6 - 73. Let t be ((-4)/(-5))/(8/o). Suppose 4 + t*k - 4 + 2*k**2 = 0. Calculate k.
-1, 0
Let y(t) be the second derivative of -t**6/300 + 2*t**5/75 - t**4/20 - 5*t**2 + 10*t. Let s(i) be the first derivative of y(i). Suppose s(a) = 0. What is a?
0, 1, 3
Factor 0*s + 3/4*s**2 - 3.
3*(s - 2)*(s + 2)/4
Let f(z) = z**2 - 6*z - 3. Let b(i) = 6*i**2 - 31*i - 15. Let h(j) = -6*b(j) + 33*f(j). Solve h(g) = 0.
-3, -1
Let g(d) = -5*d**5 - 7*d**4 + d**3 + 7*d**2 - 4. Let r(b) = -b**5 - b**4. Let m(t) = g(t) - 4*r(t). Let m(k) = 0. What is k?
-2, -1, 1
Factor 0 + 16/5*g**2 - 8/5*g + 2*g**3.
2*g*(g + 2)*(5*g - 2)/5
Let d(b) = -b**3 - 4*b**2 + 2*b - 3. Let y be d(-3). Let u be (-6)/15 + y/(-15). Factor -u - 81/5*g**2 + 36/5*g.
-(9*g - 2)**2/5
Let k be (-7)/63 + (-38)/(-18). Suppose -2/7*p + 0 + 2/7*p**k - 2/7*p**4 + 2/7*p**3 = 0. What is p?
-1, 0, 1
Let x(i) = -4361*i**2 - 648*i - 37. Let h(p) = -727*p**2 - 108*p - 6. Let j(z) = 39*h(z) - 6*x(z). Suppose j(s) = 0. Calculate s.
-2/27
Solve 36/7 - 24/7*p + 4/7*p**2 = 0.
3
Let p = 25 + -13. Let u = -8 + p. Suppose 0 + 0*q**2 + 2/7*q**5 + 2/7*q + 0*q**u - 4/7*q**3 = 0. Calculate q.
-1, 0, 1
Let a(b) be the first derivative of -3/16*b**4 + 0*b**2 - 2 + 1/12*b**3 + 3/20*b**5 + 0*b - 1/24*b**6. Factor a(k).
-k**2*(k - 1)**3/4
Let d = 1/298 - -2081/1490. Suppose -2/5*y + 6/5*y**3 - 4/5*y**5 - 7/5*y**4 + 0 + d*y**2 = 0. Calculate y.
-2, -1, 0, 1/4, 1
Let h(d) = -d - 5. Let z be h(-10). Solve -4*r - 14*r**2 + 6*r**3 + 13*r - z*r = 0 for r.
0, 1/3, 2
Suppose -4*z - 3*p - 4 = 2, 3*z + 3*p = -6. Solve 2/7*a - 1/7*a**2 + z = 0.
0, 2
Let a(s) be the third derivative of -4*s**2 + 7/8*s**4 - 1/4*s**5 + s**3 - 1/10*s**6 + 0*s + 0. Factor a(o).
-3*(o - 1)*(o + 2)*(4*o + 1)
Let f(c) be the second derivative of 5*c**4/4 - c**3 - 7*c. Factor f(t).
3*t*(5*t - 2)
Let d(w) = -8*w**4 - 19*w**3 + w**2 - 4*w. Let z(j) = -17*j**4 - 37*j**3 + j**2 - 7*j. Let c(o) = 7*d(o) - 4*z(o). Factor c(n).
3*n**2*(n + 1)*(4*n + 1)
Let r(b) be the third derivative of b**5/5 - 23*b**4/6 + 28*b**3/3 - 15*b**2. Factor r(z).
4*(z - 7)*(3*z - 2)
Let l be 102/(-20)*(-2)/9. Let m = -41/45 + l. Let -2/9*c**3 + 2/9*c**4 - m*c**2 + 2/9*c + 0 = 0. Calculate c.
-1, 0, 1
Let l(n) be the first derivative of n**5/20 - n**4/8 - n**2/2 - 3. Let o(g) be the second derivative of l(g). Find z, given that o(z) = 0.
0, 1
Let r(o) = -o**2 - 7*o + 5. Let l be r(-7). Let i(d) be the third derivative of 0*d + 0*d**4 + d**2 + 2/15*d**3 - 1/600*d**6 - 1/100*d**l + 0. Factor i(x).
-(x - 1)*(x + 2)**2/5
Let d(w) be the second derivative of 5*w**5/16 + 35*w**4/12 - 5*w**3/2 + 35*w. Factor d(m).
5*m*(m + 6)*(5*m - 2)/4
Let o(l) = -2*l - 8. Let z be o(-4). Let k(h) be the second derivative of 1/80*h**5 - 2*h + 0*h**3 + z*h**2 + 0*h**4 + 0. Let k(t) = 0. Calculate t.
0
Let s be (-20)/(-24) + (-1)/(-6)*3. Solve -s*t**2 + 2/3 + 2/3*t**4 + 2/3*t - 4/3*t**3 + 2/3*t**5 = 0 for t.
-1, 1
Let d(i) be the first derivative of 2/5*i**5 - 4/3*i**3 + 2*i + 0*i**2 + 1 + 0*i**4. Factor d(a).
2*(a - 1)**2*(a + 1)**2
Factor 5/2*z**2 + 0 - 15/2*z**3 + 0*z.
-5*z**2*(3*z - 1)/2
Let o = 5 + -3. Factor -4*y**3 - 8*y**o + 3*y + 6*y**3 + 5*y.
2*y*(y - 2)**2
Factor -3 + 5*o - o**2 - o + 0.
-(o - 3)*(o - 1)
Let g be (0 + -1)*((-35)/(-5) + -7). Let -2/9*y**4 + 0*y + 4/9*y**3 + g - 2/9*y**2 = 0. What is y?
0, 1
Let u(f) be the third derivative of -2*f**7/525 + 2*f**6/25 - 2*f**5/5 + 14*f**4/15 - 6*f**3/5 - 11*f**2. Factor u(z).
-4*(z - 9)*(z - 1)**3/5
Suppose -y - 2*y - 3*m = -18, -5*y + m = -12. Suppose 0 = 3*j - 2*a - 50, 4*a + 20 = 2*j - j. Factor -j*u - 1 + 2*u**3 - y*u**3 - 3*u**2 + 13*u.
-(u + 1)**3
Let t(x) be the third derivative of x**5/90 + x**4/12 + 2*x**3/9 - 12*x**2. Suppose t(r) = 0. What is r?
-2, -1
Let q(b) be the third derivative of b**8/20160 - b**6/720 + 2*b**5/15 + 9*b**2. Let j(r) be the third derivative of q(r). Suppose j(l) = 0. What is l?
-1, 1
Suppose -60/7*h**4 + 0 + 0*h - 16/7*h**2 - 72/7*h**3 + 50/7*h**5 = 0. What is h?
-2/5, 0, 2
Let l be (-8 - -8)*(-3)/6. Let v(i) be the third derivative of 0*i - 1/36*i**4 + 0 + 1/90*i**6 - i**2 - 7/180*i**5 + l*i**3. Factor v(m).
m*(m - 2)*(4*m + 1)/3
Suppose 6 + 8 = -b. Let f = -25/2 - b. Determine m so that 5*m**2 - f*m**3 + 1 - 9/2*m = 0.
1/3, 1, 2
Let p be (3/18)/(22/(-627)) - -5. Factor -1/4 - p*v**2 + 5/8*v.
-(v - 2)*(2*v - 1)/8
Let o = -2/43 - -92/129. Factor -2/9 - 4/9*m**3 - 2/9*m**5 - 4/9*m**2 + 2/3*m**4 + o*m.
-2*(m - 1)**4*(m + 1)/9
Let k(q) be the third derivative of -q**7/210 - q**6/60 - q**5/60 - 7*q**2. Determine l so that k(l) = 0.
-1, 0
Let c(z) be the first derivative of z**4/4 - z**2/2 - z - 5. Let b(s) = 8*s**3 + 3*s**2 - 5*s - 5. Let u(q) = -b(q) + 5*c(q). Factor u(y).
-3*y**2*(y + 1)
Let y(a) be the third derivative of 0*a + 0 + 0*a**3 + 1/240*a**5 - 1/840*a**7 - 1/480*a**6 + 1/1344*a**8 + 3*a**2 + 0*a**4. Factor y(z).
z**2*(z - 1)**2*(z + 1)/4
Let i(b) be the second derivative of 11*b + 0 + 0*b**4 - 1/18*b**3 + 0*b**2 + 1/60*b**5. Factor i(u).
u*(u - 1)*(u + 1)/3
Let u(z) be the third derivative of -289*z**7/105 - 272*z**6/15 - 148*z**5/5 + 64*z**4/3 - 16*z**3/3 - 43*z**2. Factor u(y).
-2*(y + 2)**2*(17*y - 2)**2
Let f(u) be the second derivative of 1/42*u**4 + 9/7*u**2 + 4*u - 2/7*u**3 + 0. Determine l so that f(l) = 0.
3
Let i(k) be the third derivative of 0*k + 0 + 0*k**3 + 1/540*k**6 + 0*k**4 + 1/945*k**7 - 2*k**2 + 0*k**5. Factor i(m).
2*m**3*(m + 1)/9
Let y = -3 + 8. Let g = 1546/3 - 508. Let 34/3*p**4 - 4/3*p - 10/3*p**y - 14*p**3 + 0 + g*p**2 = 0. What is p?
0, 2/5, 1
Solve -3*y**4 - 2*y**2 + 0*y**3 - 6*y**3 + 0*y**5 - 2*y**5 - 3*y**4 = 0 for y.
-1, 0
Let l = 4 - 1. Let d(b) be the first derivative of -16/5*b**5 - 2/3*b**l - 7/6*b**6 - 11/4*b**4 - 4 + 0*b**2 + 0*b. Find r such that d(r) = 0.
-1, -2/7, 0
Factor 3/2*y**5 - 12*y**4 + 0 + 27*y**3 - 81/2*y + 0*y**2.
3*y*(y - 3)**3*(y + 1)/2
Let q be 0/(1/(1/(-2))). Let u = 3 + q. Factor j**2 + 6*j**u - 5*j**3 + 7*j**3 - 2*j + 5*j**4.
j*(j + 1)**2*(5*j - 2)
Let b = 34 + -23. Solve -4 + 3*y**4 + 2 - 7*y**2 + 21*y**4 + 26*y**3 - b*y = 0.
-1, -1/2, -1/4, 2/3
Let p = 15 + -8. Let j be ((-1)/(-3))/(p/12). Determine o so that 2/7*o**4 - 4/7*o**3 + 2/7*o**5 - j*o**2 + 2/7*o + 2/7 = 0.
-1, 1
Let u(p) be the second derivative of -p**4/6 + 2*p**3/3 + p + 15. What is l in u(l) = 0?
0, 2
Factor 1/2*k**2 + 5/2*k + 2.
(k + 1)*(k + 4)/2
Let g(q) be the first derivative of -q**6/135 + q**5/90 - 2*q - 1. Let o(m) be the first derivative of g(m). Factor o(h).
-2*h**3*(h - 1)/9
Let p(l) be the first derivative of -l**3/3 + 7*l**2/2 - 3*l - 1. Let h be p(4). What is f in h*f + 4*f - f - 4 - 6*f**2 - 5*f**3 + 3*f**2 = 0?
-2, 2/5, 1
Suppose 9/7 - 1/7*h**5 + 10/7*h**2 - 3*h + 6/7*h**3 - 3/7*h**4 = 0. What is h?
-3, 1
Let n(w) be the second derivative of 31/10*w**6 - 2*w**2 + 113/20*w**5 + 0 + 9/14*w**7 + 7*w + 17/4*w**4 + 0*w**3. Factor n(q).
(q + 1)**3*(3*q + 2)*(9*q - 2)
Let q(s) be the first derivative of -s**5/20 - s**4/4 - s**3/2 - s**2/2 + s + 2. Let m(o) be the first derivative of q(o). Factor m(n).
-(n + 1)**3
Suppose 4*r - r = 0. Let n = r - 0. What is w in n + 2/9*w**2 + 2/9*w = 0?
-1, 0
Let n(d) be the first derivative of -4*d**3/3 + 8*d**2 - 12*d + 76. Suppose n(k) = 0. What is k?
1, 3
Factor 0 - 2/7*c**2 - 16/7*c**4 + 10/7*c**3 + 0*c + 8/7*c**5.
2*c**2*(c - 1)*(2*c - 1)**2/7
Factor n**3 + 80 + 96*n - n**3 + 36*n**2 + 4*n**3 + 0*n**2.
4*(n + 2)**2*(n + 5)
Let j = -2/295 + 179/295. Let x(r) = r**3 - 10*r**2 + r - 7. Let v be x(10). Let -24/5*i**2 + 0 + 12/5*i - j*i**4 + 3*i**v = 0. Calculate i.
0, 1, 2
Let s = -6 + 9. Let x = s - 1. Factor 0 + 1/3*y**3 + 0*y**x - 1/3*y.
y*(y - 1)*(y + 1)/3
Let p(c) be the second derivative of -c**4/90 + c**3/15 - 8*c. Solve p(i) = 0 for i.
0, 3
Let v be -9*((-115)/(-966) - (-2)/(-7)). Factor v - 3/4*b - 3/4*b**2.
-3*(b - 1)*(b + 2)/4
Suppose -j = -5 - 1. Let f(k) be the third derivative of 2/135*k**5 + 0*k**3 - 1/27*k**4 + 2*k**2 + 0 - 1/540*k**j + 0*k. Factor f(v).
-2*v*(v - 2)**2/9
Let q(x) = 2*x - 8. Let r be q(8). Suppose 5*c = y + 4, 0 = 4*y - 2*y + r. Let 3*j**4 + 2*j**2 - 5*j**4 + c*j**4 + 2*j**3 - 2*j + 0*j**4 = 0. Calculate j.
-1, 0, 1
Suppose 3*v = 3*f + v - 5, -5*v - 2 = -4*f. Factor -9*q + f*q**2 + 3*q + 6*q.
3*q**2
Let n(s) be the