 6. Determine l so that 3*l**2 - 2*l**y + 1 + 2*l + 0*l**2 = 0.
-1
Let f(g) be the third derivative of g**7/210 + g**6/480 - g**5/60 - g**4/96 - 6*g**2. Solve f(c) = 0 for c.
-1, -1/4, 0, 1
Let a(s) = -21*s**4 + 15*s**3 + 6*s**2 + 15*s. Let t(h) = -3*h**4 + 2*h**3 + h**2 + 2*h. Let z(q) = -2*a(q) + 15*t(q). Factor z(y).
-3*y**2*(y - 1)*(y + 1)
Let w = 3 + -1. Suppose -1 + 11 = -w*n, -4*u = -4*n - 40. Solve 1/2*p**u + 0*p - 1/2*p**3 + 1/2*p**4 - 1/2*p**2 + 0 = 0 for p.
-1, 0, 1
Factor 2/13*w**2 + 12/13*w + 0.
2*w*(w + 6)/13
Let i(t) = t**2 + 14*t + 17. Let d be i(-13). Let n be (d - 5)/(5/(-1)). Find y, given that -1/5*y**3 - 1/5*y**2 + n + 1/5*y = 0.
-1, 1
Factor -8/9*m**2 - 8/9*m**3 + 0*m - 2/9*m**4 + 0.
-2*m**2*(m + 2)**2/9
Let r(a) be the second derivative of -a**5/20 - a**4/4 - a**3/3 - a. Suppose r(g) = 0. Calculate g.
-2, -1, 0
Suppose -4*m + 20 = -0*m, 4*m = 3*k + 14. Let f(w) = w**2 - w. Let v be f(k). Find a such that 6*a**4 - 4*a - 80*a**3 + 34*a**2 + 0*a**v + 26*a**4 = 0.
0, 1/4, 2
Let d(v) = 9*v**2 - 4*v + 2. Let g(a) be the first derivative of 5*a**3/3 - a**2 + a - 4. Let c(j) = -4*d(j) + 7*g(j). Solve c(p) = 0.
1
Factor -12/5 + 21/5*u - 3/5*u**3 - 6/5*u**2.
-3*(u - 1)**2*(u + 4)/5
Let t(u) be the first derivative of 2 + 1/2*u**4 + 0*u**2 + 0*u + 1/3*u**3 + 1/5*u**5. Factor t(p).
p**2*(p + 1)**2
Let q be 1/2 - (-3)/(-18). Let b(z) be the third derivative of -1/12*z**4 + 0*z + 1/60*z**6 + 1/30*z**5 + 2*z**2 + 0 - q*z**3. Factor b(t).
2*(t - 1)*(t + 1)**2
Find f such that -2/11*f**5 + 10/11*f**4 - 2/11*f**2 - 14/11*f**3 - 8/11 + 16/11*f = 0.
-1, 1, 2
Let z = 4 + -1. Let b(a) be the second derivative of -1/3*a**z + a + 3/10*a**5 + 0*a**2 + 0 - 1/3*a**4. Factor b(x).
2*x*(x - 1)*(3*x + 1)
Factor 2/7*v**3 - 2/7 - 2/7*v + 2/7*v**2.
2*(v - 1)*(v + 1)**2/7
Factor 2*v**2 - 5*v**3 + 2*v**5 + 3*v**3 + 160*v**4 - 6*v**2 - 156*v**4.
2*v**2*(v - 1)*(v + 1)*(v + 2)
Let c(o) be the second derivative of -o**7/6300 - o**6/1800 + o**5/150 - o**4/3 - 4*o. Let h(k) be the third derivative of c(k). Let h(d) = 0. Calculate d.
-2, 1
Let l(v) = -2*v**5 + 2*v**4 + 2*v**3 + 14*v**2 - 8*v + 8. Let j(t) = -t**5 + t**4 + t**3 + 9*t**2 - 5*t + 5. Let u(q) = 8*j(q) - 5*l(q). Factor u(c).
2*c**2*(c - 1)**2*(c + 1)
Let o be (-1)/6*(70/(-25) + 2). Let g(y) be the first derivative of -1/3*y**4 + 0*y**2 + 0*y - 2/9*y**3 + 2 - o*y**5. Factor g(v).
-2*v**2*(v + 1)**2/3
Let l(j) be the first derivative of 1 - 2*j**2 - 4/3*j**3 + 0*j - 1/4*j**4. Solve l(s) = 0.
-2, 0
Let q be (-3 + 1074/360)/(2/(-5)). Let j(b) be the third derivative of q*b**4 - 1/60*b**5 + 0*b + 0*b**3 + 3*b**2 + 0. Factor j(c).
-c*(c - 1)
Factor 0 - 4/5*r**3 + 1/5*r**2 + 2/5*r - 3/5*r**4.
-r*(r + 1)**2*(3*r - 2)/5
Let x(h) be the third derivative of -h**6/240 + h**5/120 + h**4/48 - h**3/12 - 4*h**2. Factor x(o).
-(o - 1)**2*(o + 1)/2
Let w(v) = -v**2 + 5*v - 12. Let h be w(9). Let s be ((-2)/(-15))/((-4)/h). Factor -s + 24/5*j - 18/5*j**2.
-2*(3*j - 2)**2/5
Factor 2/9*l**3 - 8/9*l - 8/9 + 2/9*l**2.
2*(l - 2)*(l + 1)*(l + 2)/9
Let p(a) be the first derivative of -a**5/40 + a**4/12 + a**3/12 - a**2/2 - 2*a - 3. Let u(g) be the first derivative of p(g). Factor u(w).
-(w - 2)*(w - 1)*(w + 1)/2
Let v(u) be the third derivative of u**6/120 - u**4/12 - u**3/6 + 4*u**2. Let y be v(-1). Factor y - 2/5*i**4 - 2/5*i**2 - 4/5*i**3 + 0*i.
-2*i**2*(i + 1)**2/5
Let w(f) = f + 17. Let k(a) = 1. Let g(z) = -4*k(z) + w(z). Let x be g(-13). Factor s**2 + x + 1/3*s**4 + s**3 + 1/3*s.
s*(s + 1)**3/3
Let u(x) be the second derivative of -x**5/25 + 7*x**4/30 - 7*x**3/15 + 2*x**2/5 - 5*x. Suppose u(g) = 0. Calculate g.
1/2, 1, 2
Let b(a) be the third derivative of a**5/30 - 4*a**2. Let b(h) = 0. Calculate h.
0
Suppose 35 = 5*p - 0*g - 5*g, 2*p - 4*g - 22 = 0. Determine k so that 2*k**3 + 5*k**2 - k**2 + 2*k - 4*k**p + 4*k**3 = 0.
-1, 0
Suppose 0 = 4*q + 8*q + 14*q. Let l be ((-1)/((-10)/72))/1. Suppose q*m - 12/5*m**2 + 0 + l*m**3 - 27/5*m**4 = 0. What is m?
0, 2/3
Let s(a) be the second derivative of -a**4/12 + a**3/3 + a. Let m be s(2). Determine x, given that 1/2*x**3 - 1/2*x + m + 0*x**2 = 0.
-1, 0, 1
Suppose 46*q = 14*q - 10*q. Find t, given that 4/5 - 3/5*t**2 + q*t + 1/5*t**3 = 0.
-1, 2
Let y = -853/4230 - -10/47. Let n(l) be the third derivative of 0*l**3 + 0*l - 2*l**2 + 1/180*l**6 + 0 + 0*l**4 + y*l**5. Factor n(t).
2*t**2*(t + 1)/3
Suppose 2*v - 13 - 3 = -4*l, 0 = 4*v + 3*l - 12. Let 1/3*o + v - 1/3*o**2 = 0. Calculate o.
0, 1
Suppose 0*v - 12 = -4*v. Let h(z) be the third derivative of 1/15*z**5 + 0*z - 2/3*z**v + 1/4*z**4 + 2*z**2 + 0 - 1/20*z**6. Solve h(u) = 0 for u.
-1, 2/3, 1
Let t be (1/36)/(20/12). Let i(h) be the third derivative of t*h**5 + 0*h**4 + 0*h - h**2 + 0*h**3 + 0. Let i(d) = 0. Calculate d.
0
Let m(g) be the first derivative of 9/2*g**2 + 3*g - 9/4*g**4 - 5*g**3 + 12/5*g**5 - 2. Solve m(x) = 0 for x.
-1, -1/4, 1
Factor -5*j - 1/2*j**2 - 4 + 1/2*j**3.
(j - 4)*(j + 1)*(j + 2)/2
Factor 26*q + 2 - 4 + 8*q**2 + 8.
2*(q + 3)*(4*q + 1)
Let a(m) be the first derivative of -1/42*m**4 - 2/21*m**3 - 1/7*m**2 - 2*m + 2. Let f(o) be the first derivative of a(o). Determine h, given that f(h) = 0.
-1
Let v(s) = 22*s**2 - 10*s - 16. Let y(i) = -7*i**2 + 3*i + 5. Let m(r) = 5*v(r) + 16*y(r). Determine p so that m(p) = 0.
-1, 0
Let x(t) be the second derivative of t**8/2240 - t**6/240 - t**4/4 - 4*t. Let c(i) be the third derivative of x(i). Factor c(g).
3*g*(g - 1)*(g + 1)
Let m(c) be the second derivative of c**6/45 + c**5/30 - c**4/6 - 5*c**3/9 - 2*c**2/3 + 2*c - 49. Determine i, given that m(i) = 0.
-1, 2
Let v(g) be the first derivative of g**6/12 - g**5/10 - g**4/8 + g**3/6 + 2. Suppose v(w) = 0. What is w?
-1, 0, 1
Let a(t) = 6*t**2 + 17*t + 17. Let g(c) = 2*c**2 + 6*c + 6. Let x(o) = -6*a(o) + 17*g(o). Factor x(m).
-2*m**2
Let x be 2/(-2 + -1 + 5). Let k = x - -1/3. Find b, given that k*b + 2/3*b**2 + 0 = 0.
-2, 0
Let h = 4 - 8. Let f(a) = -5*a**3 + a**2. Let d(l) = -6*l**3 + l**2. Let r(k) = h*d(k) + 5*f(k). Factor r(p).
-p**2*(p - 1)
Factor -r**3 + 4 + 2*r + 0*r**2 - 3 + 3*r**2 - 5*r.
-(r - 1)**3
Factor -3/4*w - 3/2 + 3/4*w**2.
3*(w - 2)*(w + 1)/4
Let n(d) be the second derivative of 3*d**5/10 - 3*d**4/4 - d**3 + 15*d. Factor n(b).
3*b*(b - 2)*(2*b + 1)
Factor 3 - 3*b - 13 + 3*b**2 + 5 - 13.
3*(b - 3)*(b + 2)
Factor 11 - 4*z**2 - 11 + 4*z**3.
4*z**2*(z - 1)
Let w be (-504)/48*2/(-6) - 3. Factor -1/2*k**4 + k**3 - k + 0 + w*k**2.
-k*(k - 2)*(k - 1)*(k + 1)/2
Factor -2*u**3 - 10*u**2 + 16*u**3 + 11*u**3 + u.
u*(5*u - 1)**2
Let g(x) be the third derivative of -1/60*x**4 + 0*x + 0 + 3*x**2 - 1/525*x**7 - 2/15*x**3 + 1/50*x**5 + 1/300*x**6. Solve g(y) = 0.
-1, 1, 2
Let f(a) be the first derivative of -3*a**4/16 - a**3/12 + a**2/4 - 6. Factor f(v).
-v*(v + 1)*(3*v - 2)/4
Let u(x) be the second derivative of x**4/4 - 5*x**3 + 75*x**2/2 - 8*x. Factor u(p).
3*(p - 5)**2
Let a(i) = i**5 - 5*i**4 + 5*i**3 - 3*i**2 + 2. Let b(d) = d**4 - d**3 + d**2 - 1. Let z(n) = -3*a(n) - 6*b(n). Factor z(v).
-3*v**2*(v - 1)**3
Suppose -2*l - 5*c + 28 = 2*l, -3*c + 8 = -2*l. Find f such that 20*f - 5*f + 6 + 18*f**l - 9 = 0.
-1, 1/6
Let f(n) be the first derivative of -4*n**5/25 - n**4/5 + 16*n**3/15 + 8*n**2/5 - 24. Solve f(h) = 0 for h.
-2, -1, 0, 2
Suppose 0 = -2*r - 2*r. Let f be r + 1 + 0 + 1. Determine h, given that 0*h**f - h - h - 2*h**2 = 0.
-1, 0
Factor -2/3*j**2 + 0 + 1/6*j**3 + 1/2*j.
j*(j - 3)*(j - 1)/6
Let r = 41 + -39. Let t(x) = x**2 - 3*x - 2. Let s be t(4). Factor r*d**s - 2/3*d**3 + 2/3 - 2*d.
-2*(d - 1)**3/3
Let d be (-21)/20 + -8 + 8. Let n = -4/5 - d. What is g in 0*g**4 + 0*g**2 - n*g**5 + 1/4*g**3 + 0 + 0*g = 0?
-1, 0, 1
Suppose 5*p + 4 = 4*n + 3*p, n - 2*p + 2 = 0. Solve 2/3 - 7/3*c - c**3 + 8/3*c**n = 0.
2/3, 1
Let u = -2 + 4. Factor 2*c**4 + 2*c**2 + c**u - 4*c**3 - c**2.
2*c**2*(c - 1)**2
Let g(w) be the third derivative of -4*w**7/315 - w**6/30 - w**5/45 - 9*w**2. Factor g(s).
-4*s**2*(s + 1)*(2*s + 1)/3
Let w(g) be the third derivative of g**6/30 - 2*g**5/15 - 5*g**4/6 + 4*g**3 - 19*g**2. Let w(x) = 0. Calculate x.
-2, 1, 3
Let n(u) be the first derivative of 2*u**3/9 + 4*u**2/3 + 8*u/3 + 4. Find x such that n(x) = 0.
-2
Let c(v) be the third derivative of v**8/20160 + v**7/5040 - v**6/360 + v*