h + 1)**3
Let z(x) = -x**2. Let d(b) = b**2 + 11*b. Let v(f) = d(f) + 2*z(f). Let k be v(11). Solve 2/5*u**4 + 0*u**3 + 0*u**2 + k*u + 0 = 0 for u.
0
Factor -7*g**3 + 11*g**3 + 8*g**3 + 4*g**4 + 8*g**2.
4*g**2*(g + 1)*(g + 2)
Let s(t) be the second derivative of t**7/126 + 7*t**6/90 + 3*t**5/10 + 5*t**4/9 + 4*t**3/9 - 2*t. Factor s(w).
w*(w + 1)*(w + 2)**3/3
Suppose 3 = d - 0*d. Suppose -f + 5 = 1. Suppose -18*i**d + 6*i - 14*i**f + 10*i**2 - 4 + 12*i + 8 = 0. Calculate i.
-1, -2/7, 1
Let w(f) be the first derivative of 4*f**3/21 + 3*f**2/14 - f/7 - 6. Factor w(u).
(u + 1)*(4*u - 1)/7
Let r(f) = -2*f**4 + f**3 + 5*f**2 - f + 3. Let t(h) = 6*h**4 - 4*h**3 - 14*h**2 + 4*h - 8. Let j(n) = 8*r(n) + 3*t(n). Suppose j(p) = 0. Calculate p.
-1, 0, 1, 2
Let d be (6 + -12)*(-5)/((-40)/(-9)). Let a(p) = -p**3 + 7*p**2 + 9*p - 8. Let o be a(8). Find h, given that d*h**3 - 3/2*h**2 - 21/4*h**4 + o + 0*h = 0.
0, 2/7, 1
Let r = 15 - 12. Factor q**3 + 2*q - q**3 - q**r - q.
-q*(q - 1)*(q + 1)
Let k = 68 + -65. Let d(u) be the second derivative of 0 - 1/6*u**2 - 4*u - 5/18*u**k - 7/36*u**4 - 1/20*u**5. Factor d(n).
-(n + 1)**2*(3*n + 1)/3
Let l(f) = f**2 + 18*f + 3. Let n be l(-18). Let x be 1 - -3*n/(-27). Factor -2/3*m**2 + 1/3*m - x*m**3 + 1/3*m**5 + 1/3*m**4 + 1/3.
(m - 1)**2*(m + 1)**3/3
Suppose l = -5*h + 12, 0*l + 4 = 3*l - h. Let r(k) be the first derivative of 2/3*k**3 + k**2 - l + 0*k. Factor r(s).
2*s*(s + 1)
Let h(y) be the first derivative of -y**3/21 + 4*y**2/7 - 16*y/7 + 34. Factor h(q).
-(q - 4)**2/7
Let x be 12/2 + ((-66)/(-9) - 8). Solve 32/3 + 16*z**2 + 2/3*z**4 - 64/3*z - x*z**3 = 0 for z.
2
Let s(y) be the third derivative of y**6/33 + 53*y**5/330 + 7*y**4/33 + 4*y**3/33 + 9*y**2. Solve s(o) = 0.
-2, -2/5, -1/4
Let b(q) = -210*q**2 - 38*q + 8. Let z(l) = -420*l**2 - 75*l + 16. Let t(y) = 11*b(y) - 6*z(y). Let t(i) = 0. What is i?
-2/7, 2/15
Let i(x) be the third derivative of x**6/1440 - x**5/240 + x**4/96 - x**3/2 + 2*x**2. Let k(u) be the first derivative of i(u). Solve k(n) = 0.
1
Let k(s) be the second derivative of -s**6/10 - 3*s**5/10 - s**4/4 - s. Factor k(w).
-3*w**2*(w + 1)**2
Let w(l) be the first derivative of 3*l**5/5 + 9*l**4/4 + l**3 - 9*l**2/2 - 6*l - 7. Factor w(o).
3*(o - 1)*(o + 1)**2*(o + 2)
Let h(r) = -27*r**4 - 5*r**3 + 11*r**2 - 7*r - 4. Let z(j) = -27*j**4 - 6*j**3 + 12*j**2 - 6*j - 3. Let a(d) = 3*h(d) - 4*z(d). Suppose a(x) = 0. What is x?
-1, 0, 1/3
Let f(j) be the third derivative of j**7/315 + j**6/45 + j**5/30 - j**4/9 - 4*j**3/9 - 7*j**2. Factor f(t).
2*(t - 1)*(t + 1)*(t + 2)**2/3
Let v = 19 + -15. Let h(j) = 2*j - 6. Let l be h(v). Factor -6/5*c**l + 0 - 2/5*c - 6/5*c**3 - 2/5*c**4.
-2*c*(c + 1)**3/5
Let q(o) be the first derivative of 2*o**5/9 + 4*o**4/9 + 2*o**3/27 - 2*o**2/9 - 13. Factor q(r).
2*r*(r + 1)**2*(5*r - 2)/9
Let z(k) be the first derivative of -4*k**5 - 15*k**4/4 + 15*k**3 - 5*k**2 + 12. What is v in z(v) = 0?
-2, 0, 1/4, 1
Let j(c) = -6*c - 4. Let v be j(-2). Let r be 4/v*-2 - -5. Factor 2/7*f**3 + 0 + 2/7*f**2 - 2/7*f**r - 2/7*f.
-2*f*(f - 1)**2*(f + 1)/7
Let r(l) = -2*l**3 - 7*l**2 - l + 4. Let y(j) = -22*j**3 - 78*j**2 - 12*j + 44. Let q(o) = 68*r(o) - 6*y(o). Find k, given that q(k) = 0.
-2, -1, 1
Let k(x) = x**2 - x. Let s(n) = 10*n**2 - 6*n. Suppose 1 = -3*a + 4. Let g(d) = a*s(d) - 2*k(d). Factor g(q).
4*q*(2*q - 1)
Let x be (6/12)/((-2)/(-8)). Suppose -4*j + 5*f = -x, 4*j - 20 = -0*j - 4*f. Solve j*m**3 + 3/2*m**4 + 0*m + 0 + 0*m**2 = 0 for m.
-2, 0
Let z(h) be the third derivative of 0*h**6 - 1/735*h**7 + 0*h - 3*h**2 + 0 + 1/105*h**5 + 0*h**4 - 1/21*h**3. Factor z(b).
-2*(b - 1)**2*(b + 1)**2/7
Let j(s) be the second derivative of 5*s**7/63 + 14*s**6/45 + 23*s**5/50 + 14*s**4/45 + 4*s**3/45 - 2*s. Factor j(u).
2*u*(u + 1)**2*(5*u + 2)**2/15
Let s = 1 - -3. Let n be (-12)/(-8)*s/2. Suppose -4*t**2 + t**3 + 2*t**2 + t**n - 4*t = 0. What is t?
-1, 0, 2
Let z be (8 + -5 + 1)/6. Let x(v) be the first derivative of 0*v + z*v**2 - 2/9*v**3 - 2. Factor x(q).
-2*q*(q - 2)/3
Let j = 12/17 - 31/68. Let u(c) = c**3 - 4*c**2 + 3. Let l be u(4). What is h in -1/4*h - j*h**4 + 0 + 1/4*h**2 + 1/4*h**l = 0?
-1, 0, 1
Let p(j) = j**5 + j**4 + j**3 - j**2 - j - 1. Let u(x) = 20*x**5 + 84*x**4 + 68*x**3 + 28*x**2 + 8*x + 16. Let a(s) = -16*p(s) - u(s). Factor a(t).
-4*t*(t + 1)**3*(9*t - 2)
Factor 7*m + 8*m**3 - 7*m**3 - 6*m**2 - 8 - 2*m**3 + 8*m.
-(m - 1)**2*(m + 8)
Factor -2/5*g**2 + 0 + 2/5*g**4 - 2/5*g + 2/5*g**3.
2*g*(g - 1)*(g + 1)**2/5
Let q(j) = -11*j**2 - j. Let m be q(1). Let d be 5/21 - m/28. Find p, given that 2/3*p**3 + 0*p + 0 + 0*p**2 + d*p**4 = 0.
-1, 0
Let f(l) be the first derivative of l**4/12 - l**3/3 + 6*l + 3. Let i(c) be the first derivative of f(c). Find b, given that i(b) = 0.
0, 2
Factor -9/4*t**2 - 1 - 3*t.
-(3*t + 2)**2/4
Let h(w) be the first derivative of w**3 + 3*w**2/2 - 14. Suppose h(b) = 0. Calculate b.
-1, 0
Let i be ((-1)/3)/((-19)/114). Let k(d) be the first derivative of 2/3*d**3 - i*d - 1/2*d**4 + 3 + d**2. Factor k(p).
-2*(p - 1)**2*(p + 1)
Let k be (0 - 0) + (-3374)/35. Let h = -96 - k. Solve 0 + 0*d**3 - 2/5*d**5 + h*d + 4/5*d**4 - 4/5*d**2 = 0.
-1, 0, 1
Suppose 3*p + 23 = 4*a, 8 - 3 = -p. Factor a*q**3 + 0*q**2 + 5*q**2 - 3*q**2 - q**4 - 3*q**2.
-q**2*(q - 1)**2
Let j(r) be the second derivative of -r**7/21 + r**6/15 + r**5/5 - r**4/3 - r**3/3 + r**2 - 15*r. Factor j(w).
-2*(w - 1)**3*(w + 1)**2
Let k(m) = -m**3 - 7*m**2 - 11*m + 7. Let s be k(-4). Factor u**2 - u**s - 1/2*u**5 + 3/2*u + 1/2 - 3/2*u**4.
-(u - 1)*(u + 1)**4/2
Let a(n) = n**3 - 2*n**2 - 3*n + 5. Let y be a(3). Let l(u) be the third derivative of 1/21*u**3 + 0*u + 0 + u**2 + 1/210*u**y + 1/42*u**4. Factor l(c).
2*(c + 1)**2/7
Let z(l) be the first derivative of 3*l**5/10 + l**4/4 - l**3/2 - l**2/2 - 14. Factor z(t).
t*(t - 1)*(t + 1)*(3*t + 2)/2
Let u(a) be the first derivative of -7/6*a**4 + 5 + 4/9*a**3 + 7/3*a**2 - 4/3*a. Factor u(i).
-2*(i - 1)*(i + 1)*(7*i - 2)/3
Let f(z) be the first derivative of -z**3/6 + 3*z**2/4 - z - 4. Let f(j) = 0. Calculate j.
1, 2
Let l = -389 - -2725/7. Suppose -l + 4/7*o - 2/7*o**2 = 0. Calculate o.
1
Let i(n) be the second derivative of -3*n**5/5 - 5*n**4/3 + 8*n**3/3 + 8*n**2 + 29*n. Let i(k) = 0. Calculate k.
-2, -2/3, 1
Solve -2/5*h**2 + 18/5 + 16/5*h = 0.
-1, 9
Let r(y) = -5*y**3 - 12*y**2 + 4*y - 8. Let k be 10/(-3)*(-12)/(-5). Let b(w) = -2*w**3 - 4*w**2 + w - 3. Let c(x) = k*b(x) + 3*r(x). Factor c(g).
g*(g - 2)**2
Let b(q) be the third derivative of -q**8/336 + q**6/60 - q**4/24 + 3*q**2. Find g, given that b(g) = 0.
-1, 0, 1
Let x(m) = 5*m**2 + m + 2. Let c be x(-2). Suppose 0 = -2*t - o - 2*o + 12, 4*t + c = 5*o. Factor -1/3*d**3 + 0 + t*d + 1/3*d**2.
-d**2*(d - 1)/3
Let l(q) be the first derivative of 2/3*q**3 + 0*q**2 - 1 + 0*q - 3/2*q**4 - 8/5*q**5. Factor l(n).
-2*n**2*(n + 1)*(4*n - 1)
Suppose -3*i = -3*x + 48, x + 3*x - 64 = -2*i. Let b = x - 13. Let 6/7*u**4 + 0*u**2 + 0 - 2*u**b + 8/7*u = 0. Calculate u.
-2/3, 0, 1, 2
Suppose -3*o + 0*o = -6. Let c be (-1)/2*(-16)/o. Find p, given that -8 - 2*p**2 + c*p + 3*p + p = 0.
2
Let g = -34 + 30. Let f be (-5)/(10/g) + -2. Factor -3/5*p + 6/5*p**4 + 3/5*p**5 + f*p**3 - 6/5*p**2 + 0.
3*p*(p - 1)*(p + 1)**3/5
Let z = -47 + 52. Let b(s) be the second derivative of -2*s**3 + 0 - 1/2*s**4 + 2*s - 4*s**2 - 1/20*s**z. Factor b(g).
-(g + 2)**3
Let o be ((-40)/(-28))/5*7. Let f(p) be the second derivative of 0 + 1/4*p**3 - 2*p + 1/6*p**4 - 1/4*p**o. Factor f(z).
(z + 1)*(4*z - 1)/2
Let o(w) be the second derivative of w**7/13860 + w**6/990 + w**5/220 - w**4/2 - 3*w. Let n(l) be the third derivative of o(l). Suppose n(k) = 0. Calculate k.
-3, -1
Let y(z) be the third derivative of -z**8/1848 - z**7/385 - z**6/220 - z**5/330 + z**2. Factor y(c).
-2*c**2*(c + 1)**3/11
Let d = -8 - -13. Suppose -d*n + 4*n = -1. Let 0*x + 1/4*x**3 + n - 3/4*x**2 = 0. What is x?
-1, 2
Let f be 30/288*2/10. Let o(h) be the second derivative of -f*h**4 + 0*h**2 + 2*h + 0 + 0*h**3. Find x, given that o(x) = 0.
0
Let f(k) = 3*k - 6. Let g be f(4). Factor -10*x**2 - 16*x**3 + 2*x**4 - 3*x + g*x**3 - 5*x + 26*x**2.
2*x*(x - 2)**2*(x - 1)
Let x(y) = -y**3 - 8*y**2 - 13*y + 12. Let k be x(-5). Determine b, given that -2/3 - 6*b**k - 4/3*b