Calculate b.
5
Let x(a) be the second derivative of 3*a**5/20 + 3*a**4/2 + 6*a**3 + 12*a**2 - 4*a. Let x(l) = 0. Calculate l.
-2
Let v(d) = d**2 + 8*d + 3. Let c(t) = t**2 + 16*t + 6. Let m(x) = 4*c(x) - 7*v(x). Solve m(l) = 0 for l.
-1/3, 3
Let a(s) be the first derivative of -27*s**5/5 + 9*s**4/4 + 8*s**3 - 6*s**2 + 11. Let a(n) = 0. Calculate n.
-1, 0, 2/3
Let a(y) be the third derivative of -11/120*y**5 + 0*y + 0*y**3 - 1/60*y**7 - 6*y**2 + 1/24*y**4 + 1/15*y**6 + 0. Factor a(t).
-t*(t - 1)**2*(7*t - 2)/2
Suppose -5*f + 6 = -0*j - 2*j, j = 2*f - 2. Suppose -5*q = 9*q + 6*q. Determine d so that 2/5*d**f + q*d - 2/5 = 0.
-1, 1
Find z such that 109 - 21*z + 101 - 213 - 45*z**2 - 27*z**3 = 0.
-1, -1/3
Let m(l) = 2*l**2 + 23*l - 122. Let h be m(4). Factor -7/6*w**h + 2*w + 2/3.
-(w - 2)*(7*w + 2)/6
Let z(u) = -u**2 + 13*u - 3. Let j be z(12). Let g be (3/j)/((-2)/(-8)). Factor -2/3*x**2 + 2/3*x + g.
-2*(x - 2)*(x + 1)/3
Let q be 1/1 + -2 + 6. Factor -8*m**3 + 6*m + 12*m**2 + 19*m**q - 3*m + 8*m**5 - 36*m**4 + 2*m**3.
3*m*(m - 1)**2*(3*m + 1)**2
Let g(j) be the first derivative of -10*j**3/27 - 13*j**2/9 + 4*j/3 - 6. Suppose g(f) = 0. Calculate f.
-3, 2/5
Factor 27/7*k**2 + 3/7 + 3*k**3 + 15/7*k + 6/7*k**4.
3*(k + 1)**3*(2*k + 1)/7
Let p(g) be the second derivative of g**4/60 - 2*g**2/5 + 19*g. Factor p(d).
(d - 2)*(d + 2)/5
Factor 3*p - 9/4 - 3/4*p**2.
-3*(p - 3)*(p - 1)/4
Let i(b) be the second derivative of b**4/84 - b**3/21 - 4*b**2/7 - 41*b. Find k such that i(k) = 0.
-2, 4
Let x(a) be the first derivative of 4/15*a**5 + 0*a**2 + 0*a**3 + 0*a - 1/6*a**4 - 2 + 1/3*a**6. Factor x(r).
2*r**3*(r + 1)*(3*r - 1)/3
Let i(n) be the second derivative of -n**8/2520 - n**7/420 - n**6/180 - n**5/180 + n**3/2 + n. Let y(p) be the second derivative of i(p). Factor y(a).
-2*a*(a + 1)**3/3
Let b(l) be the third derivative of l**6/120 - l**4/8 + l**3 + l**2. Let v(d) be the first derivative of b(d). Factor v(y).
3*(y - 1)*(y + 1)
Let b(k) be the second derivative of k**6/75 - k**5/25 - k. Determine v, given that b(v) = 0.
0, 2
Let q be 2/(-3)*(-30)/5. Factor -2*g**2 + 12 + q*g**3 - 12 - 2*g**4.
-2*g**2*(g - 1)**2
Suppose 2 = 5*w - 8. Suppose 0*c**3 - w + 2*c**2 + 2*c**3 - 3*c + c**3 = 0. Calculate c.
-1, -2/3, 1
Let u(f) be the third derivative of 2*f**2 + 0*f + 1/10*f**5 + 1/60*f**6 + 0 + 1/4*f**4 + 1/3*f**3. Factor u(a).
2*(a + 1)**3
Factor -24/5*j**2 + 0*j - 21/5*j**3 + 0 + 3/5*j**4.
3*j**2*(j - 8)*(j + 1)/5
Let v(r) = r - 2. Let w be v(4). Factor w*n**2 - 2*n + 5*n + n + 2.
2*(n + 1)**2
Let i(r) be the third derivative of -r**6/420 - r**5/105 + r**4/21 + 8*r**3/21 + 9*r**2 + 5*r. Let i(a) = 0. What is a?
-2, 2
Let o(j) = j**3 + j**2 - j + 5. Let k be o(0). Factor -3*n**2 + 8*n**k - 3*n**3 + 2*n - 5*n**5 - 2*n + 3*n**4.
3*n**2*(n - 1)*(n + 1)**2
Let r = -15 + 18. Find u, given that 3*u**2 + 5*u**2 + 0*u**3 - 16*u**2 - 6*u**4 - 16*u**r = 0.
-2, -2/3, 0
Let i(o) be the first derivative of -o**7/525 + o**6/150 - o**5/150 + 2*o**2 + 5. Let f(h) be the second derivative of i(h). Factor f(d).
-2*d**2*(d - 1)**2/5
Let i(f) = f**2 - 13*f + 21. Let q be i(12). Suppose 6 = 5*o - q. Factor 0*u + 0 + 2/7*u**o + 0*u**2.
2*u**3/7
Let p(x) be the third derivative of x**7/42 + x**6/3 + 11*x**5/6 + 5*x**4 + 15*x**3/2 - 18*x**2. Let p(s) = 0. Calculate s.
-3, -1
Let y(r) = r. Let z(q) = -14. Let o(m) = y(m) - z(m). Let d be o(-14). Factor 0*p + d - 2/5*p**3 - 1/5*p**4 + 0*p**2.
-p**3*(p + 2)/5
Let q be 0*3/6 + 2. Suppose u - q*u = 0. Determine b so that 2/5*b**2 - 4/5*b + u = 0.
0, 2
Let c(p) = 4*p**5 - 13*p**4 - 3*p**3 + 27*p**2 - 33*p + 8. Let b(u) = -7*u**2 + u - u**3 + 8*u**2 + 5*u**4 - 4*u**4. Let a(q) = -5*b(q) - c(q). Factor a(s).
-4*(s - 1)**4*(s + 2)
Let -20*o - 20*o**2 - 15*o**4 + 18*o**4 - 73*o**5 + 17*o**4 + 78*o**5 + 15*o**3 = 0. What is o?
-2, -1, 0, 1
Let r(o) be the second derivative of o**5/60 - o**4/8 + o**3/3 + 2*o**2 + o. Let h(a) be the first derivative of r(a). Factor h(m).
(m - 2)*(m - 1)
Suppose 0*a + 0*a**2 + 6/5*a**4 + 0 + 0*a**3 - 2/5*a**5 = 0. What is a?
0, 3
Suppose 3 = 3*i, 0 = -5*j + j + 5*i + 7. Suppose -3*v + 18 = 3*l, -5*l = v - j*v - 2. Factor 7*d**2 + l*d**3 + 2*d + 7*d + 4 - 2 - 2*d.
(d + 1)*(d + 2)*(2*d + 1)
Let o(r) be the second derivative of -5*r**4/72 + 25*r**3/6 - 375*r**2/4 - 23*r. Factor o(c).
-5*(c - 15)**2/6
Let a(h) be the first derivative of -h**6 - 4*h**5/5 + 3*h**4 + 8*h**3/3 - 3*h**2 - 4*h - 7. What is q in a(q) = 0?
-1, -2/3, 1
Let t(r) be the second derivative of -r**6/45 - r**5/20 - r**4/36 + 6*r. Factor t(z).
-z**2*(z + 1)*(2*z + 1)/3
Let b(l) = 8*l**2 + 5. Let q(k) = 12*k**2 + 8. Let a be (-3 - 0)/((-27)/72). Let s(w) = a*b(w) - 5*q(w). Suppose s(x) = 0. What is x?
0
Suppose 2*j = -j + 9. Suppose -7 = -5*w + j. Suppose 0*c**2 + 4*c + 6 - 3*c**w + c**4 - 2*c**3 - 2 = 0. Calculate c.
-1, 2
Let n = -79 - -82. Factor -2*f + 8/5*f**2 + 4/5 - 2/5*f**n.
-2*(f - 2)*(f - 1)**2/5
Factor -2/7 + 4/7*m + 0*m**2 - 4/7*m**3 + 2/7*m**4.
2*(m - 1)**3*(m + 1)/7
Let u(t) be the second derivative of -t**4/12 + 2*t**2 + 30*t. Let u(m) = 0. What is m?
-2, 2
Let b(m) = -m**2 - 11*m + 12. Let c be b(-11). Let w be ((-4)/c)/((-9)/6). Suppose w - 2/9*k**2 + 0*k = 0. Calculate k.
-1, 1
Let g(t) = -3*t**5 - 7*t**4 - t**3 + 3*t**2 - 4*t. Let p(x) = x**4 + x**3 + x. Let f(k) = g(k) + 4*p(k). Find d such that f(d) = 0.
-1, 0, 1
Suppose 0*b = -3*b + 5*p + 23, -2*p = b - 4. Let i be 2/10 + b/(-30). Factor -4*f**2 + 2*f**4 + 1 + i*f**2 + 1.
2*(f - 1)**2*(f + 1)**2
Let m(c) = 4*c**3 - 10*c**2 + 6*c. Let h(v) = 12*v**3 - 29*v**2 + 17*v. Let z(d) = 2*h(d) - 7*m(d). Factor z(s).
-4*s*(s - 2)*(s - 1)
Let j(r) be the first derivative of 5*r**3/6 - 15*r**2/4 + 5*r + 36. Factor j(g).
5*(g - 2)*(g - 1)/2
Suppose 77 = -4*o - m, o = m - 5 - 8. Let z be 4/o + (-200)/(-90). Suppose -1/5*s + 0*s**z + 1/5*s**3 + 0 = 0. What is s?
-1, 0, 1
Suppose -l = 2*l - 6. Let z be (-5 + 3)/(l + -3). Factor 3*i**z - 2*i**3 - 4*i**2 + 3*i**2.
-2*i**2*(i - 1)
Suppose -3*t + 2*m = -10, -4*m + 3*m = 2. Suppose -4*i + i = 2*x - 10, 0 = -4*i - t*x + 10. Let 4/3*f + i - 2/3*f**2 = 0. What is f?
0, 2
Let t(o) be the first derivative of 1/90*o**5 + 0*o + 0*o**2 - 1/540*o**6 - 1 - 2/3*o**3 - 1/36*o**4. Let m(k) be the third derivative of t(k). Factor m(d).
-2*(d - 1)**2/3
Factor 6 + 11*x + 9*x + 4*x**2 + 10.
4*(x + 1)*(x + 4)
Let y(m) = m**2 + m - 1. Let k(p) be the third derivative of 7*p**4/24 - 5*p**3/3 + 4*p**2. Let d(j) = 2*k(j) - 2*y(j). Factor d(g).
-2*(g - 3)**2
Let y(l) = l**3 + 1. Let w(b) = b**3 + 22*b**2 + 24*b + 3. Suppose -16 = 3*x + n, -7 + 3 = x - n. Let r(d) = x*y(d) - w(d). Determine z so that r(z) = 0.
-2, -1, -2/3
Let f(h) be the first derivative of 4*h**5/5 + 3*h**4 + 4*h**3 + 2*h**2 + 15. Factor f(n).
4*n*(n + 1)**3
Find o, given that 0 - 10*o**2 + 0*o - 5/3*o**3 = 0.
-6, 0
Determine n so that 8*n**4 - 8*n**4 + 6*n**3 - 3*n - 17*n**5 + 14*n**5 = 0.
-1, 0, 1
Factor -3*u**2 + 6 + 3*u + 6 - 6.
-3*(u - 2)*(u + 1)
Let c = 76/423 + 2/47. Solve 0*d + c*d**4 - 2/9*d**5 + 0*d**3 + 0 + 0*d**2 = 0.
0, 1
Let b(w) be the third derivative of -w**5/16 + w**4/4 + w**3/2 - 18*w**2. Factor b(h).
-3*(h - 2)*(5*h + 2)/4
Let j = 11 - 6. Let z(o) = 14*o**3 + 38*o**2 + 16*o - 13. Let v(w) = -7*w**3 - 19*w**2 - 8*w + 6. Let g(x) = j*v(x) + 2*z(x). Factor g(u).
-(u + 1)*(u + 2)*(7*u - 2)
Let c be 16*(33/(-18) + 2 - 0). Suppose 8/9 - c*y + 10/9*y**2 = 0. What is y?
2/5, 2
Let x(q) be the third derivative of 0 - 1/5*q**3 + 0*q - 9/100*q**5 + 7/40*q**4 + 1/40*q**6 + 8*q**2 - 1/350*q**7. Factor x(c).
-3*(c - 2)*(c - 1)**3/5
Let x be (-14)/(-5)*(19 - -4). Let w = x - 64. Determine d so that 2/5*d - w + 2/5*d**2 - 2/5*d**3 = 0.
-1, 1
Let x(p) be the first derivative of -p**5/25 - p**4/20 - 3. Factor x(t).
-t**3*(t + 1)/5
Let g(f) = 3*f**3 + 5*f**2 - 11*f + 11. Let r = 22 + -14. Let h(d) = -d**3 - 2*d**2 + 4*d - 4. Let b(u) = r*h(u) + 3*g(u). Factor b(x).
(x - 1)**2*(x + 1)
Factor 2/7*g**2 + 6/7*g**3 - 4/7 - 6/7*g + 2/7*g**4.
2*(g - 1)*(g + 1)**2*(g + 2)/7
Factor g**3 - 2*g + 2*g - g + 2*g**2 + 2 - 4.
(g - 1)*(g + 1)*(g + 2)
Determine w, given that -5/6*w - 1/3*w**2 - 1/3 + 1/6*w**5 + 2/3*w**4 + 2/3*w**3 = 0.
-2, -1, 1
Let l(m) = -m**2 + m - 1. Let j(i) = -7*i**2 + 10*i - 10. Let o(k) = k**2