 + b**7/140 - b**5/40 + 17*b**3/6 - 9*b. Let r(n) be the second derivative of m(n). Factor r(g).
-3*g*(g - 1)**2*(g + 1)**2
Let f(r) = -109*r + 767. Let d be f(7). What is x in 0*x + 12*x**2 + 0 + 28/3*x**d + 20*x**3 + 4/3*x**5 = 0?
-3, -1, 0
Let i(x) be the second derivative of x**4/6 - 12*x**3 + 324*x**2 - 10*x - 5. Factor i(d).
2*(d - 18)**2
Suppose -5*z - 1 = -36. Solve 56*d**2 - 10*d**3 - 39*d**4 + z*d**3 + 54*d + 43*d**2 + 9*d**5 = 0 for d.
-1, -2/3, 0, 3
Let g(x) = -x**2 - 11*x + 1. Let y be g(-10). Let u = y - -6. Factor -4*r + u*r**2 + r**2 - 2*r - 10*r**3 - 2.
-2*(r - 1)**2*(5*r + 1)
Let a be (-18)/(-28)*(-14 - (-420)/21). Factor 75/7*v - 18*v**2 + a*v**3 - 12/7.
3*(v - 4)*(3*v - 1)**2/7
Suppose 0 = -2*w + 5*l - 2*l - 10, -17 = -5*w - 3*l. Let i be (-16)/8*w/(-4). Factor -i*p**4 + p**3 + 0 + 0*p + 0*p**2.
-p**3*(p - 2)/2
Let 8*t**2 - 3*t**3 + 7*t**4 + 7*t + 6*t**3 + t**2 + 2 - 6*t**4 + 2*t**3 = 0. Calculate t.
-2, -1
Let q(b) be the third derivative of -3*b**8/224 - b**7/70 + 13*b**6/120 + 3*b**5/10 + 5*b**4/16 + b**3/6 + 3*b**2 + 41. Solve q(w) = 0.
-1, -1/3, 2
Let q(p) be the first derivative of -2/15*p**5 + 0*p**4 + 0*p - 2/3*p**2 + 2/3*p**3 - 1. Determine o, given that q(o) = 0.
-2, 0, 1
Let z(d) be the first derivative of 0*d - 1/42*d**4 + 10/63*d**3 + 25 - 4/21*d**2. Factor z(m).
-2*m*(m - 4)*(m - 1)/21
Let z(x) be the third derivative of 1/10*x**5 - x**2 + 0*x**3 + 0 - 1/4*x**4 + 0*x - 1/80*x**6. Factor z(f).
-3*f*(f - 2)**2/2
Let x be (59/2)/((3 - 5)/(-4)). Let d = 61 - x. Factor -12/5*f**2 - 6/5*f - d*f**3 - 1/5 - 3/5*f**4.
-(f + 1)**3*(3*f + 1)/5
Let b = 1967 + -1964. Suppose 0*n + 0 - 8/5*n**b - 4/5*n**4 - 4/5*n**2 = 0. Calculate n.
-1, 0
Let q(f) be the third derivative of f**7/420 - 23*f**6/360 + 19*f**5/120 - 7*f**4/72 - 453*f**2. Solve q(w) = 0 for w.
0, 1/3, 1, 14
Let r = 67/1180 - 2/295. Let h(z) be the first derivative of 1/5*z**3 + 1/5*z - r*z**4 - 3/10*z**2 + 4. Suppose h(s) = 0. Calculate s.
1
Let h(x) be the second derivative of 2*x**6/15 - 16*x**5/5 + 30*x**4 - 400*x**3/3 + 250*x**2 - 440*x. Find p such that h(p) = 0.
1, 5
Let a(v) be the first derivative of -v**6/24 + 3*v**5/20 + v**4/8 - v**3/2 - v**2/8 + 3*v/4 - 173. Determine m, given that a(m) = 0.
-1, 1, 3
Let n(r) be the third derivative of -1/48*r**4 - 1/240*r**5 + 0*r + 22*r**2 + 1/480*r**6 + 0 + 0*r**3. Factor n(l).
l*(l - 2)*(l + 1)/4
Let j(z) be the second derivative of 2/27*z**3 + 1/9*z**2 - 35*z + 0*z**4 - 1/135*z**6 + 0 - 1/45*z**5. Factor j(c).
-2*(c - 1)*(c + 1)**3/9
Let y(o) be the third derivative of -o**6/720 + o**5/72 - o**4/36 + 3*o**2 + 23. Determine m, given that y(m) = 0.
0, 1, 4
Determine k, given that -6 - 3/2*k**2 - 12*k + 21/2*k**3 + 3/2*k**5 + 15/2*k**4 = 0.
-2, -1, 1
Let q(u) be the first derivative of 4*u**3/3 - 6*u**2 + 8*u + 38. Factor q(n).
4*(n - 2)*(n - 1)
Let 4*s**5 - 149*s**2 - 4*s**3 + 1572*s**4 + 37*s**2 - 1460*s**4 = 0. Calculate s.
-28, -1, 0, 1
Factor 6/5*h**3 + 1/5*h**4 - 1 + 4/5*h**2 - 6/5*h.
(h - 1)*(h + 1)**2*(h + 5)/5
Let n(j) = -j**2 + 6*j + 8. Let t be n(6). Let d be t*((-10)/(-4))/5 + -2. Suppose 3/2*o**d + 3*o + 0 = 0. What is o?
-2, 0
Let z(j) = -j + 7. Let s(x) = 2*x**2 - x - 1. Let d be s(2). Let b be z(d). Factor 2*a + b*a**2 + 3*a**3 - 4*a**3 - a - 2.
-(a - 2)*(a - 1)*(a + 1)
Suppose -14 = -3*h + 2*x + 65, 5*h - 3*x = 133. Suppose 10*u + h*u**2 + 0*u - 30*u**2 - 25 = 0. Calculate u.
5
Let j(k) be the first derivative of 4*k**3/3 - 26*k**2/3 - 40*k/3 - 43. Factor j(w).
4*(w - 5)*(3*w + 2)/3
Let g(i) = -i**3 - 2*i**2 - 4*i - 1. Let v be g(-1). Suppose -8*k**v + 2*k**2 + 6 - 4*k**2 + 5*k**4 - 1 = 0. What is k?
-1, 1
Factor -51/2 + 105/2*w - 57/2*w**2 + 3/2*w**3.
3*(w - 17)*(w - 1)**2/2
Let l = -1572/19 + 11061/133. Determine t so that -l*t**3 - 2/7 + 3/7*t + 1/7*t**2 + 1/7*t**4 = 0.
-1, 1, 2
Let z(p) be the third derivative of p**8/5040 - p**7/315 + 13*p**5/60 - 19*p**2. Let a(b) be the third derivative of z(b). Factor a(m).
4*m*(m - 4)
Suppose 0*m + 3*m = -2*d - 14, -5*m - 3*d - 23 = 0. Let i(k) = 15*k + 62. Let a be i(m). Find t such that 0 + 4/5*t - 4/5*t**a = 0.
0, 1
Let f(c) = -3*c**3 - 12*c**2 + 149*c - 2. Let v(a) = 48*a**3 + 192*a**2 - 2391*a + 33. Let z(s) = -33*f(s) - 2*v(s). Find d, given that z(d) = 0.
-9, 0, 5
Let d(r) be the first derivative of -r**4/4 - 2*r**3 - 4*r**2 + 2*r - 3. Let s be d(-4). Factor -2/3*g + 0*g**s + 8/9*g**3 + 2/9.
2*(g + 1)*(2*g - 1)**2/9
Let r(h) = -5*h**3 + 10*h**2 + 5*h - 5. Let g(l) = l**2. Let x(s) = 5*g(s) - r(s). Factor x(j).
5*(j - 1)**2*(j + 1)
Let s = -7739/2 + 25145/6. Let p = s + -318. Determine h so that -5/3*h**3 - 5*h**2 + 5/3*h + 5/3*h**4 + p = 0.
-1, 1, 2
Let z(q) be the first derivative of -q**6/360 + q**5/180 + q**4/72 - q**3/18 - 3*q**2/2 + 20. Let b(v) be the second derivative of z(v). Factor b(p).
-(p - 1)**2*(p + 1)/3
Let u be (-4)/10 - (-4 - (-1 + -1)). Let m(p) be the first derivative of 2/15*p**3 + 4/5*p**2 - 1 + u*p. Factor m(s).
2*(s + 2)**2/5
Let b(h) = 8*h**4 - 5*h**3 - 55*h**2 + 36*h + 12. Let o(m) = 15*m**4 - 9*m**3 - 111*m**2 + 72*m + 24. Let c(l) = 9*b(l) - 4*o(l). What is v in c(v) = 0?
-2, -1/4, 1, 2
What is k in 1/3*k**3 + 400/3*k - 40/3*k**2 + 0 = 0?
0, 20
Determine z, given that -19 + 8*z + 49*z**2 - 15*z**2 + 19*z - 34*z**3 - 10*z**4 - 5 + 7*z = 0.
-4, -1, 3/5, 1
Let s(m) be the first derivative of m**5/10 + 2*m**4/3 + m**3 - 15*m - 2. Let p(t) be the first derivative of s(t). Let p(z) = 0. What is z?
-3, -1, 0
Let s(l) be the second derivative of -l**9/75600 + l**7/12600 - l**4/6 + l**3 - 2*l. Let x(z) be the third derivative of s(z). Factor x(c).
-c**2*(c - 1)*(c + 1)/5
Solve 4/17*g**4 - 64/17*g - 24/17 + 22/17*g**3 - 22/17*g**2 = 0 for g.
-6, -1, -1/2, 2
Factor 2/11*n**3 - 82/11*n**2 + 798/11*n + 882/11.
2*(n - 21)**2*(n + 1)/11
Let f be (-74)/(-12)*3/5. Let b = 21/5 - f. Factor 1 + b*v - 1/2*v**2.
-(v - 2)*(v + 1)/2
Let f be ((-1)/3)/((-7)/42). Suppose 3*a + o - 3 = 2, 4*a - 2*o = 10. Factor -6*z**f - 4 - z - 2*z + 5*z + 8*z**a.
2*(z - 1)*(z + 2)
Let l(m) = -6*m**3 + 63*m**2 - 438*m + 1026. Let w(j) = -2 - j**3 + 6 + j - 5. Let t(x) = l(x) - 3*w(x). Let t(y) = 0. What is y?
7
Let m = -3402 - -3404. Determine r so that -4/3*r + 0*r**4 - 8/3*r**3 + 32/9*r**m + 4/9*r**5 + 0 = 0.
-3, 0, 1
Suppose -2*b + 9*b + 56 = 0. Let l = b + 8. Factor l + 4/3*h + 4/3*h**2.
4*h*(h + 1)/3
Let y(c) be the second derivative of c**5/150 + 4*c**4/45 + c**3/9 - 10*c**2/3 + 239*c. Let y(b) = 0. Calculate b.
-5, 2
Let s = -58 - -60. Factor -2*u**2 - 8*u - 16 + 8*u**2 - 4*u - s*u**2.
4*(u - 4)*(u + 1)
Let z(w) = 5*w**4 + 75*w**3 + 85*w**2 - 150*w - 345. Let v(r) = r**3 + r**2 + 2*r - 1. Let a(b) = -25*v(b) + z(b). Factor a(t).
5*(t - 2)*(t + 2)**2*(t + 8)
Let w(y) be the first derivative of -1/3*y**2 + 2*y + 1/6*y**4 - 2/3*y**3 - 8. Factor w(s).
2*(s - 3)*(s - 1)*(s + 1)/3
Let u(b) be the third derivative of b**5/30 + 49*b**4/6 + 2401*b**3/3 + 149*b**2. Factor u(h).
2*(h + 49)**2
Let r(d) = 3*d**4 + d + 3 - d**4 - 4*d + 2*d**4 - 6*d**3. Let f(s) = 11*s**4 - 17*s**3 - 8*s + 8. Let m(a) = 3*f(a) - 8*r(a). Factor m(y).
y**3*(y - 3)
Let h(r) = -12*r**3 + 378*r**2 + 765*r + 384. Let u(q) = 3*q**3 - 94*q**2 - 191*q - 96. Let p(v) = -2*h(v) - 9*u(v). Let p(j) = 0. Calculate j.
-1, 32
Factor 16/3 + 5/3*f**2 - 16/3*f - 1/6*f**3.
-(f - 4)**2*(f - 2)/6
Let m(a) be the second derivative of a**5/110 - 7*a**4/66 + 7*a**3/33 + 15*a**2/11 - 192*a. Suppose m(c) = 0. Calculate c.
-1, 3, 5
Let q(o) be the third derivative of o**9/120960 + o**8/40320 + 3*o**5/20 - 20*o**2. Let l(r) be the third derivative of q(r). Suppose l(a) = 0. What is a?
-1, 0
Let j(k) be the first derivative of -2*k**5/25 - 3*k**4/10 + 2*k**3/15 + 3*k**2/5 - 604. Let j(m) = 0. What is m?
-3, -1, 0, 1
Let m(a) be the third derivative of 0 - 9/8*a**4 - a**3 + 10*a**2 - 1/35*a**7 - 9/40*a**6 + 0*a - 7/10*a**5. What is j in m(j) = 0?
-2, -1, -1/2
Let x = 3236/5 + -647. Let s(c) be the second derivative of 0*c**2 - 2/15*c**6 - 11*c + 0*c**4 + 0 + 0*c**3 - x*c**5. Determine k, given that s(k) = 0.
-1, 0
Let t(y) = -6*y**2 - 12*y - 16. Let i be t(-5). Let b = i + 744/7. Determine o, given that 2/7*o - b*o**3 + 2/7*o**2 - 2/7*o**4 + 0 = 0.
-1, 0, 1
Let x(l) be the first derivative of l**6/600 - l**5/75 -