- 1/3*n**3 + 2*n + 1/24*n**4 - 1/720*n**6. Let x(w) be the second derivative of t(w). Factor x(j).
-(j - 2)*(j + 1)/2
Let o(h) be the second derivative of -h**7/1260 - h**2/2 + h. Let c(j) be the first derivative of o(j). Factor c(x).
-x**4/6
Let g = -99/7 + 346/21. Suppose -2/3 - r**2 + g*r = 0. What is r?
1/3, 2
Suppose 0 = -a - 0*n + 2*n, -a - 6 = -5*n. Factor -4*x**3 - 2*x**a + 4*x**2 + 0*x**3 + 3*x**3 - x**3.
-2*x**2*(x - 1)*(x + 2)
Suppose -t + 14 = -10. Let l be (-32)/t*3/(-10). Suppose 0*z + l*z**2 + 4/5*z**3 + 0 = 0. Calculate z.
-1/2, 0
Factor -12/5*z**3 + 2/5*z + 7/5*z**4 + 3/5*z**2 + 0.
z*(z - 1)**2*(7*z + 2)/5
Let u = 8744 + -498425/57. Let l = 7/19 - u. Factor l*g**2 + 2/3 + 4/3*g.
2*(g + 1)**2/3
Let f be (9/12)/((-6)/(-4)). Let l be (-6)/36 + 20/30. Determine c, given that -1/2*c**3 + 0*c - l*c**4 + 0 + f*c**2 + 1/2*c**5 = 0.
-1, 0, 1
Let b = 558 - 558. Suppose -1/5*v**3 - 1/5*v + 2/5*v**2 + b = 0. Calculate v.
0, 1
Determine i so that 4*i**4 + 95*i**2 - 127*i**2 + 4*i**4 - 8*i**3 - 28*i - 8 + 4*i**5 = 0.
-1, 2
Find j such that 24*j - 32 - 6*j**2 + 1/2*j**3 = 0.
4
Let c(f) = f**3 - 2*f**2 - f - 2. Let p be c(3). Suppose -i - i - 2*g = -12, i - 18 = -p*g. Find y such that 0*y - 2/3*y**i + 0 - 2/3*y**3 = 0.
-1, 0
Let z(n) = -n**4 + 13*n - 5*n**2 - 13*n + 4*n**3. Let m(w) = w**4 - 3*w**3 + 4*w**2. Let f(l) = 5*m(l) + 4*z(l). Factor f(x).
x**3*(x + 1)
Find f such that 4*f**5 + f**3 - 3*f**3 + 3*f**4 - f**5 - f**3 - 3*f**2 = 0.
-1, 0, 1
Let r(x) be the third derivative of 0 + 1/20*x**6 + 1/105*x**7 + 0*x - 1/4*x**4 - 3*x**2 + 1/30*x**5 - 2/3*x**3. Let r(p) = 0. What is p?
-2, -1, 1
Let t(c) be the third derivative of -c**8/336 - c**7/105 + c**6/24 + c**5/10 + 4*c**2. Factor t(q).
-q**2*(q - 2)*(q + 1)*(q + 3)
Let z(h) = 4*h**2 + 6*h - 10. Let i(p) = p**2 + 2*p - 3. Let k = 4 + -18. Let y(n) = k*i(n) + 4*z(n). Factor y(d).
2*(d - 1)**2
Suppose -20 = -5*x - 0*x. Suppose 1/2*q**x - 1/2*q**5 - 1/2*q**2 + 0*q + 0 + 1/2*q**3 = 0. What is q?
-1, 0, 1
Let i(h) be the third derivative of -h**6/480 - h**5/48 - h**4/24 + 50*h**2. Factor i(v).
-v*(v + 1)*(v + 4)/4
Let y(v) be the second derivative of 0*v**2 - 1/10*v**5 - 1/6*v**4 + 1/3*v**3 + 0 + 1/15*v**6 - 4*v. Factor y(n).
2*n*(n - 1)**2*(n + 1)
Let j(q) = -12*q**3 + 8*q - 12. Suppose 2*m + 8 = b + 6*m, 1 = m. Let p(t) = t**4 + 24*t**3 + t**2 - 15*t + 25. Let s(g) = b*p(g) + 9*j(g). Factor s(f).
4*(f - 2)*(f - 1)**2*(f + 1)
Let y be 3/((-3)/(-4)) - 0. Suppose -11 = y*j + 5*u + 1, -4*j = 2*u. Factor -1/4*m - m**j + 0.
-m*(4*m + 1)/4
Suppose 4*q - q = 36. Let a(i) = -i + 12. Let o be a(q). Find f such that o + 0*f**2 + 0*f + 1/3*f**3 = 0.
0
Let c(k) be the second derivative of -1/30*k**5 - k**2 + 3*k + 0*k**3 + 0 - 1/18*k**4. Let j(h) be the first derivative of c(h). Factor j(z).
-2*z*(3*z + 2)/3
Let k(p) = -4*p**2 + 54*p + 26. Let g(d) = -d**2 + 11*d + 5. Let h(u) = -14*g(u) + 3*k(u). Factor h(t).
2*(t + 2)**2
Let z(v) be the first derivative of v**6/5 + 3*v**5/20 - v**4/4 + 8*v - 5. Let n(r) be the first derivative of z(r). Suppose n(b) = 0. What is b?
-1, 0, 1/2
Let i(x) = -x**4. Let o(m) = -5*m**5 + 22*m**4 - 40*m**3 + 20*m**2. Let n(q) = -3*i(q) + o(q). Factor n(k).
-5*k**2*(k - 2)**2*(k - 1)
Let x(g) be the second derivative of 0*g**3 + 0*g**4 + 3*g + 0*g**2 + 0 - 1/10*g**5. Factor x(j).
-2*j**3
Factor 7*x**2 + 24 - 10*x**2 - 15*x - 6*x.
-3*(x - 1)*(x + 8)
Factor -n**2 + 8*n - 9 + 1 - 8.
-(n - 4)**2
Solve -2/3*v**3 - 4/3*v + 0 - 2*v**2 = 0 for v.
-2, -1, 0
Let l = -3 - 3. Let f be (l/15)/((-16)/10). Solve 0*k**2 + 0 - f*k**3 + 0*k = 0 for k.
0
Suppose 2*n + 0*n = -g + 11, -4*g - 21 = -5*n. Let 4/3*c**3 - 2/3*c + 4/3*c**2 - 2/3 - 2/3*c**4 - 2/3*c**n = 0. What is c?
-1, 1
Suppose -3*a + 8 = -5*y, 2*y = 3*a - 2*y - 7. Factor 4 - 2*o**2 + 3 - 6 + a.
-2*(o - 1)*(o + 1)
Factor -177 + 177 - 3*g**2 - 3*g**3.
-3*g**2*(g + 1)
Solve -3/4*g + 1/4*g**2 + 0 = 0.
0, 3
Let i(a) = -a**3 + 6*a**2 + 6*a + 9. Let t be i(7). Factor 9*z**3 - 2*z**2 + z**4 + 9*z**2 - z**t + 2*z**4.
3*z**2*(z + 1)*(z + 2)
Let z(v) = v**2 + 4*v + 1. Let u(x) = -2*x**2 - 9*x - 3. Suppose -s - 6 = 2*s. Let f be 2/2 - (s - 4). Let t(d) = f*z(d) + 3*u(d). Factor t(c).
(c - 1)*(c + 2)
Let m(o) = o**3 + 10*o**2 + 2*o + 8. Let j be m(-10). Let n be 4 - (2 - 20/j). Solve -n*u**3 - 1/3*u**2 + 0*u + 0 = 0.
-1, 0
Let i(x) be the second derivative of 1/2*x**2 + 1/12*x**4 + 1/3*x**3 + 0 - x. Solve i(g) = 0 for g.
-1
Let r(x) be the first derivative of x**6/2 + 3*x**5/5 - 7. Factor r(u).
3*u**4*(u + 1)
Let m(p) be the third derivative of p**9/11760 - p**8/6720 - p**7/8820 + p**4/3 - 7*p**2. Let g(i) be the second derivative of m(i). Find w such that g(w) = 0.
-2/9, 0, 1
Let y(a) be the second derivative of 7*a**6/240 - a**5/80 - 4*a - 4. Solve y(b) = 0 for b.
0, 2/7
Let d = 122/13 - 14627/1560. Let i(o) be the third derivative of 5/24*o**4 - 2*o**2 + 0 + 0*o - 1/15*o**5 - 1/3*o**3 + d*o**6. Suppose i(n) = 0. What is n?
1, 2
Let p(y) be the second derivative of -y**7/189 - y**6/27 - 4*y**5/45 - 2*y**4/27 + 5*y. Factor p(w).
-2*w**2*(w + 1)*(w + 2)**2/9
Let a(b) be the third derivative of b**8/168 + 2*b**7/105 + b**6/60 + b**2. Determine l so that a(l) = 0.
-1, 0
Suppose -2*b - 2*b = 5*a - 37, 2*a = -b + 10. Determine d, given that -5*d + 0*d**2 + 0*d**2 + b*d + 3*d**2 = 0.
-1, 0
Let j = -10/9 - -16/9. Factor -2/3*l**2 + 2/3 - j*l**3 + 2/3*l.
-2*(l - 1)*(l + 1)**2/3
Let n(l) be the third derivative of l**5/45 + l**4/9 - 2*l**3/3 + 5*l**2. Let n(h) = 0. Calculate h.
-3, 1
Let r(s) = -2*s**2 + 3*s - 1. Let t be r(2). Let c be (2/20)/(t/(-6)). Factor 0*n**2 + 0*n - c*n**4 + 0 + 1/5*n**3.
-n**3*(n - 1)/5
Let i(q) = -q**4 + q**3 - q**2 + 1. Let h(k) = 15*k**5 - 35*k**4 - 20*k**2 + 15*k + 25. Let d(u) = -h(u) + 30*i(u). Suppose d(t) = 0. Calculate t.
-1, 1/3, 1
Factor -3/2*a - 1/2*a**2 + 0.
-a*(a + 3)/2
Let f = 347/4 - 8659/100. Let y(z) be the first derivative of f*z**5 - 4/5*z + 1/5*z**4 - 1 - 16/15*z**3 - 1/15*z**6 + 7/5*z**2. Determine u so that y(u) = 0.
-2, 1
Let l(t) be the second derivative of t**8/6720 + t**7/2520 + t**4/12 + t. Let m(u) be the third derivative of l(u). Solve m(y) = 0 for y.
-1, 0
Let q(v) be the second derivative of v**7/42 + v**6/15 - v**5 - 2*v**4/3 + 64*v**3/3 - 64*v**2 + 14*v. Factor q(a).
(a - 2)**3*(a + 4)**2
Let x(d) = 2*d + 10. Let o be x(-5). Factor o + 1/2*m**3 + 0*m - 3/4*m**5 - 1/4*m**4 + 0*m**2.
-m**3*(m + 1)*(3*m - 2)/4
Suppose -6*r - 5 = -r. Let x be (-6)/((1 + 0)/r). Factor 0 + 2*k + 4*k**3 - x*k + 2*k**4 - 2.
2*(k - 1)*(k + 1)**3
Suppose -4*k = -k. Suppose k*a - 10 = -2*a. Factor -w**a + 0*w**5 + 2*w**4 - 4*w**4 + 3*w**5.
2*w**4*(w - 1)
Let n(i) be the third derivative of 0*i**3 + 0*i + 2/15*i**5 + 1/6*i**4 + 0 + i**2 + 1/30*i**6. Factor n(s).
4*s*(s + 1)**2
Let j(w) = -w**3 - 3*w**2 - 2*w - 2. Let u be j(-3). Let n = 24 - 21. Factor n - 2 - k**u - 1 + k**3.
-k**3*(k - 1)
Let p(a) = -a**5 - a**4 + a**2 - a. Let k(c) = -4*c**5 + 2*c**4 + 10*c**3 + 10*c**2 - 6*c. Let d(o) = -k(o) + 6*p(o). Let d(t) = 0. What is t?
-2, -1, 0
Let i(t) be the third derivative of -t**6/40 + t**5/30 + 7*t**4/24 + t**3/3 - 7*t**2. Factor i(k).
-(k - 2)*(k + 1)*(3*k + 1)
Let o(c) be the second derivative of c**5/180 - c**4/36 + c**3/27 + 18*c. What is g in o(g) = 0?
0, 1, 2
Let r = -1169/3 + 391. Solve 2*c**2 + r*c + 0 + 2/3*c**3 = 0.
-2, -1, 0
Let s(n) be the second derivative of -2*n**7/7 + 4*n**6/5 + 9*n**5/20 - 9*n**4/4 - 14*n. Factor s(t).
-3*t**2*(t + 1)*(2*t - 3)**2
Let f(c) be the first derivative of 1 - 2/21*c**4 - 2/7*c**2 - 5/21*c**3 - 2*c - 1/70*c**5. Let a(v) be the first derivative of f(v). Factor a(w).
-2*(w + 1)**2*(w + 2)/7
Let c be (-2)/(-6) - 64/(-24). Let g(r) be the first derivative of -2/9*r**c - 2/3*r**2 - 2/3*r + 2. Factor g(l).
-2*(l + 1)**2/3
Let j = -16/33 + 1451/2970. Let b(d) be the third derivative of -j*d**5 - 1/54*d**4 + 0 - 1/27*d**3 + 0*d + 3*d**2. Factor b(l).
-2*(l + 1)**2/9
Let b(n) be the first derivative of n**6/2 - 21*n**5/5 + 27*n**4/2 - 20*n**3 + 12*n**2 + 21. Suppose b(h) = 0. What is h?
0, 1, 2
Let 0 + 1/5*t**2 - 2/5*t = 0. What is t?
0, 2
Let b(u) be the second derivative of 6*u + 1/20*u**5 + 1/18*u**3 + 1/12*u**4 + 0 + 1/90*u**6 + 0*u**2. Factor b(w).
w*(w + 1)**3/3
Suppose 8*g - 5*g