65 - b**4/66 - b. Factor l(o).
2*o**2*(o - 1)*(o + 1)/11
Let c be (-5)/42 + (-5)/(-35). Let u(k) be the third derivative of 0 - 1/210*k**5 - c*k**4 - 1/21*k**3 + 0*k + k**2. Determine l, given that u(l) = 0.
-1
Let b = 52 - 252/5. Let f(x) be the first derivative of b*x + 2 + 4/5*x**2 + 2/15*x**3. What is w in f(w) = 0?
-2
Let z(i) be the third derivative of 3*i**5/80 - 5*i**4/32 + i**3/4 + 7*i**2. Factor z(x).
3*(x - 1)*(3*x - 2)/4
Factor k + 1/3*k**3 - k**2 - 1/3.
(k - 1)**3/3
Let 4/7*o**3 + 3/7*o**2 + 0*o + 0 + 1/7*o**4 = 0. Calculate o.
-3, -1, 0
Let h = -11 + 13. Suppose 0*t - 2*t = -6. Factor -5*x**2 + 50*x**t - 6*x + 25*x**h - 125*x**4 - 2*x.
-x*(5*x - 2)**2*(5*x + 2)
Factor -1/7*u + 4/7*u**2 + 0 - 1/7*u**5 - 6/7*u**3 + 4/7*u**4.
-u*(u - 1)**4/7
Let f be 1/(-4) - 2/(-8). Suppose l + f = 1. Find c such that 3*c**2 + l + 2 + c - 5 = 0.
-1, 2/3
Let l be (3 - 0 - 3)/2. Factor 3*a**3 - a**2 - a**4 + 4*a**4 + l*a**4 - 3*a - 2*a**2.
3*a*(a - 1)*(a + 1)**2
Suppose 8*p - 33 = -3*p. Let c(r) = r**3 - 6*r**2 + 5*r. Let x be c(5). Find s, given that x*s - 2/7*s**p - 2/7*s**2 + 0 = 0.
-1, 0
Let o = -5 + 7. Suppose -2*j + p - 2 = -3*j, j - 5 = o*p. Factor -n**j + n - 1/2 + 0*n**2 + 1/2*n**4.
(n - 1)**3*(n + 1)/2
Suppose 2*v - 4*b - 14 = 0, -4 = -v - b - 3. Let s(o) be the first derivative of -1 + 2/9*o**v + 0*o - 1/3*o**2. Factor s(n).
2*n*(n - 1)/3
Let l(c) be the third derivative of -c**5/180 + c**4/9 - 8*c**3/9 + 4*c**2. Factor l(j).
-(j - 4)**2/3
Let l be 15/(-18)*3/(-15). Let r(g) be the third derivative of 3*g**2 - l*g**3 - 5/24*g**4 - 7/60*g**5 + 0 + 0*g - 1/40*g**6. Factor r(n).
-(n + 1)**2*(3*n + 1)
Let h(k) = -198*k**2 + 208*k - 78. Let s(y) = 18*y**2 - 19*y + 7. Let l(f) = 6*h(f) + 68*s(f). Find j, given that l(j) = 0.
2/9, 1
Let h(z) be the first derivative of z**5/35 - 2*z**4/7 + 8*z**3/7 - 16*z**2/7 + 16*z/7 + 13. Let h(w) = 0. Calculate w.
2
Suppose 0 = 2*o + 4*n + 2, -2*n - 2 = -o + 5. Let i(w) be the first derivative of -1/6*w**2 + 1/9*w**o - 2 - 1/3*w + 1/12*w**4. Factor i(u).
(u - 1)*(u + 1)**2/3
Suppose 2*o = 3*o + 29. Let y = o - -32. Let 0*b + 6/5*b**y + 0 - 3/5*b**4 - 3/5*b**2 = 0. What is b?
0, 1
Suppose 2/11*w**5 + 54/11*w - 20/11*w**4 + 72/11*w**3 - 108/11*w**2 + 0 = 0. Calculate w.
0, 1, 3
Let v(l) = l**2 - 10*l - 9. Let g be v(11). Suppose 17 = 5*r + g. Factor -2/5*c**2 + 0*c + 2/5*c**4 + 0*c**r + 0.
2*c**2*(c - 1)*(c + 1)/5
Let v(t) be the second derivative of -t**7/2100 - t**6/900 + t**3/6 + 2*t. Let n(d) be the second derivative of v(d). Factor n(p).
-2*p**2*(p + 1)/5
Determine o so that -3*o**2 - 108 + 6*o - 6*o - 36*o = 0.
-6
Let w(y) = -4*y**4 + 6*y**3 + 6. Let m(q) = -11*q**4 + 17*q**3 + 17. Let o = -4 + 0. Let b be 25/o - 5/(-20). Let a(s) = b*m(s) + 17*w(s). Factor a(i).
-2*i**4
Find z such that 36 + 2*z**2 - 3*z**2 + 24*z + 5*z**2 = 0.
-3
Find m such that -2/5*m**2 + 2/5*m + 0 = 0.
0, 1
Let c be 12 + -9 + 1078/(-360). Let m(t) be the third derivative of 0 + 0*t + c*t**5 + t**2 + 1/9*t**3 + 1/24*t**4. Factor m(i).
(i + 1)*(i + 2)/3
Let g(q) = -q**2 + 7*q - 7. Let k be g(5). Determine x so that 0*x - 2/7*x**k + 0*x**2 + 2/7*x**4 + 0 = 0.
0, 1
Let o = -1/24 + 3/8. Suppose o*c**4 + 1/6*c**3 - 1/6*c**5 + 0 + 0*c - 1/3*c**2 = 0. What is c?
-1, 0, 1, 2
Let h(q) be the first derivative of -1 + 1/6*q**2 - 1/36*q**4 - q + 0*q**3. Let t(v) be the first derivative of h(v). Determine m, given that t(m) = 0.
-1, 1
Let l = 44 - 44. Let t(i) be the third derivative of 1/120*i**6 + 0*i**3 + 0*i + i**2 + l*i**5 + 0 - 1/24*i**4. Factor t(z).
z*(z - 1)*(z + 1)
Let g(t) be the second derivative of t**6/300 + t**5/150 - t**4/60 - t**3/15 - t**2 + t. Let b(p) be the first derivative of g(p). Factor b(l).
2*(l - 1)*(l + 1)**2/5
Let w(p) be the second derivative of -9*p**6/10 - 3*p**5/2 - p**4/4 - 40*p + 2. Factor w(j).
-3*j**2*(j + 1)*(9*j + 1)
Let d(h) = -h**3 - 4*h**2 - 2*h + 1. Let k(z) = -z**3 - 1. Let o(c) = -d(c) - k(c). Determine j so that o(j) = 0.
-1, 0
Let m be 93/12 - (-3)/12. Let 15 + 2*h - m*h**2 + 6*h**3 - 15 = 0. Calculate h.
0, 1/3, 1
Factor -4*z - z**3 + z**2 + 4*z - 1 - 2*z + 3*z.
-(z - 1)**2*(z + 1)
Suppose 0 = 3*r - 4*r + 8. Let b(h) = h - 5. Let l be b(r). Factor 2*q**2 - 4*q - 2 + q - 2*q**l + 5*q.
-2*(q - 1)**2*(q + 1)
Let v(f) = f - 1. Let o(w) = -3*w**3 - 3*w**2 + 6. Let n(u) = -o(u) - 3*v(u). Factor n(m).
3*(m - 1)*(m + 1)**2
Let v(k) = -k**3 - 2*k**2 + 16*k + 7. Let t be v(-5). Factor 20/9*u**3 + 2/9 + 10/9*u**4 + 2/9*u**5 + 20/9*u**t + 10/9*u.
2*(u + 1)**5/9
Let c = 33/1420 - -9/71. Let n(v) be the first derivative of 1 + 0*v - 1/4*v**3 + 0*v**2 + c*v**5 + 0*v**4. Factor n(m).
3*m**2*(m - 1)*(m + 1)/4
Suppose 50*o = -11*o. Factor o*z + 1/8 - 1/8*z**2.
-(z - 1)*(z + 1)/8
Let p(i) be the third derivative of i**6/200 - i**5/20 + i**4/5 - 2*i**3/5 + 11*i**2. Factor p(w).
3*(w - 2)**2*(w - 1)/5
Factor -8*y**3 + 8*y**3 + 2*y**4 + 5*y**2 - 7*y**2.
2*y**2*(y - 1)*(y + 1)
Let k(u) be the second derivative of -u**8/1512 + u**6/270 - u**4/108 - 3*u**2/2 + u. Let j(a) be the first derivative of k(a). Solve j(o) = 0 for o.
-1, 0, 1
Let s be -3 + (-2404)/(-1200) + 1. Let x(q) be the third derivative of -1/120*q**4 + 2*q**2 + 0 + 0*q + 1/30*q**3 - s*q**5 + 1/600*q**6. Solve x(a) = 0 for a.
-1, 1
Factor 0 + 0*u + u**2 - 1/2*u**3.
-u**2*(u - 2)/2
Let y be (-3)/(-4)*(-1)/((-30)/16). Let -6/5*v**3 - y*v**4 + 0*v + 0 - 4/5*v**2 = 0. What is v?
-2, -1, 0
Let o(x) be the third derivative of -x**4/24 + x**3/6 - 7*x**2. Let u be o(-2). Suppose 2/3*v**4 + 4*v**2 + 2/3 - 8/3*v**u - 8/3*v = 0. What is v?
1
Let p be (-5 + 7)/(2/1002). Let a = p - 4992/5. Factor a*j**3 + 22/5*j**2 + 0 + 4/5*j.
2*j*(j + 1)*(9*j + 2)/5
Let j(y) be the first derivative of y**5/10 + 2*y**4/9 + y**3/9 - 2*y + 3. Let p(k) be the first derivative of j(k). Factor p(m).
2*m*(m + 1)*(3*m + 1)/3
Let a(m) = -10*m**2 + 35*m - 20. Let l(q) = -q**2 + q + 1. Let g(i) = a(i) - 5*l(i). What is r in g(r) = 0?
1, 5
Let u = -14 - -16. Let d(j) = -j**3 + j**2 - j - 2. Let l be d(-2). Factor 0*b**4 + 8*b**2 + 8*b**4 + b**5 + l*b**3 + u*b - b**5 + 2*b**5.
2*b*(b + 1)**4
Let u = -9 + 12. Let j be u*(-2)/(-12)*16. Factor j*n + 4*n**2 + 2/3*n**3 + 16/3.
2*(n + 2)**3/3
Let o be (5 - 1) + 56/(-15). Let j(h) be the first derivative of -2/9*h**3 + 1/6*h**6 - 1/12*h**4 + 0*h - 1 + o*h**5 + 0*h**2. Suppose j(n) = 0. What is n?
-1, 0, 2/3
Let f be 3 - (4 - 3) - 0. Let l(v) be the first derivative of -3/2*v**6 + 20/3*v**3 - f*v**2 - 37/4*v**4 + 0*v - 1 + 6*v**5. Determine a so that l(a) = 0.
0, 2/3, 1
Let r be -1*2 - 60/(-6). Let z = r - 6. Factor 4/3 + 25/3*f**z - 20/3*f.
(5*f - 2)**2/3
Suppose h - 29 = -6*p + p, -3*p - 5*h = -35. Suppose -4*w - 24 = -4*b, -14 = -0*b - p*b + w. Factor 0 + 3/4*a**3 + 0*a + 3/4*a**b.
3*a**2*(a + 1)/4
Suppose -g - o = 2, -3*g - 4 = -g - 2*o. Let x be (g + 1)*1/(-6). Suppose 0 + 0*b + 1/6*b**3 - x*b**2 = 0. What is b?
0, 1
Determine l so that -6/7*l + 0*l**3 - 4/21 - 22/21*l**2 + 8/21*l**4 = 0.
-1, -1/2, 2
Let c(s) be the second derivative of -2*s - 1/12*s**3 + 1/40*s**5 + 0 + 1/24*s**4 - 1/4*s**2. Solve c(l) = 0.
-1, 1
Let t be (-6 - -7) + 2/(-1) + 5. Determine y so that 0*y**3 - 2/3*y**5 + 2/3*y + 4/3*y**2 - 4/3*y**t + 0 = 0.
-1, 0, 1
Suppose -3*t - 141 + 141 = 0. Determine r so that t - 4/3*r**2 - 1/3*r = 0.
-1/4, 0
Let 3 - 3 - 4*k**4 - 8*k**3 = 0. What is k?
-2, 0
Factor -8/11*x**2 + 0*x + 0 + 2/11*x**3.
2*x**2*(x - 4)/11
Let o(q) be the second derivative of -q**6/25 + q**5/25 + q**4/30 - 7*q. Let o(m) = 0. What is m?
-1/3, 0, 1
Factor 12/7*f**2 + 3/7 - 6/7*f**3 - 10/7*f + 1/7*f**4.
(f - 3)*(f - 1)**3/7
Let s = -57/2 - -29. Let q(z) be the first derivative of -1/5*z**5 - z + 1/6*z**6 + 2 - 1/2*z**4 + s*z**2 + 2/3*z**3. Factor q(n).
(n - 1)**3*(n + 1)**2
Let t = 2 + 1. Let h be 34/t + (-2)/(-3). Find o, given that 9*o**2 - 2*o - h*o**3 + 4*o**2 + 5*o**4 - 4*o**2 = 0.
0, 2/5, 1
Let q = 5 - 8. Let h be 1/(q/4)*-3. Factor -j**3 - 2*j**2 - j**4 + j**4 - 3*j**3 - 2*j**h.
-2*j**2*(j + 1)**2
Let c be 4*(-2 + 5/2). Suppose 10 = 4*q - 2. Factor -h**c - 2*h**3 + 2*h**3 - h**q.
-h**2*(h + 1)
Let b(n) = -3*n**2 + 3*n + 3. Let l(h) = -h**3 + h**2 - h - 1. Let z(y) = -b(y) - 3*l(y). Factor z(p).
3*p**3
Let l be (-36)/(-4) - (-12)/(-3). Let y = l - 5. Factor -2/9*n