)/4
Let u(a) be the second derivative of -7*a**6/60 + 19*a**5/40 + a**4/4 + a + 3. Find l, given that u(l) = 0.
-2/7, 0, 3
Solve -i**3 + 777 - 15*i - 771 - 2*i**3 + 12*i**2 = 0 for i.
1, 2
Factor -36*h - 24*h - h**2 - h**4 - 12*h**3 - 45*h**2 - 25.
-(h + 1)**2*(h + 5)**2
Factor -15*l - 5/4*l**4 + 10*l**2 + 5/4*l**3 + 0.
-5*l*(l - 2)**2*(l + 3)/4
Let g(d) = d**3 - 4*d - 2. Let s be g(-2). Let h be s*(-3 - 23/(-8)). What is k in h*k**3 + 3/4*k - 3/4*k**2 - 1/4 = 0?
1
Let w(k) be the second derivative of 1/600*k**6 + 2*k + 1/120*k**4 + 1/150*k**5 + 0*k**3 - 1/2*k**2 + 0. Let l(c) be the first derivative of w(c). Factor l(q).
q*(q + 1)**2/5
Let v(k) be the third derivative of k**6/30 + k**5/5 + k**4/2 + 2*k**3/3 + 8*k**2. Factor v(d).
4*(d + 1)**3
Factor 12 + 28*p**3 + 6*p**2 - 15*p**2 - 25*p**3.
3*(p - 2)**2*(p + 1)
Let o(c) be the first derivative of -c**5/130 - c**4/26 + 4*c - 5. Let b(s) be the first derivative of o(s). Factor b(h).
-2*h**2*(h + 3)/13
Let n(g) be the second derivative of g**7/231 - 8*g**6/165 + g**5/5 - 4*g**4/11 + 3*g**3/11 + 13*g + 1. Factor n(h).
2*h*(h - 3)**2*(h - 1)**2/11
Let v(c) be the third derivative of -1/9*c**4 + 4/27*c**3 + 5*c**2 + 0*c + 0 - 1/90*c**6 + 1/945*c**7 + 13/270*c**5. Solve v(b) = 0 for b.
1, 2
Solve k - 2*k**3 + 2*k**2 - 5 + 0*k**2 + k**3 + 3 = 0.
-1, 1, 2
Let u(i) = -i**2 + 17*i + 3. Let z(m) = -2*m**2 + 18*m + 2. Let s(x) = -6*u(x) + 5*z(x). Let s(n) = 0. Calculate n.
-2, -1
Let r(d) be the third derivative of -d**6/80 - d**5/40 - d**4/48 - d**3/3 + 4*d**2. Let x(a) be the first derivative of r(a). Suppose x(i) = 0. Calculate i.
-1/3
Let i(v) be the third derivative of 0*v**5 + 0*v**7 - 1/60*v**6 + 0*v**4 + 0*v + 1/168*v**8 + 0 + 0*v**3 - 3*v**2. Suppose i(a) = 0. Calculate a.
-1, 0, 1
Let b(o) be the second derivative of -3*o**5/20 - o**4/4 + 5*o**3/2 - 9*o**2/2 - 16*o. Factor b(f).
-3*(f - 1)**2*(f + 3)
Let s = -8461/9 + 941. Let n = 563/36 + -59/4. Factor 4/9*j**3 - s - n*j + 2/3*j**2 - 2/9*j**4.
-2*(j - 2)**2*(j + 1)**2/9
Let 0 + 4/7*n**2 + 8/7*n = 0. What is n?
-2, 0
Let k(m) be the second derivative of 3/20*m**5 - 1/2*m**4 + 0 + m + 0*m**2 + 1/10*m**6 + 0*m**3. Factor k(s).
3*s**2*(s - 1)*(s + 2)
Suppose 3*l - 4*l + 22 = 0. Let r be 92/l - (-6)/(-33). Suppose c - 4*c**2 + 0*c**5 - 4*c**3 - 2 + 6*c**r - 2*c**5 + 5*c = 0. What is c?
-1, 1
Let x be 2/(-5)*4/12*-10. Determine u, given that x - 1/3*u**2 + 5*u**3 - 4*u = 0.
-1, 2/5, 2/3
Let m(j) be the second derivative of -2*j**7/315 - j**6/225 - 5*j. Solve m(v) = 0 for v.
-1/2, 0
Let u(s) be the third derivative of 0*s + 1/12*s**4 - 1/120*s**5 + 0 - 1/3*s**3 - s**2. Determine t, given that u(t) = 0.
2
Let a(x) be the first derivative of -4*x**3/15 + 8*x**2/5 - 16*x/5 - 5. Factor a(n).
-4*(n - 2)**2/5
Let h(a) = a**3 + a**2 + 2*a. Let k(r) = 7*r**3 + 22*r**2 + 89*r + 98. Let w(s) = -6*h(s) + k(s). Factor w(p).
(p + 2)*(p + 7)**2
Let r(f) be the second derivative of f**4/42 + f**3/21 - 2*f**2/7 + 12*f. Suppose r(o) = 0. What is o?
-2, 1
What is t in t**4 - 3*t**4 - 3*t - t**4 + 3*t**2 + 3*t**3 = 0?
-1, 0, 1
Determine j so that 1/5*j**4 + 1/5*j - 1/5*j**3 - 1/5*j**2 + 0 = 0.
-1, 0, 1
Let t(v) = v**2 + v - 4. Let a be t(-3). Factor 10*i**a - 2*i + 50 - 50.
2*i*(5*i - 1)
Factor 63*n**4 - 8*n**2 + 48*n**4 + 6*n - 2*n**3 - 1 - 102*n**4 - 4*n**5.
-(n - 1)**3*(n + 1)*(4*n - 1)
Let j(s) be the first derivative of -9/20*s**4 + 3 - 1/5*s**3 + 0*s + 3/5*s**2. Determine h so that j(h) = 0.
-1, 0, 2/3
Let w be (2 + -5)*2/(-6). Suppose -w = t - 3. Let -6*f**3 + 3*f**t + 6 - 5 - 10*f**2 = 0. Calculate f.
-1, -1/2, 1/3
Let r(h) be the first derivative of 10*h**3/39 + 2*h**2/13 - 6*h/13 - 7. Let r(n) = 0. What is n?
-1, 3/5
Let z(r) be the third derivative of 0*r + 1/20*r**4 - 1/300*r**6 + 0*r**5 - 2/15*r**3 + 0 + 3*r**2. Factor z(i).
-2*(i - 1)**2*(i + 2)/5
Factor 4 + 4 + 10*t**2 - 4*t**3 - 6*t - 10*t + 2*t**3.
-2*(t - 2)**2*(t - 1)
Factor 12/5*i + 3/5*i**5 + 0 + 39/5*i**2 + 9*i**3 + 21/5*i**4.
3*i*(i + 1)**3*(i + 4)/5
Suppose -6*q + 16 = -2*q. Factor -2*u**2 + 3*u - q*u**5 - 4*u**4 - u + 6*u**2 + 2*u**5.
-2*u*(u - 1)*(u + 1)**3
Let z(u) be the second derivative of u**4/54 - 2*u**3/27 + u**2/9 - 2*u. Solve z(r) = 0.
1
Suppose -z - 3*k - 13 = -3*z, -z + 17 = -5*k. Let c(a) be the first derivative of 2/3*a**3 + 2*a - 1 + 2*a**z. Find b such that c(b) = 0.
-1
Let s(o) be the second derivative of o**7/42 + o**6/30 - 3*o**5/20 - o**4/12 + o**3/3 - 4*o. Factor s(j).
j*(j - 1)**2*(j + 1)*(j + 2)
Let d(z) be the second derivative of z**4/3 - 2*z**3 - 12*z. Factor d(c).
4*c*(c - 3)
Let j(a) be the third derivative of 5*a**5/54 - 5*a**4/27 + 4*a**3/27 + 4*a**2. Factor j(r).
2*(5*r - 2)**2/9
Suppose 3*c - 18 = -0*c. Let s be (c/(-4))/((-1)/2). Suppose l**4 + 2*l**s + 4*l**4 - 3*l**4 = 0. Calculate l.
-1, 0
Let g(b) be the third derivative of -b**5/240 - 5*b**4/96 + b**3/4 + 37*b**2. Factor g(a).
-(a - 1)*(a + 6)/4
Let y be (2 - 4/1) + 3. Let a(h) = -3*h**3 - h. Let t(u) = -u**3 - u. Let i(r) = y*a(r) - t(r). Solve i(z) = 0.
0
Let v(y) = y**3 - y**2 - 4*y + 9. Let l be v(6). Let w be 3/(-2)*(-44)/l. Factor 32/5*x**3 + w + 18/5*x + 48/5*x**2.
2*(x + 1)*(4*x + 1)**2/5
Suppose 0 = 2*y + 2*y - 16. Suppose -y*u - 3*b + 12 = 0, -2*u + 4*u - 4*b - 6 = 0. Suppose -g + 2*g**u - g**5 + 0*g**5 + 0*g**5 + 0*g**5 = 0. Calculate g.
-1, 0, 1
Let k(g) = g**2 - g + 1. Let m(n) = -12*n**2 + 2*n - 18. Let s(u) = -20*k(u) - 2*m(u). Suppose s(h) = 0. Calculate h.
-2
Let c(v) be the first derivative of -3*v**4/4 - 6. Factor c(i).
-3*i**3
Suppose -2*n**3 - 3*n**3 + n + 8*n**3 - 2*n**2 - 2*n**3 = 0. Calculate n.
0, 1
Let x be (-3)/6 - 2/4. Let i = x - -3. Solve 2 + l**2 - l + 0*l**i - 2 - 2 = 0 for l.
-1, 2
Let v(u) be the first derivative of -u**4/12 - u**3 - 4*u**2 - 16*u/3 - 1. Suppose v(d) = 0. What is d?
-4, -1
Suppose 0 - 3/4*t**5 + 0*t**4 + 3/4*t**3 + 0*t**2 + 0*t = 0. What is t?
-1, 0, 1
What is o in -126/13*o + 98/13 + 30/13*o**2 - 2/13*o**3 = 0?
1, 7
Let y(b) be the second derivative of -b**8/15680 + b**7/1960 - b**6/560 + b**5/280 - b**4/2 + 10*b. Let x(s) be the third derivative of y(s). Factor x(v).
-3*(v - 1)**3/7
Let m(s) be the third derivative of -s**8/5040 - s**7/5040 + s**3/6 + 3*s**2. Let o(h) be the first derivative of m(h). Factor o(k).
-k**3*(2*k + 1)/6
Let x = -4 + 5. Let u be 2 + x - (-3 + 4). Find i, given that -4/3*i + 0 - 2/3*i**u + 2/3*i**3 = 0.
-1, 0, 2
Let d(g) = 2*g + 81. Let l be d(0). Let t be (-18)/l + 29/9. Factor -2/3*z**2 + 0*z + 0 + 1/3*z**4 + 1/3*z**t.
z**2*(z - 1)*(z + 2)/3
Let -1/4 - 1/8*r**2 + 3/8*r = 0. Calculate r.
1, 2
Let t(x) = 2*x**3 + 4*x**2 - 4*x. Let a(u) = u**2. Let j(n) = -12*a(n) + 2*t(n). Solve j(f) = 0 for f.
-1, 0, 2
Factor -5 - f**4 + 3*f**2 - 5*f**3 + f**4 + 1 + 8*f - 2*f**4.
-(f - 1)*(f + 2)**2*(2*f - 1)
Let c(u) = u**3 - 3*u**2 - 4*u - 4. Let h be c(4). Let a be (-6)/10*h/6. Factor -2/5 - 6/5*r**2 + 6/5*r + a*r**3.
2*(r - 1)**3/5
Let f(b) be the second derivative of -b**5/60 + b**4/6 - b**3/2 + 9*b. Let f(k) = 0. What is k?
0, 3
Let k(a) be the second derivative of -1/6*a**4 + 0 + 3*a**2 - 2/3*a**3 - 3*a. Factor k(q).
-2*(q - 1)*(q + 3)
Let z be 5/10*0/6. Factor 0*g**3 + z*g + 2/9*g**4 - 4/9*g**2 + 2/9.
2*(g - 1)**2*(g + 1)**2/9
Let l = 4 - 2. Suppose 0 = l*t + 2*t. Factor 0 + 2/7*k**2 + t*k + 0*k**3 - 2/7*k**4.
-2*k**2*(k - 1)*(k + 1)/7
Suppose 6*r - 2*r + 32 = 0. Let y(a) = a**2 + 9*a + 10. Let j be y(r). Factor j*x**3 + 0*x**2 + x**3 - 2*x**2.
x**2*(3*x - 2)
Let x(f) = -2*f**3 - 6*f + 4. Let q(y) = 2*y**3 - y**2 + 7*y - 5. Let k(j) = -4*q(j) - 5*x(j). Find g, given that k(g) = 0.
-1, 0
Let r(t) be the third derivative of t**7/2520 - t**6/90 + 2*t**5/15 - t**4/24 - 3*t**2. Let f(c) be the second derivative of r(c). Solve f(j) = 0 for j.
4
Let f be (-3)/(-18) + (-4)/24. Suppose f = d + 3, 3*d - 4*d = -2*v + 9. Factor -t - t**3 + t**3 + t**v.
t*(t - 1)*(t + 1)
Let n(t) = t**3 - 8*t**2 - 11*t + 12. Let q be n(9). Let m be (q*12/(-9))/7. What is u in 8/7*u + m + 2/7*u**2 = 0?
-2
Let l = -104 - -1561/15. Let m(b) be the first derivative of 0*b**4 - 3 + 0*b**3 + 0*b + 0*b**2 - l*b**5. Let m(d) = 0. What is d?
0
Let h(c) = c - 14. Let z be h(14). Let k(t) be the third derivative of -1/180*t**5 + z*t + 0*t**3 + t**2 + 0 + 0*t**4. Find a, gi