7). Factor -1/10*s**4 + 3/5*s**m + 2/5*s**3 - 2/5*s - 1/2.
-(s - 5)*(s - 1)*(s + 1)**2/10
Let p be (314/3768)/((-1)/(-4)). Let d(g) be the second derivative of 2/3*g**2 - 1/9*g**4 + 0 - 6*g + p*g**3 - 1/10*g**5. Factor d(c).
-2*(c - 1)*(c + 1)*(3*c + 2)/3
Let y(b) = b**2 - b - 8. Let w = -3 + 7. Let s be y(w). Solve 3*u**3 - 3*u**5 + 291*u**2 + 0*u**5 - 294*u**2 + 3*u**s = 0.
-1, 0, 1
Let z be 4/(-12) + (-11 - 3751/(-330)). Let q(k) be the second derivative of z*k**4 + 0 + 1/3*k**3 + 6/5*k**2 - 50*k. Let q(p) = 0. Calculate p.
-3, -2
Factor 5/4*j**2 - 253/2*j + 7/4*j**3 + 36.
(j - 8)*(j + 9)*(7*j - 2)/4
Let g(k) be the first derivative of -k**4/18 - 14*k**3/9 + 70*k**2/9 - 32*k/3 - 5125. Solve g(p) = 0.
-24, 1, 2
Factor -573 + 4*i**2 - 551 - 92*i + 132.
4*(i - 31)*(i + 8)
Let s(q) = -q**2 + 4*q + 50. Let g be s(-10). Let p be (-246)/g + (16/20)/4. Factor -p*m + 2/15*m**2 + 242/15.
2*(m - 11)**2/15
Let v(c) be the third derivative of -c**7/126 - 25*c**6/72 - 113*c**5/36 + 125*c**4/72 + 95*c**3/3 - 4424*c**2. Suppose v(a) = 0. What is a?
-19, -6, -1, 1
Let w(n) = 4*n**3 + 433*n**2 + 115*n + 756. Let r be w(-108). Factor 2/7*d**4 + r + 0*d**2 - 2/7*d**3 + 0*d.
2*d**3*(d - 1)/7
Let i(k) be the first derivative of -4*k**6/15 + 174*k**5/25 - 67*k**4/5 - 254*k**3/15 + 138*k**2/5 + 16*k + 1818. Suppose i(s) = 0. Calculate s.
-1, -1/4, 1, 2, 20
Let d(s) be the first derivative of -s**6/120 + 21*s**5/20 + 202*s**3/3 - 118. Let q(u) be the third derivative of d(u). What is x in q(x) = 0?
0, 42
Let n(a) = a - 6. Let d be n(7). Let r be d/((-3)/(-3*4)). Factor -3*u**r + 0*u**4 + u**5 + 3*u**5 - u**5.
3*u**4*(u - 1)
Let w(f) be the first derivative of f**4/4 + 106*f**3/3 + 1550*f**2 + 15000*f - 1025. Factor w(z).
(z + 6)*(z + 50)**2
Let w(j) = j**2 - 11*j + 16. Let o be w(9). Let g be 5 + (o - -1) + -17 + 15. Factor 5*u**2 - 13*u**g + 6*u**2 - 20*u + 7*u**2.
5*u*(u - 4)
Let v(p) be the third derivative of 0 + 1/12*p**4 + 14/39*p**3 - 1/390*p**5 + 17*p**2 + 0*p. Suppose v(u) = 0. What is u?
-1, 14
Let p = 39 - 35. Let w be 18/(-2 + 1) + p. Let x(k) = 4*k**2 - 29*k - 101. Let o(m) = -m**2 + 10*m + 34. Let v(t) = w*o(t) - 4*x(t). Factor v(h).
-2*(h + 6)**2
Let q(f) = -2*f**3 - f**2 + f + 1. Let k = -94 - -97. Let r(l) = 3*l**3 + 129*l**2 - 1767*l + 8229. Let o(d) = k*q(d) + r(d). Let o(v) = 0. What is v?
14
Let h(n) be the third derivative of n**7/1680 - 7*n**5/240 - n**4/8 + 28*n**3/3 + 8*n**2 - 3*n. Let k(q) be the first derivative of h(q). Factor k(t).
(t - 3)*(t + 1)*(t + 2)/2
Let a(u) be the second derivative of -u**6/1260 + u**5/42 + 11*u**4/84 - 79*u**3/6 + 4*u + 3. Let p(i) be the second derivative of a(i). Factor p(b).
-2*(b - 11)*(b + 1)/7
Determine g, given that 6*g**2 - 11*g**2 - 3378 - 2*g**2 + 3*g**2 - 1496*g - 1074 = 0.
-371, -3
Let d(v) be the first derivative of 13*v**5/5 - 7*v**4 - 16*v**3 + 56*v**2 - 16*v - 2389. Suppose d(f) = 0. What is f?
-2, 2/13, 2
Let f be -75 - ((-496062)/(-310))/(-21). Factor 2/5*k**5 + 0 + 2*k**2 - f*k**3 - 2/5*k**4 - 4/5*k.
2*k*(k - 1)**3*(k + 2)/5
Let h = 112 + -110. Let o(j) = 2*j**2 + j - 7. Let r be o(h). Let -k**2 + 60*k + 2*k**2 - 55*k**2 - 24 - r*k**4 + 21*k**3 = 0. What is k?
1, 2
Factor 497 + 1/2*t**2 - 499/2*t.
(t - 497)*(t - 2)/2
Let n = 82 + -82. Suppose -9*g + 37 - 10 = n. Factor 3*q - 6*q**3 + 12*q**4 + 14*q**g + 10*q**3 + 12*q**2 + 6*q**5 - 3*q**5.
3*q*(q + 1)**4
Factor 6/5*p**3 + 0 + 124/5*p**2 + 16*p.
2*p*(p + 20)*(3*p + 2)/5
Factor 108/7*o - 4/7*o**2 - 200/7.
-4*(o - 25)*(o - 2)/7
Let j be (-84)/(-14) - (4 + 0) - 38. Let u = 46 + j. Factor 14*p + 6 - 2*p**5 - 5*p**2 - p**2 - u*p**4 - 12*p**3 + 10*p**2.
-2*(p - 1)*(p + 1)**3*(p + 3)
Let n(f) = 2*f**2 + 112*f + 1919. Let t be ((-14)/8)/((-3)/(-24)). Let d(h) = 4*h**2 + 220*h + 3837. Let p(r) = t*n(r) + 6*d(r). What is k in p(k) = 0?
-31
Let u = -3806 + 11419/3. Let l(s) be the first derivative of 17 - u*s**3 - 2*s + 3/2*s**2. Factor l(i).
-(i - 2)*(i - 1)
Let f be (-2 - -4)*(-19 + 4)*-6. Let v be 33/f*8 + (-2)/(-5). What is u in -v*u**3 + 0*u - 98/15*u**2 - 2/15*u**4 + 0 = 0?
-7, 0
Let z(y) be the third derivative of 5*y**5/48 - 49*y**4/64 - 3*y**3/16 - 729*y**2. What is t in z(t) = 0?
-3/50, 3
Let g(v) be the second derivative of v**4/12 - v**3/6 + v**2 + 2*v + 50. Let n(p) = -20*p**2 + 14*p - 44. Let o(r) = -44*g(r) - 2*n(r). Factor o(u).
-4*u*(u - 4)
Let y(a) = 2*a**3 + 16*a**2 - 30*a + 20. Suppose 3*h - 42 = 17*h. Let t(j) = -2*j**3 - 15*j**2 + 30*j - 19. Let o(f) = h*y(f) - 4*t(f). Factor o(g).
2*(g - 1)**2*(g + 8)
Factor -152/5*n - 4/5*n**2 - 276.
-4*(n + 15)*(n + 23)/5
Let j(r) = r + 1. Let z be j(1). Let -t**5 + 372*t**2 - t**5 - 386*t**z + 14*t**4 + 2*t**3 = 0. Calculate t.
-1, 0, 1, 7
Let u(k) be the third derivative of k**7/280 + 9*k**6/320 - 17*k**5/160 + 3*k**4/32 + 1079*k**2. Find t, given that u(t) = 0.
-6, 0, 1/2, 1
Let j(l) be the first derivative of -l**4 + 12*l**3 - 30*l**2 + 28*l - 626. Factor j(b).
-4*(b - 7)*(b - 1)**2
Let c(y) = 2*y**4 - 7*y**3 + 7*y - 5. Let q(p) = 2*p**4 - 6*p**3 + 6*p - 4. Let l(r) = -2*c(r) + 3*q(r). Suppose l(x) = 0. What is x?
-1, 1
Suppose 0 = 2*k - 3*a - 9, -3*k + 2*k = -5*a - 8. Suppose -m = -h - 4 + 2, k*m - 27 = -4*h. Factor i**4 - 44*i**2 + 3*i**h + 48*i**2 + i**3.
i**2*(i + 2)**2
Let f(z) be the second derivative of -3*z + 1/30*z**5 - 14 + 169/3*z**2 + 65/3*z**3 + 3/2*z**4. Solve f(m) = 0.
-13, -1
Factor -108/7 - 15*b + 3/7*b**2.
3*(b - 36)*(b + 1)/7
Suppose 0 = -23*u + u + 44. Factor 2*r**u - 24*r + 6*r - 22 + 2.
2*(r - 10)*(r + 1)
Let -472/15 - 476/15*k**2 - 946/15*k - 2/15*k**3 = 0. What is k?
-236, -1
Let w(p) be the second derivative of -3/5*p**4 + 2 - 4*p - 13/50*p**5 - 1/50*p**6 + 7/10*p**2 - 1/5*p**3. Solve w(v) = 0 for v.
-7, -1, 1/3
Factor 64/5 - 52/5*h - 13/5*h**2 + 1/5*h**3.
(h - 16)*(h - 1)*(h + 4)/5
Let r(k) be the second derivative of 3*k**5/20 - 11*k**4/4 + 7*k**3/2 + 441*k**2/2 + k + 14. Let r(s) = 0. What is s?
-3, 7
Suppose -12 = 2*z + 3*s, z + 19 = 3*s + 4. Let b(v) = 12*v**3 + 3*v**2 + 3*v. Let a(x) = -x**3 - x**2. Let u(y) = z*a(y) - b(y). Let u(w) = 0. What is w?
0, 1
Let j(d) = 4*d**3 + 10*d**2 + 13*d - 3. Let h(m) = 9*m**3 + 20*m**2 + 25*m - 7. Let y(l) = -18*l + 105. Let f be y(6). Let r(b) = f*h(b) + 7*j(b). Factor r(o).
o*(o + 2)*(o + 8)
Let m(k) = 16*k**2 + 28*k + 30. Let f(d) = 18*d**2 + 26*d + 29. Let s(i) = 6*f(i) - 7*m(i). Determine w so that s(w) = 0.
-9, -1
Let g(k) be the second derivative of 2025/2*k**3 - 1/42*k**7 + 345/2*k**4 - 293/10*k**5 + 0 + 131*k + 43/30*k**6 + 3375/2*k**2. Factor g(y).
-(y - 15)**3*(y + 1)**2
Let m(r) be the first derivative of r**6/50 - 9*r**5/100 + r**4/10 - 67*r - 55. Let y(g) be the first derivative of m(g). Factor y(f).
3*f**2*(f - 2)*(f - 1)/5
Let y(f) be the second derivative of f**7/840 - 11*f**6/480 + 7*f**5/48 - 25*f**4/96 + 50*f**2 + 3*f. Let g(u) be the first derivative of y(u). Factor g(r).
r*(r - 5)**2*(r - 1)/4
Let f(b) be the second derivative of -b**4/12 + 31*b**3/6 - 110*b**2 + b + 138. Factor f(r).
-(r - 20)*(r - 11)
Let v(m) be the first derivative of 72*m + 15*m**5 - 435/4*m**4 - 245 + 254*m**3 - 210*m**2. Factor v(c).
3*(c - 3)*(c - 2)*(5*c - 2)**2
Let j(x) = -15*x - 133. Suppose 3*f + 3 = 0, 0 = 6*n - 2*n + 2*f + 38. Let s be j(n). Factor -200/3 - 2/3*w**3 - 160/3*w + 38/3*w**s.
-2*(w - 10)**2*(w + 1)/3
Factor -85/4*w**2 + w**3 + 461/4*w - 55/2.
(w - 11)*(w - 10)*(4*w - 1)/4
Let o(s) be the second derivative of s**6/45 + 46*s**5/15 + 962*s**4/9 - 2944*s**3/3 + 3072*s**2 - 2*s. Factor o(u).
2*(u - 2)**2*(u + 48)**2/3
Let b = 524687 - 524684. Find g, given that 5/2*g**b - 1/4*g**2 + 1/4*g**4 + 0 - 5/2*g = 0.
-10, -1, 0, 1
Let s = -200 - -205. Suppose -5*p + 2*h - 10 = -36, -4*p = -4*h - 28. Solve -o**2 + 0*o**3 + o**p + 0 - 1/2*o**s + 1/2*o = 0 for o.
-1, 0, 1
Let t = 1882/3 - 3134/5. Let z(j) be the second derivative of 5*j + 1/9*j**3 - t*j**5 - 64/135*j**6 + 10/27*j**4 + 0 - 1/9*j**2. What is b in z(b) = 0?
-1, -1/4, 1/4
Let j(s) = 3*s**3 + 40*s**2 - 27*s + 14. Let a be j(-14). Let t(x) be the third derivative of 0*x + 0 + 1/3*x**4 + a*x**3 + 15*x**2 + 1/15*x**5. Factor t(v).
4*v*(v + 2)
Let t(n) be the first derivative of -n**4/26 - 10*n**3/39 + 125*n**2 + 56250*n/13 - 7786. Factor t(q).
-2*(q - 45)*(q + 25)