 + 22. Factor b(k).
3*(k - 2)*(k - 1)
Let j(d) be the second derivative of -d**4/36 + 4*d**3/9 - 8*d**2/3 - 10*d. Factor j(p).
-(p - 4)**2/3
Let r = -686585/66 - -10403. Let w = r + 157/22. What is f in -34/3*f**3 + 10/3*f**4 + 4/3 + 14*f**2 - w*f = 0?
2/5, 1
Let h(z) = z**2 + 4*z - 1. Let f(q) be the third derivative of q**5/60 + 5*q**4/24 - q**3/3 - 2*q**2. Let a(r) = 2*f(r) - 3*h(r). Find t, given that a(t) = 0.
-1
Let n be (-4)/6 - 94/3. Let i = n - -69/2. Factor 1 + 3/2*l - i*l**2.
-(l - 1)*(5*l + 2)/2
Let t(a) = -21*a**4 + 7*a**3 + 20*a**2 - 7*a - 9. Let q(k) = -20*k**4 + 8*k**3 + 20*k**2 - 8*k - 8. Let p(c) = -5*q(c) + 4*t(c). Find l, given that p(l) = 0.
-1, -1/4, 1
Let y(n) be the first derivative of -2*n**5/5 + n**4 - 2*n**2 + 2*n - 6. Factor y(b).
-2*(b - 1)**3*(b + 1)
Let d(v) be the third derivative of v**5/210 - 11*v**4/42 + 121*v**3/21 + 12*v**2. Solve d(a) = 0.
11
Suppose -w + 3*w = 13*w. Let -2/7*j**4 - 8/7*j + 0*j**2 + 6/7*j**3 + w = 0. Calculate j.
-1, 0, 2
Factor -2/11*b - 2/11*b**2 + 0.
-2*b*(b + 1)/11
Factor 0 + 12*t**2 - 9*t**4 + 3*t**5 + 0.
3*t**2*(t - 2)**2*(t + 1)
Let i be (-270)/(-63) - 4/14. Let p(f) be the first derivative of 1/6*f**6 + 2/3*f**3 - 2 + 1/2*f**2 - 1/5*f**5 - f - 1/2*f**i. Factor p(d).
(d - 1)**3*(d + 1)**2
Suppose -2*x = -2*m - 18 + 2, -32 = -4*x - 2*m. Let l be x/(-12) - 34/(-6). Solve 3*u + 9*u**2 + u**4 - 3*u**2 - 7*u**4 - 3*u**l = 0 for u.
-1, 0, 1
Let f(g) be the first derivative of g**6/150 + 3*g**5/100 + g**4/30 + 5*g - 4. Let l(m) be the first derivative of f(m). Factor l(n).
n**2*(n + 1)*(n + 2)/5
Let w(k) be the first derivative of -2*k**4/3 + 10*k**3/9 - k**2/3 + 2. Factor w(q).
-2*q*(q - 1)*(4*q - 1)/3
Let k(x) be the second derivative of 0 - 1/80*x**6 - 3*x + 1/4*x**3 + 3/40*x**5 - 3/16*x**4 + x**2. Let d(j) be the first derivative of k(j). Factor d(u).
-3*(u - 1)**3/2
Determine p, given that 15/4*p**3 + 0 - 3/2*p + 3/4*p**2 + 3/2*p**4 = 0.
-2, -1, 0, 1/2
Let n be (8 - 1)*(-81)/(-189). Determine j, given that 0 + 3/4*j + 3/2*j**2 + 3/4*j**n = 0.
-1, 0
Let h(m) be the first derivative of -m**6/6 - 4*m**5/5 - 3*m**4/4 + 4*m**3/3 + 2*m**2 - 3. Factor h(a).
-a*(a - 1)*(a + 1)*(a + 2)**2
Suppose -6 = 2*j, 0*c + 2*c = 3*j + 19. Suppose 3*a - c*a = 0. Factor -1 - 3*q**2 + 4*q**2 + a.
(q - 1)*(q + 1)
Factor 1/2*w**2 - 1/4*w + 1/4*w**5 + 0 - 1/2*w**4 + 0*w**3.
w*(w - 1)**3*(w + 1)/4
Suppose -5 = -5*y, 4*c - 12*y - 5 = -9*y. Suppose 0 + 1/6*k**3 - 1/3*k**c + 0*k = 0. What is k?
0, 2
Let p(w) be the third derivative of w**7/315 - w**6/360 + w**4/24 + w**2. Let b(c) be the second derivative of p(c). Solve b(z) = 0.
0, 1/4
Let z(b) be the second derivative of 14*b**6/15 - 12*b**5/5 + b**4 + 4*b**3/3 + 8*b. Suppose z(p) = 0. What is p?
-2/7, 0, 1
Let j = 6 + -2. Factor 1/3 + 256/3*f**j + 256/3*f**3 + 32*f**2 + 16/3*f.
(4*f + 1)**4/3
Let n(v) be the second derivative of v**7/189 - 2*v**6/135 + v**4/27 - v**3/27 - 7*v. Let n(a) = 0. Calculate a.
-1, 0, 1
Let o(t) be the third derivative of t**6/840 - t**4/14 + 8*t**3/21 - 36*t**2. Suppose o(d) = 0. What is d?
-4, 2
Let x(r) be the first derivative of 15*r**6/8 - 3*r**5 - 25*r**4/4 + 25*r**3/6 + 55*r**2/8 + 5*r/2 - 17. Suppose x(z) = 0. Calculate z.
-1, -1/3, 1, 2
Let i(y) be the first derivative of 1/5*y**5 - 4*y + y**3 - y**4 + 2*y**2 - 2. Suppose i(m) = 0. Calculate m.
-1, 1, 2
Let b(z) be the third derivative of 4*z**2 + 0*z - 1/60*z**5 + 1/8*z**4 - 1/3*z**3 + 0. Factor b(q).
-(q - 2)*(q - 1)
Let w = 1/86 - -251/602. Let -w*v**3 - 15/7*v + 12/7*v**2 + 6/7 = 0. What is v?
1, 2
Let g(i) be the first derivative of i**6/42 + 6*i**5/35 + 13*i**4/28 + 4*i**3/7 + 2*i**2/7 + 22. Suppose g(k) = 0. What is k?
-2, -1, 0
Let y(v) be the second derivative of v**7/315 + v**6/90 + v**5/90 + 4*v**2 + 5*v. Let x(p) be the first derivative of y(p). Factor x(a).
2*a**2*(a + 1)**2/3
Let g(q) be the second derivative of 2*q**6/105 - q**5/7 + 3*q**4/7 - 2*q**3/3 + 4*q**2/7 - 17*q. Factor g(n).
4*(n - 2)*(n - 1)**3/7
Let a(n) be the first derivative of -n**8/42 - 2*n**7/35 - n**6/30 + 7*n**2/2 + 2. Let m(d) be the second derivative of a(d). Factor m(r).
-4*r**3*(r + 1)*(2*r + 1)
Let c = 529/2 + -245. Solve 63/2*z**4 - 25*z**2 - 4 + c*z**3 - 22*z = 0.
-2/3, -2/7, 1
Let u be 2*-1*-1 + -5 + 8. Let y(q) be the first derivative of 0*q**2 - 1 - 1/5*q**4 + 0*q - 2/25*q**u - 2/15*q**3. Factor y(n).
-2*n**2*(n + 1)**2/5
Let o = -27349/5 - -5289. Let x = -180 - o. Solve -6/5*k**3 + 6/5*k**5 + x*k**4 + 0 + 0*k - 4/5*k**2 = 0 for k.
-1, -2/3, 0, 1
Let p(c) = -c**3 - 9*c**2 - 27*c - 22. Let d(n) = -n**3 - 9*n**2 - 27*n - 23. Let z(q) = 5*d(q) - 4*p(q). Let z(i) = 0. What is i?
-3
Factor -5*c**2 - 5 + 9*c**3 + 4*c - 19*c + c**3 + 5*c**3 + 10*c**4.
5*(c - 1)*(c + 1)**2*(2*c + 1)
Factor -x - 2*x**4 + 2*x**3 + 0*x**2 - x**2 - 2*x**2 - 2 - x**5 + 7*x**2.
-(x - 1)**2*(x + 1)**2*(x + 2)
Factor 22 - 15*s**2 - 3*s - 14*s - 27 + 2*s - 5*s**3.
-5*(s + 1)**3
What is u in -9/5*u**2 - 1/5*u**3 - 3*u + 5 = 0?
-5, 1
Let l be ((-32)/(-25))/1 + 0. Let f(v) be the first derivative of 12/5*v**4 + 0*v - 6/5*v**3 - l*v**5 + 1/5*v**2 - 1. Factor f(u).
-2*u*(u - 1)*(4*u - 1)**2/5
Let m(c) be the second derivative of c**6/90 - c**4/12 + c**3/9 + 14*c. Determine w so that m(w) = 0.
-2, 0, 1
Let x(z) be the third derivative of -z**5/15 - z**4/6 - 7*z**2 + 1. Factor x(i).
-4*i*(i + 1)
Let p = 3 + -4. Let g be (-1)/(-2)*(-1 - p). Suppose -1/2*b**3 + g + 0*b + 1/2*b**2 = 0. Calculate b.
0, 1
Let v(j) be the second derivative of -j**7/42 + j**6/30 + j**5/20 - j**4/12 + 3*j. Suppose v(k) = 0. What is k?
-1, 0, 1
Find z, given that 0 - 2*z**4 + 14/5*z**3 + 0*z - 4/5*z**2 = 0.
0, 2/5, 1
Factor 0*q - 1/3*q**3 - 1/3*q**5 - 2/3*q**4 + 0 + 0*q**2.
-q**3*(q + 1)**2/3
Let p(g) = -g**2 - g - 1. Let t(j) = -j**3 - 4*j**2 - 4*j - 4. Let o(z) = -12*p(z) + 3*t(z). Factor o(d).
-3*d**3
Let b(x) = 3 - 4 - x + 2*x + 3*x**2 + 0*x. Let m be b(1). Let 0*j**2 + 1/5*j**4 + 0*j + 0 - 1/5*j**m = 0. What is j?
0, 1
Let x(v) be the third derivative of -v**6/900 + v**5/75 - v**4/20 + 4*v**3/45 - 14*v**2. Solve x(i) = 0 for i.
1, 4
Factor -1/5*z**3 - 4*z - 16/5 - 8/5*z**2.
-(z + 2)**2*(z + 4)/5
Let y(k) be the third derivative of k**8/2520 - k**7/1260 + k**3/6 - 5*k**2. Let c(s) be the first derivative of y(s). Factor c(x).
2*x**3*(x - 1)/3
Factor 5*s**5 - 31*s**2 + 43*s**3 + 12*s**4 - 19*s**2 + 15*s - 42*s**4 + 17*s**3.
5*s*(s - 3)*(s - 1)**3
Let g(p) be the first derivative of 2*p**6/27 - 11*p**4/9 - 8*p**3/9 + 56*p**2/9 + 32*p/3 + 5. Suppose g(z) = 0. Calculate z.
-2, -1, 2, 3
Let h(m) = m**2 - 6*m - 9. Let t(g) = -g**2. Let q(f) = -h(f) - 2*t(f). Find y, given that q(y) = 0.
-3
Suppose 2*n = 5*l + 20 - 0, 3*l + 12 = -n. Suppose -2*r = -n*r - 6. Solve 0*t + 0 + 0*t**2 + 2/3*t**4 + 0*t**r = 0 for t.
0
Let v(o) be the third derivative of 0*o**3 + 0*o + 0 + 1/10*o**6 - 1/6*o**4 + 0*o**5 + 4/105*o**7 + 3*o**2. Determine j, given that v(j) = 0.
-1, 0, 1/2
Suppose 6*y**2 + 0*y + y + 0*y**3 + 2*y**3 + 3*y = 0. What is y?
-2, -1, 0
Let a(u) = 4*u**2 - 4 - 3*u**2 + u**2 - 2*u. Let j(f) = 2*f + 2. Let b(r) = r + 1. Let p(d) = -5*b(d) + 3*j(d). Let m(i) = -a(i) - 4*p(i). Factor m(l).
-2*l*(l + 1)
Let l(c) = 2*c. Let h be l(-3). Let b be (h/15)/(2/(-20)). Factor 1/2*j**3 + 5/4*j**b + 0*j**2 - 7/4*j**5 + 0*j + 0.
-j**3*(j - 1)*(7*j + 2)/4
Factor k**3 + 0*k - 2 - 6*k**2 - 3*k**3 - 6*k.
-2*(k + 1)**3
Let o(y) be the third derivative of -2/75*y**5 + 0*y**3 - 8*y**2 - 1/75*y**6 + 0 + 0*y**4 + 0*y - 1/525*y**7. Factor o(p).
-2*p**2*(p + 2)**2/5
Determine k so that 4 + k**2 - k**2 + k**3 - 3*k**2 = 0.
-1, 2
Let g = 24 - 19. Let x(z) = -5*z**3 - 3*z**2 + 5*z. Let v(k) = -9*k**3 - 5*k**2 + 9*k. Let f(h) = g*x(h) - 3*v(h). Factor f(m).
2*m*(m - 1)*(m + 1)
Let y(u) be the third derivative of -u**5/20 - 5*u**4/8 - 3*u**3 - 6*u**2. Find s, given that y(s) = 0.
-3, -2
Let y = -3 - -7. Suppose 3*c - 23 = -4*f, -y*f - 2*c + 22 = -0*f. Factor 5*j**f + 7*j**2 - 5*j**3 - 7*j**4 - 2*j + 2*j**3 + 0*j**3.
j*(j - 1)**2*(j + 1)*(5*j - 2)
Let k(s) be the first derivative of -3 + 0*s + 12*s**3 + 9/2*s**4 + 3/5*s**5 + 12*s**2. Factor k(a).
3*a*(a + 2)**3
Let o be 2 - (-6)/(-8)*2. Suppose -22 = 2*r - 26. Factor -o*d**r - 1/2 - d.
-(d + 1)**2/2
Factor -2 + n**3 - 98*n + 4 + 9