*4. Factor -6*a + a**3 - 9/2 - v*a**2.
(a - 3)*(a + 1)*(2*a + 3)/2
Let i(c) = -3*c**4 + 29*c**3 - 18*c**2 - 106*c + 5. Let a(z) = 4*z**4 - 43*z**3 + 26*z**2 + 158*z - 7. Let b(o) = 5*a(o) + 7*i(o). Factor b(f).
-f*(f - 2)*(f + 2)*(f + 12)
Let f(l) be the first derivative of -4*l**3 + 3/2*l**2 - 3/4*l**4 - 3 + 12*l. Find k such that f(k) = 0.
-4, -1, 1
Let l(c) = -8*c**5 - 81*c**4 - 121*c**3 - 18*c**2 - 9*c. Let v(z) = -2*z**5 - 20*z**4 - 30*z**3 - 4*z**2 - 2*z. Let s(d) = 4*l(d) - 18*v(d). Factor s(h).
4*h**3*(h + 2)*(h + 7)
Let b(r) be the second derivative of -r**4/24 - r**3/3 - r**2 - 256*r. Determine i so that b(i) = 0.
-2
Let s = 10906 - 10903. Factor 0 + 1/4*h**4 - 1/2*h**s + 0*h**2 + 0*h.
h**3*(h - 2)/4
Let c(b) be the third derivative of -b**6/540 - 2*b**5/135 - b**4/27 - 106*b**2. Factor c(z).
-2*z*(z + 2)**2/9
Let i(m) be the third derivative of 7*m**6/180 - m**5/30 - m**4/9 - 79*m**2. Factor i(d).
2*d*(d - 1)*(7*d + 4)/3
Factor 0 + 0*o + 3/2*o**2 + 3/4*o**3.
3*o**2*(o + 2)/4
Solve 28/9*k + 2/9*k**3 + 14/9*k**2 + 16/9 = 0 for k.
-4, -2, -1
Factor 2*v**2 - 42 + 0*v**2 + 24 + 0*v**2 - 8*v**2 + 21*v.
-3*(v - 2)*(2*v - 3)
Let h = 28 + -24. Find q, given that -h*q**2 - 2 + 2*q**2 + 10*q**2 + 7*q + q**2 = 0.
-1, 2/9
Let t be 1/(-2)*((-16)/(-4) + -10). Factor -l**4 - 2 - l**5 + 2*l - 4*l + 1 + 2*l**2 + l + 2*l**t.
-(l - 1)**2*(l + 1)**3
Let a(r) be the second derivative of -r**6/90 + r**3/2 + 4*r. Let t(o) be the second derivative of a(o). Suppose t(f) = 0. What is f?
0
Let m(i) be the third derivative of -i**5/80 - 119*i**4/32 - 59*i**3/4 - 17*i**2 - 2. Solve m(o) = 0 for o.
-118, -1
Solve -7*r**2 - 9*r**2 + 12*r**2 + 36*r - 28 + 1 - 5 = 0.
1, 8
What is y in -1366*y**2 + 24*y - 4*y**4 + 10*y**3 + 22*y**3 + 1314*y**2 = 0?
0, 1, 6
Let h(k) be the third derivative of -k**7/630 - 2*k**6/45 + 19*k**4/24 + 8*k**2. Let g(x) be the second derivative of h(x). Solve g(b) = 0.
-8, 0
Let u(c) = 20*c**2 + 12*c - 8. Let x(d) be the first derivative of 40*d**3/3 + 12*d**2 - 16*d + 11. Let v(h) = 5*u(h) - 2*x(h). Find g such that v(g) = 0.
-1, 2/5
Suppose -13*v - 18*v + v = 0. Let y(q) be the third derivative of 0*q + 0*q**3 + 0 + v*q**4 + 1/60*q**6 + 1/75*q**7 - 1/75*q**5 - 10*q**2. Factor y(s).
2*s**2*(s + 1)*(7*s - 2)/5
Suppose -7*y = -23 - 5. Factor 8*v**3 - 9 + 5 + 2*v**4 + 8*v**2 + y.
2*v**2*(v + 2)**2
What is q in -21*q**3 + 8*q**4 - 23*q**4 + 6*q**3 + 6*q**2 + 10*q**4 + 14*q**4 = 0?
0, 2/3, 1
What is g in g**2 - 1/8*g**3 - 13/8*g + 3/4 = 0?
1, 6
Suppose -623 - 472 = -15*v. Solve -v + 12*b**2 + 73 + b**4 - 13*b**3 = 0 for b.
0, 1, 12
Let v(o) be the third derivative of 5*o**2 + 1/15*o**3 + 0 + 1/300*o**5 + 0*o + 1/40*o**4. What is n in v(n) = 0?
-2, -1
Let a(y) = 14*y**3 + 6*y**2 - y - 13. Let t(h) = 5*h**3 + 2*h**2 - 4. Let q(b) = -4*a(b) + 11*t(b). Factor q(w).
-(w - 2)*(w + 2)**2
Suppose -13*j - 54 = -29*j - 2*j. Factor 5/3*p**4 + 20/3*p**2 + 0*p + 0 - 20/3*p**j.
5*p**2*(p - 2)**2/3
Suppose 0 = 3*p - 2*r + 7*r - 21, -8 = 2*p - 4*r. Solve 21*s**2 - 11*s**p + 2*s**4 - 10*s**2 = 0.
0
Let l(a) be the first derivative of 0*a - 13 + 1/3*a**3 + 1/2*a**2. Solve l(y) = 0.
-1, 0
Factor -3*k + 7/3*k**4 - 2/3 + 3*k**3 - 5/3*k**2.
(k - 1)*(k + 1)**2*(7*k + 2)/3
Suppose 4*i + 17 = 45. Find s, given that 2*s**2 - 6*s + i - 3 + 0*s**2 = 0.
1, 2
Let h(r) be the second derivative of -3/20*r**5 - 1/5*r**6 + 0*r**4 - r - 12 + 0*r**3 + 0*r**2 - 1/14*r**7. Let h(p) = 0. What is p?
-1, 0
Let a(r) be the second derivative of -r**6/70 + 9*r**5/70 - r**4/4 - 3*r**3/7 + 12*r**2/7 + 19*r - 4. What is z in a(z) = 0?
-1, 1, 2, 4
Suppose -2*z + 2*x = 0, -4*x = -2 - 6. Let i = z - -52. Factor 147/2*l**5 + 327/2*l**3 + 0 + 6*l - 189*l**4 - i*l**2.
3*l*(l - 1)**2*(7*l - 2)**2/2
Let f(r) be the second derivative of -r**7/70 + 7*r**6/50 - 21*r**5/50 + 2*r**4/5 - 16*r - 4. Find j such that f(j) = 0.
0, 1, 2, 4
Let h(k) be the first derivative of 3*k**4/4 + 5*k**3 + 9*k**2/2 - 27*k + 73. Solve h(r) = 0 for r.
-3, 1
Let x(k) be the third derivative of -64*k**7/735 + 17*k**6/35 - 163*k**5/210 + k**4/4 + 2*k**3/21 + 37*k**2. What is n in x(n) = 0?
-1/16, 1/4, 1, 2
Suppose -5*j = 3*y - 134, -j + 62 = j + 4*y. Suppose -4*h - j = -25. Factor -1/3*s**3 + 1/3*s + h*s**2 + 0.
-s*(s - 1)*(s + 1)/3
Let o = 2144/17 + -126. Determine c so that 2/17*c - o*c**3 - 6/17*c**2 + 4/17 + 2/17*c**4 = 0.
-1, 1, 2
Let m(l) be the third derivative of -l**5/480 - 53*l**4/96 + 36*l**2. Factor m(s).
-s*(s + 106)/8
Let c = -29 - -37. Solve -16*y**4 - 4*y**5 + 3*y**3 + c - 19*y**3 + 20*y + 5*y**2 + 3*y**2 = 0.
-2, -1, 1
Let l(y) be the third derivative of y**9/5040 + y**8/2520 - 2*y**5/5 + 9*y**2. Let z(q) be the third derivative of l(q). Factor z(k).
4*k**2*(3*k + 2)
Let r(g) be the third derivative of 1/15*g**5 + 14*g**2 + 0 + 0*g**3 + 0*g + 1/3*g**4. Suppose r(s) = 0. What is s?
-2, 0
Let r(v) be the first derivative of -5*v**6/6 - v**5 + 5*v**4/2 + 10*v**3/3 - 5*v**2/2 - 5*v + 130. Factor r(f).
-5*(f - 1)**2*(f + 1)**3
Let x(q) be the second derivative of q**7/1512 - q**6/72 + 5*q**5/72 - 13*q**4/12 + 31*q. Let k(i) be the third derivative of x(i). Solve k(z) = 0 for z.
1, 5
Let k(y) = y + 1. Let v be k(7). Let i = -3 + v. Factor i - 3 + 2 + 2*o**2 - 6*o.
2*(o - 2)*(o - 1)
Let d = 22 + -19. Factor -5*v + 17*v**3 + 5*v**4 + v - 7*v**d - 5*v**2 - 6*v.
5*v*(v - 1)*(v + 1)*(v + 2)
Let q(t) be the first derivative of -2/57*t**3 + 3/38*t**4 - 3/19*t**2 + 4/19*t - 2/95*t**5 + 10. Determine v, given that q(v) = 0.
-1, 1, 2
Let v(n) be the first derivative of 4*n**5/5 - 4*n**3 + 4*n**2 + 6. Determine h so that v(h) = 0.
-2, 0, 1
Let l(c) be the first derivative of 9 + 2/3*c**2 + 1/6*c**3 - 1/36*c**4 - 2*c. Let a(v) be the first derivative of l(v). Factor a(h).
-(h - 4)*(h + 1)/3
Let v = 1120 + -1120. Let d(r) be the second derivative of 1/3*r**4 + 5*r + 1/5*r**5 + v*r**3 + 0 + 0*r**2. Find m such that d(m) = 0.
-1, 0
Let h = 383/290 + -177/145. Let -11/10*d**2 - 1/10*d**4 + 9/10*d**3 + 0 + 2/5*d - h*d**5 = 0. Calculate d.
-4, 0, 1
Suppose -6*r + 12*r = -24. Let j be r + 4 + -4 + 9. Find v, given that -4/5*v**2 + 2/5 - 2/5*v + 2/5*v**4 - 2/5*v**j + 4/5*v**3 = 0.
-1, 1
Let z(g) be the second derivative of g**6/6 + 3*g**5/4 + 5*g**4/12 - 5*g**3/2 - 5*g**2 + g + 43. Let z(h) = 0. Calculate h.
-2, -1, 1
Determine c, given that c**2 + 729 - 25*c**2 + 0*c**2 + 54*c + 25*c**2 = 0.
-27
Let v(q) = q**2 - 3*q + 3. Let b be v(3). Let y = -1 + b. Suppose 6*z - 3*z**4 + z**2 - 3*z**4 + 3*z**4 + y*z**2 - 6*z**3 = 0. What is z?
-2, -1, 0, 1
Suppose -7*t + 16*t - 38*t = 0. Factor 0 - 2/7*z**4 + t*z + 6/7*z**3 - 4/7*z**2.
-2*z**2*(z - 2)*(z - 1)/7
Let g(m) = 1. Let z be 24/14 + -2 - (-690)/161. Let c(j) = 2*j**2 - 10*j + 4. Let p(k) = z*g(k) + c(k). Factor p(b).
2*(b - 4)*(b - 1)
Let c be (-4500)/(-495) - (-1)/(-11). Let s be (c/(-12))/((-4)/(-3) - 2). What is d in 0 - s*d + 3/8*d**2 = 0?
0, 3
Let g(s) be the first derivative of -6 - 1/5*s**3 - 2/5*s + 7/10*s**2 + 4/25*s**5 - 2/5*s**4. Find z, given that g(z) = 0.
-1, 1/2, 2
Suppose -9*j - 23 = -41. Let k(h) be the second derivative of 0*h**2 - 14/27*h**4 + j*h + 23/30*h**5 + 0 - 14/27*h**6 + 4/27*h**3 + 25/189*h**7. Solve k(t) = 0.
0, 2/5, 1
Let r(m) be the first derivative of m**6/360 + 4*m**5/15 + 32*m**4/3 - 3*m**3 - 34. Let a(i) be the third derivative of r(i). Let a(v) = 0. What is v?
-16
Let o(a) = 10*a**4 + 25*a**3 + 5. Let b(t) = -15*t**4 + 10*t**4 - 12*t**3 + 2 - 5. Let q(h) = -5*b(h) - 3*o(h). Determine u so that q(u) = 0.
-3, 0
Let c(f) = 4*f - 33. Let x be c(8). Let h be 5*(0 + x)/(5/(-2)). Let h*i**2 - 4/3*i + 0 = 0. Calculate i.
0, 2/3
Suppose 27*u - 95 = u + 9. Solve -2/5*n**5 - 8/5*n**u + 0 - 12/5*n**3 - 2/5*n - 8/5*n**2 = 0 for n.
-1, 0
Solve 9/8*u - 3/8 + 9/8*u**4 - 3/8*u**5 - 3/4*u**3 - 3/4*u**2 = 0.
-1, 1
Let d be (6 + (-16)/4)*2. Let h(f) = -80*f**d + 71*f**4 + 6*f**2 - 3*f**2 - 6*f. Let m(y) = 19*y**4 - 6*y**2 + 13*y. Let n(x) = 13*h(x) + 6*m(x). Factor n(v).
-3*v**2*(v - 1)*(v + 1)
Let v be ((-6)/(-4))/((-27)/(-288)). Suppose 12*l**3 - 12 - l - 20*l**2 + 6*l - l + v = 0. Calculate l.
-1/3, 1
Factor -779*g - 71*g**2 - 1573*g + 391*g**3 + 239*g**2 - 394*g**3.
-3*g*(g - 28)**2
Factor 30 - 2*y**2 - 95*y - 22 - 2*y**3 + 103*y.
-2*(y - 2)*(y + 1)*(y + 2)
Find d,