- 41 - 12*a**2 - 65*a + 9.
-4*(a + 4)*(3*a + 2)
Let w(s) be the first derivative of -4*s**3/9 + 11*s**2/9 + 4*s/9 - 19. Suppose w(y) = 0. Calculate y.
-1/6, 2
Let i(h) be the third derivative of 0 - 1/15*h**5 - 5*h**2 + 0*h**3 + 1/3*h**4 + 0*h. What is t in i(t) = 0?
0, 2
Let f(v) = v**2 + 4*v - 3. Let b be f(-5). Suppose 2*r = -2*j + 14, 18 = j - b*j + 4*r. Find g such that -2*g + 5 - 2*g**2 + j*g**4 + 2*g**3 - 5 = 0.
-1, 0, 1
Suppose -11*g + 9*g + 2 = 0. Let f(l) = 3*l**5 + 3*l**4 + 6*l**3 + 6*l**2 + 6. Let v(s) = -s**4 + s**2 + 1. Let z(c) = g*f(c) - 6*v(c). Factor z(u).
3*u**3*(u + 1)*(u + 2)
Let t(u) be the second derivative of -4/21*u**3 + u + 2/35*u**5 + 1/14*u**4 - 4/7*u**2 + 0 + 1/105*u**6. Determine c so that t(c) = 0.
-2, -1, 1
Let i = -16 + 10. Let j(g) = g**3 + g - 1. Let d(u) = -4*u**3 - 2*u**2 - 4*u + 3. Let p(h) = i*j(h) - 2*d(h). Factor p(y).
2*y*(y + 1)**2
Suppose 0 = -b - 3*v + 4*v + 4, 4*b + 5*v = 7. Suppose -c + b*c = 0. What is k in 2 + 1 + 0 + c*k**2 - 3*k**2 = 0?
-1, 1
Let d(p) be the third derivative of p**6/600 + p**5/50 + p**4/10 + 4*p**3/15 + 6*p**2. Determine g so that d(g) = 0.
-2
Factor -64/3 - 4/3*u**2 + 32/3*u.
-4*(u - 4)**2/3
Let o(q) be the third derivative of 0*q + 1/25*q**5 + 1/350*q**7 + 0*q**4 + 1/50*q**6 + 0*q**3 + q**2 + 0. Factor o(w).
3*w**2*(w + 2)**2/5
Let q(c) be the second derivative of -c**4/4 + 2*c**3 - 9*c**2/2 - 15*c. Solve q(g) = 0 for g.
1, 3
Find q, given that 13*q**4 + 5*q**3 - q**3 - 6*q**2 - 16*q**4 + 5*q**3 = 0.
0, 1, 2
Let b be (40/24*-1)/((-10)/12). Factor 2/5 - 1/5*w - 1/5*w**b.
-(w - 1)*(w + 2)/5
Factor 21/10*x**2 + 3/10 + 9/10*x**3 - 17/10*x.
(x + 3)*(3*x - 1)**2/10
Let h(y) = y**2 - 12*y - 21. Let b(s) be the first derivative of -4*s**3/3 + 30*s**2 + 104*s - 3. Let t(j) = 3*b(j) + 14*h(j). Factor t(w).
2*(w + 3)**2
Let y(k) = 2*k + 35. Let p be y(-16). Find t, given that -2/9*t**p + 2/9*t - 2/9*t**4 + 2/9*t**2 + 0 = 0.
-1, 0, 1
Suppose 0 = -3*x + 7*x - 20. Suppose 2*w**2 - w**2 + w**2 - x*w**3 = 0. Calculate w.
0, 2/5
Let y(b) = -b**3 - 3*b**2 + 3. Let n be y(-3). Factor -5*o**n + 1 + 3 + 20*o**2 - 16*o - 3*o**2.
-(o - 2)*(o - 1)*(5*o - 2)
Let r(m) be the second derivative of -2*m**6/15 - 2*m**5/5 + 4*m**3/3 + 2*m**2 - 16*m. What is s in r(s) = 0?
-1, 1
Let y be 10/9 + 2/(-3). Let a(b) be the first derivative of 4/3*b - 1/3*b**2 + 1 + 1/6*b**4 - y*b**3. Factor a(i).
2*(i - 2)*(i - 1)*(i + 1)/3
Factor 0*o + 2/13*o**2 - 18/13.
2*(o - 3)*(o + 3)/13
Let c(w) be the third derivative of 0 + 0*w + 1/36*w**6 - 1/9*w**3 + w**2 - 5/36*w**4 - 1/30*w**5 + 4/315*w**7. Suppose c(f) = 0. Calculate f.
-1, -1/4, 1
Let y(d) be the second derivative of d**4/4 + d**3/2 - 7*d. Determine t so that y(t) = 0.
-1, 0
Suppose -29*x + u + 1 = -32*x, -2*x + 5 = -5*u. Suppose -1/7*m**5 + 0 + 1/7*m**3 + 0*m**2 + x*m + 0*m**4 = 0. What is m?
-1, 0, 1
Let z(a) be the third derivative of a**6/30 - a**5/15 - 15*a**2. Factor z(v).
4*v**2*(v - 1)
Let d(k) be the first derivative of -k**8/840 + k**7/105 - k**6/30 + k**5/15 - k**4/12 - 5*k**3/3 - 5. Let b(n) be the third derivative of d(n). Factor b(a).
-2*(a - 1)**4
Let a(t) = -3*t**4 - 32*t**3 + 139*t**2 - 5*t - 864. Let v(b) = -5*b**4 - 48*b**3 + 208*b**2 - 8*b - 1296. Let c(f) = 8*a(f) - 5*v(f). Factor c(z).
(z - 6)**3*(z + 2)
Let g = 16 - 10. Suppose g*s - 4*s = 0. Factor -1/3*w**3 + s*w**2 + 1/3*w + 0.
-w*(w - 1)*(w + 1)/3
Let i(f) be the first derivative of 2*f**5/25 + f**4/10 - 2*f**3/15 - f**2/5 - 4. Factor i(p).
2*p*(p - 1)*(p + 1)**2/5
Let o be (27/(-21))/(6/(-16)). Let 2/7 + 26/7*i**2 + o*i**3 + 8/7*i**4 + 12/7*i = 0. Calculate i.
-1, -1/2
Let y(r) = -r**2 - 4*r - 1. Let g be y(-3). What is i in -4 - 3*i**4 + 4 + i**4 + g*i**2 = 0?
-1, 0, 1
Factor 0 - 3/2*r**2 - 3/2*r**5 + 3/2*r**4 + 0*r + 3/2*r**3.
-3*r**2*(r - 1)**2*(r + 1)/2
Let d(c) be the first derivative of c**4/8 - 11*c**3/18 + 5*c**2/12 + c/2 + 23. Find o such that d(o) = 0.
-1/3, 1, 3
Let y = 10 + -9. Suppose 5 = 3*k - y. Suppose 3/2*s**k + 5/2*s + 1 = 0. Calculate s.
-1, -2/3
Let y(z) = 74*z**4 - 163*z**3 + 98*z**2 - 5*z - 4. Let w(a) = 221*a**4 - 489*a**3 + 295*a**2 - 14*a - 13. Let r(s) = 4*w(s) - 14*y(s). Solve r(g) = 0.
-2/19, 1/4, 1
Let g be 8/12 - 29/48. Let a = 19/48 - g. Solve 0 + 1/3*j + a*j**2 = 0.
-1, 0
Suppose -11*s = -14*s - 12*s. Let a(f) be the first derivative of 1/3*f**2 + s*f - 1/9*f**3 + 1. Factor a(k).
-k*(k - 2)/3
Factor -20*h**2 + 5*h + 4*h**4 + 150*h**3 - 13*h - 154*h**3 - 4*h.
4*h*(h - 3)*(h + 1)**2
Let u(a) be the first derivative of -a**3 - 3*a**2 - 3*a - 1. Suppose u(v) = 0. What is v?
-1
Let z(q) be the third derivative of -q**4/24 - q**3/2 + 4*q**2. Let t be z(-5). Factor -9*a**3 + 4*a**t - 3*a**4 - 9*a**4 + 2*a**4 + 3*a**3.
-2*a**2*(a + 1)*(5*a - 2)
Suppose -15 = -5*m - 5. Let c(g) be the second derivative of -1/18*g**3 + m*g + 0*g**2 + 0 + 1/12*g**4 + 1/90*g**6 - 1/20*g**5. Factor c(k).
k*(k - 1)**3/3
Let z be (0 - -3)*8/12. Factor -f**3 - 3*f**z + 1 + 3*f + 2*f**2 - 2*f.
-(f - 1)*(f + 1)**2
Factor -100*l**4 + 127*l**3 + 13*l**3 - 88*l**2 + 44*l**2 + 4*l.
-4*l*(l - 1)*(5*l - 1)**2
Let t = 243/20 - 47/4. Factor -2/5*g**3 + 2/5*g - t*g**2 + 2/5.
-2*(g - 1)*(g + 1)**2/5
Suppose -2*n - 8 = -n + 2*d, 5*n - 4*d - 30 = 0. Suppose -2*u + 14 = 4. Let -1/2*i**4 - 1/2 - i**3 + i**n + 1/2*i + 1/2*i**u = 0. What is i?
-1, 1
Suppose 0 = 8*i - 4*i + 108. Let v(d) = 6*d**3 + 111*d**2 - 105*d + 69. Let n(q) = -q**3 - 16*q**2 + 15*q - 10. Let m(b) = i*n(b) - 4*v(b). Factor m(o).
3*(o - 2)*(o - 1)**2
Let i(n) = n**2 + n + 1. Let k(x) = -8*x**2 - 11*x - 8. Let m(c) = -5*i(c) - k(c). What is v in m(v) = 0?
-1
Let m(f) be the third derivative of -f**7/210 + f**6/120 + f**5/60 - f**4/24 + 7*f**2. Factor m(t).
-t*(t - 1)**2*(t + 1)
Solve 3*l + 5*l - 2*l**2 - 18 + 10 = 0 for l.
2
Let s(i) be the first derivative of -i**4/30 + 2*i + 2. Let h(o) be the first derivative of s(o). Find c, given that h(c) = 0.
0
Let 4107*l**4 - l + 2*l**5 - l**5 - 2*l**2 - 4105*l**4 = 0. Calculate l.
-1, 0, 1
Let d(m) be the third derivative of m**6/24 - 13*m**5/4 + 845*m**4/8 - 10985*m**3/6 - 2*m**2 + 6*m. What is q in d(q) = 0?
13
Suppose 0 = 13*k - 11*k - 10. Let v = 1 + 5. Factor 8/3*s**k + v*s**3 - 2/3*s**2 - 22/3*s**4 - 2/3*s + 0.
2*s*(s - 1)**3*(4*s + 1)/3
Let m(r) = 4*r**3 + r**2 - 2. Let v be m(-1). Let h be (3/9)/(v/(-30)). Determine a so that -1/2*a**3 + 1/2*a + 0 + 1/2*a**4 - 1/2*a**h = 0.
-1, 0, 1
Let q(m) be the second derivative of -2/15*m**3 - 3/50*m**5 + 0*m**2 + 3*m + 1/6*m**4 + 0. Suppose q(t) = 0. Calculate t.
0, 2/3, 1
Factor 0 + 0*i**2 + 1/4*i**5 - 3/2*i**3 - 1/4*i**4 + 0*i.
i**3*(i - 3)*(i + 2)/4
Let u be (-4)/14 + 4/14 + 0. Let f(l) be the third derivative of 0 - 1/9*l**3 + 1/18*l**4 + u*l + 4*l**2 - 1/90*l**5. Factor f(o).
-2*(o - 1)**2/3
Let i(x) = x**3 + 8*x**2 + 7*x + 2. Let b be i(-7). Suppose -2*w**2 + 3*w**2 + w**b = 0. What is w?
0
Let a(r) be the first derivative of r**8/8400 - r**7/1400 + r**6/600 - r**5/600 - r**3/3 - 5. Let u(i) be the third derivative of a(i). Factor u(d).
d*(d - 1)**3/5
Determine o so that -o**4 + 13 - o**2 - 7*o**2 - 5 + 10*o**2 + 12*o - 3*o**3 = 0.
-2, -1, 2
Let l(b) be the first derivative of 0*b + 1/8*b**2 - 1 + 1/3*b**3 - 1/16*b**4 - 1/5*b**5. Determine u, given that l(u) = 0.
-1, -1/4, 0, 1
Let q(c) = -c - 1. Let n be q(2). Let x = n + 3. Determine o so that -21/5*o**3 - 3*o**2 + 6/5*o + x = 0.
-1, 0, 2/7
Let c(o) = 30*o**3 + 17*o**2 - 9*o + 4. Let f(t) = 15*t**3 + 8*t**2 - 5*t + 2. Let r(h) = h**2. Let b be r(-2). Let l(j) = b*c(j) - 9*f(j). Factor l(z).
-(z + 1)*(3*z - 1)*(5*z - 2)
Let b = -31/15 + 113/45. Factor 2/3*a**2 - 8/9 - 2/9*a**4 - 8/9*a + b*a**3.
-2*(a - 2)**2*(a + 1)**2/9
Let g(z) be the second derivative of -5*z**7/6 - 2*z**6 - 3*z**5/4 + 5*z**4/6 - 46*z. Factor g(t).
-5*t**2*(t + 1)**2*(7*t - 2)
Let d(h) = -h**5 + h**3 + h**2 + h + 1. Let g(j) = -5*j**5 + j**4 + 5*j**3 + 3*j**2 + 4*j + 4. Let s(u) = -20*d(u) + 5*g(u). Let s(x) = 0. Calculate x.
-1, 0, 1
Let j(c) = c + 1. Let m be j(1). Suppose 5 = -o + 4*q + 1, 3*q = 5*o - 31. Factor -5*f - 2*f + o*f**3 - m + 2*f**4 - 4*f**2 + 4*f**4 - f.
2*(f - 1)*(f + 1)**2*(3*f + 1)
Let w be (510/20)/(-17 - 1). Let p = w + 5/3. Suppose 0 - 1/4*l + p*l**2 = 0. What is l?
0, 1
Let u(s) = -4*s - 2. Le