 Let r(q) = -20*q**3 + 75*q**2 - 24*q - 7. Let a(n) = 3*r(n) + 7*x(n). Let a(h) = 0. Calculate h.
0, 2/5, 3
Let l(a) be the second derivative of -1/105*a**6 + 0*a**2 + 0 + 1/35*a**5 - 4*a + 0*a**3 - 1/42*a**4. Factor l(i).
-2*i**2*(i - 1)**2/7
Let x(g) be the second derivative of -g**6/15 + g**4/6 + 4*g. Suppose x(y) = 0. What is y?
-1, 0, 1
Let b(t) = -t**3 + 13*t**2 + 2. Let j be b(13). Let g(z) be the second derivative of -1/6*z**4 - 1/3*z**3 + 0 - 1/3*z**j - 1/30*z**5 - 3*z. Factor g(r).
-2*(r + 1)**3/3
Factor 0*h**3 + 3*h**2 + 2*h**3 - 3*h**3 + 2*h**3 + 2*h.
h*(h + 1)*(h + 2)
Let d(o) = -618*o**2 - 100*o - 11. Let r(y) = -619*y**2 - 100*y - 10. Let q(t) = -6*d(t) + 7*r(t). Factor q(p).
-(25*p + 2)**2
Let d = -2047/194 - -5/97. Let g = -10 - d. Factor 0*u**3 + g*u**2 - 1/4*u**5 - 1/2*u**4 + 0 + 1/4*u.
-u*(u - 1)*(u + 1)**3/4
Let z(v) = v**3 - v + 1. Let y(h) = -4*h**5 - 4*h**4 - 4*h**3 + 4*h**2 + 8*h - 8. Let u(i) = y(i) + 8*z(i). Let u(a) = 0. Calculate a.
-1, 0, 1
Factor 0 - 2/3*q**4 + 2*q**3 + 2/3*q**2 - 2*q.
-2*q*(q - 3)*(q - 1)*(q + 1)/3
Suppose -4*o**3 - o**3 + 3*o**3 - 9*o**2 + 8 + 3*o**2 = 0. What is o?
-2, 1
Suppose -2*h = 7 + 3, 0 = -5*s - 3*h + 80. Suppose 2*z = 5*l - s, 5*z + 3*l + 1 = 31. Factor -2/9*x**z + 4/9*x**4 + 0*x**2 - 2/9*x**5 + 0*x + 0.
-2*x**3*(x - 1)**2/9
Suppose 3*a = -a + 12. Let f be (-5)/((-30)/(-4))*-3. Factor -6*z**3 + 6*z**3 - 2*z**a - 2*z**2 + 4*z**f.
-2*z**2*(z - 1)
Let n = -4296/5 + 861. Find c, given that n*c + 1/5 + 24/5*c**2 + 16/5*c**3 = 0.
-1, -1/4
Find b, given that -16/3*b + 4/3*b**2 - 20/3 = 0.
-1, 5
Let d(z) be the first derivative of -z**4/6 + 2*z**3/9 + z**2/3 - 2*z/3 - 9. Factor d(u).
-2*(u - 1)**2*(u + 1)/3
Let d(y) be the first derivative of 7*y**6/12 + y**5/15 - 7*y**4/8 - y**3/9 - 34. What is l in d(l) = 0?
-1, -2/21, 0, 1
Let x(h) be the second derivative of 7/4*h**4 - 8/3*h**3 - 2*h**2 + 27/10*h**5 + 0 + 5*h. Factor x(n).
(2*n - 1)*(3*n + 2)*(9*n + 2)
Let t(o) = -12*o**3 + 4*o**2 + 12*o - 4. Let r(b) = -11*b**3 + 4*b**2 + 11*b - 4. Let u(x) = -2*r(x) + 3*t(x). Factor u(d).
-2*(d - 1)*(d + 1)*(7*d - 2)
Let q(y) = 2*y**2 + 2*y - 4. Let k(x) = 4*x**2 + 3*x - 8. Let a(i) = -4*k(i) + 7*q(i). Find c such that a(c) = 0.
-1, 2
Solve 6/7*j**3 + 4/7*j**4 + 0 - 6/7*j**5 - 4/7*j**2 + 0*j = 0.
-1, 0, 2/3, 1
Suppose -5*l + 6 - 6 = 0. Let l + 0*g + 1/2*g**2 = 0. Calculate g.
0
Let k(a) = -a**3 + 5*a**2 - 3*a - 4. Let c be k(3). Let c*q**2 - 3*q**2 + 4*q - 8*q + 2*q**3 = 0. What is q?
-2, 0, 1
Factor 3/5 + 6/5*m + 3/5*m**2.
3*(m + 1)**2/5
Let j(a) = 16*a + 258. Let b be j(-16). Factor 0*d**b + 2/9*d**3 + 0 - 2/9*d.
2*d*(d - 1)*(d + 1)/9
Let w(j) be the third derivative of j**8/840 - 4*j**7/525 + j**6/75 + j**5/75 - j**4/12 + 2*j**3/15 + j**2 - 6. Factor w(h).
2*(h - 2)*(h - 1)**3*(h + 1)/5
Factor -2/11*l**2 + 0 + 0*l - 2/11*l**3.
-2*l**2*(l + 1)/11
Factor 4*n**3 + 6*n**3 - 2*n**4 - 3*n**4 - 5*n**2.
-5*n**2*(n - 1)**2
Let b(p) be the third derivative of -5/72*p**4 - p**2 + 0*p + 0 + 1/72*p**6 + 1/18*p**3 - 2/315*p**7 + 1/60*p**5. Let b(n) = 0. Calculate n.
-1, 1/4, 1
Let l be (1/(-2))/(8 + 147/(-18)). Find b, given that 3*b**5 + 67/3*b**l + 8*b - 4/3 - 19*b**2 - 13*b**4 = 0.
2/3, 1
Factor 0 - 12/7*i**2 - 8/7*i**3 - 4/7*i.
-4*i*(i + 1)*(2*i + 1)/7
Let l(f) be the first derivative of f**3/12 - 5*f**2/4 + 9*f/4 - 57. Suppose l(i) = 0. What is i?
1, 9
Let v = 642/5 + -128. Let o(n) be the first derivative of 7/2*n**2 + v*n**5 - 2*n - 1/6*n**6 - 1 + 1/2*n**4 - 8/3*n**3. Solve o(j) = 0.
-2, 1
Let r(f) = -f**4 - f**3 + f**2 - f - 1. Let s(x) = 10*x**4 + 16*x**3 - 4*x**2 + 8*x + 6. Let m(u) = -12*r(u) - s(u). Suppose m(l) = 0. What is l?
-1, 1, 3
Let d(j) = 5*j**4 + 3*j**3 - 15*j**2 - 7*j + 8. Let s(x) = -5*x**4 - 2*x**3 + 15*x**2 + 8*x - 7. Let z(t) = -3*d(t) - 2*s(t). Factor z(h).
-5*(h - 1)**2*(h + 1)*(h + 2)
Let p(g) be the third derivative of g**5/120 - g**4/12 + g**3/3 + g**2. Factor p(b).
(b - 2)**2/2
Solve 31*c + 2*c**2 - 40 - 8*c**2 + c**2 - c = 0.
2, 4
Let s(o) be the third derivative of -o**8/50400 + o**7/2100 - o**6/200 + o**5/20 - 3*o**2. Let c(i) be the third derivative of s(i). Factor c(a).
-2*(a - 3)**2/5
Let d(t) be the third derivative of t**8/448 + t**7/280 - 3*t**6/160 - t**5/80 + t**4/16 + 12*t**2 - 5. Determine s so that d(s) = 0.
-2, -1, 0, 1
Let b(o) = -o + 5. Let m be b(2). Suppose 3*g - 5*h = 4, -3 = -4*h + 13. Factor -5*x**4 - 6*x**4 + 0*x**4 - m*x**4 + g*x + 10*x**3 + 32*x**2.
-2*x*(x - 2)*(x + 1)*(7*x + 2)
Suppose -4*n + 143 = 3*u, -5*u + 56 = 4*n - 97. Solve 29*g - 7*g + n*g**2 - 6*g + 2 = 0.
-1/4
Let k(h) = -3*h**3 - h**2 - 19*h - 17. Let x be k(-1). What is p in 3/2*p**2 + 0*p - 3/2*p**x + 3/4*p**5 - 3/4*p**3 + 0 = 0?
-1, 0, 1, 2
Let x(r) = -2*r**3 + 4*r**2 + 2*r - 2. Let p(b) = b**2. Let n = -2 - 0. Let k(u) = n*p(u) + x(u). Suppose k(d) = 0. Calculate d.
-1, 1
Let h(r) = r**2 + 23*r + 5. Let y be h(-23). Factor 0 + 0*t**4 + 1/2*t + 1/2*t**y - t**3 + 0*t**2.
t*(t - 1)**2*(t + 1)**2/2
Suppose t = 2*z - 6, -13 = -4*z + 3*z - 2*t. Find a, given that 7*a**3 - z*a + 3*a**2 + 0*a**2 + 7*a + 6*a**2 = 0.
-1, -2/7, 0
Let t(p) be the third derivative of p**6/320 + p**5/80 + 7*p**2. Suppose t(q) = 0. What is q?
-2, 0
Let d(o) = 4*o**5 - 12*o**4 + 12*o**3 - 4*o**2 - 5*o. Let v(j) = -2*j**5 + 6*j**4 - 6*j**3 + 2*j**2 + 3*j. Let t(i) = 3*d(i) + 5*v(i). Factor t(b).
2*b**2*(b - 1)**3
Let b(y) be the first derivative of -y**9/10584 + y**7/2940 - 2*y**3/3 + 1. Let d(f) be the third derivative of b(f). What is w in d(w) = 0?
-1, 0, 1
Factor -1/2 + 1/2*h**2 + 0*h.
(h - 1)*(h + 1)/2
Let o = -12 + 21. Suppose -5*l - 5 = 5*p - 0, 3*l = -o. Factor 5*z**2 - 5*z**p - z**3.
-z**3
Let r(m) be the third derivative of m**8/5040 + m**7/1260 + m**6/1080 + m**3/6 - 2*m**2. Let s(j) be the first derivative of r(j). Factor s(f).
f**2*(f + 1)**2/3
Let g be ((-3)/(-3))/((-4)/(-8)). Factor -1/4*m**g - 1/4*m**3 + 0 + 0*m.
-m**2*(m + 1)/4
Let o(x) = -2 + 4 + 8*x**2 + 9*x - 23*x**2 + 9. Let u(f) = 7*f**2 - 4*f - 5. Let l(m) = -6*o(m) - 13*u(m). Factor l(j).
-(j + 1)**2
Let l be (-9)/(-5) + (-18)/(-15). Let 20/9*i**2 - 20/9*i**l - 2/9*i**5 + 10/9*i**4 + 2/9 - 10/9*i = 0. What is i?
1
Let v(i) be the second derivative of -1/30*i**5 + 0*i**2 + 0*i**3 - 1/45*i**6 - 1/189*i**7 - 1/54*i**4 - 2*i + 0. Let v(g) = 0. Calculate g.
-1, 0
Let m be (6/4)/((-12)/(-16)). Suppose -4*k + 5*s + 11 + 7 = 0, k - m*s - 6 = 0. Factor 2/11*o**k + 2/11*o - 2/11*o**3 - 2/11.
-2*(o - 1)**2*(o + 1)/11
Let m(s) be the second derivative of 1/40*s**5 + 0 - 4*s + 0*s**2 + 0*s**3 + 1/60*s**6 + 0*s**4. Factor m(k).
k**3*(k + 1)/2
Let m(z) be the third derivative of z**6/30 - z**5/15 - z**4/6 + 2*z**3/3 + 2*z**2. Factor m(d).
4*(d - 1)**2*(d + 1)
Factor -1/4*t**3 - 1/12*t**4 - 1/12*t**2 + 1/4*t + 1/6.
-(t - 1)*(t + 1)**2*(t + 2)/12
Let o(m) be the third derivative of 1/330*m**5 + 0*m**4 + 0*m**3 + 0 - 1/660*m**6 + 0*m - 3*m**2. Factor o(g).
-2*g**2*(g - 1)/11
Factor 32*s + 8*s**2 + 128/3 + 2/3*s**3.
2*(s + 4)**3/3
Find q such that 0*q - 2/7*q**2 - 2/7*q**3 + 0 = 0.
-1, 0
Let v(n) be the first derivative of -n**6/30 - n**5/20 + n**4/12 + n**3/6 - 3*n - 2. Let o(d) be the first derivative of v(d). Factor o(y).
-y*(y - 1)*(y + 1)**2
Let 3*f**3 + 0*f**3 + f**2 - 7*f**2 = 0. What is f?
0, 2
Let d(a) be the first derivative of a**3/21 - 3*a**2/14 - 26. Factor d(p).
p*(p - 3)/7
Let f(d) be the third derivative of 3/40*d**6 - 1/10*d**5 + 0*d + d**3 - 3*d**2 - 3/8*d**4 + 0. Factor f(x).
3*(x - 1)*(x + 1)*(3*x - 2)
Let o(y) be the first derivative of 1/12*y**4 - 5 + 0*y + 0*y**3 - 1/6*y**2. What is h in o(h) = 0?
-1, 0, 1
Let q be (1*-3)/((-2)/4). Suppose x = q*x. Factor -1/4*l + x + 1/4*l**2.
l*(l - 1)/4
Solve -1/8*s**3 + 1/8*s**2 + 0*s + 0 = 0.
0, 1
Let u(j) be the second derivative of -j**4/18 + j**2/3 + 9*j. Factor u(p).
-2*(p - 1)*(p + 1)/3
Let w(y) be the first derivative of y**7/147 - y**5/35 + y**3/21 + y - 2. Let d(m) be the first derivative of w(m). Factor d(t).
2*t*(t - 1)**2*(t + 1)**2/7
Let u(y) be the third derivative of 1/60*y**4 - y**2 + 0*y + 2/15*y**3 + 0 - 1/150*y**5. Factor u(p).
-2*(p - 2)*(p + 1)/5
Let o(h) = -2*h**4 - 2*h**3 - 2*h + 2. Suppose 0*y = 5*y + 110. Let m(f) = 10*f**4 + 11*f**3 + f**2 + 11*f - 11. Let s(d) = y*o(d) - 4*m(d)