15
Let t = -1 + 5/4. Let u be 84/(-12) + (-1 - -9) - (-9)/(-12). Factor -u*x - t*x**2 + 0.
-x*(x + 1)/4
Let j = -94739/4368 + 282/13. Let d(f) be the third derivative of -5*f**2 + 0*f**4 - 1/105*f**7 + 0 + 0*f**3 + 0*f**5 + j*f**8 + 0*f + 1/120*f**6. Factor d(p).
p**3*(p - 1)**2
Suppose -74*s - 3 = -75*s. Let -4*y - 4*y**s - 18*y**4 - 25*y**3 - 4*y**5 - 18*y**2 + y**3 = 0. Calculate y.
-2, -1, -1/2, 0
Let v(k) be the third derivative of -1/224*k**8 + 1/16*k**4 + 0*k + 0*k**6 + 0*k**3 - 12*k**2 - 1/20*k**5 + 0 + 1/70*k**7. Factor v(s).
-3*s*(s - 1)**3*(s + 1)/2
Let j(a) be the third derivative of -a**7/315 + a**5/30 + a**4/18 + 20*a**2 - 4. Factor j(t).
-2*t*(t - 2)*(t + 1)**2/3
Factor 0 + 12/17*q**3 + 16/17*q**2 - 2/17*q**5 + 0*q**4 + 6/17*q.
-2*q*(q - 3)*(q + 1)**3/17
Let d = -5 - -14. Suppose -2*g + 15 = d. Determine j so that 3/5*j**4 - 3/5*j**5 + 9/5*j**3 + 6/5*j + 0 - g*j**2 = 0.
-2, 0, 1
Let x(h) be the second derivative of -h**7/21 + h**6/15 + h**5/2 - h**4/6 - 8*h**3/3 - 4*h**2 - h + 15. Determine f so that x(f) = 0.
-1, 2
Let x = -7389 - -7393. Suppose 3/2*j + 0*j**3 + 0 - 3/4*j**x + 9/4*j**2 = 0. Calculate j.
-1, 0, 2
Let w(h) be the first derivative of 3/5*h**3 + 0*h**2 + 0*h - 3/20*h**4 + 6. Find i, given that w(i) = 0.
0, 3
Let h = 5372 + -5370. Find y, given that -12/7*y + 1/7*y**h + 36/7 = 0.
6
Let b = -13 - -16. Suppose 0 = -4*y + 2*y - 2, -5 = -2*a - b*y. Solve -2*s**3 - 4*s**2 + a + 0 + 0*s**3 + 2*s = 0.
-2, -1, 1
Factor -148955/3*j - 5/3*j**4 + 0 - 155*j**3 - 4805*j**2.
-5*j*(j + 31)**3/3
Let a(h) be the third derivative of 5*h**8/504 + 67*h**7/945 + 101*h**6/540 + 19*h**5/90 + h**4/27 - 4*h**3/27 - 24*h**2 + h. Suppose a(f) = 0. What is f?
-2, -1, -2/3, 1/5
Let k = 2049/100 - 506/25. Let -t + k*t**2 + 1 = 0. What is t?
2
Let g(w) be the second derivative of 3*w**5/20 - 2*w**4 + 5*w**3/2 + 75*w**2 - 37*w. Factor g(q).
3*(q - 5)**2*(q + 2)
Let c(b) = b**2 + 6*b + 7. Let f be c(-5). Suppose 0 = 3*a + 5*y - 11, f*y - 4 = -4*a + 6*y. Find i, given that -6 - 4*i - 2/3*i**a = 0.
-3
Factor -21*t + 1744748 - 1744748 + 3*t**3 + 18*t**2.
3*t*(t - 1)*(t + 7)
Let h(u) be the second derivative of u**4/3 - 10*u**3/3 + 8*u**2 + 139*u. Find p such that h(p) = 0.
1, 4
Let t(l) be the second derivative of l**6/60 - l**5/8 + l**4/8 + 3*l**3/4 + 47*l - 1. Determine g so that t(g) = 0.
-1, 0, 3
Let p = -9/4 + 73/36. Let r = p - -5/9. Factor 2/3*i**3 + 2/3*i**2 - r*i**4 - 1/3*i**5 - 1/3*i - 1/3.
-(i - 1)**2*(i + 1)**3/3
Find l, given that -74/3*l**2 + 14/3*l**3 - 8 + 104/3*l = 0.
2/7, 2, 3
Factor 0 + 5/2*g**3 + 50*g - 105/2*g**2.
5*g*(g - 20)*(g - 1)/2
Let v(c) be the second derivative of -c**7/210 - c**6/120 + c**5/60 + c**4/24 - 5*c**2 + 13*c. Let o(x) be the first derivative of v(x). Factor o(m).
-m*(m - 1)*(m + 1)**2
Let l(n) = -16*n**2 + 34*n - 33. Let c(m) = -3*m**2 + 7*m - 6. Let z(g) = -22*c(g) + 4*l(g). Factor z(b).
2*b*(b - 9)
Let t(n) be the second derivative of -2*n**6/15 - 9*n**5/5 - 8*n**4 - 32*n**3/3 - n + 101. Let t(z) = 0. What is z?
-4, -1, 0
Let a(s) = 59*s**2 + 205*s + 60. Let g(y) be the third derivative of y**5/3 + 17*y**4/6 + 10*y**3/3 + 15*y**2. Let q(c) = 6*a(c) - 17*g(c). Factor q(i).
2*(i + 5)*(7*i + 2)
Factor 51/4 + 12*n - 3/4*n**2.
-3*(n - 17)*(n + 1)/4
Let o = 18 - -67. Suppose 4*x - o = 2*k - 19, 43 = 3*x + 5*k. What is a in -x*a**2 - 15*a**2 - 6 + 4*a**2 + 21*a - 3*a**4 + 15*a**3 = 0?
1, 2
Suppose -10*x + 12 = -6*x. Suppose 0 = x*d + 9, -2*j = -3*d - 13. Determine i, given that 6*i**3 + 10*i**4 + 0*i - 10*i**2 + j*i - 4*i**5 - 4*i**5 + 0*i = 0.
-1, 0, 1/4, 1
Factor 4/5*j**2 + 0 - 4/5*j**4 + 16/5*j**3 - 16/5*j.
-4*j*(j - 4)*(j - 1)*(j + 1)/5
Let p(b) be the second derivative of 37/90*b**5 + 1/189*b**7 - 10/9*b**4 + 0*b**2 + 0 - 2/27*b**6 - 28*b + 4/3*b**3. Solve p(l) = 0.
0, 2, 3
Let q(f) = -34*f**2 + 474*f + 30. Let x be q(14). Factor -3/2*y**x + 0 - 3/2*y.
-3*y*(y + 1)/2
Let m be ((-256)/(-80))/(5 + (-1 - 158/40)). Determine s, given that 4*s**4 + 76*s**2 + 25*s**3 + 112*s + 1/4*s**5 + m = 0.
-4, -2
Let t = 7 - 2. Let r(q) = q + 9. Let y be r(-7). Determine n so that 12*n**2 - t*n**y + n**3 - 3*n**2 = 0.
-4, 0
Let m(u) = -29*u**2 + 105*u + 9. Let j(t) = -13*t**2 + 52*t + 4. Let p(r) = 9*j(r) - 4*m(r). Factor p(f).
-f*(f - 48)
Let v(f) be the third derivative of 0*f - 10*f**2 + 10/3*f**3 + 0*f**4 + 0 - 1/4*f**5 + 1/24*f**6. Factor v(w).
5*(w - 2)**2*(w + 1)
Let n(x) be the third derivative of -x**6/40 + 7*x**4/8 - 3*x**3 + 234*x**2. Determine u, given that n(u) = 0.
-3, 1, 2
Factor 0 + 2/15*c**4 + 2/3*c**3 + 2/5*c**2 - 6/5*c.
2*c*(c - 1)*(c + 3)**2/15
Let f be 2/3 + 10*2/15. Determine u, given that -5/3*u + 0*u**f + 5/3*u**3 + 0 = 0.
-1, 0, 1
Let q(s) be the first derivative of s**4/16 + s**3/4 - s + 2. Factor q(l).
(l - 1)*(l + 2)**2/4
Let u(f) = -f - 1. Let m(n) = n**2 - 18*n - 2. Let v(i) = 5*m(i) - 10*u(i). Let v(t) = 0. What is t?
0, 16
Solve -4 + 2801*r**5 + 5*r**4 + 2 + 2 - 2800*r**5 + 4*r**3 = 0.
-4, -1, 0
Factor -4*r**3 - 10*r**4 - 2 + 241*r**2 - 229*r**2 - 2*r + 2*r**5 + 4*r**5.
2*(r - 1)**3*(r + 1)*(3*r + 1)
Let b = -128/13 + 9229/936. Let r(s) be the third derivative of 0*s - 7*s**2 + b*s**4 + 1/9*s**3 - 1/180*s**5 + 0. Determine w, given that r(w) = 0.
-1, 2
Let z = -1466/5 - -5879/20. Let -3/4*i + 1/2*i**3 + 1/4*i**5 - 1/2*i**2 + z*i**4 - 1/4 = 0. Calculate i.
-1, 1
Let k(a) = a**2 - 4*a - 3. Let b be k(7). Let z = 21 - b. Find d, given that -2 - 2*d - d - z*d**2 + 2*d**2 = 0.
-2, -1
Let -5/7*v**3 + 0 - v + 13/7*v**2 - 1/7*v**4 = 0. What is v?
-7, 0, 1
Let h = 178/93 + -1876/775. Let x = 4/25 - h. What is i in 1/3*i**2 + 0 - x*i = 0?
0, 2
Let x(r) be the third derivative of -r**10/378000 - r**9/75600 - 17*r**5/60 - 18*r**2. Let q(y) be the third derivative of x(y). Factor q(o).
-2*o**3*(o + 2)/5
Let x(p) be the second derivative of -p**5/4 + 5*p**4/2 - 15*p**3/2 + 106*p. Factor x(q).
-5*q*(q - 3)**2
Suppose 112 + 4/7*z**2 + 16*z = 0. What is z?
-14
Let q = 1/5172 + 31025/36204. Factor -12/7*j**2 - 27/7*j - q.
-3*(j + 2)*(4*j + 1)/7
Let h(x) = 2*x - 13. Let k be h(11). Let q = 11 - k. Determine j so that -q - 5*j - j + 2*j**5 - 2*j**4 - 4*j**4 + 4*j**3 + 4*j**2 + 4 = 0.
-1, 1
Let o(r) be the second derivative of r**6/24 + r**5/3 + 5*r**4/8 - 23*r**2/2 - 3*r. Let l(i) be the first derivative of o(i). Determine s so that l(s) = 0.
-3, -1, 0
Let g = 2204/23 - 33014/345. Factor -4/15*d**2 + 2/15 - 4/15*d**3 + 2/15*d + 2/15*d**4 + g*d**5.
2*(d - 1)**2*(d + 1)**3/15
Let u(x) be the first derivative of x**6/3 - 76*x**5/15 + 32*x**4/9 + 68*x**3/9 - 73*x**2/9 + 8*x/3 + 345. Suppose u(r) = 0. What is r?
-1, 1/3, 1, 12
Let f(t) be the second derivative of 6859*t**5/12 - 1805*t**4/4 + 285*t**3/2 - 45*t**2/2 + t + 55. Factor f(k).
5*(19*k - 3)**3/3
Factor 48/5*m**3 + 0*m + 16*m**2 + 0 + 4/5*m**4.
4*m**2*(m + 2)*(m + 10)/5
Suppose -58/5*b**2 - 42/5*b**3 - 4/5 - 2*b**4 - 6*b = 0. Calculate b.
-2, -1, -1/5
Let o(b) be the first derivative of -5 - 1/3*b**3 + 1/4*b**4 - b**2 + 0*b. Determine p so that o(p) = 0.
-1, 0, 2
Let m = 624 - 6239/10. Factor 1/5*c**4 + 0 - 1/10*c**3 - m*c**5 + 0*c + 0*c**2.
-c**3*(c - 1)**2/10
Suppose s = -5 + 20. Suppose -p + s = -5*r, -2*r = 6 - 0. Factor 0*v + p + 1/2*v**2.
v**2/2
Find z, given that 0*z + 1/3*z**4 + 1/3*z**3 + 0 + 1/9*z**2 + 1/9*z**5 = 0.
-1, 0
Let d be (-250)/(-100)*(-12)/(-15). Factor 3*x**3 + 3/4*x**4 + 27/4 - 9*x - 3/2*x**d.
3*(x - 1)**2*(x + 3)**2/4
Let k(s) be the second derivative of s**6/30 + 19*s**5/100 + 7*s**4/20 + s**3/6 - s**2/5 + 127*s. Solve k(y) = 0 for y.
-2, -1, 1/5
Let x = 65 - 60. Let a(r) = -3*r**3 - 3*r**2 - 4*r. Let t(h) = 3*h**3 + 4*h**2 + 5*h. Let w(u) = x*t(u) + 6*a(u). Factor w(f).
-f*(f - 1)*(3*f + 1)
Let i(x) be the first derivative of 26 + 0*x**2 + 5/4*x**4 - 5/3*x**3 + 0*x. Factor i(w).
5*w**2*(w - 1)
Let v(a) be the third derivative of -a**5/15 - 3*a**4/2 - 40*a**3/3 + 8*a**2 + 12. Factor v(y).
-4*(y + 4)*(y + 5)
Let d(m) be the first derivative of 4*m**3/3 + 10*m**2 - 24*m + 455. Solve d(f) = 0 for f.
-6, 1
Solve -3969 + 25*f + 2434*f**2 + 101*f - 1219*f**2 - 1216*f**2 = 0 for f.
63
Let l = -1/5819 + 110567/34914. Find z, given that -3/2*z**3 + 1 - l*z + 7/2*z**2 + 1/6*z**4 = 0.
1, 6
Let f(y) = y**3 + y**2 - 2*y + 1. Let r(c) = c**4 + 6*c