n**2 + 33*n - 12. Let g(p) be the first derivative of -p**4/4 + p**2/2 - p + 3. Let v(o) = -18*g(o) + m(o). Solve v(w) = 0.
-2, -1
Let w be -38*5/50 - -4. Let p(x) be the second derivative of -1/5*x**2 + 0 - w*x**3 - 1/10*x**4 - 1/50*x**5 - x. Factor p(l).
-2*(l + 1)**3/5
Solve 32/3 - 16/3*q + 2/3*q**2 = 0 for q.
4
Let a(g) = -11*g**2 + 8*g - 4. Let l(o) = -6*o**2 + 4*o - 2. Suppose -v = -6*v - 20. Let q(t) = v*a(t) + 7*l(t). Factor q(f).
2*(f - 1)**2
Let z be 5 + 5/((-135)/123). Factor 2*t**2 - 22/9*t + z.
2*(t - 1)*(9*t - 2)/9
Let b be 0/(1/2*4). Factor 0*i + b - 5*i**2 - 6*i + 2 - 3*i**2.
-2*(i + 1)*(4*i - 1)
Let l(w) be the second derivative of -1/60*w**6 + 0*w**3 + 0 - 1/24*w**4 + 0*w**2 + 1/20*w**5 + 3*w. Solve l(r) = 0.
0, 1
Let c be -2 + (-12)/(-1 - 2). Factor -5*k - 2 - k + 3*k - 2*k**2 + 4*k**c.
(k - 2)*(2*k + 1)
Let q(u) = -10*u**4 - 3*u**3 + 3*u**2 - 12*u. Suppose 35 - 211 = -4*d. Let p(h) = -h**4 - h. Let s(t) = d*p(t) - 4*q(t). Let s(a) = 0. Calculate a.
0, 1
Let t(a) be the second derivative of a**4/3 + 8*a**3/3 - 12*a. Determine z so that t(z) = 0.
-4, 0
Determine l, given that 8*l + l**3 + 4*l**4 - 5*l**3 - 4*l**3 - 4 = 0.
-1, 1
Let l(r) be the first derivative of r**3/3 + r**2 + r - 1. Let a(u) = u**2 + 2*u + 1. Let b = -6 - -11. Let w(j) = b*l(j) - 4*a(j). Factor w(h).
(h + 1)**2
Let c(b) = -b**2 - 14*b + 14. Let q be c(-12). Suppose -2*j = -j - q. Find u such that 69*u**2 - 24*u - 21*u**3 + 12 - j*u + 2*u = 0.
2/7, 1, 2
Let d be (-2)/2*(-2)/4. Determine n, given that 1/2*n**3 + d*n**2 - 1/2*n - 1/2 = 0.
-1, 1
Let u = 16 + -16. Let m(s) be the second derivative of -s**2 + 5/12*s**4 + 2*s - 1/2*s**3 + 3/10*s**5 + u. Determine h so that m(h) = 0.
-1, -1/2, 2/3
Let m(u) be the first derivative of 256*u**5/3 - 320*u**4/3 + 160*u**3/3 - 40*u**2/3 + 5*u/3 + 8. Factor m(x).
5*(4*x - 1)**4/3
Let d(u) be the third derivative of -2*u**7/15 + 19*u**6/30 - 8*u**5/15 - 2*u**4/3 - u**2. Solve d(w) = 0 for w.
-2/7, 0, 1, 2
Let d(l) be the second derivative of l**4/2 + 5*l**3/3 - 2*l**2 - 2*l. Let d(x) = 0. Calculate x.
-2, 1/3
Let u = -7 + 11. Factor 2*j**u + 0*j**2 - 2*j**3 + j - 2*j**2 + j.
2*j*(j - 1)**2*(j + 1)
Let 0 - 1/7*y**4 + 5/7*y**3 - 3/7*y**5 + 1/7*y**2 - 2/7*y = 0. Calculate y.
-1, 0, 2/3, 1
Let d be -6 + 1 + 5 + 3/1. Determine m, given that -54/5*m**d + 54/5*m**2 - 2/5*m**5 + 0 + 0*m + 18/5*m**4 = 0.
0, 3
Let i(k) = -5*k**5 + 6*k**4 - 2*k**3 - 6*k**2 + 7*k. Let j(z) = -24*z**5 + 30*z**4 - 10*z**3 - 30*z**2 + 34*z. Let v(y) = -14*i(y) + 3*j(y). Solve v(s) = 0.
-1, 0, 1, 2
Let b(v) be the first derivative of 0*v + v**2 - 5 - 3/4*v**4 + v**3 - 2/5*v**5. Find t, given that b(t) = 0.
-2, -1/2, 0, 1
Let z be 4/(-6)*(8 - 5). Let y be (6 + z + -3)*0. Find k, given that -1/4*k**2 + 0 - 1/4*k**3 + y*k = 0.
-1, 0
Find j, given that 0 - 51/8*j**2 - 51/8*j**3 + 15/2*j**5 - 9/8*j + 51/8*j**4 = 0.
-1, -3/5, -1/4, 0, 1
Let f(n) be the second derivative of -n**8/13440 + n**7/5040 + n**6/720 + n**4/12 - 6*n. Let o(a) be the third derivative of f(a). Solve o(t) = 0.
-1, 0, 2
Let a(q) = -q + 10. Let v be a(4). Suppose 3*k - 6 = n, -8*n + v = -3*n + 3*k. Suppose 2/7*m + 2/7*m**3 + 4/7*m**2 + n = 0. Calculate m.
-1, 0
Suppose 0 = -5*n + 3*w + 10, -w + 3 = n + 1. Factor 2 + 0*x + 5*x - x + n*x**2.
2*(x + 1)**2
Suppose 3*q = 2*m + 12, 0 = 3*q - 4*m - m - 21. Suppose -8*k**4 + 5*k - 24*k**2 + 14*k**4 + 24*k**4 - q*k**3 + 3*k = 0. Calculate k.
-1, 0, 2/5, 2/3
Let p(m) be the first derivative of -m**8/5040 + m**7/2520 + m**3 - 3. Let u(d) be the third derivative of p(d). Factor u(i).
-i**3*(i - 1)/3
Let p(w) be the second derivative of w**4/24 - w**2 - 24*w. Solve p(o) = 0 for o.
-2, 2
Let a(c) be the first derivative of -2*c**3/21 - 2*c**2/7 - 2*c/7 - 1. Let a(h) = 0. Calculate h.
-1
Let s(o) be the second derivative of -o**7/840 - o**6/60 - o**5/10 - o**4/3 - o**3 - 8*o. Let n(y) be the second derivative of s(y). What is v in n(v) = 0?
-2
Let b(j) = -4*j**2 + j. Let q be b(-1). Let a be 10/(-150) - 2/q. Factor a*x + 2/3 - 1/3*x**2.
-(x - 2)*(x + 1)/3
Let f(a) be the first derivative of -1/10*a**4 + 1 + 2/15*a**3 + 0*a + 0*a**2. Find p such that f(p) = 0.
0, 1
Let r(p) be the third derivative of 0*p**4 + 1/420*p**6 + 0 - 1/210*p**5 + p**2 + 0*p + 0*p**3. What is k in r(k) = 0?
0, 1
Let q(p) be the third derivative of 0*p**3 + 0*p + 1/32*p**4 + 2*p**2 + 1/896*p**8 + 1/560*p**7 - 1/160*p**5 + 0 - 3/320*p**6. Suppose q(r) = 0. What is r?
-2, -1, 0, 1
Factor -14*k**2 - 2*k**2 + 10*k**2 - 2*k**3.
-2*k**2*(k + 3)
Let m be (36 - 40)/(18/(-4)). Suppose m*v**3 + 0 - 4/9*v - 14/9*v**2 = 0. What is v?
-1/4, 0, 2
Let s = 568/9 - 63. Let v(f) be the third derivative of 0*f + s*f**3 + 0 - 1/90*f**5 - f**2 + 0*f**4. Factor v(n).
-2*(n - 1)*(n + 1)/3
Let l(w) be the third derivative of w**8/20160 + w**7/1680 + w**6/360 + w**5/60 - w**2. Let j(n) be the third derivative of l(n). Factor j(s).
(s + 1)*(s + 2)
Factor 0 - 2/7*y**3 + 10/7*y**2 - 8/7*y.
-2*y*(y - 4)*(y - 1)/7
Let o(v) be the third derivative of -v**9/52920 + v**8/23520 + v**7/8820 - v**6/2520 + v**4/12 + 8*v**2. Let f(q) be the second derivative of o(q). Factor f(n).
-2*n*(n - 1)**2*(n + 1)/7
Let u be 20/(-4) - 99/(-18). Factor 0 - u*r**2 - r.
-r*(r + 2)/2
Let u(h) = h**2 + 5*h + 3. Let p be u(-4). Let z be (p/(-2))/(7/70). Suppose 5/2*q - z*q**4 + 1 - 3/2*q**5 + 0*q**2 - 5*q**3 = 0. What is q?
-1, 2/3
Suppose 5*w = -3*u + 6, 10 = 5*u - 5*w - 0*w. Factor 0 + 6/7*k**5 + 8/7*k**u + 32/7*k**3 + 0*k + 26/7*k**4.
2*k**2*(k + 2)**2*(3*k + 1)/7
Let o(z) be the second derivative of 0*z**3 + 3/50*z**5 - 1/105*z**7 - 1/15*z**4 + 0*z**6 + 0*z**2 + 6*z + 0. Factor o(h).
-2*h**2*(h - 1)**2*(h + 2)/5
Let w = -73 - -75. Factor 0 + 3/4*b - 3/4*b**3 + 0*b**w.
-3*b*(b - 1)*(b + 1)/4
Let i(k) be the second derivative of -k**5/5 - 5*k**4/12 - k**3/6 - 18*k. Factor i(l).
-l*(l + 1)*(4*l + 1)
Determine x so that 1/6*x**3 + 1/2*x**2 + 1/6 + 1/2*x = 0.
-1
Let t(l) = 6*l**3 - 7*l**2 - l + 2. Let q(w) = 9*w**3 - 11*w**2 - w + 3. Let x(v) = -5*q(v) + 8*t(v). Suppose x(k) = 0. What is k?
-1, 1/3, 1
Let u = 8 + -12. Let y(f) be the first derivative of -2*f**3/3 - f**2 + 5*f - 1. Let r(k) = 2*k**2 + 2*k - 4. Let d(g) = u*y(g) - 5*r(g). Factor d(n).
-2*n*(n + 1)
Let i(o) be the second derivative of o**7/3780 - o**6/405 + o**5/135 + o**3/6 + 5*o. Let u(c) be the second derivative of i(c). Factor u(v).
2*v*(v - 2)**2/9
Suppose 0 = 5*v + 3*n - 75, 3*n + 2*n + 15 = v. Suppose -18*i = -13*i - v. Suppose -1/5 - 3/5*d**2 + 3/5*d + 1/5*d**i = 0. What is d?
1
Let c(p) be the first derivative of 6*p**5/25 - 3*p**4/20 - 3*p**3/5 + 3*p**2/10 + 3*p/5 - 25. Solve c(w) = 0 for w.
-1, -1/2, 1
Let k(v) = -3*v**4 - 9*v**3 + 10*v**2 + 4*v. Let i(o) = -5*o**4 - 17*o**3 + 19*o**2 + 7*o. Let n(r) = 4*i(r) - 7*k(r). Factor n(q).
q**2*(q - 3)*(q - 2)
Let i be ((-5)/2)/(8/(-16)). Factor n**3 + 4*n**4 - 2*n**5 - i*n**3 - 4*n**4 + 6*n**4.
-2*n**3*(n - 2)*(n - 1)
Let v(c) be the second derivative of 0 - 2*c + 4/21*c**3 - 1/42*c**4 - 4/7*c**2. Factor v(s).
-2*(s - 2)**2/7
Find c such that -2/3*c**2 - 2*c + 0 = 0.
-3, 0
Let k(u) be the first derivative of u**7/2520 + u**6/1080 - u**3/3 + 2. Let t(x) be the third derivative of k(x). Suppose t(l) = 0. What is l?
-1, 0
Suppose -3/2*r**3 - 15/2*r - 6*r**2 - 3 = 0. What is r?
-2, -1
Factor 1/3*d**4 + 0 + 0*d + 2/3*d**2 - d**3.
d**2*(d - 2)*(d - 1)/3
Let d(x) = 6*x**3 + 3*x + 3. Let p(b) = b**4 + 6*b**3 + 2*b + 2. Let t(o) = -2*d(o) + 3*p(o). Factor t(z).
3*z**3*(z + 2)
Let n(o) be the second derivative of -o**6/60 - o**5/10 - 5*o**4/24 - o**3/6 - 16*o. Factor n(f).
-f*(f + 1)**2*(f + 2)/2
Let h(q) be the first derivative of 2/15*q**3 - 1/5*q**2 - 4/5*q - 2. Solve h(g) = 0.
-1, 2
Solve 0 - 3/2*p**4 + 1/2*p**3 - p + 3/2*p**2 + 1/2*p**5 = 0.
-1, 0, 1, 2
Let d(p) be the third derivative of p**8/50400 + p**7/6300 + p**6/1800 - p**5/20 - 4*p**2. Let k(a) be the third derivative of d(a). Factor k(m).
2*(m + 1)**2/5
Let c(b) be the second derivative of -b**6/540 + b**5/270 - 3*b**2/2 + b. Let j(r) be the first derivative of c(r). Factor j(f).
-2*f**2*(f - 1)/9
Factor -4*y**3 - 27 - 18*y**2 - 36*y - 1/3*y**4.
-(y + 3)**4/3
Factor 2*c**2 + 3*c**3 - 3*c**3 - 2*c**4 + 0*c**3 + 4*c**3 - 4*c.
-2*c*(c - 2)*(c - 1)*(c + 1)
Let l(p) =