.
1
Let w(j) = 43*j**3 + 8*j**2 - 13*j + 5. Let p(n) = -21*n**3 - 4*n**2 + 7*n - 3. Let a(y) = -5*p(y) - 3*w(y). Factor a(c).
-4*c*(2*c + 1)*(3*c - 1)
Suppose -10/13*c**4 - 2/13 + 12/13*c**2 + 4/13*c**3 - 6/13*c**5 + 2/13*c = 0. Calculate c.
-1, 1/3, 1
Let q(n) = 7*n**3. Let b(g) = -3*g**3. Let p(r) = 15*b(r) + 6*q(r). Suppose p(u) = 0. What is u?
0
Let o(t) be the first derivative of -2*t**3/21 - 5*t**2/7 + 12*t/7 + 11. Factor o(w).
-2*(w - 1)*(w + 6)/7
Suppose 4*y + 3*p = 17, -3*y - 3*p + 6 = -6. Factor 0 - 6/13*b**3 + 2/13*b**2 + 0*b - 2/13*b**y + 6/13*b**4.
-2*b**2*(b - 1)**3/13
Suppose -100 - 44 = -12*c. Factor -17/2*j**3 + 1 - 13/2*j + 2*j**4 + c*j**2.
(j - 2)*(j - 1)**2*(4*j - 1)/2
Let o(f) = -f**4 + f**3 - f**2 + f + 1. Let m(u) = -28*u**4 + 20*u**3 + 100*u**2 + 108*u + 32. Let q(s) = -m(s) + 8*o(s). Let q(r) = 0. What is r?
-1, -2/5, 3
Let n(r) be the second derivative of r**4/4 - 3*r**3/2 + 29*r. What is f in n(f) = 0?
0, 3
Let a(u) be the first derivative of 2*u**6/15 - 2*u**5/5 + 4*u**3/3 - 2*u**2 + 6*u/5 + 25. Determine d so that a(d) = 0.
-3/2, 1
Let r be 2/(-8) + (-41)/(-4). Solve -16 + r*s + 21*s**2 - 34*s + 28*s**3 + 84*s**4 + 36*s**5 - 89*s**2 - 40*s = 0 for s.
-1, -2/3, 1
Let l(v) be the third derivative of v**6/4 + 5*v**5/12 - 5*v**4/3 - 5*v**3/2 + 29*v**2. Factor l(o).
5*(o - 1)*(2*o + 3)*(3*o + 1)
Factor 1/3*g**3 + 1/3*g**2 - 2/3*g + 0.
g*(g - 1)*(g + 2)/3
Let f(u) = -6*u**3 - 6*u**2 - 3. Let s(h) = 2*h**3 - h**3 - 6*h**3 - 16*h**2 + 11*h**2 - 2. Let r(t) = 2*f(t) - 3*s(t). Let r(x) = 0. What is x?
-1, 0
Let 0 - 8/9*d + 2/9*d**2 = 0. Calculate d.
0, 4
Let s(y) be the third derivative of -1/2*y**3 + 1/20*y**5 + 2*y**2 + 1/8*y**4 - 1/40*y**6 + 0*y + 0. Factor s(u).
-3*(u - 1)**2*(u + 1)
Suppose d + 5*l - 4 = 0, -3*d = 5*l - 2 - 0. Let z be (9 - d)*(-5)/(-10). Let 0*u + 0 + 3/4*u**3 + 0*u**2 - 3/2*u**z + 3/4*u**4 = 0. What is u?
-1/2, 0, 1
Let c(q) = -q**3 - 5*q**2 - 4*q + 4. Let r be c(-4). Let f be (-1)/(-4) + 7/4. Suppose -2*z**3 + 3*z**3 + f*z**2 - 2*z**r - 2*z + z**3 = 0. Calculate z.
-1, 0, 1
Let g be 2 + ((-66)/(-36))/11*-8. Suppose 0 + 0*q + g*q**2 - 2/3*q**4 + 0*q**3 = 0. Calculate q.
-1, 0, 1
Factor 12*z**2 - 26*z**3 + 2*z + 6*z**3 + 6*z.
-4*z*(z - 1)*(5*z + 2)
Factor 10/13*c**2 - 4/13*c - 2/13*c**4 + 0 - 6/13*c**3 + 2/13*c**5.
2*c*(c - 1)**3*(c + 2)/13
Suppose 3*y + 0*y - 4*z = -4, 3*z = -2*y + 3. Suppose y = 4*u - 28 - 20. Determine v, given that u - 11*v - 2*v + v + 3*v**2 = 0.
2
Let b = -167/2 - -84. Let t(d) be the first derivative of 4/3*d**3 + 4 + 0*d - d**2 - b*d**4. Determine v, given that t(v) = 0.
0, 1
Let d be 1 - 2*(-2)/2. Factor 3*y**d - 3*y**3 + 2*y - 2*y**3.
-2*y*(y - 1)*(y + 1)
Factor 0 - 2/7*n**2 - 2/7*n.
-2*n*(n + 1)/7
Let l(p) be the first derivative of -1 + 1/20*p**5 - 1/6*p**3 + 1/60*p**6 - 2*p + 0*p**4 - 1/4*p**2. Let y(a) be the first derivative of l(a). Factor y(q).
(q - 1)*(q + 1)**3/2
Let u be (-32)/18 - (-8)/(-36). Let g be (-868)/(-16) + u/8. Factor 54*y**2 - 2*y**3 + y - g*y**2 + y**5.
y*(y - 1)**2*(y + 1)**2
Suppose -5 = -m - 31. Let u = m + 80/3. Factor -2/3 - 4/3*j - u*j**2.
-2*(j + 1)**2/3
Let j be (-161)/735 - (-6)/21. Let q = 3/5 + j. What is t in 1/3*t**3 - 1/3*t**4 + t**2 - q - 1/3*t = 0?
-1, 1, 2
Let d be 12*(2 - (-9)/(-6)). Suppose 0 = -5*o + 21 - d. Determine z so that -2/7 - 6/7*z**2 + 6/7*z + 2/7*z**o = 0.
1
Let i(l) be the third derivative of -l**7/1470 - l**6/420 - l**5/420 + l**2. Suppose i(d) = 0. Calculate d.
-1, 0
Suppose 11*d - 68 = 7*d. Let p = d + -14. Factor -8/9*o**2 - 2/9*o**5 - 8/9*o**4 + 0 - 4/3*o**p - 2/9*o.
-2*o*(o + 1)**4/9
Let v be 5/(-30) - (-67)/6. What is h in -10*h**3 - h + 0*h + v*h**3 = 0?
-1, 0, 1
Let x(u) be the first derivative of 0*u**2 - 1 + 2/15*u**5 + 0*u - 4/27*u**3 - 1/18*u**4. Factor x(k).
2*k**2*(k - 1)*(3*k + 2)/9
Suppose -s = 3*s - 8. Suppose -1 = i + a, s*a + 3 + 3 = 0. Factor 4*t**2 - 3*t**i + t**3 - 2*t**3 - 2*t**2.
-t**2*(t + 1)
Let r = 10 + -5. Factor s + 5*s**3 - s**3 - r*s**3.
-s*(s - 1)*(s + 1)
Solve 67*i**3 + 80*i - 240*i - 2 + 31*i**3 - 238*i**2 - 22 = 0 for i.
-2/7, 3
Factor -9*b**4 + 3*b - 4*b + b - 6*b**3.
-3*b**3*(3*b + 2)
Let y = 33/140 + 1/20. Suppose 2/7 + y*b**2 - 4/7*b = 0. What is b?
1
Let s(n) = 4*n. Let g be s(3). Factor 15*o**4 + g*o**3 - 7*o**4 + 8*o**2 + o + o + 2*o**5.
2*o*(o + 1)**4
Let z(a) be the first derivative of 2*a**3 - 33*a**2/2 - 18*a + 8. Factor z(f).
3*(f - 6)*(2*f + 1)
Let n(u) be the second derivative of -u**5/90 + u**3/27 + u. Factor n(f).
-2*f*(f - 1)*(f + 1)/9
Let m(v) = -v**2 - 5*v - 2. Let i be m(-4). Let -f - 3*f**2 - 2*f**i + 0*f**2 + 3*f**2 - f**3 = 0. What is f?
-1, 0
Suppose 7*d - 53 = -11. Suppose -17 + d*v**2 - 2*v + 17 = 0. What is v?
0, 1/3
Let u be (5 - 4) + 4/2. Find s, given that -6/7*s**2 - 2/7*s**u - 4/7*s + 0 = 0.
-2, -1, 0
Let y be (-114)/24 + 4 - (-4 - -2). Find w such that 7/4*w**2 + 1/4 - y*w - 3/4*w**3 = 0.
1/3, 1
Let i(l) be the first derivative of 7*l**5/30 - 3*l**4/8 - 5*l**3/18 + 3*l**2/4 - l/3 + 9. Determine f, given that i(f) = 0.
-1, 2/7, 1
Determine w, given that 0*w**2 + 0*w + 0 - 2*w**4 + 0*w**3 - 2/5*w**5 = 0.
-5, 0
Let u = 11 - 8. Find y, given that -y**3 - 4*y**3 + 2 - 2*y**5 + 4*y**2 + 2*y + 4*y + y**u - 6*y**4 = 0.
-1, 1
Let x(u) = u**2 - 2*u - 3. Let t be (-16)/(-7) - 4/14. Let c(r) = r**2 - 4*r + 4. Let s be c(3). Let p(o) = -o**2 + 1. Let f(g) = s*x(g) + t*p(g). Factor f(b).
-(b + 1)**2
Let 6/7*c**5 - 6/7*c**3 - 2/7*c**4 + 2/7*c**2 + 0*c + 0 = 0. Calculate c.
-1, 0, 1/3, 1
Suppose 4*y - 25 = -1. Suppose -y*o = -7*o. Solve -1/2 + 3/4*h + o*h**2 - 1/4*h**3 = 0 for h.
-2, 1
Suppose 0 = -2*c + 3*w + 10, 0 = 5*c - 4*w + 2*w - 36. Find b such that -b**2 - 4*b**3 - 11*b**2 + c*b**3 + 8*b = 0.
0, 1, 2
Determine n, given that 4*n - 3*n**2 - 4*n**3 + 7*n**2 + 0*n**3 - 4*n**4 = 0.
-1, 0, 1
Let a(w) = -9*w + 51. Let g be a(5). Let x(y) be the second derivative of 0 - 2*y + 0*y**2 + 1/12*y**4 + 1/6*y**3 - 1/20*y**5 - 1/30*y**g. Factor x(h).
-h*(h - 1)*(h + 1)**2
Let v = -415/3 - -139. Factor v*y**2 - 2/3 + 0*y.
2*(y - 1)*(y + 1)/3
Let a(r) be the third derivative of 0 + 3/70*r**7 - 1/2*r**3 - 2*r**2 - 1/112*r**8 + 3/8*r**4 + 0*r - 1/10*r**5 - 1/20*r**6. Solve a(l) = 0.
-1, 1
Let v = -3 + 5. Factor m + v*m**2 + 2*m - 3*m - 2*m.
2*m*(m - 1)
Let t(a) be the first derivative of -a**4 + 60*a**3 - 1350*a**2 + 13500*a + 2. Determine p, given that t(p) = 0.
15
Let b(s) be the third derivative of s**6/80 + s**5/60 - s**4/48 + 13*s**2. Factor b(k).
k*(k + 1)*(3*k - 1)/2
Suppose 6*p = 9*p - 5*s + 20, 20 = p + 5*s. Let d(r) be the third derivative of 0*r**3 + 0 + r**2 + 1/12*r**4 + 1/24*r**6 + 7/60*r**5 + p*r. Factor d(g).
g*(g + 1)*(5*g + 2)
Let f(g) be the first derivative of g**4/2 - 2*g**3 - g**2 + 6*g - 22. Factor f(j).
2*(j - 3)*(j - 1)*(j + 1)
Determine n so that n - 10*n**2 - 3*n - 20*n**3 + 32*n**3 = 0.
-1/6, 0, 1
Suppose 8/7 - 2/7*f**2 + 6/7*f = 0. What is f?
-1, 4
Let v be 3 + -2*3/(-6). Let w = 8 - v. Determine o so that 4 - w - 2*o**3 = 0.
0
Let r(s) be the second derivative of 0*s**3 - 8/45*s**6 + 0 + 4*s + 0*s**2 - 2/15*s**5 + 0*s**4 + 5/63*s**7. Factor r(l).
2*l**3*(l - 2)*(5*l + 2)/3
Let a(z) be the second derivative of 3/10*z**6 + 3*z + 0*z**2 + 3/4*z**5 - 1/2*z**3 + 0 - 2/7*z**7 - 3/4*z**4. Suppose a(k) = 0. Calculate k.
-1, -1/4, 0, 1
Find c, given that 6/13*c**4 + 0*c + 2/13*c**5 - 2/13*c**3 + 0 - 6/13*c**2 = 0.
-3, -1, 0, 1
Determine u, given that -2*u**2 - 1 - 3 + 6 = 0.
-1, 1
Let p(d) be the second derivative of -d**4/6 - 7*d**3/27 + 2*d**2/9 + 8*d. Let p(w) = 0. Calculate w.
-1, 2/9
Let y(j) be the third derivative of -1/8*j**4 + 0*j**5 + 1/120*j**6 - 1/3*j**3 + 0*j + 3*j**2 + 0. Solve y(q) = 0 for q.
-1, 2
Let o be 0*(-3 + 2) - -2. Let p be 11/12 + (-6)/9. Factor 1/4*g**o - p*g + 0.
g*(g - 1)/4
Factor -3/5*i**5 + 3/5 - 6/5*i**3 + 6/5*i**2 - 9/5*i**4 + 9/5*i.
-3*(i - 1)*(i + 1)**4/5
Suppose 33 = i - 3. Let k be 10/36 + 8/i. Factor 1/2 + 1/2*l**3 - k*l - 1/2*l**2.
(l - 1)**2*(l + 1)/2
Let l(h) = 7*h**4 - h**3 - 4*h**2 + 7*h. Let j(c) = -34*c**4 + 6*c**3 + 20*c**2 - 34*c. Let k(g) = -3*j(g) - 14*l(g). Factor k(o).
4*o*(o - 1)**2*(o + 1)
Let f(y) = y**2 + y - 3. Let s be f(-2). Let d(n) = n**3 - n**2 - 3*n - 1. Let a be d(s). What is r in 1/4*r - 1/4*r*