et o(i) be the second derivative of 9/10*i**5 + 7/4*i**4 + 0 - 1/2*i**3 + i - 3*i**2. Find u, given that o(u) = 0.
-1, -2/3, 1/2
Suppose 0*a = -a. Let l(k) be the third derivative of 2/9*k**4 - 1/9*k**3 - k**2 - 8/45*k**5 + 0 + a*k. Find i, given that l(i) = 0.
1/4
Suppose -19 - 5 = -3*w. Suppose -12 = 4*i - w*i. Factor 6*y**3 + y - 2 - y**4 + 2 - 3*y**i - 3*y**2.
-y*(y - 1)**3
Let m(v) = -v**3 + v**2 - 1. Let y(k) = 2*k**2 - 6*k - 6. Let r(j) = -2*m(j) + y(j). Solve r(l) = 0.
-1, 2
Let d(r) = 5*r**2 - 3*r. Let x(c) = -16*c**2 + 8*c - 1. Let o(v) = 7*d(v) + 2*x(v). Find h, given that o(h) = 0.
-1/3, 2
Let g(b) be the third derivative of -11*b**6/240 - 13*b**5/120 - b**4/24 - 51*b**2. Factor g(d).
-d*(d + 1)*(11*d + 2)/2
Let l(h) be the first derivative of 4*h**3/3 - 4*h**2 - 12*h - 5. Determine a so that l(a) = 0.
-1, 3
Find y, given that -2*y**3 - 2*y**4 + 2 - 2 + 6*y**3 = 0.
0, 2
Let p(v) be the third derivative of -v**5/510 - v**4/204 + 2*v**3/51 + 14*v**2. Factor p(w).
-2*(w - 1)*(w + 2)/17
Suppose -6*u + y + 9 = -3*u, u - 5*y = 17. Factor -k + 0*k**u + k + 2*k**2 - 2*k**3.
-2*k**2*(k - 1)
Let u(f) be the third derivative of f**5/300 + f**4/60 + 8*f**2. Solve u(s) = 0 for s.
-2, 0
Solve -z**2 + 0 + 0*z - 1/2*z**4 - 3/2*z**3 = 0.
-2, -1, 0
Let l(r) be the first derivative of -1/3*r**3 + 0*r - 1/4*r**4 + 1/5*r**5 + 1/2*r**2 + 1. What is k in l(k) = 0?
-1, 0, 1
Factor 16/5*s**2 + 2/5*s**3 + 26/5*s + 12/5.
2*(s + 1)**2*(s + 6)/5
Suppose 2 = -2*a + 4, -h + 5 = a. Factor -40*t + 3 + 9*t**2 + 3*t**2 + 5 + h.
4*(t - 3)*(3*t - 1)
Let g(d) = 2*d**2 + 13*d + 4. Let k(b) = -b**2 - 7*b - 2. Let w(t) = -4*g(t) - 7*k(t). Factor w(a).
-(a + 1)*(a + 2)
Let y be -2 - ((-140)/105)/((-20)/(-54)). Factor -2/5*t**3 + 6/5*t**2 - y + 0*t.
-2*(t - 2)**2*(t + 1)/5
Let v(o) be the second derivative of o**4/18 - 4*o**3/9 - 5*o**2/3 + 12*o. Factor v(j).
2*(j - 5)*(j + 1)/3
Let u(h) = 3*h**2 + 3*h - 6. Let f(z) = 8*z**2 + 9*z - 17. Suppose -3*r - 2*b + 4*b = -18, r + 3*b - 6 = 0. Let y(m) = r*f(m) - 17*u(m). Solve y(i) = 0.
0, 1
Let q = -5 + 6. Determine m so that 2*m**2 + 3 - q + m - 3*m**2 = 0.
-1, 2
Let j be (10/(-15) - -2)*(-3)/(-2). Factor 0*c**3 + 1/2*c**4 + 0 - 1/4*c + 1/4*c**5 - 1/2*c**j.
c*(c - 1)*(c + 1)**3/4
Suppose 4*n - 4 = -2*g + 8, 0 = 4*g + 3*n - 24. Factor 8 - 9*a**4 + 2*a**2 + 4*a**2 + 9*a - 5 - g*a**3 - 3*a**5.
-3*(a - 1)*(a + 1)**4
Suppose -4 + 6 = o. Factor j + 1 + 3*j - 4*j - j**o.
-(j - 1)*(j + 1)
Let t(d) be the second derivative of -4/3*d**3 - 5/3*d**4 + 0 + d**2 - 5/6*d**5 - d. Let v(g) be the first derivative of t(g). Factor v(i).
-2*(5*i + 2)**2
Let c be (-2)/(-3) + (-4)/6. Let g = -128 - -898/7. Factor -g*x**3 + 0*x**2 + c*x + 0.
-2*x**3/7
Let f(t) be the third derivative of -t**8/42 + 22*t**7/105 + 2*t**6/15 - 49*t**5/15 - 28*t**4/3 - 32*t**3/3 - 31*t**2. Suppose f(o) = 0. What is o?
-1, -1/2, 4
Factor -6 + 7 - 27*j**2 - 7 - 33*j.
-3*(j + 1)*(9*j + 2)
Let g(p) be the first derivative of -2*p**5/75 - p**4/10 - 4*p**3/45 - 17. What is y in g(y) = 0?
-2, -1, 0
Let x = 9 + -9. Let l(a) be the third derivative of x*a + 0*a**5 + 1/210*a**8 + 1/300*a**6 + 0*a**3 - 2*a**2 - 1/105*a**7 + 0 + 0*a**4. Factor l(w).
2*w**3*(w - 1)*(4*w - 1)/5
Let m = 24 - 13. Let i(l) = -8*l**3 + 4*l**2 + 4. Let f(n) = -n**4 + 24*n**3 - 12*n**2 - 11. Let t(r) = m*i(r) + 4*f(r). Factor t(q).
-4*q**2*(q - 1)**2
Let x(s) = -s + 33. Let g be x(28). Factor 0*l**4 + 0*l + 0*l**2 - 2/3*l**g + 0 + 0*l**3.
-2*l**5/3
Let s(w) be the second derivative of w**6/40 + w**5/10 + w**4/8 + 3*w**2/2 - w. Let k(l) be the first derivative of s(l). Let k(t) = 0. Calculate t.
-1, 0
Let x(r) be the third derivative of -r**8/336 - 11*r**7/210 - 17*r**6/60 - 23*r**5/30 - 29*r**4/24 - 7*r**3/6 + 25*r**2. Factor x(h).
-(h + 1)**4*(h + 7)
Factor -26 + 25*t**3 + 11 + 15 + 10*t**2 + t.
t*(5*t + 1)**2
Let z(s) be the first derivative of s**4/8 + s**3/2 + 3*s**2/4 + s/2 - 7. Let z(y) = 0. What is y?
-1
Let b(q) be the first derivative of q**6/27 + 2*q**5/15 + q**4/6 + 2*q**3/27 - 2. Factor b(m).
2*m**2*(m + 1)**3/9
Let m(g) be the first derivative of g**7/147 - g**6/210 - g**5/42 + g**4/42 + g**2/2 + 2. Let k(v) be the second derivative of m(v). Solve k(f) = 0 for f.
-1, 0, 2/5, 1
Let u(f) be the third derivative of -f**8/1512 + f**7/945 + f**6/540 - f**5/270 - 7*f**2. Factor u(z).
-2*z**2*(z - 1)**2*(z + 1)/9
Let u(b) be the second derivative of -b**4/42 + 2*b**3/21 - b**2/7 + 13*b. Factor u(i).
-2*(i - 1)**2/7
Let u(p) be the first derivative of p**6/3 + 4*p**5/5 - p**4 - 16*p**3/3 - 7*p**2 - 4*p + 1. Let u(w) = 0. What is w?
-1, 2
Factor -1/5*a**2 + 1/5*a**4 - 1/5*a**3 + 1/5*a + 0.
a*(a - 1)**2*(a + 1)/5
Let b(f) be the third derivative of f**6/780 + 2*f**5/65 + 15*f**4/52 + 50*f**3/39 - 34*f**2. Find o such that b(o) = 0.
-5, -2
Suppose 27/5*q**2 + 33/5*q - 3/5*q**4 + 12/5 + 3/5*q**3 = 0. Calculate q.
-1, 4
Let c(a) be the third derivative of a**5/15 + 2*a**4 + 24*a**3 + 2*a**2 - 42. Solve c(r) = 0 for r.
-6
Determine j, given that 4/5 - 2/5*j**2 + 2/5*j = 0.
-1, 2
What is h in 3*h**3 + 9*h**4 - 3*h**4 + 3*h**5 - 2*h**4 + 2*h**4 = 0?
-1, 0
Let m(t) be the first derivative of -t**4/4 + 2*t**3/3 + 10. Factor m(u).
-u**2*(u - 2)
Let k(s) = 3*s**4 + 7*s**3 + 30*s**2 - 53*s - 53. Let c(v) = -v**4 - 4*v**3 - 15*v**2 + 26*v + 26. Let u(f) = 13*c(f) + 6*k(f). Factor u(z).
5*(z - 2)**2*(z + 1)**2
Let m(d) be the second derivative of 0*d**3 + 0*d**4 - 11*d + 0*d**2 + 0*d**5 + 0 - 1/75*d**6 + 1/105*d**7. Let m(t) = 0. Calculate t.
0, 1
Let j = -130 - -134. Find k such that 1/4*k - 1/4 + 9/4*k**2 + k**j + 11/4*k**3 = 0.
-1, 1/4
Let s(i) be the third derivative of 3*i**2 + 0*i - 1/15*i**5 + 0 + 1/2*i**3 - 1/3*i**4 - 1/180*i**6. Let f(h) be the first derivative of s(h). Factor f(t).
-2*(t + 2)**2
Let l(t) be the third derivative of t**8/128 + t**7/35 + t**6/80 - 2*t**2 - 17*t. Factor l(r).
3*r**3*(r + 2)*(7*r + 2)/8
Factor -10/3*t**4 + 0*t**2 + 0*t + 14/3*t**5 - 4/3*t**3 + 0.
2*t**3*(t - 1)*(7*t + 2)/3
Let s(f) = -f**5 - 11*f**4 - 4*f**3 + 4*f**2 + 4*f - 4. Let k(d) = -d**5 - 21*d**4 - 7*d**3 + 8*d**2 + 7*d - 7. Let p(y) = 4*k(y) - 7*s(y). Factor p(m).
m**2*(m - 2)*(m - 1)*(3*m + 2)
Let c = -2 + 11. Let t be c/(-3) - -3 - -2. Factor 0 - 1/4*h - 1/4*h**t.
-h*(h + 1)/4
Let q(r) be the first derivative of r**6/6 + 7*r**5/5 - r**4/2 - 14*r**3/3 + r**2/2 + 7*r + 57. Suppose q(z) = 0. Calculate z.
-7, -1, 1
Let p(x) be the second derivative of 1/2*x**3 - 5*x - 9/4*x**2 + 0 - 1/24*x**4. Factor p(g).
-(g - 3)**2/2
Let u(c) be the first derivative of -5*c**4/4 + 5*c**3 - 5*c**2 + 4. Factor u(m).
-5*m*(m - 2)*(m - 1)
Let r(w) be the third derivative of w**6/180 + w**5/60 - w**4/24 - w**3/9 + 4*w**2. Determine u, given that r(u) = 0.
-2, -1/2, 1
Let d(v) = -2*v**3 - 2*v**2 + 2*v + 3. Let f be d(-2). Factor -96*p + 12 - 4 - f*p**2 + 4 + 196*p**2.
3*(7*p - 2)*(9*p - 2)
Solve -40/19*v**3 + 0 + 0*v - 8/19*v**5 + 8/19*v**2 + 34/19*v**4 = 0.
0, 1/4, 2
Suppose 2*g + 3*g = 15. Let v be (-2)/g + 12/6. Factor -2/3*j**4 + 0 - v*j**3 - 2/3*j**2 + 0*j.
-2*j**2*(j + 1)**2/3
Let a(o) be the third derivative of -o**7/1260 - o**6/540 + o**5/90 - 5*o**3/6 + o**2. Let i(u) be the first derivative of a(u). Solve i(z) = 0 for z.
-2, 0, 1
Let g be 2*(-2 - -1) - -7. Let n(w) be the first derivative of 0*w**3 - 1/2*w**2 + 1/4*w**4 - 2 - 1/10*w**g + 1/2*w. Factor n(v).
-(v - 1)**3*(v + 1)/2
Let h(g) be the third derivative of g**6/300 + g**5/75 - g**4/60 - 2*g**3/15 + g**2. Factor h(w).
2*(w - 1)*(w + 1)*(w + 2)/5
Let f = -8098 - -15789/2. Let y = f - -240. Let -y*l**2 + 86*l**3 + 7*l - 1/2 + 32*l**5 - 88*l**4 = 0. Calculate l.
1/4, 1
Let h(g) be the third derivative of -g**6/30 - g**5/5 - g**4/3 - 6*g**2. Factor h(k).
-4*k*(k + 1)*(k + 2)
Let a(t) be the first derivative of -t**4/22 + 2*t**3/11 - 2*t**2/11 + 23. Solve a(b) = 0 for b.
0, 1, 2
Factor -7/3*m - 2/3 - 5/3*m**3 - 3*m**2 - 1/3*m**4.
-(m + 1)**3*(m + 2)/3
Let k(p) be the second derivative of 5/9*p**3 - 2/9*p**4 + 0 - 2/3*p**2 - 4*p + 1/30*p**5. Find s such that k(s) = 0.
1, 2
Let i(s) be the second derivative of 1/150*s**6 + 0*s**2 - 2*s + 0 + 1/30*s**4 - 3/100*s**5 + 0*s**3. What is u in i(u) = 0?
0, 1, 2
Let z be (3 - 1) + 3/(-2). Determine i, given that 3/2*i - 1 - z*i**2 = 0.
1