. Let g be b(4). Find m, given that g*m - 2*m**2 - 4 + 2*m + m = 0.
1, 2
Let n(v) be the first derivative of -v**6/3 + 2*v**5/5 + v**4 - 4*v**3/3 - v**2 + 2*v + 5. What is r in n(r) = 0?
-1, 1
Let m be (20/(5/(-1)))/(-6). Let f(s) be the first derivative of -1/2*s**4 + m*s**3 + s**2 + 0*s - 3 - 2/5*s**5. Factor f(u).
-2*u*(u - 1)*(u + 1)**2
Let p(l) be the third derivative of -l**5/45 - 2*l**4/9 - 8*l**3/9 - 6*l**2. Solve p(h) = 0 for h.
-2
Factor 0 + 0*d**3 + 0*d - 1/2*d**2 + 1/2*d**4.
d**2*(d - 1)*(d + 1)/2
Let p = -2 - -5. Determine j so that -4*j**4 + 0*j + j + 4*j**2 - p*j + 2*j**5 = 0.
-1, 0, 1
Factor 0 + 28/9*p**3 + 44/9*p**2 + 4/9*p**4 + 20/9*p.
4*p*(p + 1)**2*(p + 5)/9
Factor 2*z**5 - 3*z**4 + 0*z - 4*z - 8*z**2 + 11*z**4 + 2*z**5.
4*z*(z - 1)*(z + 1)**3
Let a(k) = k**4 + k**2 - k + 1. Let t(x) = 5*x**4 - 12*x**3 - 25*x**2 + 16*x + 8. Let l(n) = -4*a(n) - t(n). Suppose l(b) = 0. Calculate b.
-1, -2/3, 1, 2
Determine u so that -8*u**2 + 4*u + 5*u**3 + 4*u**3 - 5*u**3 = 0.
0, 1
Let b(r) be the second derivative of r**6/30 - 3*r**5/80 - r**4/48 + 7*r. Factor b(u).
u**2*(u - 1)*(4*u + 1)/4
Let g = 71/54 - -1/54. Solve -z**5 + 4/3*z**2 - g*z - 4/3*z**4 + 7/3*z**3 + 0 = 0.
-2, -1, 0, 2/3, 1
Let s(m) = 22*m**3 + 28*m**2 - m. Let i(q) = 7*q**3 + 9*q**2. Let j(x) = 14*i(x) - 4*s(x). Factor j(z).
2*z*(z + 1)*(5*z + 2)
Determine p, given that 2/7*p**2 + 0 - 2/7*p = 0.
0, 1
Let f(y) be the third derivative of -2/27*y**5 + 0*y**3 + 4*y**2 - 2/27*y**4 - 1/30*y**6 + 0*y - 1/135*y**7 + 0 - 1/1512*y**8. Let f(o) = 0. Calculate o.
-2, -1, 0
Let v(k) be the first derivative of k**8/672 + k**7/105 + k**6/60 - 2*k**2 + 4. Let d(z) be the second derivative of v(z). Factor d(i).
i**3*(i + 2)**2/2
Factor -2/7*o**2 + 0 - 6/7*o.
-2*o*(o + 3)/7
Let c = 25/21 + -6/7. Let d(t) be the second derivative of 1/20*t**5 - c*t**2 + 7/18*t**3 + 0 - 2/9*t**4 + t. Suppose d(n) = 0. What is n?
2/3, 1
Let o(y) be the first derivative of 14*y**5/15 - 5*y**4/6 - 4*y**3/9 + 2. Solve o(w) = 0.
-2/7, 0, 1
Factor 2*c**2 - 97*c**3 + 95*c**3 + 2*c**2.
-2*c**2*(c - 2)
Let v(x) = -4*x**3 - 2*x**2 + 10*x. Let f(r) = 4*r**3 + r**2 - 11*r. Let u(h) = -2*f(h) - 3*v(h). Solve u(a) = 0.
-2, 0, 1
Let k = -267/4 + 67. Factor -9/4 - 3/2*o - k*o**2.
-(o + 3)**2/4
Let q(l) be the first derivative of -l**7/70 - l**6/20 - l**5/20 - 2*l**2 + 1. Let b(x) be the second derivative of q(x). Factor b(a).
-3*a**2*(a + 1)**2
Let v(f) = 4*f**3 - f**2 - 7*f - 2. Let h(o) = -4*o**3 + 2*o**2 + 8*o + 2. Let n be (2/(-3))/((-5)/(-30)). Let g(m) = n*v(m) - 3*h(m). Factor g(w).
-2*(w - 1)*(w + 1)*(2*w + 1)
Factor 2/7*q + 1/7*q**2 + 0.
q*(q + 2)/7
Suppose -12*j**2 + 19*j**4 - 47*j**3 + 38*j - 8 - 34*j**2 - 7*j**4 + 9*j**5 + 6*j = 0. Calculate j.
-2, 1/3, 2
Suppose 0*f + 0 - 1/2*f**3 - 3/2*f**4 + f**2 = 0. What is f?
-1, 0, 2/3
Let o(d) be the first derivative of -1/2*d**3 + 0*d**2 + 2 + 3/2*d. Factor o(w).
-3*(w - 1)*(w + 1)/2
Let u(h) be the first derivative of -2*h**3/3 + 9*h**2/2 - 4*h + 20. Factor u(f).
-(f - 4)*(2*f - 1)
Let f(m) be the second derivative of 3*m**6/10 + 33*m**5/20 + 11*m**4/4 + m**3/2 - 3*m**2 + 20*m. Factor f(q).
3*(q + 1)**2*(q + 2)*(3*q - 1)
Let x = 29/52 - 3/52. Let 1/4 - x*i - 1/4*i**4 + 0*i**2 + 1/2*i**3 = 0. What is i?
-1, 1
Let v(f) be the second derivative of f**4/6 + 11*f**3/15 + 2*f**2/5 + 51*f. Factor v(a).
2*(a + 2)*(5*a + 1)/5
Let l be 1/3*-5*-3. Suppose l*z - 10 = c, -4 = -2*z + 4*c - 5*c. Factor 2/9*k**z + 2/9*k - 2/9*k**3 - 2/9.
-2*(k - 1)**2*(k + 1)/9
Let y(s) be the third derivative of -1/70*s**7 + 1/6*s**3 + 1/336*s**8 + 3*s**2 + 0 - 1/8*s**4 + 1/30*s**5 + 1/60*s**6 + 0*s. Suppose y(x) = 0. What is x?
-1, 1
Let n(j) = -2*j + 2*j**3 + 9*j - 3*j - 3. Let d(p) = 11*p**3 + 23*p - 17. Let r(u) = 6*d(u) - 34*n(u). Factor r(y).
-2*y*(y - 1)*(y + 1)
Factor 6 + 23*n**2 - 119*n**3 + 35*n**3 + 10*n + 106*n**2 - 61*n.
-3*(n - 1)*(4*n - 1)*(7*n - 2)
Suppose 0*y + 4*y - 8 = 0. Let m(q) be the first derivative of 4*q**2 - 8/3*q**3 + 0*q + y + 1/2*q**4. Factor m(d).
2*d*(d - 2)**2
Solve -130*a + 2*a**3 + a**3 + 124*a + 3*a**2 = 0 for a.
-2, 0, 1
Factor -2/3*z**5 - 6*z**3 + 14/3*z**2 + 0 - 4/3*z + 10/3*z**4.
-2*z*(z - 2)*(z - 1)**3/3
Let l(p) = -p**5 + p**3 + 1. Let i(o) = -8*o**5 - 2*o**4 + 9*o**3 + 2*o**2 - o + 9. Let c(k) = -4*i(k) + 36*l(k). Factor c(v).
-4*v*(v - 1)**3*(v + 1)
Suppose -4*z + c = -0 - 8, 0 = -4*c. Determine n so that -2*n**3 - 2 + n + z*n**2 - 3*n + 4*n**3 + 0*n**3 = 0.
-1, 1
Let f(c) be the third derivative of 0 + 1/168*c**8 + 0*c + 1/3*c**3 + c**2 + 1/12*c**4 + 1/105*c**7 - 1/30*c**6 - 1/15*c**5. Factor f(u).
2*(u - 1)**2*(u + 1)**3
Let i(r) = 149*r**2 + 124*r + 25. Let s(x) = 150*x**2 + 123*x + 24. Let f(h) = 3*i(h) - 2*s(h). Factor f(z).
3*(7*z + 3)**2
Factor -5*d + 58 + d**2 - 5*d - 33.
(d - 5)**2
Factor 8 - 3*j**4 - 2 + 7*j**2 + 3*j**3 + 2*j - 17*j + 2*j**2.
-3*(j - 1)**3*(j + 2)
Let v(o) be the third derivative of -o**6/80 + 3*o**4/16 - o**3/2 - 6*o**2. Factor v(f).
-3*(f - 1)**2*(f + 2)/2
Let c be (-19)/(-7) - (-2)/7. Let h(a) be the first derivative of 0*a + 0*a**2 + 0*a**c - 2/15*a**5 - 1/18*a**4 + 2. Find x such that h(x) = 0.
-1/3, 0
Let n be 4/(-63) - (-4)/(-18). Let r = n - -13/21. Let -r*o**2 + 0 + 1/3*o = 0. What is o?
0, 1
Let c(s) = -27*s**2 + 28*s**2 - 6*s + 2 - s. Let y be c(7). Factor 0 + 2/3*w**4 - 2/3*w**y - 2/3*w**5 + 0*w + 2/3*w**3.
-2*w**2*(w - 1)**2*(w + 1)/3
Let f(n) be the second derivative of n**7/840 - n**6/120 + n**5/40 - n**4/24 - 2*n**3/3 + 5*n. Let z(w) be the second derivative of f(w). Factor z(a).
(a - 1)**3
Suppose -2*f = -3*s + 100, 90 = -0*s + 3*s + 3*f. Let v be s/10 + (-2)/10. Factor -9*u**3 - 4*u**2 - u**4 - u**4 + v*u**3.
-2*u**2*(u + 1)*(u + 2)
Let n(z) be the first derivative of z**4/24 - z**2/12 + 15. Factor n(o).
o*(o - 1)*(o + 1)/6
Factor 20 + 13*x + 24*x + 8*x + 5*x**3 + 48*x**2 - 18*x**2.
5*(x + 1)**2*(x + 4)
Let i(j) = j + 9. Let c be i(-6). Let u(z) be the first derivative of -2/33*z**c - 1 + 0*z**2 + 0*z. Determine g so that u(g) = 0.
0
Let j(f) be the first derivative of -f**3/6 + f/2 - 1. Factor j(t).
-(t - 1)*(t + 1)/2
Suppose 1881 = -4*v + 473. Let f = -3868/11 - v. Factor f*h - 2/11*h**4 + 2/11 - 4/11*h**3 + 0*h**2.
-2*(h - 1)*(h + 1)**3/11
Let a be ((-2)/6)/(4/(-72)). Factor -4*y**3 - y**4 + 3*y**2 - a*y**2 + y**3 - y.
-y*(y + 1)**3
Factor 6*q - 71*q - 3*q**2 - 31*q - 768.
-3*(q + 16)**2
Let v(r) be the second derivative of 9*r**5/10 + 29*r**4/6 + 8*r**3 + 4*r**2 + 2*r - 47. Solve v(h) = 0.
-2, -1, -2/9
Let v be (-3)/(9/(-3)) - -3. Factor 0 + 0*l + 4/5*l**3 - 1/5*l**v - 4/5*l**2.
-l**2*(l - 2)**2/5
Suppose 21*s - 92 = -2*s. Solve 4/5*u**s - 4/5*u**2 - 8/5*u**3 + 0 + 8/5*u = 0 for u.
-1, 0, 1, 2
Let l(o) = -10*o + 84. Let h be l(8). Factor -h*t - 2/3*t**2 - 6.
-2*(t + 3)**2/3
Factor 0 - 4/9*b**2 - 2/3*b**3 - 2/9*b**4 + 0*b.
-2*b**2*(b + 1)*(b + 2)/9
Let q(g) = -21*g**3 + 36*g + 42. Let d(o) = 3*o**3 - 5*o - 6. Let p(r) = 27*d(r) + 4*q(r). Determine v so that p(v) = 0.
-1, 2
Let p(o) be the first derivative of 0*o**4 + 0*o**2 - 1/360*o**5 + 1/3*o**3 + 1/1080*o**6 + 0*o - 2. Let i(g) be the third derivative of p(g). Factor i(m).
m*(m - 1)/3
Suppose -2*c + 7 = -3*o, -10 + 4 = -5*c - 4*o. Let q(h) be the first derivative of 2 - 12*h**4 + 2*h + 2/3*h**3 + 6*h**c + 32/5*h**5. Factor q(s).
2*(s - 1)**2*(4*s + 1)**2
Let h(a) be the third derivative of -a**7/1680 + a**6/240 - a**5/120 - a**3/6 + 3*a**2. Let w(p) be the first derivative of h(p). Factor w(j).
-j*(j - 2)*(j - 1)/2
Let k(f) be the third derivative of -f**8/16800 + f**4/8 - 2*f**2. Let x(y) be the second derivative of k(y). What is z in x(z) = 0?
0
Let i = 1255 + -2509/2. Suppose -5/2*s**3 - i*s**2 + 5/2*s + 1/2 = 0. What is s?
-1, -1/5, 1
Let w(s) be the first derivative of -4*s**5/5 - 15*s**4/4 - 16*s**3/3 - 3*s**2/2 + 2*s + 3. Solve w(r) = 0.
-2, -1, 1/4
Factor 0*k**3 + 0*k - 8 - 1/2*k**4 + 4*k**2.
-(k - 2)**2*(k + 2)**2/2
Let t(s) be the first derivative of s**5/130 + 2*s**4/39 + 4*s**3/39 - 2*s + 3. Let n(v) be the first derivative of t(v). Let n(i) = 0. Calculate i.
-2, 0
Let q(u) = -2*u - 12. Let d be q(-8). Suppose -d*k = k. Factor 0*s**2 + s - 4*s**4 + k*s**2 - s**3 + 4*s**2.
-s*(s - 1)*(s + 1)*(4*s + 1)
Suppose 11*c = -c + 5*c. Let a(o) be the 