = 0.
-1, 1
Let b(a) = -a**3 - a**2 - 1. Let m(c) = 3*c**4 + 15*c**3 + 9*c**2 + 18. Let w(t) = 15*b(t) + m(t). Suppose w(j) = 0. Calculate j.
-1, 1
Let j = 117 + -817/7. Suppose 4/7*x**3 - 12/7*x**5 + j*x**2 + 0 + 0*x - 10/7*x**4 = 0. What is x?
-1, -1/3, 0, 1/2
Let k(z) be the first derivative of -11*z**3/4 + z**2 + z/4 - 37. Factor k(f).
-(3*f - 1)*(11*f + 1)/4
Let t(v) be the third derivative of -1/10*v**5 - 1/8*v**6 + 0 + 0*v**3 + 0*v**4 + 0*v + 2*v**2. Suppose t(u) = 0. Calculate u.
-2/5, 0
Let f = 162 + -289. Let u = 639/5 + f. Find s, given that 4/5 + 1/5*s**2 + u*s = 0.
-2
Let c(w) be the second derivative of 1/4*w**2 + 0 - 1/3*w**3 + 1/60*w**6 - 1/10*w**5 + 1/4*w**4 - 2*w. Let c(o) = 0. Calculate o.
1
Let s(k) = 8*k + 132. Let d be s(-16). Let x be 4/(-14) + 26/42. Factor -1/3*g**5 - 2/3*g**2 + x*g + 2/3*g**d + 0 + 0*g**3.
-g*(g - 1)**3*(g + 1)/3
Let v be 92/69 + (-4)/6. What is w in -v*w + 1/3 + 1/3*w**2 = 0?
1
Let q(h) be the first derivative of 4*h**5/15 + 4*h**4/3 + 4*h**3/3 + 16. Factor q(c).
4*c**2*(c + 1)*(c + 3)/3
Let b(h) be the third derivative of -h**9/272160 + h**7/7560 + h**6/1620 - h**5/20 + 4*h**2. Let j(l) be the third derivative of b(l). Factor j(f).
-2*(f - 2)*(f + 1)**2/9
Let f(j) be the first derivative of 1/24*j**4 + 0*j - 2 + 1/60*j**5 - 1/2*j**2 - 1/3*j**3. Let s(k) be the second derivative of f(k). Solve s(x) = 0 for x.
-2, 1
Let b(t) be the first derivative of -t**4/16 - 7*t**3/6 - 25*t**2/8 - 3*t - 29. Find l such that b(l) = 0.
-12, -1
Let p(f) = -f - 1. Let k be p(-6). Find s, given that 4*s**2 - 8*s**4 - 6*s**k + 2*s**3 - 41 + 41 = 0.
-1, 0, 2/3
Let y(d) = -35*d**4 - 125*d**3 - 155*d**2 - 15*d - 15. Let o(s) = 5*s**4 + 18*s**3 + 22*s**2 + 2*s + 2. Let a(p) = -15*o(p) - 2*y(p). Factor a(q).
-5*q**2*(q + 2)**2
Let p(o) be the third derivative of o**5/60 - o**4/12 - o**2. Suppose p(m) = 0. What is m?
0, 2
Let z(k) be the second derivative of k**4/15 + 2*k**3/5 - 8*k**2/5 - k. Factor z(c).
4*(c - 1)*(c + 4)/5
Let o be 19/5 - 8/10. Suppose 2*g - 3*g**o - 65 - 4*g**2 + 65 + 5*g**3 = 0. What is g?
0, 1
Let l