) be the second derivative of -p**6/50 + 3*p**5/25 - p**4/10 - 2*p**3/5 + 9*p**2/10 - 81*p. Determine t, given that v(t) = 0.
-1, 1, 3
Let m(b) be the first derivative of b**3/21 - 11*b**2/7 + 121*b/7 + 114. Solve m(t) = 0.
11
Solve -25/6*b**2 - b + 0 + 27/2*b**3 + 13/6*b**5 - 21/2*b**4 = 0.
-2/13, 0, 1, 3
Let l(s) be the second derivative of -s**4/90 + 4*s**3/45 + 4*s**2/5 + 37*s - 2. Factor l(q).
-2*(q - 6)*(q + 2)/15
Factor 3/5*f**2 + 0*f - 1/10*f**3 + 0.
-f**2*(f - 6)/10
Let r(m) = -m**2 + 4*m - 2. Let c(d) = 5*d**2 - 173*d - 281. Let i(q) = c(q) - r(q). Find b, given that i(b) = 0.
-3/2, 31
Let z(c) = -c**2 - 2*c + 4. Let v be z(-2). Let q be 8/4*3 - v. Determine f, given that 0*f**4 - 20*f**3 - 12*f + 62*f**q + 4*f**4 - 34*f**2 = 0.
0, 1, 3
Let i = 211 + -211. Let r(x) be the second derivative of i - 4/27*x**3 + 1/54*x**4 - 2*x + 4/9*x**2. Factor r(g).
2*(g - 2)**2/9
Suppose -4*c = -7*c - 15. Let g(q) = 3*q**2 + 9*q. Let i(w) = 2*w**2 + 4*w. Let u(b) = c*g(b) + 9*i(b). Determine a, given that u(a) = 0.
0, 3
Let h(i) be the second derivative of -5/2*i**4 + 0*i**2 - 3/5*i**6 - 1/14*i**7 - 9/5*i**5 - 3 - 3/2*i**3 + 10*i. What is c in h(c) = 0?
-3, -1, 0
Let d(o) be the second derivative of -o**5/50 - 7*o**4/10 - 13*o**3/5 - 19*o**2/5 + 130*o. Factor d(c).
-2*(c + 1)**2*(c + 19)/5
Let m(n) be the second derivative of 333/5*n**5 - 139/3*n**4 - 234/5*n**6 - 4*n**2 + 33*n + 18*n**3 + 0 + 72/7*n**7. Suppose m(o) = 0. What is o?
1/4, 1/3, 2
Let c = -3652 + 18264/5. Let c - 3/5*p**2 + 11/5*p = 0. What is p?
-1/3, 4
Suppose 6*o - 3 = -3*k + 3*o, -1 = -3*k - 4*o. Let s(t) = -2*t. Let y be s(-2). Factor 2*q**4 - k*q**3 + 3*q**2 + q**3 - 9*q**2 - y + 10*q.
2*(q - 1)**3*(q + 2)
Let z = 1260 + -3778/3. Solve -2*g**3 + 0*g**2 + 0*g + 0 - z*g**4 = 0 for g.
-3, 0
Let o(f) be the third derivative of 1/240*f**5 + 1/96*f**4 + 0*f + 5*f**2 - 1/480*f**6 - 1/24*f**3 + 0. Determine m, given that o(m) = 0.
-1, 1
Let t(s) be the third derivative of -s**7/105 + s**6/12 - 4*s**5/15 + s**4/3 + 45*s**2. Factor t(z).
-2*z*(z - 2)**2*(z - 1)
Let x = -3 - -3. Suppose 5*j + x*j = 55. Factor 4*s**2 - j + 17*s + 15 + 2*s**2 - 7*s.
2*(s + 1)*(3*s + 2)
Let g(t) = -t**2 + 25*t - 144. Let c be g(10). Let y(w) be the second derivative of 0 + 0*w**3 - 1/3*w**4 + 0*w**5 + 7*w + w**2 + 1/15*w**c. Factor y(q).
2*(q - 1)**2*(q + 1)**2
Let f(u) be the first derivative of -u**3/9 - 22*u**2/3 - 484*u/3 + 10. Solve f(h) = 0 for h.
-22
Factor 28*i + 44*i + 10*i**2 - 20*i + 28 + 10*i**2 - 4*i**3.
-4*(i - 7)*(i + 1)**2
Let p(j) = 76*j**3 + 276*j**2 + 584*j + 320. Let r(s) = 7*s**3 + 25*s**2 + 53*s + 29. Let q(w) = 3*p(w) - 32*r(w). Factor q(m).
4*(m + 1)*(m + 2)*(m + 4)
Let s = -1307 + 422163/323. Let g = 640/969 + s. Let 1/2*a**5 + 29/6*a**3 + 0 + g*a + 10/3*a**2 + 8/3*a**4 = 0. What is a?
-2, -1, -1/3, 0
What is y in 1/3*y**2 + 3844/3 - 124/3*y = 0?
62
Let l(c) = -c**2 - 7*c - 1. Let m be l(-7). Let y = 4 + m. Factor -4*r + 2*r**2 - r + y*r.
2*r*(r - 1)
Solve -8/9 + 4/3*c**3 - 2/9*c**4 - 26/9*c**2 + 8/3*c = 0.
1, 2
Let d(m) be the third derivative of -m**10/50400 + m**8/2240 - m**7/840 + 4*m**5/15 + 17*m**2. Let s(v) be the third derivative of d(v). Factor s(j).
-3*j*(j - 1)**2*(j + 2)
Let h(c) = -2*c**3 + 2*c**2 - 8*c - 8. Let q(g) = g**3 - g**2 + 3*g + 3. Let f be 168/60 - (-3)/15. Let y(j) = f*h(j) + 8*q(j). Solve y(a) = 0 for a.
0, 1
Let l(k) be the first derivative of 8/3*k**2 - 23 + 2/27*k**3 + 32*k. Factor l(o).
2*(o + 12)**2/9
Factor -15/2*x + 0 + 23/2*x**2 + 1/2*x**4 - 9/2*x**3.
x*(x - 5)*(x - 3)*(x - 1)/2
Let d(y) = -171*y**2 + 420*y + 69. Let b(u) = 42*u + 2 + 5 - 91*u**2 + 74*u**2. Let k(j) = 21*b(j) - 2*d(j). Let k(i) = 0. Calculate i.
-1/5, 3
What is o in -8/3*o**2 + 0 + 2/3*o**3 + 8/3*o = 0?
0, 2
Let o be (-8190)/1176 - (-2 + (-5)/1). Let u(m) be the second derivative of 0 + 5*m + 2/7*m**3 - o*m**4 - 6/7*m**2. Suppose u(s) = 0. Calculate s.
2
Let d = -108 + 110. Factor -8*r**2 - r + 12*r**2 - r + d*r**5 - 4*r**4.
2*r*(r - 1)**3*(r + 1)
Suppose -6*a + 826 = 8*a. Factor -65*t**3 - 86*t**5 - a*t**4 + 300*t**2 - 180*t + 9*t**4 + 81*t**5.
-5*t*(t - 1)**2*(t + 6)**2
Factor 0 + 3/2*x**3 - 3/2*x + 0*x**2.
3*x*(x - 1)*(x + 1)/2
Let a = -33 - -37. Let f(u) = -5*u**3 + 5*u**2 + 4*u. Let z(o) = o**3 + o. Let n(j) = a*z(j) - 2*f(j). Factor n(c).
2*c*(c - 1)*(7*c + 2)
Let q(c) = c**2 + 7*c - 6. Let r(g) = 2*g**2 + 12*g - 12. Let t(v) = -5*q(v) + 3*r(v). Factor t(y).
(y - 2)*(y + 3)
Let y be (20/(-30))/((-4)/18). Factor -11*o - 12*o**y + 5*o + 3*o**4 + 17*o**2 - 2*o**2.
3*o*(o - 2)*(o - 1)**2
Let g(t) = -t**2 + 2*t - 1. Let k(x) = 15*x**2 + 18*x + 18. Let l(y) = 18*g(y) + k(y). Determine i so that l(i) = 0.
0, 18
Factor -2*b**2 - 1/4*b**3 + 1/4*b + 2.
-(b - 1)*(b + 1)*(b + 8)/4
Find z such that 285*z + 9*z**2 + 3*z**2 + 4*z**2 - 17*z**2 + 6*z**2 = 0.
-57, 0
Let v = 137/62 - 53/31. Factor -v*p**4 + 0*p + 1/2*p**2 - 1/2*p**5 + 0 + 1/2*p**3.
-p**2*(p - 1)*(p + 1)**2/2
Let s(o) be the first derivative of 29 + 0*o - 35/6*o**3 + 1/2*o**5 + 0*o**4 - 15/2*o**2. Let s(g) = 0. Calculate g.
-2, -1, 0, 3
Factor 55*k - 176*k**2 + 344*k**2 + 45 + 15 - 55*k**3 + 5*k**4 - 233*k**2.
5*(k - 12)*(k - 1)*(k + 1)**2
Suppose -3*n + 32 = 29. Suppose 5*d - n + 3 = -l, -6 = -3*d + 3*l. Factor 0 - 2/9*r**3 - 2/9*r**2 + d*r.
-2*r**2*(r + 1)/9
Let t(p) be the second derivative of p**6/285 + 2*p**5/95 - 16*p**3/57 - 16*p**2/19 + 81*p. Factor t(i).
2*(i - 2)*(i + 2)**3/19
Let d(n) be the third derivative of -3/70*n**7 + 0*n**3 - 27*n**2 + 1/40*n**6 + 1/112*n**8 + 0*n + 0 - 1/4*n**4 + 3/20*n**5. Find r, given that d(r) = 0.
-1, 0, 1, 2
Let r be (-2)/(-6) + 2387/21. Suppose 0 = -9*a + 7*a + r. Factor 0*w - 29 - 2*w**2 + a + 4*w - 22.
-2*(w - 3)*(w + 1)
Factor 273*i**3 + 18*i**2 + 279*i**3 - 540*i**3 + 2*i**4 + 11*i - 3*i.
2*i*(i + 1)**2*(i + 4)
Let t = -25 + 33. Suppose -5*r = t*r - 3*r. Suppose c**3 + 1/2*c**2 + 1/2*c**4 + r + 0*c = 0. Calculate c.
-1, 0
Let k be 2/(-80)*(-4)/12. Let y(w) be the third derivative of 0 + k*w**4 + 0*w - 1/300*w**5 + 3*w**2 + 1/15*w**3. Factor y(f).
-(f - 2)*(f + 1)/5
Suppose -13 = -6*i - 1. Find u such that -u**4 - u**i - 3*u**4 + 2*u**4 + 3*u**2 = 0.
-1, 0, 1
Let b(j) = -2*j**3 + j**2 + 3*j + 1. Let u be b(2). Let s be (34/u - 1)/((-56)/40). Solve -12/7 - 3/7*q**4 - s*q**2 - 36/7*q - 18/7*q**3 = 0.
-2, -1
Let n(j) = -7*j**2 + j**3 - 10*j + 4*j - 4*j**3 + 9*j**3. Let o(d) = -d**3 + d**2 + d. Let v(u) = 4*n(u) + 28*o(u). Factor v(r).
-4*r*(r - 1)*(r + 1)
Let v(o) = 4*o**3 - 46*o**2 + 72*o - 36. Let j(c) = -12*c**3 + 139*c**2 - 214*c + 108. Let i(y) = -2*j(y) - 7*v(y). Find k, given that i(k) = 0.
1, 9
Factor -910/3*y**2 - 155/3 - 205*y + 5/3*y**5 - 45*y**4 - 590/3*y**3.
5*(y - 31)*(y + 1)**4/3
Suppose -3*p = -8*p + 15. Let v be (p/5)/(13/65). Solve 3*q**3 - 4 - 15*q + v*q**4 - 9*q**2 - 7 + 5 = 0.
-1, 2
Let j(a) = -a**2 + 12*a - 7. Let g be j(11). Let r(f) be the first derivative of -12*f + 4/3*f**3 + g*f**2 - 6. Factor r(c).
4*(c - 1)*(c + 3)
Factor 3/2 - 3*p**2 + 3/2*p**4 + 0*p**3 + 0*p.
3*(p - 1)**2*(p + 1)**2/2
Let p = 167/4 - 39. Let z be (-7 + 110/16)*(-42)/3. Factor -7/4*d - p*d**2 + 9/4*d**4 + z*d**3 + 1/2.
(d - 1)*(d + 1)**2*(9*d - 2)/4
Let b(j) = 4*j**4 - 36*j**3 + 9*j**2 + 100*j + 79. Let c(n) = 3*n**4 - 24*n**3 + 6*n**2 + 66*n + 53. Let m(h) = 5*b(h) - 7*c(h). Factor m(k).
-(k - 2)*(k + 1)**2*(k + 12)
Let k(d) = 67*d + 406. Let u be k(-6). Let w(q) be the first derivative of 0*q - 11*q**3 + 5 + 3*q**2 + 27/5*q**5 + 9*q**u. Factor w(c).
3*c*(c + 2)*(3*c - 1)**2
Let c(f) be the third derivative of f**6/480 - 11*f**5/240 + 5*f**4/48 - 2*f**2 - 48*f. Factor c(s).
s*(s - 10)*(s - 1)/4
Let z(i) be the third derivative of i**7/280 - i**6/120 + 10*i**3/3 - 14*i**2. Let g(y) be the first derivative of z(y). Factor g(s).
3*s**2*(s - 1)
Suppose -4*o = 3*n - 0*n - 11, 2*n - 5*o = 15. Suppose -5*p + n*p - 10*p - 2*p + 10 + 2*p**2 = 0. What is p?
1, 5
Let j(a) be the first derivative of -a**5/45 - a**4/9 + 17*a**2/2 + 19. Let p(n) be the second derivative of j(n). Factor p(o).
-4*o*(o + 2)/3
Let x(g) = -8*g**2 - 104*g + 216. Let w(v) = -6*v**2 - 104*v + 216. Let d(i) = 6*w(i) - 4*x(i). Factor d(h).
-4*(h - 2)*(h + 54)
Let i = 1467 - 1461. Let a(t) be the first derivative of 4*t**5 - 2/3*t