n(k) = -6*f(k) + z(k). Factor n(s).
s*(s - 2)*(s + 16)
Let h(z) be the first derivative of z**7/2100 - z**6/300 - 4*z**3 + 10. Let j(v) be the third derivative of h(v). Determine u so that j(u) = 0.
0, 3
Let v = 501642/143 - 3508. Let q = v + 149/429. Factor 1/3*f**2 - q*f - 2/3.
(f - 2)*(f + 1)/3
Let u(g) = 63*g + 1138. Let d be u(-18). Let s(m) be the first derivative of d*m**2 - 11 + 4*m + 4/3*m**3. Factor s(n).
4*(n + 1)**2
Suppose 77/2*n - 49/6 - 137/3*n**2 + 35/6*n**4 + 9*n**3 + 1/2*n**5 = 0. What is n?
-7, 1/3, 1
Let t = 146 - 139. Let j be (t/14)/(3 + (-1 - 1)). Factor 0 + j*y**4 + 1/2*y**3 - 1/2*y**2 - 1/2*y.
y*(y - 1)*(y + 1)**2/2
Suppose -4*y + 3*y - 35 = -5*z, 2*z - 4*y = -4. Suppose 3*c = 5*c - z. Factor 6*m - 4*m - c*m**3 + 3*m**5 + 3*m**5 - 4*m**5.
2*m*(m - 1)**2*(m + 1)**2
Let f be -10*(-9 + (-464)/(-40) - 3). Find q, given that 6/11*q**5 + 12/11*q**2 - 4/11 - 8/11*q**f + 2/11*q - 8/11*q**3 = 0.
-1, -2/3, 1
Let a be (3 + -3)/(-1 - (5 + -7)). Let d(c) be the third derivative of -1/12*c**4 - 1/105*c**7 + 0 + 3*c**2 + 0*c + 1/60*c**6 + 1/30*c**5 + a*c**3. Factor d(b).
-2*b*(b - 1)**2*(b + 1)
Let h(z) be the first derivative of -z**6/360 + z**5/40 - z**4/12 - 22*z**3/3 - 27. Let k(g) be the third derivative of h(g). Factor k(p).
-(p - 2)*(p - 1)
Let g(a) = 873*a**3 + 1530*a**2 - 396*a + 28. Let y(c) = -13971*c**3 - 24480*c**2 + 6336*c - 450. Let i(t) = 33*g(t) + 2*y(t). Suppose i(f) = 0. What is f?
-2, 2/17
Suppose -4*j + 3*h = -8, 36*h = 31*h. Let f(c) be the second derivative of -4*c + 0*c**j - 1/6*c**3 + 0 + 1/12*c**4. Determine m so that f(m) = 0.
0, 1
Let i(y) = 6*y**2 - y. Let q(n) = -25*n**2 + 18*n - 24. Let z(x) = 4*i(x) + q(x). Factor z(o).
-(o - 12)*(o - 2)
Let i(q) be the first derivative of q**3/27 + 8*q**2/9 - 51. Find f such that i(f) = 0.
-16, 0
Let r(q) = -q + 8. Let g = -3 + 9. Let n be r(g). Factor -2 + n - 3*x**2 + 3.
-3*(x - 1)*(x + 1)
Let u(k) be the first derivative of -2*k**6/3 - 8*k**5/5 + 29*k**4 - 184*k**3/3 - 40*k**2 + 224*k + 58. Find l such that u(l) = 0.
-7, -1, 2
Factor 18*w**2 + 36*w + 4*w - 166*w**2 + 1369*w**3 - 1341*w**3.
4*w*(w - 5)*(7*w - 2)
Let u(n) be the first derivative of -n**4/8 - 4*n**3/3 + 108. What is h in u(h) = 0?
-8, 0
Factor 10/11*z + 2/11*z**3 - 12/11*z**2 + 0.
2*z*(z - 5)*(z - 1)/11
Let c(n) = 19*n**3 + 635*n**2 + 7217*n - 2121. Let i(u) = -9*u**3 - 318*u**2 - 3609*u + 1060. Let r(d) = 2*c(d) + 5*i(d). Let r(j) = 0. What is j?
-23, 2/7
Let s(a) = -3*a**3 - 13*a**2 - 31*a - 19. Let c be s(-10). Suppose -c + 1991 - 3*i**4 - 3*i**3 + 6*i**2 = 0. What is i?
-2, 0, 1
Factor 3 - 4*c**2 + 0*c**2 - 23 - 14*c - 10*c.
-4*(c + 1)*(c + 5)
Let i(w) be the second derivative of -2/15*w**6 + 0 + 8*w**2 - 4/5*w**5 + 8/3*w**3 - 4*w - w**4. Let i(v) = 0. What is v?
-2, -1, 1
Suppose 20 = -u + 5*x, 0 = 2*u + 4*x - 9*x + 15. Factor -3 + 2*f + 5*f - 5 + u*f - 4*f**2.
-4*(f - 2)*(f - 1)
Let d be (4 + -1 + -3)/2. Suppose 4*i + q - 4 = d, 3*q = -10*i + 5*i - 2. Find c, given that 0 + 3/4*c**3 + c**4 + 1/4*c**5 - c**i - c = 0.
-2, -1, 0, 1
Let a(p) = -p**3 + 4*p**2 - p + 1. Let v(z) = -z**3 + 9*z**2 - 11*z - 7. Let t(x) = 2*a(x) - v(x). Find j, given that t(j) = 0.
-3, -1, 3
Let c(p) = 56*p**2 - 152*p - 39. Let a(n) = 14*n**2 - 38*n - 10. Let l(w) = -9*a(w) + 2*c(w). Factor l(k).
-2*(k - 3)*(7*k + 2)
Let y be ((-6)/(-4))/((-1)/(-2)). Let l(d) be the first derivative of -3*d**2 - 3*d**y + 0*d**2 + 3 + 2*d**3 - 3*d. Let l(r) = 0. Calculate r.
-1
Let o(w) be the second derivative of w**2 + 0 + 2/15*w**3 - 1/20*w**4 - 1/30*w**5 - 3*w. Let k(f) be the first derivative of o(f). Solve k(x) = 0 for x.
-1, 2/5
Let s be 2 + -6 - (-1 - -6). Let v be s/(-15) + (-2)/10. Factor v*t**2 + 6/5*t + 4/5.
2*(t + 1)*(t + 2)/5
Let j(f) be the first derivative of 1 + 90*f + 5/4*f**4 - 20/3*f**3 - 15/2*f**2. What is d in j(d) = 0?
-2, 3
Let i = -1215 - -41315/34. Let n = 1/51 + i. Factor 0 - n*m**2 + 0*m + 1/6*m**3.
m**2*(m - 1)/6
Let z(s) = -3*s**2 + 5*s + 6. Let p(d) = 4*d**2 - 6*d - 7. Let u(x) = -2*p(x) - 3*z(x). Factor u(t).
(t - 4)*(t + 1)
Let o(g) be the first derivative of -g**6/9 + 158*g**5/15 - 533*g**4/2 + 338*g**3 - 199. Factor o(u).
-2*u**2*(u - 39)**2*(u - 1)/3
Let a be (-4)/22 + 520/(-44). Let m be a/(-9)*(-6)/(-4). Factor 3*i**3 - m*i**3 + 6*i**2 - 2*i**2 - 3*i**3.
-2*i**2*(i - 2)
Let k(p) be the second derivative of -p**5/70 - p**4/7 + 5*p**3/7 - 8*p**2/7 - 48*p. Determine y, given that k(y) = 0.
-8, 1
Let o(b) = 3*b + 8. Let w be o(-6). Let v be (-2)/w - 70/(-25). Find n such that 0 - 15*n - 2*n**3 - 12*n**2 - n**v - 6 = 0.
-2, -1
Let p = -1806 - -1810. Factor 9/7*a**5 + 0*a + 3*a**3 - 6/7*a**2 - 24/7*a**p + 0.
3*a**2*(a - 1)**2*(3*a - 2)/7
Let y(t) be the second derivative of t**5/110 + 5*t**4/66 - 4*t**3/11 - 36*t**2/11 + 88*t. Factor y(c).
2*(c - 3)*(c + 2)*(c + 6)/11
Suppose -2*d - 31 + 35 = 0. Find r such that 696*r + 480*r**3 + 1280*r**d + 584*r + 5*r**5 + 18*r**4 + 62*r**4 = 0.
-4, 0
Let 106/3 + 2/3*m**2 + 36*m = 0. Calculate m.
-53, -1
Let l = 72515/9 - 8057. Suppose 0 + 4/9*y**3 + 0*y**2 - l*y - 2/9*y**5 + 0*y**4 = 0. Calculate y.
-1, 0, 1
Let o(l) be the third derivative of -l**6/120 - 2*l**5/15 - 13*l**4/24 - l**3 + 62*l**2. Factor o(g).
-(g + 1)**2*(g + 6)
Let s(n) be the first derivative of -2*n**7/945 - n**6/180 - n**5/270 - 6*n**2 + 19. Let p(x) be the second derivative of s(x). Suppose p(w) = 0. What is w?
-1, -1/2, 0
Let a(r) be the third derivative of r**7/504 - r**5/6 - 13*r**4/24 - 2*r**2. Let f(z) be the second derivative of a(z). Solve f(c) = 0 for c.
-2, 2
Let r(j) be the third derivative of -8/105*j**7 - 31*j**2 + 4/3*j**3 + 5/6*j**4 + 0*j - 2/15*j**6 + 0 + 2/15*j**5 - 1/84*j**8. Factor r(n).
-4*(n - 1)*(n + 1)**3*(n + 2)
Let t(b) = -b + 1. Let g be t(-1). Suppose g*n - 3 - 11 = 0. Determine j, given that 7 + 2*j**2 - n + 2*j**2 - 4*j**3 = 0.
0, 1
Let d(r) be the first derivative of r**5/390 - r**4/52 + 2*r**3/39 + 4*r**2 + 6. Let k(j) be the second derivative of d(j). Factor k(c).
2*(c - 2)*(c - 1)/13
Suppose 0*t = -5*t + 85. Factor 10*d**2 + 3*d**2 - 12*d**3 - 35*d + 20 - 3*d**2 + t*d**3.
5*(d - 1)**2*(d + 4)
Let q(f) = 3*f**2 - 72*f + 53. Let a(w) = -6*w**2 + 147*w - 105. Let s(d) = -4*a(d) - 9*q(d). Factor s(z).
-3*(z - 19)*(z - 1)
Let m(q) = q + 12. Let x be m(-6). Let d be x/9*(-15)/(-2). Find f such that 132*f**4 + 20*f + 124*f**2 + 28*f**d - 16 - 20*f + 212*f**3 = 0.
-2, -1, 2/7
Suppose -7*l - 14 + 70 = 0. Let u = -7 + 10. Find i such that -3*i**2 - 2*i**2 + 2 - 9*i + i**u + 3*i**2 + l*i = 0.
-1, 1, 2
Let t = 3 + 1. Let k be -3*((-64)/12)/t. Factor i**4 - 2*i**3 - i**4 + k*i**3 + i**4 + i**2.
i**2*(i + 1)**2
Let t(y) be the second derivative of -y**7/21 - y**6/5 + 17*y**5/10 + 13*y**4/2 + 20*y**3/3 - 420*y + 1. Solve t(v) = 0.
-5, -1, 0, 4
Let z = 204 + -199. Let n(k) be the second derivative of 0 + 1/2*k**2 + 7*k + 1/30*k**6 + 2/3*k**3 + 1/2*k**4 + 1/5*k**z. Suppose n(m) = 0. Calculate m.
-1
Let y(c) be the second derivative of c**4/42 + 46*c**3/21 - 47*c**2/7 - 34*c + 1. Factor y(s).
2*(s - 1)*(s + 47)/7
Let d be ((-4)/(-14))/(3/21). Let n be d/(-3 + (-24)/(-4)). Determine q, given that 2/3*q - 4/3*q**2 - n*q**3 + 4/3 = 0.
-2, -1, 1
Let -2/3 - 770/3*s - 148225/6*s**2 = 0. What is s?
-2/385
Let y(z) be the second derivative of z**7/2520 + z**6/720 - 7*z**4/12 + 2*z. Let r(p) be the third derivative of y(p). Suppose r(s) = 0. Calculate s.
-1, 0
Let v(i) be the third derivative of -i**6/1440 - i**5/480 + i**4/48 - 4*i**3 - 8*i**2. Let z(q) be the first derivative of v(q). Factor z(y).
-(y - 1)*(y + 2)/4
Solve 1/9*k**3 + 0 + 8/9*k**2 + 7/9*k = 0.
-7, -1, 0
Let x = -119/110 + -9/11. Let z = x + 17/5. Solve -3/2*t**2 - 21/4*t + 9/4*t**3 - z = 0 for t.
-1, -1/3, 2
Let i(o) be the second derivative of o**6/40 - 5*o**5/16 + 65*o**4/48 - 55*o**3/24 + 3*o**2/2 + 128*o + 1. Let i(u) = 0. What is u?
1/3, 1, 3, 4
Suppose 2*v - 4*g = -3*v + 22, -g - 3 = 0. Factor 34 - 3*b**4 + 6*b**3 - 3*b**v - 34.
-3*b**2*(b - 1)**2
Let h(s) be the second derivative of 4*s**5/25 + 7*s**4/15 - 11*s**3/5 - 9*s**2/5 - 58*s. Determine m, given that h(m) = 0.
-3, -1/4, 3/2
Let p(q) be the first derivative of 5/4*q**2 + 0*q - 10 + 125/8*q**4 - 25/3*q**3. Suppose p(t) = 0. What is t?
0, 1/5
Let j(b) = -3*b**5 +