f**2 + 186*f + 147. Let z(i) = i**2 + 53*i + 42. Let b(h) = -5*k(h) + 18*z(h). Find j such that b(j) = 0.
-7, -1
Let w(j) be the second derivative of -5*j**4/12 - 5*j**3/6 + 9*j. Factor w(x).
-5*x*(x + 1)
Let v(r) be the first derivative of 0*r - 1 - 3/10*r**4 - 1/5*r**2 + 8/15*r**3. Solve v(a) = 0 for a.
0, 1/3, 1
Factor 3/5*i - 12/5 - 3/5*i**3 + 12/5*i**2.
-3*(i - 4)*(i - 1)*(i + 1)/5
Let c be (-2)/5 - 221/(-65). Factor 3*i - 3*i**c + 0*i**2 - 6*i + 6*i**2.
-3*i*(i - 1)**2
Let b(x) = -5*x - 11. Let u be b(-4). Suppose 4*z + 1 = u. Solve 2/3 + y + 1/3*y**z = 0 for y.
-2, -1
Let g = 4/89 + 514/445. Factor -2/5*j**2 - g + 8/5*j.
-2*(j - 3)*(j - 1)/5
Let x be (266/228)/(1/2) + -1. Factor 0 - 2*b**3 + 2/3*b**4 + x*b**2 + 0*b.
2*b**2*(b - 2)*(b - 1)/3
Let b(s) be the first derivative of -s**7/420 + s**6/30 - 3*s**5/20 - 5*s**3/3 + 8. Let m(y) be the third derivative of b(y). Determine g so that m(g) = 0.
0, 3
Let v(z) = z**3 - 7 - 8*z - 6 + 4 + 5*z**2. Let p be v(-6). Factor 2*s - 18*s**2 + 8*s**4 - 23*s**p - 18*s**4 + 4 - 3*s**3.
-2*(s + 1)**3*(5*s - 2)
Let j(q) be the third derivative of 0 - 1/2520*q**8 + 0*q**5 + 0*q**4 + 4*q**2 + 0*q**3 + 0*q**6 + 0*q - 2/1575*q**7. Solve j(c) = 0 for c.
-2, 0
Let n(y) be the first derivative of 4/5*y - 1 + 6/25*y**5 + 38/15*y**3 - 13/10*y**4 - 11/5*y**2. Determine i so that n(i) = 0.
1/3, 1, 2
Let v = -119/6 - -41/2. Let f be -3 + (-1)/((-1)/3). Suppose f + 2*s**3 + v*s + 2/3*s**4 + 2*s**2 = 0. What is s?
-1, 0
Factor 1/3*w**2 + 2*w + 3.
(w + 3)**2/3
Let r be 6/(-10) + 6 + 68/(-20). Factor -5/3*b**3 - 2/3 - 4*b**r - 3*b.
-(b + 1)**2*(5*b + 2)/3
Suppose -3*l + 6 = -3. Let p(k) be the second derivative of 0*k**5 - k - 1/15*k**6 + 0 - k**2 + 1/3*k**4 + 0*k**l. Factor p(u).
-2*(u - 1)**2*(u + 1)**2
Let x(i) be the first derivative of 2*i**2 - 8/5*i**5 - 4 + 0*i + 0*i**4 - 2/3*i**6 + 8/3*i**3. Factor x(n).
-4*n*(n - 1)*(n + 1)**3
Suppose 0 = -4*p - 4*k + 60, 4*k = -5*p + 52 + 24. Factor -p*t**2 - t**4 - 15*t**4 - 24*t**3 - 7*t - 4*t**5 + 2*t + t.
-4*t*(t + 1)**4
Let d(w) = 8*w**2 - 53*w + 77. Let a(n) = -4*n**2 + 26*n - 38. Let h(t) = 5*a(t) + 2*d(t). Let h(o) = 0. Calculate o.
3
Suppose -2*j = 2*v - 4, -4*j - v - 5 = -7. Find q such that 2/5*q + 4/5*q**2 - 6/5*q**3 + j = 0.
-1/3, 0, 1
Let f(x) be the first derivative of x**7/420 + x**6/60 - x**4/3 - x**3 - 2. Let a(v) be the third derivative of f(v). Factor a(g).
2*(g - 1)*(g + 2)**2
Let r(d) be the third derivative of d**6/24 - d**5/4 + 8*d**2. Solve r(h) = 0.
0, 3
Let w(z) be the first derivative of -3*z**5/20 + 11*z**4/16 - 11*z**3/12 + z**2/8 + z/2 - 8. Find g, given that w(g) = 0.
-1/3, 1, 2
Let n(g) be the second derivative of g**6/90 - g**5/15 + g**4/6 - 2*g**3/3 - 3*g. Let k(r) be the second derivative of n(r). Solve k(y) = 0 for y.
1
Let u(x) be the third derivative of 3*x**6/80 + x**5/40 - x**4/8 - 13*x**2. Factor u(j).
3*j*(j + 1)*(3*j - 2)/2
Let y(p) be the second derivative of -p**7/3780 - p**6/270 - p**5/45 - p**4/12 + 3*p. Let l(s) be the third derivative of y(s). Factor l(w).
-2*(w + 2)**2/3
Find k such that -3/2*k - 7/6*k**2 - 1/3 = 0.
-1, -2/7
Let v(s) be the first derivative of 7*s**6/3 + 32*s**5/5 + 11*s**4/2 + 4*s**3/3 - 11. Factor v(n).
2*n**2*(n + 1)**2*(7*n + 2)
Factor -11*s**2 - 27*s + 27*s + 3*s**2 - 4*s**3.
-4*s**2*(s + 2)
Find k such that -2 - 1/2*k**2 - 121/2*k**5 + 16*k - 319/2*k**4 - 235/2*k**3 = 0.
-1, 2/11
Let a(t) = -3*t**3 - 7*t**2 + 3*t - 2 - 10*t - 1. Let c(l) = -4*l**3 - 8*l**2 - 8*l - 4. Let f(p) = -6*a(p) + 5*c(p). Factor f(k).
-2*(k - 1)**2*(k + 1)
Let h(p) be the third derivative of -p**8/40320 + p**7/1260 - p**6/90 + p**5/10 + 10*p**2. Let x(j) be the third derivative of h(j). Factor x(o).
-(o - 4)**2/2
Let u(b) be the first derivative of -b**8/840 + 2*b**7/525 + b**6/300 - b**5/75 + b**2 - 9. Let x(t) be the second derivative of u(t). What is f in x(f) = 0?
-1, 0, 1, 2
Let m(h) be the second derivative of 0*h**3 + 0 + 1/2*h**2 + 2*h - 1/12*h**4. Suppose m(x) = 0. Calculate x.
-1, 1
Let w = -8/13 - -29/26. Factor -1 - 3/2*u + u**2 + 0*u**4 - w*u**5 + 2*u**3.
-(u - 2)*(u - 1)*(u + 1)**3/2
Factor -3 + 3/8*p**2 - 3/4*p.
3*(p - 4)*(p + 2)/8
Suppose 4*t + 0 - 8 = 0. Suppose l**t + 4*l - 4*l**2 - 3*l**3 - 5*l - 5*l**4 + 4*l**4 = 0. Calculate l.
-1, 0
Let a(n) = -n**3 + n**2 - n + 1. Let z be a(0). Factor -3*r + z - 4 + 6*r**2 + 5 - 5*r.
2*(r - 1)*(3*r - 1)
Let q(t) be the second derivative of -7*t**5/330 + 5*t**4/132 + 2*t**3/33 - t**2/2 - t. Let i(k) be the first derivative of q(k). Factor i(x).
-2*(x - 1)*(7*x + 2)/11
Determine b so that -9*b**3 - 3*b**2 - 6*b**5 + 3*b**5 - 7*b**4 - 5*b**4 + 3*b**4 = 0.
-1, 0
Let a(r) = r**2 + 16*r + 10. Let g be a(-11). Let c be (-99)/g - 1*2. Factor 1/5*y**2 + 0*y - c.
(y - 1)*(y + 1)/5
Let i(m) = 2*m**5 - 10*m**4 + 4*m**3 + 4*m**2 + 10*m + 10. Let h(k) = k**4 - k**3 - k - 1. Let v(p) = 10*h(p) + i(p). Factor v(z).
2*z**2*(z - 1)**2*(z + 2)
Let f(s) = -s**2 - s + 1. Let u(v) = 5*v**3 - 6*v**2 - v + 1. Let i(k) = -f(k) + u(k). Suppose i(x) = 0. Calculate x.
0, 1
Factor 2*a - 12*a**2 - 2*a**3 + 3*a**4 + 10*a**2 - a**4.
2*a*(a - 1)**2*(a + 1)
Factor 0*z**2 - 2*z**2 + 4*z + 0*z**2 + 3*z**2.
z*(z + 4)
Let c be 589/155 + 1/5. Factor 0 + 1/3*r**2 + 0*r + 1/3*r**c - 2/3*r**3.
r**2*(r - 1)**2/3
Factor -18*t - 14 - 32*t**3 - 51*t**2 - t**2 + 4*t**2 + 12.
-2*(t + 1)*(4*t + 1)**2
Factor -1/2*c + 7/2*c**2 + 0 + 9/2*c**4 - 15/2*c**3.
c*(c - 1)*(3*c - 1)**2/2
Factor o**3 + 2*o**4 - 2*o**2 + 0*o**4 - 2*o + o**3 + 0*o.
2*o*(o - 1)*(o + 1)**2
Let d be (-4)/6 + (-2808)/(-2754). What is k in d*k + 2/17*k**2 + 0 = 0?
-3, 0
Let t(h) = h - 1. Let l be t(1). Suppose l = -3*o - 5*a + 1, a = 4*o - 2*a - 11. Suppose 10/3*z**o + 14/3*z + 4/3 = 0. Calculate z.
-1, -2/5
Suppose -2 = s + 2*d - 4*d, d = 4*s - 13. Solve -3*v**2 + 24*v**s - 27*v**4 + 6*v**2 = 0.
-1, 0, 1
Let v be (2/(-160))/(15/(-15)). Let n(g) be the second derivative of 0*g**2 - 1/48*g**4 + 3*g + v*g**5 + 0 + 0*g**3. Factor n(a).
a**2*(a - 1)/4
Let a(p) be the first derivative of 0*p**3 - 1 - 2*p + 0*p**2 + 1/18*p**4. Let z(l) be the first derivative of a(l). Find b, given that z(b) = 0.
0
Let w(x) be the third derivative of 0*x + 0 - 1/36*x**4 - 3*x**2 - 1/18*x**3 - 1/180*x**5. Determine u, given that w(u) = 0.
-1
Let h(x) be the first derivative of -3*x**4/10 - 8*x**3/15 + 4*x**2/5 - 11. Determine m so that h(m) = 0.
-2, 0, 2/3
Let p(a) = -6*a**4 + 22*a**3 - 14*a**2 + 10*a - 6. Let z(m) = 12*m**4 - 43*m**3 + 28*m**2 - 19*m + 11. Let b(j) = 11*p(j) + 6*z(j). Suppose b(c) = 0. What is c?
0, 2/3, 1
Let p(b) be the first derivative of -b**3 + 9*b**2/2 - 6*b + 1. Factor p(d).
-3*(d - 2)*(d - 1)
Let h(l) = -25*l**3 - 25*l**2 + 40*l - 50. Let a(v) = v**3 + 1. Let x(d) = -30*a(d) - h(d). Find y, given that x(y) = 0.
1, 2
Let i(m) = -4*m - 5. Let n be i(-2). Factor -n + 3 + 24*w**2 + 16*w + 9*w**3 + 4 - 3*w**2.
(w + 1)*(3*w + 2)**2
Let s = 3 - 2. Suppose 0 = 4*o - s + 9, 2*y + 4*o = -8. Solve 1/5*j**5 + 0*j + 0 + 1/5*j**3 + 2/5*j**4 + y*j**2 = 0 for j.
-1, 0
Let u(w) be the first derivative of 0*w**2 + 0*w + 3/10*w**5 - 3 + 0*w**3 + 0*w**4. What is z in u(z) = 0?
0
Suppose -6*x + 20 = -2*x. Let -9*y**3 - 4*y**5 + 5*y**x - 15*y**2 + 2*y**5 + 3*y**4 - 6*y = 0. What is y?
-1, 0, 2
Let p(j) be the second derivative of -j**5/40 + j**4/12 + j**3/12 - j**2/2 - 3*j. Factor p(b).
-(b - 2)*(b - 1)*(b + 1)/2
Let z(c) be the third derivative of c**6/480 + 8*c**2. Factor z(u).
u**3/4
Let t(a) be the first derivative of -a**5/50 - a**4/15 - a**3/15 + 3*a - 2. Let k(x) be the first derivative of t(x). Factor k(i).
-2*i*(i + 1)**2/5
Let b(y) be the third derivative of -y**8/672 + y**7/630 + y**6/72 - y**5/30 + y**4/6 + 4*y**2. Let l(f) be the second derivative of b(f). Factor l(v).
-2*(v - 1)*(v + 1)*(5*v - 2)
Factor 47 - 47 + 2*g**3 - 2*g.
2*g*(g - 1)*(g + 1)
Let d(m) = m**3 + m**2 - m - 1. Let l(i) = i**5 - 5*i**4 + 6*i**3 - 4*i**2 + i + 1. Let a(z) = d(z) + l(z). Factor a(g).
g**2*(g - 3)*(g - 1)**2
Let c be 81/42*(140/(-24))/(-5). Let n(l) be the first derivative of 0*l - 3 - 5/6*l**6 + 12/5*l**5 + 0*l**2 - c*l**4 + 2/3*l**3. Factor n(s).
-s**2*(s - 1)**2*(5*s - 2)
Let p be (-80)/(-2)*(-4)/(-10). Let w = 16 - p. Factor 0*k**2 - 2/5*k**5 - 2/5*k**4 + 0 + w*k + 0*k**3.
