 + 317/8. Let r(b) be the first derivative of -3/16*b**2 + w*b - 12 - 1/32*b**4 + 1/8*b**3. Let r(j) = 0. Calculate j.
1
Let o = 3316/9 - 368. Factor 2/9*a**2 + 2/3*a + o.
2*(a + 1)*(a + 2)/9
Suppose 2*t - 293 = -5*x - 2*t, x - 4*t - 73 = 0. Let o = x - 43. Factor 24*s**2 + 0*s - 6*s - 45*s**2 - o*s**3 + 3*s**3.
-3*s*(s + 1)*(5*s + 2)
Let o(j) be the second derivative of j**4/48 + j**3/24 - j**2/4 - 46*j. Factor o(u).
(u - 1)*(u + 2)/4
Let d(j) = -6*j**5 - 7*j**4 - 6*j**3 + 2*j**2 - 8*j. Let h(s) = -s**5 - s**4 - 2*s**3 - s. Let y(x) = d(x) - 5*h(x). Let y(v) = 0. What is v?
-3, -1, 0, 1
Suppose -21 - 39 = k. Let v = -58 - k. Factor 1/4*z**4 + 1/4*z + 1/4*z**5 - 1/2*z**3 - 1/2*z**v + 1/4.
(z - 1)**2*(z + 1)**3/4
Let i(x) = 11*x**3 - 14*x**2 + 4. Let g(w) = -9*w**3 + 15*w**2 - 3. Let r(o) = -4*g(o) - 3*i(o). What is j in r(j) = 0?
0, 6
Let d(h) = -h**2 + 14*h + 2. Let l be d(10). Suppose 6 - l*z**2 + 62*z**2 + 9*z - 6*z**3 - 29*z**2 = 0. What is z?
-2, -1/2, 1
Let p = 2259 + -2259. Factor -21*y**3 + 9/2*y**4 + p - 2*y + 25/2*y**2.
y*(y - 4)*(3*y - 1)**2/2
Factor 2*y**2 + 27*y**2 - 25*y**2 - 236*y.
4*y*(y - 59)
Let v be (268/670)/(16/10). Let 1/4 + 3/4*m + v*m**3 + 3/4*m**2 = 0. What is m?
-1
Let r(i) = -2*i**4 - 8*i**3 + 2*i**2 + 2*i. Let x(d) = d**4 + 8*d**3 - d**2 - 3*d. Let k(v) = -5*r(v) - 6*x(v). Find c such that k(c) = 0.
-1, 0, 1, 2
Factor 1/6*x**4 + 0 + 5/3*x + 17/6*x**2 + 4/3*x**3.
x*(x + 1)*(x + 2)*(x + 5)/6
Let k(w) = -w**2 + 32*w - 58. Let v be k(24). Let f = -134 + v. Find m such that f*m + 0*m**2 + 0*m**3 - 1/4*m**4 + 0 = 0.
0
Suppose 20/7*a**4 + 72/7*a + 2/7*a**5 + 0 + 120/7*a**2 + 74/7*a**3 = 0. Calculate a.
-3, -2, 0
Let s(j) be the first derivative of -22 - 1/4*j**2 - 1/18*j**3 + 2/3*j. Factor s(m).
-(m - 1)*(m + 4)/6
Suppose 3*d**4 - 9*d**4 + 45*d**3 + 9*d**4 - 105*d**2 + 2*d**4 + 55*d = 0. Calculate d.
-11, 0, 1
Let h(m) be the first derivative of m**9/18144 + m**8/5040 - m**6/1080 - m**5/720 + m**3 - 19. Let q(d) be the third derivative of h(d). Factor q(s).
s*(s - 1)*(s + 1)**3/6
Let a(m) be the first derivative of 2*m**6/15 + 14*m**5/25 + 3*m**4/10 + 53. Solve a(p) = 0.
-3, -1/2, 0
Let a(j) = 3*j**3 + 9*j**2 + 3*j. Let k(c) = -2*c**3 - 5*c**2 - 2*c. Let b(f) = -3*a(f) - 5*k(f). Factor b(l).
l*(l - 1)**2
Let m(g) = -11*g + 37. Let y be m(3). Let a(k) be the first derivative of -2/33*k**3 + 0*k**2 - 1/22*k**y + 7 + 0*k. Suppose a(t) = 0. What is t?
-1, 0
Suppose 3*o - 4 = 2*o. Let l be (-5)/(-10) + 22/o. Factor -9*x**3 - 5*x**2 + 10*x**3 + l*x**2.
x**2*(x + 1)
Let q(r) = r**2 - 33*r - 537. Let d be q(45). Factor 15/8*h - 3/8*h**d + 3/8*h**2 + 9/8.
-3*(h - 3)*(h + 1)**2/8
Let j(o) be the second derivative of -o**6/72 + o**5/9 - 5*o**4/24 + 9*o**2/2 + 7*o. Let r(s) be the first derivative of j(s). Determine p, given that r(p) = 0.
0, 1, 3
Let g = -10797 - -1360439/126. Let n = 5/14 - g. Factor -4/9*i - 2/9 - n*i**2.
-2*(i + 1)**2/9
Let n(z) = -7*z - 9. Let c = -31 + 24. Let t be n(c). Suppose t*x**2 - x**4 - 40*x**2 = 0. Calculate x.
0
Let z(t) be the second derivative of -t**7/42 + 3*t**5/20 - t**4/6 + 17*t - 5. What is j in z(j) = 0?
-2, 0, 1
Let t(g) = 5*g**3 - 31*g**2 + 72*g - 4. Let c(m) = 36*m**3 - 216*m**2 + 504*m - 30. Let d(j) = -2*c(j) + 15*t(j). Let d(p) = 0. What is p?
0, 3, 8
Let z be (-261)/(-315) - (48/(-15))/(-4). Let p(q) be the first derivative of 0*q**2 - 2 + 0*q + 1/14*q**4 + z*q**5 + 1/21*q**3. Factor p(x).
x**2*(x + 1)**2/7
Let q(u) be the first derivative of u**6/5 - 3*u**5/20 - 3*u**4/2 + 7*u**3/2 - 3*u**2 - 24*u - 11. Let m(d) be the first derivative of q(d). Factor m(c).
3*(c - 1)**2*(c + 2)*(2*c - 1)
Let s(d) = d**3 - 5*d**2 + 3*d. Let n be s(4). Let r(l) = 5*l**2 - 5*l - 11. Let i(y) = 2*y**2 - 2*y - 4. Let g(b) = n*r(b) + 11*i(b). Factor g(p).
2*p*(p - 1)
Let i(l) be the first derivative of 4*l**3/3 - 10*l**2 + 24*l + 69. What is s in i(s) = 0?
2, 3
Let d(u) = -7*u**2. Suppose 21 + 39 = 4*q. Let t(g) = -28*g + 28*g + q*g**2. Let l(a) = 13*d(a) + 6*t(a). Factor l(h).
-h**2
Let h(c) be the third derivative of -c**5/30 + 7*c**4/6 + c**2 + 10*c. Factor h(w).
-2*w*(w - 14)
Let u = -10/171 - -4838/855. Factor 44/5*t**2 - 8/5*t + 0 + u*t**4 - 64/5*t**3.
4*t*(t - 1)**2*(7*t - 2)/5
Let i(q) be the third derivative of q**8/100800 + q**7/2100 + q**6/100 + 19*q**5/30 + 42*q**2. Let d(g) be the third derivative of i(g). Factor d(o).
(o + 6)**2/5
Let d(f) = f**3 + 9*f**2 + 2. Let u be d(-9). Factor 6*v**u + 117 - 107 - v**2 + 15*v.
5*(v + 1)*(v + 2)
Let c be 4/(-20) - (44/(-20) + 0). Suppose 3*l**2 - l**4 + 3 - l**2 + 2*l**2 - 8*l + c*l**2 = 0. Calculate l.
-3, 1
Let z(s) be the second derivative of 0 - 1/12*s**4 + 1/20*s**5 + 1/60*s**6 - 1/12*s**3 + 9*s + 1/4*s**2 - 1/84*s**7. Factor z(r).
-(r - 1)**3*(r + 1)**2/2
Let q = 727 - 727. Let k(p) be the third derivative of q + 0*p - 1/80*p**6 + 8*p**2 + 1/6*p**3 + 1/16*p**4 - 1/420*p**7 - 1/120*p**5. Let k(h) = 0. Calculate h.
-2, -1, 1
Let l(d) be the second derivative of 1/12*d**4 + 1/6*d**3 + 10*d + 0 - 1/20*d**5 - 1/2*d**2. Factor l(v).
-(v - 1)**2*(v + 1)
Let l(g) = 5*g**3 - 3*g**2 + 8. Suppose 2*j = 5*v + 19, 9 = -4*v + v. Let f(p) = p**3 + p**2. Let z(r) = j*l(r) - 6*f(r). Find k, given that z(k) = 0.
-1, 2
Suppose -9*k + 80 = -4*k. Let i be (-36)/16*k/(-6). Let i*n**3 - n + 22*n**3 + 16*n**2 - 16*n**4 + 7*n - 22*n - 12*n**5 = 0. What is n?
-2, -1, 0, 2/3, 1
Let k be (-2)/(8/(-1)) - 45/(-100). Let o(p) be the second derivative of 8*p**2 + 1/15*p**6 - k*p**5 + 0 - 20/3*p**3 - 5*p + 3*p**4. Factor o(u).
2*(u - 2)**3*(u - 1)
Let -18/7*x**3 + 0*x + 0*x**2 + 6/7*x**4 + 0 = 0. What is x?
0, 3
Let y(p) be the first derivative of p**3/2 + 3*p**2/2 - 9*p/2 + 267. Factor y(b).
3*(b - 1)*(b + 3)/2
Let k be 0 - (-25)/4 - (145 - 139). Suppose 0 = 2*s - 5*s. Solve 1/2*z**2 - 1/4*z - k*z**3 + s = 0 for z.
0, 1
Let y(a) = a + 1. Let p(t) = -16*t + 5. Let h(g) = p(g) - 3*y(g). Let w be h(-1). Factor 30*q - w*q + 3*q**3 - 8*q**3 - 14*q + 10*q**2.
-5*q*(q - 1)**2
Let t(w) = -w**2 + w - 5. Let a(m) = 5*m**2 + 14*m - 70. Let s(b) = 5*a(b) + 30*t(b). Let s(k) = 0. What is k?
10
Let h(u) be the third derivative of u**7/42 - 4*u**6/3 + 32*u**5 - 1280*u**4/3 + 10240*u**3/3 - 276*u**2. Factor h(g).
5*(g - 8)**4
Let i be -1 + 35/5 - -2. Let v(g) = -6*g**2 + 14. Let u(x) = x**2 + x**2 + 0 - 5. Let w(c) = i*u(c) + 3*v(c). Solve w(k) = 0 for k.
-1, 1
Let j(t) be the third derivative of 0*t**3 + 0*t - 19*t**2 - 1/168*t**7 + 1/48*t**5 + 0 + 0*t**6 + 0*t**4. Factor j(c).
-5*c**2*(c - 1)*(c + 1)/4
Let b(k) be the third derivative of -k**7/1680 - k**6/120 - k**5/80 + k**4/24 + 7*k**3/48 - 57*k**2 + 2*k. Determine a, given that b(a) = 0.
-7, -1, 1
Let h(v) = -4*v**2 + 4*v. Let y(m) = -17 + 3*m + 17 - 4*m. Let z(f) = -h(f) - 4*y(f). Suppose z(i) = 0. Calculate i.
0
Let x(q) be the first derivative of 0*q**5 + 5 - 1/540*q**6 + 0*q + 1/108*q**4 + 0*q**3 + 7/2*q**2. Let t(m) be the second derivative of x(m). Factor t(l).
-2*l*(l - 1)*(l + 1)/9
Let x(s) = -s**3 + 2*s**2 + 8*s + 3. Let v(j) = 23*j - 42. Let o be v(2). Let u be x(o). Factor 0*z**2 + 12/5*z + 0 - 3/5*z**u.
-3*z*(z - 2)*(z + 2)/5
Let l(c) be the first derivative of c**4/3 - 2*c**3 - 23*c + 23. Let u(y) be the first derivative of l(y). Factor u(v).
4*v*(v - 3)
Let a(q) be the second derivative of 2*q**6/5 - 9*q**5/20 - 9*q**4/4 - q**3 - 2*q + 5. Factor a(x).
3*x*(x - 2)*(x + 1)*(4*x + 1)
Let g = 188 - 188. Let k(a) be the first derivative of 12/5*a**5 + 4 + 0*a + 2/3*a**3 + 2/3*a**6 + g*a**2 + 9/4*a**4. Solve k(o) = 0 for o.
-2, -1/2, 0
Let d(u) be the first derivative of -1/10*u**5 + 0*u + 21 - 7/12*u**3 - 13/32*u**4 - 5/16*u**2. Factor d(h).
-h*(h + 1)**2*(4*h + 5)/8
Factor 27*j**2 - 3*j**2 + 6*j**4 - 9*j**3 + 3*j**5 + j**4 - 12*j - 13*j**4.
3*j*(j - 2)*(j - 1)**2*(j + 2)
Let a(w) = 67*w**3 + 5 - 34*w**3 + w**2 - 34*w**3 - 5*w. Let r be a(1). Factor r + 4/5*i**2 - 4/5*i.
4*i*(i - 1)/5
Let s(c) be the third derivative of 0 - 6/5*c**5 + 0*c + 13*c**2 + 7/30*c**6 - 16/3*c**3 - 2/105*c**7 + 10/3*c**4. Factor s(p).
-4*(p - 2)**3*(p - 1)
Let k(q) = 10*q**4 + 27*q**3 - 29*q**2 - 67*q - 7. Let l(g) = 7*g**4 + 18*g**3 - 19*g**2 - 45*g - 5. Let c(n) = 5*k(n) - 7*l(n). Factor c(z).
z*(z - 2)*(z + 1)*(z + 10)
Let v(y) be the second derivativ