/7
Let g(l) be the second derivative of l**5/10 + 7*l**4/12 - l**3/6 + 29*l. Let j(w) = 11*w**3 + 41*w**2 - 7*w. Let k(v) = 34*g(v) - 6*j(v). Factor k(r).
2*r*(r - 2)**2
Factor -1/4*k**2 + 3*k - 5.
-(k - 10)*(k - 2)/4
Let k(i) be the first derivative of -i**6/24 - 3*i**5/20 + 9*i**4/8 - i**3/3 - 3*i**2 + 664. Find d such that k(d) = 0.
-6, -1, 0, 2
Let m(r) be the third derivative of 0*r + 2/735*r**7 - 2/21*r**4 + 0 - 7*r**2 + 0*r**3 - 1/15*r**5 - 1/105*r**6. Factor m(q).
4*q*(q - 4)*(q + 1)**2/7
Let c(a) be the first derivative of -a**3/12 + 21*a**2/8 + 11*a/2 - 268. Factor c(h).
-(h - 22)*(h + 1)/4
Let s(u) be the first derivative of -12/7*u**2 + 26/7*u - 2/21*u**3 - 29. What is a in s(a) = 0?
-13, 1
Let g(f) be the second derivative of 49*f**5/100 - 7*f**4/6 - 26*f**3/15 - 4*f**2/5 + 3*f + 51. Factor g(w).
(w - 2)*(7*w + 2)**2/5
Factor -1/9*f**4 + 0 + 46/9*f**2 + 0*f + 7/3*f**3.
-f**2*(f - 23)*(f + 2)/9
Let w(j) be the third derivative of j**10/50400 - j**8/5600 + j**6/1200 - 7*j**4/12 + 7*j**2. Let f(n) be the second derivative of w(n). What is p in f(p) = 0?
-1, 0, 1
Suppose 4*i = -2*y - 30, -2*y - 4 = -4*i - 14. Let g = 0 - i. Factor -3*o**4 - 2*o**5 - 3*o**4 + 4*o**5 + o**g.
3*o**4*(o - 2)
Suppose -589*w**2 + 605*w**2 + 112*w - 40*w**4 - 4*w**5 - 85*w**3 + w**3 = 0. What is w?
-7, -2, 0, 1
Let y(q) be the first derivative of -2/55*q**5 + 1/22*q**4 + 2/33*q**3 - 12 - 1/11*q**2 + 0*q. Factor y(g).
-2*g*(g - 1)**2*(g + 1)/11
Let k = 69 + -75. Let f(v) = -v**3 + 3*v**2 + 4*v + 6. Let o(g) = 3*g**3 - 8*g**2 - 11*g - 17. Let j(c) = k*o(c) - 17*f(c). Suppose j(m) = 0. Calculate m.
-2, -1, 0
Determine a so that 5*a - 5*a + 9*a**4 - 16*a**3 + 348*a**2 - 352*a**2 = 0.
-2/9, 0, 2
Let p be 3108/1591 - (-12)/258. Find a, given that 3/5*a**p - 12/5 + 3/5*a**3 - 12/5*a = 0.
-2, -1, 2
Let m(i) = -i + 9. Let v be m(5). Suppose 5*r - 9 = 6. Suppose 2/7*z + 0 - 1/7*z**2 + 1/7*z**v - 2/7*z**r = 0. What is z?
-1, 0, 1, 2
Let z(x) = x**2 - x - 17. Let c be z(5). Factor 4*o**3 - 3*o**3 + 2*o**3 + o**c - 12*o + 8*o**2.
4*o*(o - 1)*(o + 3)
Let k be (9/126)/(4/42). Let f(w) be the first derivative of k*w**4 + w**3 + 3 + 0*w + 0*w**2. Let f(d) = 0. Calculate d.
-1, 0
Let o(l) be the third derivative of -l**7/1260 + l**6/120 + l**5/10 + 5*l**4/18 + 216*l**2. Factor o(r).
-r*(r - 10)*(r + 2)**2/6
Let l(x) be the first derivative of x**5/20 - x**3/2 - x**2 - 11*x - 13. Let t(v) be the first derivative of l(v). Factor t(u).
(u - 2)*(u + 1)**2
Let w(n) be the first derivative of n**4/26 - 4*n**3/39 + 513. Factor w(f).
2*f**2*(f - 2)/13
Let l be (-2)/7 + (-2 - ((-2960)/112)/5). Let j = -1/40 + 47/280. Suppose -j*o**l - 2/7*o + 0 - 3/7*o**2 = 0. What is o?
-2, -1, 0
Let b be -3*(-3)/18 - 45/(-18). Factor -25*q**2 + b*q**2 + 5*q**3 + 10*q + 7*q**2.
5*q*(q - 2)*(q - 1)
Let k = 88 + -85. Suppose -k*d - 4*j - 6 = 2, -4*j - 8 = 0. Solve 12/7*o**4 + 0 + 6/7*o**2 - 3/7*o**5 + d*o - 15/7*o**3 = 0.
0, 1, 2
Let g(o) be the second derivative of 4*o**6/165 + 9*o**5/110 + o**4/33 + 143*o. Factor g(v).
2*v**2*(v + 2)*(4*v + 1)/11
Let x(a) be the second derivative of 1/10*a**5 + 2/3*a**4 - 4*a + 2*a**2 + 5/3*a**3 + 0. Factor x(t).
2*(t + 1)**2*(t + 2)
Let q(g) be the third derivative of g**8/252 + g**7/126 - 47*g**6/360 + g**5/45 + 17*g**4/18 + 8*g**3/9 + 95*g**2. Suppose q(w) = 0. Calculate w.
-4, -1, -1/4, 2
Determine t so that -15*t**3 + 3*t + 4 - 20*t**3 - 27*t**3 + 13*t + 46*t**3 - 4*t**2 = 0.
-1, -1/4, 1
Let a(h) be the third derivative of h**5/12 + 25*h**4/12 + 40*h**3/3 + 246*h**2. Suppose a(c) = 0. Calculate c.
-8, -2
Let d(j) be the third derivative of -j**8/448 - j**7/40 - 3*j**6/32 - 9*j**5/80 + 7*j**2 - 5*j. Factor d(c).
-3*c**2*(c + 1)*(c + 3)**2/4
Factor 15*q**2 + 324 + 4484*q + 317*q**2 + 4*q**3 - 3832*q.
4*(q + 1)**2*(q + 81)
Let b(d) = d**2 - 8*d + 15. Let k be b(6). Let -c**3 - 7*c**k + 2 + 4*c**4 - 12*c**2 + 32*c - 18 = 0. Calculate c.
-2, 1, 2
Factor -7 + a**2 - 2*a + 2 + a**2 + 1.
2*(a - 2)*(a + 1)
Let s(g) be the first derivative of g**3 + 3*g**2/2 + 2*g + 1. Let p be s(-2). Find t such that 2*t**2 + 0*t + 2*t + 9 - t**2 - p*t = 0.
3
Let r(c) = 6*c**2 - 20*c + 122. Let i(b) = 8*b**2 - 24*b + 121. Let a(q) = 4*i(q) - 5*r(q). Factor a(z).
2*(z - 7)*(z + 9)
Let s(j) = j**3 - 8*j**2 - j - 6. Let z be s(6). Let t be 3*8/z*-7. Factor -22*h**t - 10*h**2 - 3*h**3 - 5*h**3 + 4 + 16*h**5 + 28*h**4 - 8*h.
4*(h - 1)*(h + 1)**3*(4*h - 1)
Let v = -506 - -513. Let i(x) be the second derivative of 7*x + 2/11*x**2 - 6/55*x**6 - 4/33*x**4 + 0 + 1/5*x**5 - 1/11*x**3 + 5/231*x**v. Factor i(p).
2*(p - 1)**4*(5*p + 2)/11
Let d(f) = f**3 - 15*f**2 + 14*f. Suppose -j + 3*r = 2 - 10, -2*j = -4*r - 20. Let b be d(j). Factor 2/5*x + b - 2/5*x**2.
-2*x*(x - 1)/5
Let x(c) = 3*c**2 + 15*c - 70. Let i be x(-8). Find p such that 1/5*p + 1/5*p**i + 0 = 0.
-1, 0
Let s(d) be the first derivative of -2*d**3/9 + 38*d**2/3 - 74*d/3 - 161. Determine a so that s(a) = 0.
1, 37
Suppose -4*z + 725 = -175. Solve 2*q - 47*q + 21*q**2 + 4*q**2 + 285*q**3 + z*q**4 - 10 = 0 for q.
-1, -1/3, 2/5
Let k(m) be the second derivative of -3*m**5/140 - 75*m**4/14 - 5625*m**3/14 - m - 446. Factor k(r).
-3*r*(r + 75)**2/7
Let j be 4/26 - (-4522)/182. Determine z so that 45*z**4 - j*z**2 - 15*z**3 + 5*z**5 + 48*z**4 - 88*z**4 - 10*z = 0.
-1, 0, 2
Let v(g) be the first derivative of g**5/20 - g**3/4 + g**2/4 - 121. Determine m, given that v(m) = 0.
-2, 0, 1
Let g(d) be the third derivative of d**5/15 - d**4/2 + 335*d**2. Find u such that g(u) = 0.
0, 3
Let k(q) = 2*q - 4. Let d be k(4). Suppose -5*z + d*p + 0 = -24, -4*z + 17 = -p. What is i in -i - 5/2*i**5 + 7/2*i**3 - 3/2*i**2 + 3/2*i**z + 0 = 0?
-1, -2/5, 0, 1
Factor -26*o + 35*o - 6*o**2 + 39*o - 140 + 2*o**2.
-4*(o - 7)*(o - 5)
Let g be 5/(20/16) + 6123/3. Determine s so that g - 3*s**5 + 3*s**4 - 3*s**2 + 9*s**3 - 2045 - 6*s = 0.
-1, 0, 1, 2
Let y(x) = 7*x**2 - 95*x - 66. Let o(d) = 14*d**2 - 192*d - 130. Let k(h) = -3*o(h) + 5*y(h). Determine s so that k(s) = 0.
-4/7, 15
Find r such that -8/11*r**4 - 34/11*r**3 - 26/11*r - 4/11 - 48/11*r**2 = 0.
-2, -1, -1/4
Suppose -4*j = 2*x - 30 + 4, -3*x = -15. Let 2*n**j + 4*n - 6*n**2 + 303*n**3 - 303*n**3 = 0. Calculate n.
-2, 0, 1
Factor 1/3*f**3 + 13/3*f**2 - 13/3 - 1/3*f.
(f - 1)*(f + 1)*(f + 13)/3
Let i(q) = -6*q**2 + 4*q + 38. Let p(j) be the first derivative of -j**4/4 + 11*j**3/3 - 7*j**2/2 - 77*j - 6. Let v(d) = 5*i(d) + 2*p(d). What is l in v(l) = 0?
-3, 2
Let l(a) = -3*a**3 - 131*a**2 - 253*a - 130. Let k(h) = -2*h**3 - 66*h**2 - 126*h - 64. Let t(u) = -5*k(u) + 2*l(u). Factor t(o).
4*(o + 1)**2*(o + 15)
Let k = -19 - -4. Let t = k - -27. Factor 4*d**2 - 4*d**3 - 8*d**2 - t*d + 4 + 16*d**2.
-4*(d - 1)**3
Let w(o) be the third derivative of -1/32*o**5 + 0*o + 0*o**4 + 0*o**3 + 0 + 3/160*o**6 - 1/560*o**7 + 4*o**2. Factor w(b).
-3*b**2*(b - 5)*(b - 1)/8
Let h(v) = -3*v**3 - 5*v**2 - 5*v - 3. Let u(w) = 2*w**3 + 6*w**2 + 4*w. Let q(j) = 3*h(j) + 4*u(j). Suppose q(y) = 0. Calculate y.
-1, 1, 9
Suppose 3*r = -0*r - 255. Let w = r + 87. Factor -3*q - 27/2*q**3 + 0 - 21/2*q**w - 3/2*q**5 - 15/2*q**4.
-3*q*(q + 1)**3*(q + 2)/2
Suppose -92 = 4*f - 4*w, 9*w - 5*w = -2*f - 40. Let j be 7/f - 2/(-4). Find t, given that 2/11*t**4 + 2/11 + 2/11*t**5 + j*t - 4/11*t**3 - 4/11*t**2 = 0.
-1, 1
Let a(q) = -q**3 + q**2 - 2. Let t(v) = -3*v**3 - 51*v**2 - 52*v - 4. Let h(i) = 2*a(i) - t(i). Factor h(p).
p*(p + 1)*(p + 52)
Suppose -b - 4 = -6. Factor 6*k**2 + 2*k - 168 + 168 + 2*k + b*k**3.
2*k*(k + 1)*(k + 2)
Let q = -750 + 3752/5. Determine s, given that -q*s**4 - 2/5*s**2 + 6/5*s - 6/5*s**3 + 4/5 = 0.
-2, -1, 1
Let r(v) be the second derivative of v**7/180 + 23*v**6/540 + v**5/9 + v**4/9 + 4*v**3 + 8*v. Let h(x) be the second derivative of r(x). Factor h(g).
2*(g + 1)*(g + 2)*(7*g + 2)/3
Find i such that 14/3*i - 6*i**2 - 14/3*i**3 - 2/3*i**4 + 20/3 = 0.
-5, -2, -1, 1
Let -4 + 2/3*d**5 + 0*d**4 - 16/3*d**3 + 14/3*d + 4*d**2 = 0. Calculate d.
-3, -1, 1, 2
Let f(s) be the second derivative of -s**6/40 - 3*s**5/20 - s**4/16 + 3*s**3/4 - s - 10. Factor f(o).
-3*o*(o - 1)*(o + 2)*(o + 3)/4
Let b(q) = -q**2 - 8*q - 11. Let p be b(-5). Suppose -p*i = -4*m - 8*i + 20, -9 = -3*i. Factor -4/7*o**m + 4/7*o + 0.
-4*o*(o - 1)/7
Let t(h) be