 152. Determine l, given that -t*l + 0 - i*l**2 = 0.
-2, 0
Let n(l) be the third derivative of -l**8/80640 - l**7/6720 - l**6/1440 - l**5/20 + 5*l**2. Let v(s) be the third derivative of n(s). Factor v(x).
-(x + 1)*(x + 2)/4
Let m(n) be the third derivative of -n**8/30240 + n**7/7560 - n**5/60 - 3*n**2. Let d(h) be the third derivative of m(h). Suppose d(l) = 0. Calculate l.
0, 1
Let j be (-16)/(-6)*(146/28 + -5). Factor 0*v - 2/7*v**3 - 2/7*v**4 + j*v**2 + 0.
-2*v**2*(v - 1)*(v + 2)/7
Let i = -13 + 21. Let -i*v**2 + 6*v + 0*v**3 + 2*v**3 - 4 + 5*v - v = 0. What is v?
1, 2
Let t(m) be the first derivative of -m**6/10 - m**5/25 + 9*m**4/20 + 3*m**3/5 + m**2/5 - 5. Suppose t(o) = 0. Calculate o.
-1, -1/3, 0, 2
Suppose 4*a - 1 - 7 = 0. Suppose -4*s = -2*g - s + 16, -a*g - s = -8. Let -4*c**5 - c**3 + c**2 + 2*c**3 + 3*c**g - c**4 = 0. Calculate c.
-1, 0, 1
Solve 4/5*q - 4/5*q**2 - 8/5*q**3 + 0 = 0 for q.
-1, 0, 1/2
Let c(a) = a**5 - 4*a**4 + 4*a**3 + 4*a**2 - 4*a + 4. Let i(g) = -g**5 + 4*g**4 - 4*g**3 - 5*g**2 + 5*g - 5. Let l(h) = -5*c(h) - 4*i(h). Factor l(v).
-v**3*(v - 2)**2
Factor -6 + 5*g - 15*g + 13*g + 3*g**2.
3*(g - 1)*(g + 2)
Let q(g) = g**2 + 10*g - 6. Let r be q(-11). Suppose -r + 1 = -2*k. Factor 0*n - 1/4*n**k + 1/4.
-(n - 1)*(n + 1)/4
Let h(f) be the first derivative of 21*f**5/10 - 57*f**4/8 + 15*f**3/2 - 3*f**2/4 - 3*f - 55. Suppose h(j) = 0. What is j?
-2/7, 1
Let s(u) be the third derivative of -1/420*u**7 + 0*u**3 + 1/120*u**6 + 0 + 0*u**5 + 0*u**4 + 0*u + 7*u**2. Determine m so that s(m) = 0.
0, 2
Let g(b) = 6*b**2 - 149*b - 1280. Let j(h) = h**2 - 30*h - 256. Let t(d) = -2*g(d) + 11*j(d). Let t(s) = 0. Calculate s.
-16
Let s be (-1 - (1 + -2))*(2 + -1). Let z = 11 - 11. Factor s*r**2 + 1/4*r**3 + 0 + z*r.
r**3/4
Let z be (2/6)/(5/60). Let s be 6/z - 15/(-10). Find a such that 2*a**s + 1/2*a - 5/2*a**2 + 0 = 0.
0, 1/4, 1
Factor p**2 + 0 - 1/2*p**4 - 1/2*p**3 + 0*p.
-p**2*(p - 1)*(p + 2)/2
Let g(t) be the third derivative of -t**8/2016 - t**7/1260 + t**6/720 + t**5/360 - t**2. Factor g(f).
-f**2*(f - 1)*(f + 1)**2/6
Let y(s) = -81*s**4 - 288*s**3 - 624*s**2 - 576*s - 159. Let g(k) = 5*k**4 + 18*k**3 + 39*k**2 + 36*k + 10. Let o(l) = -33*g(l) - 2*y(l). Factor o(t).
-3*(t + 1)**2*(t + 2)**2
Let k = 39 - 60. Let c = -19 - k. Factor 2/3*g + 2/3*g**c + 0 + 1/6*g**3.
g*(g + 2)**2/6
Suppose 15/7*s + 3/7*s**3 + 12/7*s**2 + 6/7 = 0. Calculate s.
-2, -1
Let c(t) be the second derivative of 7*t**5/120 - t**4/6 + t**3/12 + t**2/6 - t. Factor c(b).
(b - 1)**2*(7*b + 2)/6
Let v = -13 - -9. Let f(x) = x**2 + 3*x - 1. Let n be f(v). Factor -4 + 6*i - 2*i**n + 2 - 2.
-2*(i - 1)**2*(i + 2)
Let o(u) = -u + 1. Let q be o(-5). Factor 2*v**3 + 3*v - q*v**3 + 6*v**4 - 5*v**3 + 0*v**3.
3*v*(v - 1)**2*(2*v + 1)
Let p(g) be the first derivative of g**6/135 + g**5/90 - g**4/54 - g**3/27 - 2*g + 3. Let a(s) be the first derivative of p(s). What is k in a(k) = 0?
-1, 0, 1
Let f = 419/2 + -208. Factor -f*i**2 - 1/2 - 3/2*i - 1/2*i**3.
-(i + 1)**3/2
Let q(y) be the second derivative of 0*y**2 + 4/15*y**3 - 2/15*y**4 + 2*y + 0 + 1/50*y**5. Factor q(b).
2*b*(b - 2)**2/5
Let r(c) be the third derivative of c**7/70 - c**6/20 + c**5/20 + 16*c**2. Determine a, given that r(a) = 0.
0, 1
Let p be 3*21*4/36. Let d(a) be the second derivative of 0 - 3*a + 1/60*a**6 + 0*a**3 + 1/168*a**p + 0*a**2 + 1/80*a**5 + 0*a**4. Let d(u) = 0. What is u?
-1, 0
Suppose -4*l + 2 + 2 = -5*w, 5*l = 5. Let h be (0 + 1)*17/((-680)/(-16)). Let w*j + 2/5*j**2 - h = 0. Calculate j.
-1, 1
Let f(i) = 15*i**4 + 28*i**3 - i**2 - 7. Let k(l) = -5*l**4 - 9*l**3 + 2. Let d(p) = 2*f(p) + 7*k(p). Let d(t) = 0. What is t?
-1, -2/5, 0
Let w = 1 - 6. Let h = -5 - w. Factor 0*u**2 + h + 1/4*u**3 - 1/4*u.
u*(u - 1)*(u + 1)/4
Let x(r) be the second derivative of r**5/80 + r**4/12 + 5*r**3/24 + r**2/4 - 6*r. Solve x(m) = 0.
-2, -1
Let g(z) be the second derivative of -z**5/3 - z**4/3 - z**2/2 - 4*z. Let s(j) be the first derivative of g(j). Factor s(w).
-4*w*(5*w + 2)
Factor -7 - 1 + 0*q**2 + 4*q**2 + 4*q.
4*(q - 1)*(q + 2)
Let d(b) be the second derivative of b**6/15 - b**5/5 + b**4/6 - 4*b. Factor d(f).
2*f**2*(f - 1)**2
Let s = -7 - -4. Let a = s + 6. Let 2*y - 1 - 3*y**2 + y**3 + y + 0*y**a = 0. What is y?
1
Let f = 1212877/4436660 + 2/13049. Let r = f - 2/85. Solve -1/4*j**2 + r*j + 1/2 = 0 for j.
-1, 2
Let c = -1481699/330 - -4490. Let h(r) be the third derivative of 0 + 0*r**4 - 2*r**2 + 0*r - c*r**5 + 0*r**3. Factor h(q).
-2*q**2/11
Let f = 34 + -34. Suppose f = -5*o + o. Factor -3/4*i**5 + o - 3/4*i**4 + 0*i**3 + 0*i + 0*i**2.
-3*i**4*(i + 1)/4
Let q(z) be the second derivative of z**8/30240 - z**7/11340 - z**4/12 + 4*z. Let t(i) be the third derivative of q(i). Find u such that t(u) = 0.
0, 1
Suppose 2*m = 8, 12 = 2*w + 3*m - 0. Let k(c) be the second derivative of -9/80*c**5 + w*c**2 + 0 + 1/8*c**4 + 3*c - 1/24*c**3. Factor k(t).
-t*(3*t - 1)**2/4
Suppose 7*j = 14 + 14. Let d(p) be the second derivative of 2/3*p**2 + 0 + p - 1/12*p**j - 1/60*p**5 + 0*p**3. Factor d(v).
-(v - 1)*(v + 2)**2/3
Let -3/5 - 15*b**2 + 6*b = 0. What is b?
1/5
Let p(j) be the first derivative of -j**4/8 - 3*j**3/4 - 5*j**2/4 - 3*j/4 - 51. Factor p(n).
-(n + 1)*(n + 3)*(2*n + 1)/4
Let z(h) be the first derivative of -4*h**5/5 + h**4 + 4*h**3/3 - 2*h**2 - 5. Factor z(q).
-4*q*(q - 1)**2*(q + 1)
Factor 2*p - 2/5*p**2 - 6/5 - 2/5*p**3.
-2*(p - 1)**2*(p + 3)/5
Suppose 4*y - 30 = -5*r, -5*y - r + 20 + 7 = 0. Let z(w) be the second derivative of -w**3 + 5/12*w**4 + 5/24*w**y + 2/3*w**2 + 0 + 3*w. Factor z(t).
(t + 2)*(5*t - 2)**2/6
Let s(x) be the second derivative of 1/24*x**4 + 5/168*x**7 - 1/15*x**6 + 0*x**2 + 0*x**3 + 1/80*x**5 + 0 - 6*x. Find m such that s(m) = 0.
-2/5, 0, 1
Let l = -4284/5 - -862. Let d = -419/5 - -433/5. Determine w, given that 0 + 46/5*w**4 + l*w**2 + 54/5*w**3 + d*w**5 + 4/5*w = 0.
-1, -2/7, 0
Let l = -12 - -12. Let d(v) be the first derivative of 2/27*v**3 + 0*v + l*v**2 + 2. Factor d(w).
2*w**2/9
Let o be -3 - 57*(0 + -1). Suppose -48*j - 6*j**2 - o - 21*j - 12*j**2 + 15*j - 2*j**3 = 0. What is j?
-3
Let m(f) be the third derivative of f**6/180 - f**5/10 + 3*f**4/4 + f**3/2 - 6*f**2. Let t(l) be the first derivative of m(l). Factor t(y).
2*(y - 3)**2
Let r(v) = v**2 + 10*v - 9. Let s be r(-11). Let k(y) be the first derivative of -s - 1/3*y**3 - y + y**2. Factor k(c).
-(c - 1)**2
Determine w so that 1/5*w**2 + 2/5*w - 1/5*w**3 + 0 = 0.
-1, 0, 2
Factor -49*q**3 + 17*q**3 + 0*q**4 - 3*q**4 + 28*q**2 + 7*q**4.
4*q**2*(q - 7)*(q - 1)
Let s(v) be the second derivative of v**6/1080 + v**5/360 + v**3/3 - 7*v. Let t(i) be the second derivative of s(i). Factor t(x).
x*(x + 1)/3
Factor -24*w**2 + 2*w + 88/3*w**3 + 4/3.
2*(2*w - 1)**2*(11*w + 2)/3
Let s(u) be the first derivative of 0*u**2 + 3 + 0*u + 1/3*u**3. Factor s(m).
m**2
Let m = -6 - -6. Suppose -2 = -l - 5, m = 3*r - 5*l - 21. Suppose -q**2 - q**r + 5*q - 3 - 1 + q = 0. Calculate q.
1, 2
Let x(f) = f**3 + 6*f**2 + f - 2. Let c be x(-5). Factor 3*g - 2 - 1 - 3 + c*g**2.
3*(2*g - 1)*(3*g + 2)
Find g such that 3*g**3 + 6*g**3 - 8*g**2 + 8 - 5*g**3 - 4*g = 0.
-1, 1, 2
Let a(y) = -y**4 - y**3 - y**2 - y. Let h(k) = -k**4 - k**3 - 5*k**2 - 3*k + 2. Let x(z) = 2*a(z) - h(z). Factor x(d).
-(d - 1)**2*(d + 1)*(d + 2)
Suppose -3*w + 3*f = -3, -4*f + 2 = -0*w + 2*w. Let z(g) = 2*g**3 - 2*g**2 - 4*g - 6. Let q(u) = u**2 + u + 1. Let k(h) = w*z(h) + 6*q(h). Factor k(c).
2*c*(c + 1)**2
Suppose -t - 72 + 74 = 0. Find w such that -2/3*w - w**t + 4/3*w**4 + 4/3*w**3 + 1/3 = 0.
-1, 1/2
Let v be (-15)/20*(10/3)/(-5). Factor -2*f**4 + 1/2*f**5 - 2*f**2 + 3*f**3 + 0 + v*f.
f*(f - 1)**4/2
Find z such that -4/5*z - 2/5*z**2 - 2/5 = 0.
-1
Let w be ((-3)/(-2) - 0)*6. Factor 98*d**4 + 8*d**2 - 29*d**2 + 42*d**3 + 8*d - w*d**2 - 18*d**2.
2*d*(d + 1)*(7*d - 2)**2
Find l such that l**2 + 1/2*l**3 + 0 + 1/2*l = 0.
-1, 0
Let q = -41/12 - -19/4. Let -5/3*f + 1/3 + q*f**2 = 0. What is f?
1/4, 1
Let v(i) = i**2 + i. Suppose -2*u = 2*u - 4. Let p be v(u). Suppose -p*r**2 + 10/7*r + 4/7 = 0. What is r?
-2/7, 1
Let h(t) be the third derivative of t**7/168 - t**6/96 - t**5/12 + 5*t**4/24 + 9*t**2. Factor h(c).
5*c*(c - 2)*(c - 1)*(c + 2)/4
Suppose -2*u - 7 - 5 = -4*n, 4*u + 4 = 3*n