- s**3. Let x(f) = f**5 - f**3 + f + 1. Let z(k) = -i(k) - 6*x(k). Factor z(a).
2*a**2*(a - 1)*(a + 1)**2
Let g(j) be the third derivative of 0*j**4 + 0 + 0*j**5 - 2*j**2 + 1/420*j**6 + 0*j + 0*j**3 - 2/735*j**7 + 1/1176*j**8. Determine w, given that g(w) = 0.
0, 1
Let z(g) be the second derivative of g**7/2520 - g**6/1080 - g**5/360 + g**4/72 + 2*g**3/3 + 2*g. Let d(b) be the second derivative of z(b). Factor d(u).
(u - 1)**2*(u + 1)/3
Suppose 0 = -4*j + 12*j. Factor -10/7*k**3 - 2/7*k**2 + j*k + 0.
-2*k**2*(5*k + 1)/7
Factor z**3 + 0 + 1/4*z**2 - 1/2*z - 3/4*z**4.
-z*(z - 1)**2*(3*z + 2)/4
Let a(k) be the first derivative of -3*k**5/5 - 3*k**4/4 + 3*k**3 + 3*k**2/2 - 6*k - 22. Factor a(l).
-3*(l - 1)**2*(l + 1)*(l + 2)
Suppose -81 = -13*c - 14*c. Let 1 + 1/2*l**2 - 5/2*l**c - 3/2*l**4 + 5/2*l = 0. Calculate l.
-1, -2/3, 1
Suppose -5*c + 35 = -0*c + 5*b, -c - 4*b = -16. Let r(x) be the third derivative of 0*x**3 + 1/60*x**5 + 0*x + 0 - x**2 - 1/24*x**c. What is w in r(w) = 0?
0, 1
Let a(h) be the third derivative of h**5/90 - 11*h**4/18 + 121*h**3/9 + 4*h**2 - 2*h. Determine c, given that a(c) = 0.
11
Let p(g) be the first derivative of g**5/5 + g**4/2 - g**3 - 30. Determine r so that p(r) = 0.
-3, 0, 1
Factor w**4 - 190 - 4*w**5 + 8*w + 6*w**3 + 187 + 3*w**5 + 3*w - 14*w**2.
-(w - 1)**4*(w + 3)
Factor 48/7 + 27/7*j**3 + 3/7*j**4 + 12*j**2 + 108/7*j.
3*(j + 1)*(j + 2)**2*(j + 4)/7
Let o(j) = -j**2 - 6*j - 3. Let g be o(-4). Let k = g + -3. Factor 3*u + 2*u**2 - 3*u - k*u.
2*u*(u - 1)
Let g(r) be the second derivative of r**5/70 + 2*r**4/21 + 5*r**3/21 + 2*r**2/7 + 6*r. Suppose g(c) = 0. What is c?
-2, -1
Let g(z) be the second derivative of -2*z**5/15 + z**4/6 + z**3 + 2*z**2/3 - 17*z. Factor g(h).
-2*(h - 2)*(h + 1)*(4*h + 1)/3
Let d(i) be the first derivative of i**4/36 - i**2/6 + 2*i - 2. Let q(s) be the first derivative of d(s). Determine f so that q(f) = 0.
-1, 1
Let g be 0 - (2 + 7 + -3). Let d be (-35)/(-15) + 2/g. Factor -8/7 - 8/7*l - 2/7*l**d.
-2*(l + 2)**2/7
Determine o so that 4/3 - 2/15*o**3 + 4/15*o**2 + 26/15*o = 0.
-2, -1, 5
Let j(u) = 40*u**5 + 57*u**4 + 3*u**3 + 7*u**2. Let k(n) = -20*n**5 - 28*n**4 - 2*n**3 - 3*n**2. Let l(p) = -3*j(p) - 7*k(p). Factor l(i).
5*i**3*(i + 1)*(4*i + 1)
Let v = -5/8 - -23/24. Let f(s) be the first derivative of -2 + 1/6*s**4 - v*s**2 - 2/3*s**3 + 4/15*s**5 + 2/3*s. Solve f(y) = 0.
-1, 1/2, 1
Let z(w) be the second derivative of w**7/35 + 8*w**6/75 - w**4/3 - w**3/5 + 2*w**2/5 - 11*w. Suppose z(a) = 0. What is a?
-2, -1, 1/3, 1
Suppose 0 = -2*g + 4*g - 4. Let t(a) be the third derivative of 0*a**4 - 1/420*a**6 - 2*a**g + 0 + 0*a + 0*a**3 + 0*a**5. Suppose t(m) = 0. Calculate m.
0
Let r be 4/2 + 1248/(-720). Factor -r - 2/15*m + 2/15*m**2.
2*(m - 2)*(m + 1)/15
Let v(f) be the second derivative of -f**8/3360 + f**7/560 - f**6/240 + f**5/240 - f**3/3 + 2*f. Let p(y) be the second derivative of v(y). Factor p(b).
-b*(b - 1)**3/2
Let q be 36/189*3/(-6)*-12. Factor -80/7*s**2 + 234/7*s**3 + q*s - 162/7*s**4 + 0.
-2*s*(s - 1)*(9*s - 2)**2/7
Let j(s) be the third derivative of s**5/40 - 7*s**4/16 + 5*s**3/2 - 22*s**2. Factor j(t).
3*(t - 5)*(t - 2)/2
Suppose 2*w - 4 = -0*w. Suppose -3*d - 3*d + 0*d - 3*d**w - 3 = 0. What is d?
-1
Let f(w) be the third derivative of w**7/280 - 7*w**6/160 + 3*w**5/16 - 9*w**4/32 - 5*w**2. Suppose f(a) = 0. What is a?
0, 1, 3
Let s be ((-18)/4)/((-15)/8*2). Let k(z) be the first derivative of -2/3*z**6 + 0*z**2 - 2/3*z**3 + 0*z + 0*z**4 + 2 + s*z**5. Factor k(b).
-2*b**2*(b - 1)**2*(2*b + 1)
Let a(z) be the third derivative of z**7/420 + z**6/120 + z**5/120 - 11*z**2. Let a(h) = 0. Calculate h.
-1, 0
Let h(x) be the first derivative of 0*x**2 + 1/2*x**4 - 2/3*x**3 + 2/5*x**5 - 1/3*x**6 - 3 + 0*x. What is r in h(r) = 0?
-1, 0, 1
Suppose s = 2*p + 3*s + 6, p = 3*s + 17. Factor 0 + 4/3*o**p + 2/3*o**3 + 2/3*o.
2*o*(o + 1)**2/3
Let v(n) be the second derivative of -1/6*n**3 - 1/120*n**6 + 0*n**2 - 3*n + 0 - 3/20*n**5 - 9/8*n**4. Let j(q) be the second derivative of v(q). Factor j(i).
-3*(i + 3)**2
Suppose -m + m**3 + 0*m**3 - 3*m - 4*m**2 + 8*m**4 - 7*m**4 = 0. Calculate m.
-2, -1, 0, 2
Let m(l) be the first derivative of -l**6/540 - l**5/135 - l**4/108 + l**2 - 2. Let a(i) be the second derivative of m(i). Factor a(h).
-2*h*(h + 1)**2/9
Let w(g) be the second derivative of g**7/420 - g**6/180 - g**3/3 - g. Let v(b) be the second derivative of w(b). Let v(j) = 0. What is j?
0, 1
Suppose u + 3*l = 6, 3*u + 5*l - 8 = 6. Factor -3 + 13*a**u + 3*a**5 + 15*a + 21*a**3 - 30*a**2 + 3*a**3 - 15*a**4 - 7*a**3.
3*(a - 1)**5
Let d(k) be the third derivative of 4*k**2 - 1/30*k**5 - 1/525*k**7 + 1/30*k**4 + 1/75*k**6 + 0*k + 0*k**3 + 0. Determine f, given that d(f) = 0.
0, 1, 2
Let o(h) be the second derivative of h**5/5 + 3*h**4/10 - h**3/5 - 2*h**2/5 + 10*h. Solve o(y) = 0.
-1, -2/5, 1/2
Let n = 26/115 - -4/23. Factor -n*o**3 + 0 + 0*o - 2/5*o**2.
-2*o**2*(o + 1)/5
Let p(s) be the second derivative of 2*s**6/5 - 2*s**5/15 - 12*s**4 + 112*s**3/3 - 64*s**2/3 - 61*s. Determine j, given that p(j) = 0.
-4, 2/9, 2
Let q(v) be the first derivative of -2*v**5/25 + 4*v**4/5 + 38*v**3/15 + 2*v**2 + 2. Factor q(x).
-2*x*(x - 10)*(x + 1)**2/5
Find n, given that 2*n**3 + 21*n**2 - 11*n**3 + 0 + 8*n - 23*n + 3 = 0.
1/3, 1
Suppose -3*p = -4*x + 1 - 2, -3*p = 3*x - 15. Solve 2/7 - 4/7*m**x + 0*m**3 + 0*m + 2/7*m**4 = 0 for m.
-1, 1
Let n(s) = 6*s**5 - 2*s**4 - 3*s**3 - 2*s**2 - 3*s + 4. Let u(c) = c**5 - c**4 - c**3 + 1. Let p(f) = -4*n(f) + 20*u(f). Solve p(w) = 0 for w.
-1, 1
Suppose -7 - 1 = -4*b. Let i = 8 - b. Factor i*g**5 - 3*g**5 + 0*g**4 - g**4.
g**4*(3*g - 1)
Let r be 30/100*(-32)/(-6). Factor 4/5*i**4 - 2*i**3 + r*i**2 + 0 - 2/5*i.
2*i*(i - 1)**2*(2*i - 1)/5
Factor 9*j**4 - 2*j**2 - 24*j**3 - 2*j**2 - j + 21*j**3 - j**2.
j*(j - 1)*(3*j + 1)**2
Let m = 37 - 35. Let f(o) be the second derivative of 2/15*o**5 - 2*o - 1/6*o**4 + 0 - 2/9*o**3 + 4/45*o**6 + 1/3*o**m. Factor f(l).
2*(l + 1)**2*(2*l - 1)**2/3
Let r(t) be the second derivative of 3*t**5/140 - 3*t**4/28 + t**3/7 + 5*t. Suppose r(x) = 0. What is x?
0, 1, 2
Let d(m) be the second derivative of m**7/21 - m**6/15 - m**5/10 + m**4/6 - 7*m. Let d(z) = 0. What is z?
-1, 0, 1
Suppose 0 + 4/5*j - 6/5*j**3 - 2/5*j**2 + 2/5*j**4 + 2/5*j**5 = 0. Calculate j.
-2, -1, 0, 1
Let y = 12 - 10. Factor 2*m + 2*m - 1 - 4*m - 3*m**y - 4*m.
-(m + 1)*(3*m + 1)
Suppose -2 = 2*q + 10. Let o be (q - -9)/((-3)/(-4)). Factor -7/3*s**2 - 5/3*s**o + 0 + 1/3*s**5 + 3*s**3 + 2/3*s.
s*(s - 2)*(s - 1)**3/3
Let s(r) = r**2 + r + 1. Let c(w) = -2*w**2 - 6*w - 10. Let v = -7 + 13. Let u(d) = v*s(d) + c(d). Let u(k) = 0. Calculate k.
-1, 1
Let a be (6 - 34/6)*0. Factor a - 4/13*g - 2/13*g**2 + 2/13*g**3.
2*g*(g - 2)*(g + 1)/13
Suppose 0*c - 19 = -3*o - 5*c, o - 8 = -2*c. Let f be o/4*(7 + -7). Suppose -1/3 + 1/3*k**2 + f*k = 0. Calculate k.
-1, 1
Factor -3/4*p - 3/2 + 3/4*p**2.
3*(p - 2)*(p + 1)/4
Let w(b) be the second derivative of -3*b**5/20 - b**4/6 + b**3/3 + b**2 + b. Let f be w(-2). Factor -6 + 4*p + 6 - f*p**2.
-2*p*(7*p - 2)
Let v = -12020/4632987 - -2/17223. Let r = 896/269 - v. Suppose 2/3 - 16/3*y**4 - 2/3*y**3 - 8/3*y**5 + r*y + 14/3*y**2 = 0. What is y?
-1, -1/2, 1
Let o(c) be the second derivative of 0 + 1/7*c**3 + 0*c**2 + 1/42*c**4 + 4*c. Factor o(y).
2*y*(y + 3)/7
Let r(b) be the third derivative of b**5/15 - 14*b**2. Factor r(v).
4*v**2
Let s(o) be the second derivative of 1/9*o**3 + 1/54*o**4 + 0 + 2/9*o**2 + 3*o. Factor s(c).
2*(c + 1)*(c + 2)/9
Let q(p) = 3*p - 20. Let y be q(8). Let d(r) = 2*r - 8. Let f be d(y). Let f*b**2 + 2/11*b**3 + 4/11 - 6/11*b = 0. What is b?
-2, 1
Let z = -1512/5 - -322. Let l(h) be the first derivative of -4*h**2 - 16*h**3 + 2 + 0*h + z*h**5 - 21/2*h**4. Suppose l(f) = 0. Calculate f.
-2/7, 0, 1
Let l(u) be the second derivative of u**5/10 + u**4/6 - 4*u. Determine z, given that l(z) = 0.
-1, 0
Factor -19 + 27 + x**2 - 14 - x.
(x - 3)*(x + 2)
Let q(v) be the first derivative of -v**4/28 - 2*v**3/21 - v**2/14 - 5. Factor q(s).
-s*(s + 1)**2/7
What is f in 0 + 4/9*f**2 + 2/9*f**3 + 2/9*f = 0?
-1, 0
Let o(d) be the first derivative of -d**9/16632 + d**8/9240 + d**7/4620 - d**6/1980 + d**3/3 + 5. Let y(a) be the third deriv