given that l(h) = 0.
-2/7, -1/6, 2/3, 1
Let l(v) be the third derivative of -1/160*v**6 + 0 - 1/280*v**7 + 0*v + 0*v**4 - 1/240*v**5 + 0*v**3 - 3*v**2 - 1/1344*v**8. Find i such that l(i) = 0.
-1, 0
Let f(l) be the second derivative of -5*l**7/14 - 4*l**6/5 + 3*l**5/5 + 5*l**4/2 + l**3/2 - 3*l**2 + 5*l. Solve f(g) = 0 for g.
-1, 2/5, 1
Let c(v) be the second derivative of -v**6/120 - v**5/40 + v**3/6 - 3*v. Let n(p) be the second derivative of c(p). Suppose n(x) = 0. What is x?
-1, 0
Let m(k) = 3 - 17*k - 6*k**2 + 4*k**2 - 11 + 0. Let b be m(-8). Suppose 0 + 1/3*w**2 + b*w = 0. Calculate w.
0
Let q(k) be the second derivative of 1/42*k**4 - 1/70*k**5 + 1/21*k**3 - 1/7*k**2 + 0 - 5*k. Factor q(n).
-2*(n - 1)**2*(n + 1)/7
Let b(z) = -2*z - 15. Let k(g) = -9*g - 1. Let s be k(1). Let i be b(s). Solve 0*x**i - 2*x**3 - x - x**5 + 3*x**4 + x = 0.
0, 1, 2
Let y = 15 - 11. Factor -t**2 + y*t**2 + 0*t**3 + t**3 - 4 + 0*t**2.
(t - 1)*(t + 2)**2
Let z(q) = q + 9. Let k be z(-8). Let n be 4 + (-1 - k/(-1)). Factor -2 - 2*u**n + 2.
-2*u**4
Solve -9*r**4 + 14*r**3 + 9*r**5 + 10*r**3 + 12*r**2 - 6*r**5 - 30*r**5 = 0 for r.
-2/3, 0, 1
Let g(o) = -o**2 + o + 2. Let v be g(2). Solve -h**4 - 2*h**5 - 3*h**4 - 2*h**3 + v*h**3 + 0*h**3 = 0 for h.
-1, 0
Let g(r) be the third derivative of r**6/1080 - r**5/180 + r**4/108 + 8*r**2. Suppose g(k) = 0. What is k?
0, 1, 2
Let t(k) be the second derivative of -k**4/4 + 2*k**3 - 6*k**2 - 2*k. Find p, given that t(p) = 0.
2
Suppose 3*v = -1 + 16. Factor -12*c**2 - 3*c**4 - 5 + 4 + c + 10*c**3 + v*c.
-(c - 1)**3*(3*c - 1)
Let r(g) be the first derivative of -3*g**5/20 + g**4/4 - 4*g + 3. Let o(h) be the first derivative of r(h). Find b such that o(b) = 0.
0, 1
Let r(x) be the second derivative of -1/15*x**6 - 1/12*x**4 + 0 - 2*x + 0*x**2 - 1/12*x**3 + 7/40*x**5. Factor r(c).
-c*(c - 1)**2*(4*c + 1)/2
Let u(x) = -2*x + 13*x**2 - 5*x - 4*x**2. Let m(t) = 5*t**2 - 4*t. Let y(i) = -11*m(i) + 6*u(i). Find n such that y(n) = 0.
0, 2
Let t be 880/420 - 6/14. Let 2/3*s**2 + 0 + 0*s + 7/3*s**3 + t*s**4 = 0. What is s?
-1, -2/5, 0
Let q = -148643/3042 + -70/169. Let n = 99/2 + q. Factor 0 - n*p**2 + 0*p.
-2*p**2/9
Let j(w) = -2*w - 4. Let h be j(-3). Suppose -k + h = -0*k. Factor 0 + a**k - 1/2*a - 1/2*a**3.
-a*(a - 1)**2/2
Let y(i) be the third derivative of 0 + 1/66*i**4 + 1/330*i**5 + 0*i + 1/33*i**3 + 5*i**2. Find k, given that y(k) = 0.
-1
Let a(d) = -2*d**3 - 6*d**2 + 4*d + 4. Let c(l) = 8 - 3*l**3 + 5*l + 5*l - l - 13*l**2 - l. Let v(j) = -5*a(j) + 2*c(j). Solve v(r) = 0.
-1, 1
Factor 0*p**2 + 0*p - 11/3*p**4 - p**5 + 0 + 4/3*p**3.
-p**3*(p + 4)*(3*p - 1)/3
Let k(c) = -c**2 - 6*c + 20. Let n be k(-8). Solve 0 - 1/5*r**3 + 1/5*r**n + 0*r + 0*r**2 = 0 for r.
0, 1
Let s(f) be the second derivative of 0*f**3 + 0*f**2 + 0*f**4 + 0 - f - 1/20*f**5 + 1/30*f**6. Find h, given that s(h) = 0.
0, 1
Let t(l) = -2*l**2 - 14*l. Let a be t(-6). Let n be 4/a - 275/(-12). Find r such that -3/4 - n*r**2 - 15/2*r + 24*r**5 + 24*r**4 - 33/2*r**3 = 0.
-1, -1/2, -1/4, 1
Let g = 234/5 - 46. Suppose -g - 2/5*b + 2/5*b**2 = 0. What is b?
-1, 2
Let x(t) be the third derivative of t**7/245 + t**6/35 + 3*t**5/35 + t**4/7 + t**3/7 + 19*t**2. What is l in x(l) = 0?
-1
Let q(s) be the first derivative of 1/18*s**4 - 1/18*s**3 - s - 2 + 0*s**2 - 1/60*s**5. Let j(n) be the first derivative of q(n). Factor j(a).
-a*(a - 1)**2/3
Suppose 0 = 67*j - 65*j - 10. Let t(q) be the third derivative of 0 - 1/60*q**j + 0*q - 1/180*q**6 - 1/72*q**4 + 2*q**2 + 0*q**3. Factor t(s).
-s*(s + 1)*(2*s + 1)/3
Suppose -10 = -8*a + 3*a. Let t = 0 + a. Factor -2 + g**t + g + 2.
g*(g + 1)
Solve 16*a**3 - a**5 + 0*a**2 - 94*a**4 + 8 + 82*a**4 + 3*a**5 + 4*a**2 - 18*a = 0 for a.
-1, 1, 4
Let h(u) be the third derivative of 0 - 7/24*u**4 + 4*u**2 - 13/120*u**6 + 2/105*u**7 + 1/4*u**5 + 0*u + 1/6*u**3. Factor h(s).
(s - 1)**3*(4*s - 1)
Suppose -34 + 34 = -15*c. Factor 0*h + c*h**2 + 0 + 8/5*h**4 + 8/5*h**3 + 2/5*h**5.
2*h**3*(h + 2)**2/5
Let b be 3/6*-3*-2. Suppose b*c + 0*c = 0. Determine k, given that c + 1/2*k - 3/2*k**3 + k**2 = 0.
-1/3, 0, 1
Suppose -5*l + 3*l = -b - 2, 14 = 5*b - 2*l. Let -f + 0*f**3 + 4*f - b*f + f**3 = 0. What is f?
-1, 0, 1
Suppose 0 = -4*i + d - 0*d + 19, -5*d - 31 = -4*i. Factor -48*y**3 + 2 - y**4 + 5*y**4 + 13*y**4 - 16*y + y**i + 44*y**2.
2*(y - 1)**2*(3*y - 1)**2
Let c = 0 - 0. Suppose f + 4 = -2*l, 2*l = -c*l - 6. Suppose -1/4 - 1/4*w + 1/4*w**f + 1/4*w**3 = 0. Calculate w.
-1, 1
Let f(y) be the second derivative of y**6/15 + y**5/5 - y**4/6 - 2*y**3/3 - 14*y. What is j in f(j) = 0?
-2, -1, 0, 1
Let l = 1162/5 + -231. Factor 4/5*h**5 + 1/5*h**2 - l*h**4 + 0 + 2/5*h**3 + 0*h.
h**2*(h - 1)**2*(4*h + 1)/5
Factor 12 - 11 + 0*u**2 - u**2.
-(u - 1)*(u + 1)
Let i(l) = l**3 - 7*l**2 + 7*l - 4. Let f be i(6). Find a such that -a**2 - 3 + a**3 + f - a + 2*a**2 + 0*a**2 = 0.
-1, 1
Let l(y) be the second derivative of -y**4/36 + y**3/9 - y**2/6 + 5*y. Factor l(h).
-(h - 1)**2/3
Let a(d) = -2*d**2 - 46*d - 288. Let q(r) = 2*r**2 + 45*r + 288. Let n(y) = 6*a(y) + 4*q(y). Factor n(h).
-4*(h + 12)**2
Let s(u) = 15*u**4 - 5*u**3 - 10*u**2 + 10*u. Let n(b) = 44*b**4 - 16*b**3 - 31*b**2 + 29*b. Let i(g) = 6*n(g) - 17*s(g). What is h in i(h) = 0?
-1, 0, 2/9, 2
Let l(f) = f**3 - 9*f**2 + 6. Let t be l(9). Solve -6*a - 9 - 4*a**2 + t + a**2 = 0 for a.
-1
Let s(u) = -16*u**2 - 5*u + 11. Let w(d) = -3*d**2 - d + 2. Let y(h) = 2*s(h) - 11*w(h). Factor y(k).
k*(k + 1)
Let c be (-2 - -1)/((-3)/(-6)). Let x be c/(-12) - 68/(-24). Factor 1/5*d**2 - 1/5 - 4/5*d**x + 4/5*d.
-(d - 1)*(d + 1)*(4*d - 1)/5
Let g be (-3)/(-14)*68/102. Factor g + 5/7*h**5 + 26/7*h**2 + 9/7*h + 34/7*h**3 + 3*h**4.
(h + 1)**4*(5*h + 1)/7
Factor 1/2*u**3 + 1/4 - 1/4*u - 1/4*u**5 + 1/4*u**4 - 1/2*u**2.
-(u - 1)**3*(u + 1)**2/4
Let o(p) be the second derivative of 2/9*p**3 + 1/18*p**4 - 1/30*p**5 - 9*p + 0 + 0*p**2. Factor o(a).
-2*a*(a - 2)*(a + 1)/3
Let d = -1/85 + 88/255. Let o(r) be the first derivative of 1/2*r**2 - 1 + d*r**3 - 1/4*r**4 - r. Factor o(z).
-(z - 1)**2*(z + 1)
Let s(c) = 9*c - 3. Let a be s(5). Factor -8*v**2 - 21*v**3 - 16*v**5 - 11*v**3 - 2*v**5 - a*v**4.
-2*v**2*(v + 1)*(3*v + 2)**2
Let l(w) be the third derivative of 0*w**3 + 9/10*w**6 + 1/84*w**8 - 6/35*w**7 + 8*w**2 - 9/5*w**5 + 0 + 0*w**4 + 0*w. Factor l(o).
4*o**2*(o - 3)**3
Let k(j) be the first derivative of 7 - 1/12*j**3 - 1/20*j**5 + 0*j**2 + 0*j - 1/8*j**4. Solve k(s) = 0 for s.
-1, 0
Let k be (-2 - -4) + -2 + -6. Let v be ((-3)/k)/((-6)/(-3)). Solve 0*z - v*z**2 + 1/4 = 0.
-1, 1
Suppose 4*h**2 - 3*h**2 - 6*h**2 + 5*h = 0. Calculate h.
0, 1
Let x(q) be the first derivative of 2*q**4/3 + 4*q**3/3 - 12*q**2 + 32*q/3 + 69. Factor x(z).
4*(z - 2)*(z + 4)*(2*z - 1)/3
Let l(s) = 9*s**2 + 206*s + 1089. Let v(b) = 6*b**2 + 137*b + 726. Let k(n) = 5*l(n) - 8*v(n). Find z, given that k(z) = 0.
-11
Let g(x) = x - 1. Let r(d) = 2*d - 14. Let z(s) = 3*g(s) - r(s). Let v be z(-8). Factor 4/7*n**5 + 2/7*n**v + 0*n**2 + 0 + 0*n + 6/7*n**4.
2*n**3*(n + 1)*(2*n + 1)/7
Suppose 0 - 6/5*f**2 - 1/5*f**3 - 9/5*f = 0. What is f?
-3, 0
Let w(y) be the second derivative of y**3 + 3*y - 1/6*y**4 - 2*y**2 + 0. Solve w(x) = 0 for x.
1, 2
Let j(x) be the second derivative of 3*x**5/25 - 2*x**4/15 - 2*x**3/5 + 4*x**2/5 - 12*x. Factor j(w).
4*(w - 1)*(w + 1)*(3*w - 2)/5
Determine c, given that 0 + 1/2*c + 1/2*c**2 = 0.
-1, 0
Let f(l) = l**2 - 2*l - 11. Let y be f(-5). Factor 44*q - 16*q**5 - q**2 - y*q**4 - 9*q**3 - 44*q.
-q**2*(q + 1)*(4*q + 1)**2
Let x(n) be the third derivative of -n**6/360 + n**4/24 + n**3/9 - 6*n**2. Factor x(s).
-(s - 2)*(s + 1)**2/3
Let b(n) = 3*n**2 + 3*n - 3. Let p be (0 - -1)*(9 - 6). Let x(h) = 3*h**2 + 4*h - 4. Let i(y) = p*x(y) - 4*b(y). Find s, given that i(s) = 0.
0
Let m be 4/(-18)*12/(-8)*1. Factor m*s + 0 + 1/3*s**2.
s*(s + 1)/3
Let q(o) be the first derivative of o**3 - 1/5*o**5 + 1 + 0*o + o**2 + 0*o**4. Suppose q(s) = 0. Calculate s.
-1, 0, 2
Let w(v) be the first derivative of -v**7/105 - v**6/75 + v**5/50 + v**4/30 + 5*v - 3. Let u(m) be the first derivative of w(m). Factor u(f).
-2*f**2*(f - 1)*(f + 1)**2/5
Let n(d) = -7*d**3 + 15*d**2 - 8*d. Let z(t) = -2*t**3 + 4*t**2 - 2*t. Let v(h) = 6*n(h) - 22*z(h). Factor v(o