x(s) = 4*l(s) + 7*v(s). Factor x(i).
i*(i + 1)*(i + 2)**2
Let k(w) be the second derivative of w**4/21 - 4*w**3/21 + 13*w. Determine c, given that k(c) = 0.
0, 2
Let d(m) = -m**3 - m**2 + 7. Let j be d(0). Suppose -j = 5*v - 27. Find r, given that -10*r + 5*r**2 + v*r + 4 - 3*r**2 = 0.
1, 2
Factor c**4 + 1/2*c + 0 - 1/2*c**5 - c**2 + 0*c**3.
-c*(c - 1)**3*(c + 1)/2
Let i = 1 + -1. Let m be i + -1 - (-17 - -16). Factor m*c - 1/4*c**2 + 1/4.
-(c - 1)*(c + 1)/4
Let q = -14 + 14. Let v(z) be the second derivative of 0*z**3 + 1/60*z**5 + 1/90*z**6 + q*z**2 + 0 + 2*z + 0*z**4. Factor v(l).
l**3*(l + 1)/3
Let u(o) be the third derivative of o**8/168 - o**7/105 - o**6/60 + o**5/30 + 5*o**2. Factor u(t).
2*t**2*(t - 1)**2*(t + 1)
Let w be 18/(-126) + (-25)/(-126). Let x(u) be the second derivative of -w*u**4 - 1/9*u**2 + 0 + 1/90*u**5 + 1/9*u**3 - u. Solve x(j) = 0.
1
Let r(q) be the third derivative of -q**5/180 - 4*q**2. Solve r(g) = 0.
0
Let s(x) be the second derivative of x**5/20 - x**4/4 + x**3/3 - x. Factor s(u).
u*(u - 2)*(u - 1)
Let s(h) be the third derivative of 0*h + 2/3*h**3 + 0 - 1/60*h**6 - 1/15*h**5 - h**2 + 1/12*h**4. Determine k so that s(k) = 0.
-2, -1, 1
Let x(o) be the third derivative of 1/48*o**4 + 0*o**3 + 0 + 5*o**2 - 1/120*o**5 + 0*o. Suppose x(b) = 0. What is b?
0, 1
Suppose -2*y = y + z, y - 4*z = 0. Factor y - 2/3*l - 2/3*l**3 + 4/3*l**2.
-2*l*(l - 1)**2/3
Let w = -577 + 1161/2. Factor -t + 0 - 3/2*t**4 - 4*t**3 - w*t**2.
-t*(t + 1)**2*(3*t + 2)/2
Let x(v) be the first derivative of v**6/2 + 3*v**5/5 - 3*v**4/4 - v**3 + 5. Find w, given that x(w) = 0.
-1, 0, 1
Let h(u) be the second derivative of 5*u**3/6 - 3*u. Let s be h(1). Factor 6*d**s - 9*d**5 + 0*d**3 - 2*d**3 - 5*d**4.
-d**3*(d + 1)*(3*d + 2)
Suppose 0 = 3*s - 4 - 5. Let r be 8/(-12) + (-16)/(-6). Suppose -l**4 - l**3 - r*l**5 - s*l**4 - l**3 = 0. What is l?
-1, 0
Let k(a) be the third derivative of a**5/270 - a**4/54 - a**3/9 + 2*a**2. Factor k(p).
2*(p - 3)*(p + 1)/9
Factor -1/5*k**3 - 2/5*k**2 + 1/5*k + 2/5.
-(k - 1)*(k + 1)*(k + 2)/5
Let h be 12/(-6) + 4/(64/36). Factor -1/4*t + 0 + h*t**2.
t*(t - 1)/4
Let d = 10 - 8. Find u, given that -9*u**4 + 3*u**d + u**2 - 12*u**3 + 0*u**5 + 7*u**5 = 0.
-1, 0, 2/7, 2
Let s(r) be the second derivative of -r**6/240 - 7*r**5/160 - 5*r**4/32 - 13*r**3/48 - r**2/4 + 13*r. Let s(z) = 0. Calculate z.
-4, -1
Factor -k + 1/2*k**2 + 0.
k*(k - 2)/2
Let l(u) = -3*u**2 - 8*u + 12. Suppose -4*t - 24 = 24. Let v(j) = j**2 + 1. Let r(x) = t*v(x) - 3*l(x). Factor r(q).
-3*(q - 4)**2
Factor -12*f**3 + 2*f**3 + 10*f**3 + 3*f**3 - 6*f**2.
3*f**2*(f - 2)
Let l be (6/36)/((-3)/(-9)). Let z be 0 + 6 + -2 + 0. Factor 2*k**2 + 0 + l*k - 2*k**z - 1/2*k**3.
-k*(k - 1)*(k + 1)*(4*k + 1)/2
Let n(j) = 2*j**3 + 2*j - 2. Let g be n(1). Factor -g*z**3 - 2 + 2*z + 3/2*z**2 + 1/2*z**4.
(z - 2)**2*(z - 1)*(z + 1)/2
Let p(k) be the second derivative of k**7/63 - k**5/10 + k**4/9 - 11*k. Factor p(x).
2*x**2*(x - 1)**2*(x + 2)/3
Let k(y) be the third derivative of -y**6/480 - y**5/60 - y**4/32 + 38*y**2. Determine l, given that k(l) = 0.
-3, -1, 0
Let j = -445/2 - -224. Factor 0 - j*s**4 + 3/2*s**2 - 3/2*s**3 + 3/2*s.
-3*s*(s - 1)*(s + 1)**2/2
Let s(h) be the third derivative of -h**5/20 + h**4/4 + 3*h**3/2 - 7*h**2. Factor s(v).
-3*(v - 3)*(v + 1)
Let z(j) be the first derivative of -j**4/18 - 4*j**3/9 - j**2 - 8*j/9 - 9. Factor z(q).
-2*(q + 1)**2*(q + 4)/9
Let g = -2/47 + 198/235. Factor 0*n**2 - 2/5 + 2/5*n**4 + 4/5*n - g*n**3.
2*(n - 1)**3*(n + 1)/5
Let q = 12/29 - 50/261. Factor -q*c**3 + 0 + 0*c - 2/9*c**2.
-2*c**2*(c + 1)/9
Let d(f) be the second derivative of -f**5/10 - 4*f**4/9 + 5*f**3/9 + 2*f**2 - 9*f. Suppose d(w) = 0. What is w?
-3, -2/3, 1
Suppose 11 = 2*j - 2*v + 3, -2*j + 5*v = 1. Factor 2*p**3 + 10*p**2 - 2*p**2 + 4 + 17*p - j*p.
2*(p + 1)**2*(p + 2)
Solve -100*t**2 - 16 + 0*t**4 - 28*t**4 + 4*t**5 + 386*t**3 - 310*t**3 + 64*t = 0.
1, 2
Let n(l) be the first derivative of 0*l - 6 - 1/10*l**4 + 2/5*l**2 - 2/15*l**3. Let n(f) = 0. What is f?
-2, 0, 1
Let m = -77 + 77. Let l(d) be the first derivative of 4/5*d**3 - 9/10*d**4 + 3 + 8/25*d**5 - 1/5*d**2 + m*d. Factor l(w).
2*w*(w - 1)**2*(4*w - 1)/5
Let u(v) be the second derivative of 0 - 1/21*v**7 - v + 0*v**3 + 0*v**2 + 1/10*v**5 + 1/15*v**6 - 1/6*v**4. Let u(p) = 0. What is p?
-1, 0, 1
Let k = 112 - 112. Let m(d) be the third derivative of 1/60*d**5 - 1/48*d**4 + k*d - 1/240*d**6 + 0 + 3*d**2 + 0*d**3. Determine l, given that m(l) = 0.
0, 1
Let s(v) be the second derivative of -2/7*v**2 + 1/21*v**3 + 1/42*v**4 + 0 + 2*v. Find k, given that s(k) = 0.
-2, 1
Let r = -18 + 21. Factor -r*l**3 + l**3 - 28*l**4 + 26*l**4.
-2*l**3*(l + 1)
Let c(v) be the third derivative of v**8/10080 + v**7/1440 - v**6/720 + v**5/20 - v**2. Let i(w) be the third derivative of c(w). Find d, given that i(d) = 0.
-2, 1/4
Find q such that 10/9*q**4 + 0 - 2*q**3 + 14/9*q**2 - 4/9*q - 2/9*q**5 = 0.
0, 1, 2
Let v = 35 + -349/10. Let i(b) be the first derivative of 1/20*b**4 + 1/5*b - 1/15*b**3 - v*b**2 - 3. Solve i(x) = 0.
-1, 1
Let i = 816 + -4203/5. Let w = i + 25. Factor -w*l**4 + 0 - 2/5*l**2 - 4/5*l**3 + 0*l.
-2*l**2*(l + 1)**2/5
Determine u so that -1/4 - 1/4*u + 1/4*u**2 + 1/4*u**3 = 0.
-1, 1
Let l(j) = -2*j - 6. Let c be l(-4). Let -1 - 4*w**2 + 2*w + 3*w**c + 0 = 0. Calculate w.
1
Solve 12*b**4 - 8*b**4 + 0*b**4 - 5*b**3 + b**2 = 0 for b.
0, 1/4, 1
Let w(k) be the third derivative of k**5/40 - k**4/2 + 4*k**3 - 7*k**2. Factor w(z).
3*(z - 4)**2/2
Let n(f) = -7*f**3 + 23*f**2 - 35*f + 19. Let z(t) = 20*t**3 - 68*t**2 + 104*t - 56. Let k(l) = -8*n(l) - 3*z(l). Find y such that k(y) = 0.
1, 2
Factor -1/7*m**3 + 0*m**2 + 2/7*m**4 - 1/7*m**5 + 0 + 0*m.
-m**3*(m - 1)**2/7
Let u(l) be the third derivative of l**6/900 - l**5/225 - 26*l**2. Factor u(x).
2*x**2*(x - 2)/15
Suppose -3*z = -4*z. Suppose -3*x + 3*t = 2*x - 5, -4*t + 1 = x. Factor -l + 2*l**2 - x + 0*l + 2*l + z.
(l + 1)*(2*l - 1)
Let o(p) be the first derivative of -2*p**3/27 + 10*p**2/9 - 50*p/9 + 6. Determine v, given that o(v) = 0.
5
Suppose -2/3*n**2 + 0 - 2/3*n = 0. What is n?
-1, 0
Suppose b + 8 = 3*b. Let s(p) = -p**2 - 8. Let o(d) = -d**2 + d - 7. Let j(x) = b*o(x) - 3*s(x). Solve j(l) = 0.
2
Let v(z) = -1. Let r(a) = a - 2. Let o(y) = r(y) - 2*v(y). Let x(h) = -h**5 + 5*h**4 - 10*h**3 + 10*h**2 - 11*h + 1. Let n(i) = -6*o(i) - x(i). Factor n(c).
(c - 1)**5
Let -4*f**2 + 2*f**3 - 4*f + 2*f**3 - 73*f**4 + 77*f**4 = 0. What is f?
-1, 0, 1
Suppose -2*c - c = 6. Let w(j) = j**3 + 4*j**2 + 3*j. Let a be w(c). Let -1 + a - 3 + 2*p**2 = 0. Calculate p.
-1, 1
Let x(j) be the third derivative of -j**7/630 - j**6/360 + j**5/180 + j**4/72 - 3*j**2. Find s, given that x(s) = 0.
-1, 0, 1
Let h(q) = -1 - 7*q**2 - 2*q + 3 - 3. Let r(v) = -6*v**2 - 2*v. Let s(p) = -4*h(p) + 5*r(p). Suppose s(k) = 0. Calculate k.
-2, 1
Determine j, given that -2*j + 2*j**3 + 0*j + 0*j**3 = 0.
-1, 0, 1
Let u(y) = 3*y**4 + 0*y**4 - 4*y**4 + 6*y**3 - 4 + 4*y. Let o(j) = j**4 - 13*j**3 - 9*j + 9. Let d(s) = 4*o(s) + 9*u(s). Factor d(t).
-t**3*(5*t - 2)
Let h(b) be the third derivative of -b**6/120 + b**5/20 - b**4/8 + b**3/3 - b**2. Let x(f) be the first derivative of h(f). Factor x(r).
-3*(r - 1)**2
Let a(l) be the second derivative of -1/12*l**7 - 3/8*l**4 + 1/8*l**5 + 1/6*l**3 - l + 0 + 3/20*l**6 + 0*l**2. Solve a(y) = 0 for y.
-1, 0, 2/7, 1
Let m(r) be the third derivative of -r**8/10080 - r**7/1080 + r**6/180 - r**5/60 + 3*r**2. Let g(y) be the third derivative of m(y). Factor g(n).
-2*(n + 3)*(3*n - 2)/3
Let l(f) be the third derivative of -1/42*f**4 + 0 + 3*f**2 + 0*f - 1/21*f**3 - 1/210*f**5. Factor l(s).
-2*(s + 1)**2/7
Let q(d) be the second derivative of 2*d**6/15 - 3*d**5/5 - d**4 + 14*d**3/3 + 12*d**2 + 7*d + 1. Factor q(z).
4*(z - 3)*(z - 2)*(z + 1)**2
Let f(b) be the third derivative of -1/9*b**3 + 0*b + 0 - 1/90*b**5 + b**2 - 1/18*b**4. Factor f(m).
-2*(m + 1)**2/3
Suppose -5*k - 45 = 3*g, -3*k + 4*g - 6*g - 28 = 0. Let d = k + 6. Factor 2/3*w - 4/3*w**2 + 2/3*w**3 + d.
2*w*(w - 1)**2/3
Let i(x) be the third derivative of x**9/90720 - x**5/60 - x**2. Let z(o) be the third derivative of i(o). Solve z(s) = 0.
0
Let v(m) be the third derivative of -3/40*m**5 - 7/48*m**4 - 1/