1)**2/9
Let s(v) be the second derivative of 3*v**5/40 + 3*v**4/8 + 3*v**3/4 + 3*v**2/4 + 2*v. Find j, given that s(j) = 0.
-1
Factor 11*u**3 - 7*u + u**3 + 4*u**4 - 9*u.
4*u*(u - 1)*(u + 2)**2
Let d(k) be the first derivative of -k**4/10 - 4*k**3/5 - 50. Let d(t) = 0. What is t?
-6, 0
Let k(x) be the first derivative of 5*x**6/33 + 16*x**5/55 - 2*x**4/11 - 20*x**3/33 - x**2/11 + 4*x/11 + 19. Suppose k(w) = 0. Calculate w.
-1, 2/5, 1
Let q(d) = -6*d**2 - 45*d - 54. Let x(g) = 3*g**2 + 23*g + 27. Let k(o) = -5*q(o) - 9*x(o). Factor k(z).
3*(z + 3)**2
Let h(z) = -z + 5. Let s be h(12). Let i(n) = -14*n**3 - 43*n**2 + 17*n. Let u(c) = -21*c**3 - 64*c**2 + 25*c. Let r(p) = s*i(p) + 5*u(p). Factor r(y).
-y*(y + 3)*(7*y - 2)
Solve 72 + 3*n**2 - 3*n**3 - 139 + 67 = 0 for n.
0, 1
Let q(d) be the first derivative of d**4/4 - 2*d**3/3 + d**2 + 1. Let x be q(2). Suppose -t**4 + t**2 + 6*t**5 - 5*t**5 + 3*t**3 - x*t**3 = 0. What is t?
-1, 0, 1
Factor o + 5*o - 2*o**2 + 7 - 13 + 2.
-2*(o - 2)*(o - 1)
Let s(h) be the third derivative of -h**6/600 + h**4/120 + 22*h**2. Factor s(o).
-o*(o - 1)*(o + 1)/5
Let p(w) = 2*w**3 - 4*w**2 + 14*w - 8. Let j(q) = q**2 + q - 1. Let o(u) = -4*j(u) + p(u). Let o(t) = 0. What is t?
1, 2
Solve -23*i**2 + 4 - 10 - 9*i + 20*i**2 = 0.
-2, -1
Find r such that -12/5*r - 3/5*r**2 - 4/5 + r**3 = 0.
-1, -2/5, 2
Let w(l) be the first derivative of -l**3/3 - l**2 + 3*l - 4. Let w(q) = 0. What is q?
-3, 1
What is a in -32/3*a + 110/3*a**2 + 8/9 - 242/9*a**3 = 0?
2/11, 1
Let h(p) be the first derivative of -p**3/12 + p**2/4 + 3*p/4 + 6. Let h(z) = 0. Calculate z.
-1, 3
Let h be (-12)/45*(-1)/4. Let d(g) be the second derivative of -1/18*g**4 + 0*g**3 + 0 + 2*g + 0*g**2 - 1/45*g**6 - h*g**5. Determine j, given that d(j) = 0.
-1, 0
Let g(k) be the first derivative of -k**4/16 + 3*k**3/4 - 27*k**2/8 + 27*k/4 + 6. Factor g(c).
-(c - 3)**3/4
Let n(h) be the second derivative of -h**5/10 - h**4/3 - h**3/3 + 2*h. Factor n(q).
-2*q*(q + 1)**2
Let w(f) = f**4 + 9*f**3 - 19*f**2 - 53*f - 10. Let u(g) = 3*g**3 - 6*g**2 - 18*g - 3. Let y(d) = -8*u(d) + 3*w(d). Factor y(r).
3*(r - 2)*(r + 1)**3
Suppose -3*d + 5*d = 0. Let x be (3 + d)/3 - 0. Let i(f) = -4*f**3 - 4*f**2 + 5*f. Let r(p) = p**3 + p**2 - p. Let t(l) = x*i(l) + 5*r(l). Solve t(v) = 0.
-1, 0
Let g(h) = 9*h**5 - 5*h**4 - 4*h**3 - 7. Let s(d) = -5*d**5 + 3*d**4 + 2*d**3 + 4. Let f(p) = -4*g(p) - 7*s(p). Determine m so that f(m) = 0.
-2, 0, 1
Let s = 7589/16 - 474. Let v(o) be the second derivative of -5/12*o**4 + s*o**5 + 1/6*o**3 + o + 0 + 0*o**2. Suppose v(n) = 0. Calculate n.
0, 2/5
Let t(c) = 10*c**4 + 5*c**3 - 5*c**2 + 5*c - 5. Let u(a) = 9*a**4 + 4*a**3 - 5*a**2 + 6*a - 6. Let g(s) = 6*t(s) - 5*u(s). Factor g(v).
5*v**2*(v + 1)*(3*v - 1)
Let u(y) be the third derivative of y**10/50400 + y**9/6720 + y**8/2240 + y**7/1680 - y**5/60 - 7*y**2. Let f(t) be the third derivative of u(t). Factor f(h).
3*h*(h + 1)**3
Let y(v) be the first derivative of -1/4*v**2 + 1 + v - 1/2*v**3. Suppose y(a) = 0. Calculate a.
-1, 2/3
Let b be (-70)/(-462)*51/(-28). Let z = -2/77 - b. Factor -1/2 - h**2 - 5/4*h - z*h**3.
-(h + 1)**2*(h + 2)/4
Let l be ((-46)/24 - -2)/1. Let g(r) be the first derivative of -1/4*r**2 + l*r**3 - 2 + 0*r. Factor g(a).
a*(a - 2)/4
Let o(a) be the third derivative of 0*a**4 + 0 + 0*a + 1/168*a**8 + 1/105*a**7 + 0*a**3 - 1/30*a**5 - 1/60*a**6 - 2*a**2. Suppose o(u) = 0. What is u?
-1, 0, 1
Suppose -2*d - 10 = -7*d. Factor t + 3*t**d + 27 - t + 6*t + 12*t.
3*(t + 3)**2
Let v(f) be the first derivative of -5*f**6/12 + 3*f**5/10 + f**4/4 - 6. Determine d so that v(d) = 0.
-2/5, 0, 1
Let t(o) be the third derivative of -o**7/350 + o**5/50 - o**3/10 - 6*o**2. Determine n so that t(n) = 0.
-1, 1
Let v = 571/10 + -57. Let g(i) be the first derivative of -v*i**2 + 0*i - 2 + 1/15*i**3. Factor g(m).
m*(m - 1)/5
Let z(w) be the second derivative of w**4/3 - 2*w**3/3 + 2*w. What is q in z(q) = 0?
0, 1
Let f(q) be the second derivative of -q**4/4 - q**3 - 3*q**2/2 + 5*q. Factor f(o).
-3*(o + 1)**2
Let h be (-7 + 1)/(-4 - 0) + 2. Factor -h*f**2 - f**3 + 7/2*f**4 + 0 + f.
f*(f - 1)*(f + 1)*(7*f - 2)/2
Factor 28*n + 5*n**5 - 8*n**4 + 9*n**3 - 5 - n**3 + 32*n**2 + 13 - 9*n**5.
-4*(n - 2)*(n + 1)**4
Let y = 17/39409 - -5548696/18482821. Let a = -1/67 + y. Solve -2/7*w**3 + a*w + 8/7*w**2 - 8/7*w**4 + 0 = 0 for w.
-1, -1/4, 0, 1
Let l(i) = -15*i**3 + 6*i**2 - 3*i. Let p(b) = -29*b**3 + 12*b**2 - 5*b. Let m(d) = -11*l(d) + 6*p(d). Determine x, given that m(x) = 0.
-1/3, 0, 1
Let x(u) = -5*u**2 + 11*u. Let z(f) = f. Let g(w) = -x(w) + z(w). Factor g(s).
5*s*(s - 2)
Let l be 1*((-12)/(-40) + (-2)/(-10)). Find o such that -1/2*o**4 + 0 + 0*o**2 + 0*o + l*o**3 = 0.
0, 1
Let -1/4*j**3 + 0 + 1/4*j**2 + 0*j = 0. Calculate j.
0, 1
Let s(z) = -z**4 - 4*z**3 - 4. Let j(k) = k**4 + 4*k**3 - k**2 + 5. Let d be (-40)/12 - (-4)/(-6). Let h(n) = d*j(n) - 5*s(n). Suppose h(f) = 0. What is f?
-2, 0
Let f = -14 + 36. Let s = 26 - f. Determine h so that 2/7*h**3 - 2/7*h**5 + 0*h - 2/7*h**s + 2/7*h**2 + 0 = 0.
-1, 0, 1
Let z(q) be the third derivative of 2*q**2 + 1/12*q**4 + 1/480*q**6 + 0*q + 0 + 1/48*q**5 + 1/6*q**3. What is k in z(k) = 0?
-2, -1
Let b be -4*(2 - (-604)/(-296)). Let t = 166/111 - b. Solve t + 14/3*y + 4*y**2 = 0.
-2/3, -1/2
Suppose 21/8*k - k**2 - 9/4 + 1/8*k**3 = 0. What is k?
2, 3
Let c = -15 + 18. Let p(x) be the first derivative of 1/14*x**4 + 0*x - 3 - 4/21*x**c + 1/7*x**2. What is d in p(d) = 0?
0, 1
Let s(r) be the second derivative of -r**6/105 + r**5/35 - 2*r**3/21 + r**2/7 + 20*r. Find d, given that s(d) = 0.
-1, 1
Let x be 2*(2 + (-3)/6). Let l(s) be the first derivative of 0*s**4 + 2/45*s**5 + x - 4/27*s**3 + 0*s**2 + 2/9*s. Factor l(f).
2*(f - 1)**2*(f + 1)**2/9
Let k(t) be the third derivative of -t**8/84 + 4*t**7/315 + 29*t**6/270 + 2*t**5/135 - 10*t**4/27 - 16*t**3/27 - 9*t**2. Solve k(r) = 0.
-1, -2/3, 1, 2
Let j(p) = -p**2 - p. Let f(h) = 9*h**2 - h + 8. Let v be -1 - -1 - (-13 - -27). Let r(w) = v*j(w) - 2*f(w). Find g, given that r(g) = 0.
2
Let b(p) = -3*p**2 - 4. Let v = 19 + -12. Let m(z) = 7 + 3 - 1 + 0 + v*z**2. Let c(r) = 9*b(r) + 4*m(r). Factor c(k).
k**2
Suppose -2*i = 2*i - 24. Let y be (-17)/((-3)/(i - 3)). Find x such that 14*x**2 - 1 + 2*x + y*x**3 + 1 - x**3 - 32*x**4 = 0.
-1/4, 0, 1
Let f(o) = 14 + 15*o + 10*o**3 + 7*o + 28*o**2 + 4*o**2 + 18*o**3. Let u(b) = -b**3 - b - 1. Let n(l) = 2*f(l) + 28*u(l). Find r such that n(r) = 0.
-2, -2/7, 0
Let n(t) be the second derivative of -t**7/210 - t**6/50 - t**5/100 + t**4/20 + t**3/15 + 4*t - 15. Determine m so that n(m) = 0.
-2, -1, 0, 1
Suppose 5*g + 20 = 5*u, 0*u = -2*u + 3*g + 12. Let v(x) be the first derivative of -2 - 2/3*x**3 + u*x**2 + 0*x. Suppose v(l) = 0. Calculate l.
0
Let r = 9 - 5. Suppose -12*h**4 - 4*h**3 + 9*h**4 - 4 + 3*h**2 + 4*h + 4*h**r = 0. What is h?
-1, 1, 2
Let p(u) be the second derivative of u**7/84 - u**5/20 + u**3/12 + 21*u. Find v, given that p(v) = 0.
-1, 0, 1
Let g = 8 - 6. Suppose g*l - 5 = -1. Let -1 - o**l + 2*o + o**4 + o**2 - 2*o**3 = 0. Calculate o.
-1, 1
Let w(h) = h**2 + 4*h - 1. Let b(n) be the third derivative of n**5/30 + 7*n**4/24 - n**3/3 + n**2. Let k(m) = 4*b(m) - 7*w(m). Factor k(g).
(g - 1)*(g + 1)
Let b(m) be the second derivative of -m - 5/3*m**3 - 2*m**2 + 1/5*m**5 + 0 - 1/6*m**4. What is d in b(d) = 0?
-1, -1/2, 2
Let k(m) be the third derivative of 0*m + 0 + 1/30*m**5 - 10*m**2 + 1/12*m**4 - 2/3*m**3. Suppose k(u) = 0. Calculate u.
-2, 1
Let p be 4/(-4)*(-5 + 3). Let b(s) be the first derivative of -1 - 1/8*s**4 - 1/6*s**3 + 1/4*s**p + 1/10*s**5 + 0*s. Factor b(c).
c*(c - 1)**2*(c + 1)/2
Let n be (-16)/(-14) + (-102)/(-119). Find v such that -7/3*v**5 - 34/3*v**n + 8/3 - 20/3*v + 17/3*v**3 + 16/3*v**4 = 0.
-1, 2/7, 2
Factor -8/19*i**3 + 4/19*i**2 - 2/19*i**4 - 18/19 + 24/19*i.
-2*(i - 1)**2*(i + 3)**2/19
Let p be (-1 + -1)*(1196/600 - 2). Let x(h) be the third derivative of -2*h**2 - 1/300*h**6 - p*h**5 + 2/15*h**3 + 0 + 0*h + 1/60*h**4. What is b in x(b) = 0?
-2, -1, 1
Let u be 20/(-6) - (-28)/(-35)*-5. Solve -1/3*r**3 - r**2 - u*r + 0 = 0 for r.
-2, -1, 0
Let q be (1/(-5))/((165/50)/(-11)). Let f(x) be the second derivative of -q*x**2 + x**3 + 0 - 3*x - 7/18*x**4. D