st derivative of 0*s**2 - 8/21*s**3 - 2/7*s**5 - 4/7*s**g + 0*s - 1/21*s**6 + 4. Let n(p) = 0. What is p?
-2, -1, 0
Let q(y) = -y**3 + 4*y**2 + 8*y - 7. Let w be q(5). Let z = w - 8. Factor 2/5*l**4 + 4/5*l**3 + z*l**2 - 2/5 - 4/5*l.
2*(l - 1)*(l + 1)**3/5
Let j(r) be the second derivative of 5/3*r**3 + 0 - 5/2*r**2 + 5/4*r**4 + r. Let j(z) = 0. What is z?
-1, 1/3
Let f(p) = p**3 - 15*p**2 - p + 25. Let h be f(15). Factor 5*k**2 - 3 + 5*k - h*k + 3.
5*k*(k - 1)
Let q(f) be the second derivative of -f**4/12 + 67*f**3/6 + 69*f**2 - 204*f - 1. Let q(w) = 0. What is w?
-2, 69
Let z(s) be the first derivative of s**4/3 - 20*s**3/3 + 18*s**2 - 11*s - 38. Let g(i) be the first derivative of z(i). Factor g(k).
4*(k - 9)*(k - 1)
Factor -96/5*p + 3/5*p**2 + 768/5.
3*(p - 16)**2/5
Let l(x) be the second derivative of 0*x**2 + 0*x**5 + 1/147*x**7 + 2/105*x**6 - 1/21*x**3 - 26*x - 1/21*x**4 + 0. What is w in l(w) = 0?
-1, 0, 1
Let i(v) = -3*v**4 - v**3 + v**2 + 11*v + 6. Let o(p) = 4*p**4 - 11*p - 6. Let w(u) = 6*i(u) + 4*o(u). Factor w(a).
-2*(a - 2)*(a + 1)**2*(a + 3)
Factor -28*a**2 - 2*a**3 - 3 + 4*a + 70*a**2 - a**4 - 38*a**2 - 2*a.
-(a - 1)**2*(a + 1)*(a + 3)
Factor -2/13*o**2 + 0*o + 32/13.
-2*(o - 4)*(o + 4)/13
Let a = -7 - -2. Let f(h) = 9*h**3 - 8*h**2 + 8. Let m(t) = 15 + t**2 + 6*t**3 - 6*t**2 - 10. Let x(o) = a*f(o) + 8*m(o). Factor x(s).
3*s**3
Let t be 0/1 - 9/((-45)/10). Let i be (4 + -6 + t)*(2 + -1). Factor 3/5*l**2 - 2/5*l + i - 1/5*l**4 + 0*l**3.
-l*(l - 1)**2*(l + 2)/5
Let d = -1867/15 - -249/2. Let v(t) be the second derivative of 13*t + 0*t**3 + 1/18*t**4 - d*t**5 + 0 + 0*t**2. Suppose v(y) = 0. Calculate y.
0, 1
Let m(z) be the first derivative of -z**6/1620 - z**5/135 - 2*z**3/3 - 9*z**2 + 44. Let i(v) be the third derivative of m(v). Factor i(d).
-2*d*(d + 4)/9
Let o(w) be the second derivative of -w**4/4 + 4*w**3 + 6*w - 4. Find t, given that o(t) = 0.
0, 8
Let q(i) = -i**3 - 13*i**2 - 17*i + 3. Let x be q(-12). Factor -x*m**5 - 6*m**2 - 37*m**5 - 6*m**2 - 72*m**3 - 135*m**4 + 25*m**5.
-3*m**2*(m + 1)*(5*m + 2)**2
Factor 1/8*s**3 + 11/8*s + 9/8*s**2 - 1/8*s**4 + 1/2.
-(s - 4)*(s + 1)**3/8
Let r(k) be the second derivative of k**7/280 + k**6/120 - k**5/20 - 5*k**3/2 - 7*k. Let a(c) be the second derivative of r(c). Factor a(j).
3*j*(j - 1)*(j + 2)
Suppose -2*y + 4*k = k - 5, -3*y - k = -13. Let d(i) be the second derivative of 0*i**2 + 1/8*i**y + 1/4*i**3 + 6*i + 0. Factor d(t).
3*t*(t + 1)/2
Factor -4/5*u**3 + 16*u**2 + 0 - 76/5*u.
-4*u*(u - 19)*(u - 1)/5
Suppose 3*r - 2*k = 8, -4*r + 3*k + 10 = -1. Suppose r*f - o = -2*f + 17, 5 = f - o. Factor -7*w**3 + 22 - 12*w**2 - 22 + f*w.
-w*(w + 2)*(7*w - 2)
Let f(j) = -j**5 + 4*j**4 + 7*j**3 + 7*j**2 - j - 6. Let y(x) = -x**5 + 5*x**4 + 8*x**3 + 8*x**2 - x - 7. Let a(w) = -6*f(w) + 5*y(w). Let a(n) = 0. What is n?
-1, 1
Let n(w) be the second derivative of w**7/36 + w**6/15 + w**5/40 - w**4/36 - 149*w. Factor n(l).
l**2*(l + 1)**2*(7*l - 2)/6
Let k(g) = 4*g**3 + 1. Let a(q) = -41*q**3 - 2*q**2 - 11. Let s(d) = 2*a(d) + 22*k(d). Factor s(j).
2*j**2*(3*j - 2)
Let f(a) be the second derivative of -2*a**6/15 + a**5/10 + a**4/6 - 512*a. Factor f(s).
-2*s**2*(s - 1)*(2*s + 1)
Let n(d) be the third derivative of -13*d**6/20 - 118*d**5/45 - 121*d**4/36 - 2*d**3/9 + 32*d**2. Factor n(x).
-2*(x + 1)**2*(117*x + 2)/3
Let n(w) be the second derivative of w**7/2 - 26*w**6/15 + 21*w**5/10 - w**4 + w**3/6 - 20*w - 1. Determine l so that n(l) = 0.
0, 1/7, 1/3, 1
Suppose -2*i + 39 = 5*l, 0 = 2*l + 5*i - 6*i - 12. Let m be (-6)/(-42)*l/10. Factor 1/10*j**5 - 1/10*j**3 + 0 + 0*j - m*j**2 + 1/10*j**4.
j**2*(j - 1)*(j + 1)**2/10
Let o(t) be the second derivative of t**5 + 29*t**4/6 + 20*t**3/3 + 4*t**2 + 84*t. Factor o(c).
2*(c + 2)*(2*c + 1)*(5*c + 2)
Let g = -18 - -24. Suppose 0 = 2*p - g*p. Factor 1/2*y**4 + 0 - 1/2*y**2 - 1/2*y**3 + p*y + 1/2*y**5.
y**2*(y - 1)*(y + 1)**2/2
Factor -50*o - 25*o + 10*o**2 - 87 + 14 - 20 - 87 + 5*o**3.
5*(o - 4)*(o + 3)**2
Factor -37 - 15*y - y**2 + 56 - 45.
-(y + 2)*(y + 13)
Let y(h) be the second derivative of -1/14*h**3 + 0 - 1/70*h**5 - 6*h - h**2 + 3/56*h**4. Let k(f) be the first derivative of y(f). Suppose k(l) = 0. What is l?
1/2, 1
Let n(p) be the third derivative of 4*p**7/105 - 7*p**6/30 + 2*p**5/5 + p**4/6 - 4*p**3/3 - 11*p**2. What is r in n(r) = 0?
-1/2, 1, 2
Let u be -44*2/(-28) + (-3)/21. Factor -o**u + 4*o + 8*o**2 - 3*o**3 - 3 - 5.
-4*(o - 2)*(o - 1)*(o + 1)
Let m = 430/1281 + -1/427. Let s(f) be the second derivative of -7*f + 0 - m*f**3 + 0*f**2 - 1/6*f**4. Determine a, given that s(a) = 0.
-1, 0
Suppose 3*g - 2*a - 13 = -a, 4*g - 8 = -a. Let v be (7 + 164/(-23))/(21/(-483)). Factor v*l**4 + 0 - l**g - 1/3*l - 5/3*l**2.
l*(l - 1)*(3*l + 1)**2/3
Solve 52*u**3 + 31*u - 58*u + 32*u**2 + 4*u**4 + 27*u + 18*u**4 + 2*u**5 = 0 for u.
-8, -2, -1, 0
Let s(o) be the third derivative of o**8/33600 + o**7/4200 - o**5/150 - 5*o**4/24 + 30*o**2. Let c(p) be the second derivative of s(p). Factor c(x).
(x - 1)*(x + 2)**2/5
Let c = -15 + 18. Let q = 51 - 30. Factor -q*b - c*b**2 - 37*b**2 + 15 + 48*b**3 + 3.
(3*b + 2)*(4*b - 3)**2
Let p(c) = 32*c**4 + 60*c**3 - 48*c**2 - 220*c - 96. Let s(y) = 13*y**4 + 24*y**3 - 19*y**2 - 88*y - 38. Let g(t) = 5*p(t) - 12*s(t). Factor g(z).
4*(z - 2)*(z + 1)**2*(z + 3)
Let d(l) be the second derivative of 22/3*l**3 + 1/5*l**5 + 7/3*l**4 - 16*l + 0 + 10*l**2. Determine m, given that d(m) = 0.
-5, -1
Let c be (-480)/432*(-24)/10. Determine o, given that -20*o**3 + c + 50/3*o**4 - 22/3*o**2 + 8*o = 0.
-2/5, 1
Let a(n) = 4*n**4 + 4*n**3 - 2*n**2 - 4*n + 2. Let o(t) = 5*t**4 + 5*t**3 - 2*t**2 - 5*t + 3. Let y(d) = -3*a(d) + 2*o(d). Factor y(i).
-2*i*(i - 1)*(i + 1)**2
Let l(x) be the first derivative of x**3/7 - 237*x**2/7 - 477*x/7 + 236. Factor l(j).
3*(j - 159)*(j + 1)/7
Let g(q) = -9*q**2 + 91*q - 521. Let z(u) = -14*u**2 + 136*u - 776. Let j(v) = 8*g(v) - 5*z(v). Factor j(l).
-2*(l - 12)**2
Factor 20*d - 48/7 + 94/7*d**2 + 2*d**3.
2*(d + 3)*(d + 4)*(7*d - 2)/7
Let u(f) be the third derivative of f**9/3360 + f**8/5040 + f**5/60 + 5*f**4/24 + 4*f**2 - 5. Let p(y) be the third derivative of u(y). Factor p(o).
2*o**2*(9*o + 2)
Let b(s) be the second derivative of -s**5/120 - 43*s**4/72 - 110*s**3/9 + 121*s**2/3 + 45*s. Factor b(n).
-(n - 1)*(n + 22)**2/6
Let r = -3 - -7. Suppose -3*a + 5*a - r = 0. Suppose -2*w + 0*w + 0*w + 4*w - 2*w**a = 0. What is w?
0, 1
Let t(q) be the third derivative of -q**5/210 - 13*q**4/21 - 676*q**3/21 + 249*q**2. Factor t(f).
-2*(f + 26)**2/7
Let c(y) = -y**4 - y**2 - y - 1. Suppose 0 = 3*i - 2*i - 1. Let r(q) = -10*q**4 + 36*q**3 - 18*q**2 + 10*q + 6. Let o(d) = i*r(d) + 6*c(d). Factor o(p).
-4*p*(p - 1)**2*(4*p - 1)
Suppose -10*d + 14*d = -10*d. Find k such that 3/4*k**4 + d*k**3 + 3/2*k + 0 - 9/4*k**2 = 0.
-2, 0, 1
Suppose -202*w + 408 + 102 = -298. What is z in 3/2*z**3 + 0 + 0*z - 1/4*z**2 + z**5 - 9/4*z**w = 0?
0, 1/4, 1
Let 5*k**4 - 74*k - 105*k**3 - 103*k - 1000 + 590*k**2 - 123*k = 0. What is k?
-1, 2, 10
Let c(y) be the third derivative of -3*y**6/220 + y**5/330 + 3*y**4/44 - y**3/33 + 2*y**2 - 60. Find s, given that c(s) = 0.
-1, 1/9, 1
Let k(v) be the second derivative of v**8/20160 - v**7/3360 + v**6/2160 - 25*v**3/6 - 33*v. Let c(r) be the second derivative of k(r). Factor c(m).
m**2*(m - 2)*(m - 1)/12
Let y(b) be the second derivative of 7*b**6/135 + b**5/6 + b**4/6 + b**3/27 + b - 87. Factor y(z).
2*z*(z + 1)**2*(7*z + 1)/9
Let y be (32/(-192))/(-1 - (-20)/22). Factor w + w**3 + 1/6 + y*w**2.
(w + 1)*(2*w + 1)*(3*w + 1)/6
Let q(u) = -6*u**5 + 17*u**4 + 12*u**3 - 23*u. Let m = 61 - 55. Let n(x) = x**5 - 3*x**4 - 2*x**3 + 4*x. Let v(j) = m*q(j) + 34*n(j). Factor v(k).
-2*k*(k - 1)**2*(k + 1)**2
Let f be 2/2 + 50/(-12). Let r = f + 7/2. Factor -2/3*z**4 + 2/3*z**2 + 0*z**3 + 0 + r*z - 1/3*z**5.
-z*(z - 1)*(z + 1)**3/3
Let f = -7 - -10. Let x(s) = s**2 - 4*s - 2. Let o be x(5). Factor -f*t**4 + 2*t - 4*t - 6*t**o + 3*t**2 + 3*t**3 + 5*t.
-3*t*(t - 1)*(t + 1)**2
Let c(n) be the second derivative of 24*n**5/5 - 2*n**4 + n**3/4 + 3*n - 9. Find k, given that c(k) = 0.
0, 1/8
Suppose 3*f - 2*g - 18 = 0, -f - 3*g + 7 = -4*g. Suppose 3*n - 2*h = -0*n + 16, 0 = 3*n + h - 10. Find q, given that -4*q**n 