Factor -2/7*s**4 + 2/7*s**k + 2/7*s - 4/7*s**3 - 2/7 + 4/7*s**2.
2*(s - 1)**3*(s + 1)**2/7
Let t(v) = v**2 + 54*v - 55. Let x(y) = -3*y**2 - 106*y + 109. Let q(s) = 5*t(s) + 3*x(s). Find b, given that q(b) = 0.
-13, 1
Let r(s) be the first derivative of 2/3*s**2 + 40 + 1/9*s**3 + 4/3*s. Factor r(l).
(l + 2)**2/3
Suppose 5*l - 269 - 266 = 0. Suppose -5*d + n + 43 = -l, -3*d + 90 = -2*n. Factor -d*f**2 + 15*f + f**3 + 9*f + 8 + 7*f**3.
2*(f - 2)**2*(4*f + 1)
Let g(z) be the first derivative of z**8/560 - z**7/350 - z**6/100 - 13*z**2/2 - 11. Let n(c) be the second derivative of g(c). Factor n(d).
3*d**3*(d - 2)*(d + 1)/5
Factor -28/3*l + 1/3*l**3 - 1/3*l**4 + 16/3 + 4*l**2.
-(l - 2)**2*(l - 1)*(l + 4)/3
Let u be (2/14 - 3059/(-196))/(21/14). Let 0 + 3/4*o**5 + 11/2*o**4 + 9/4*o + 13*o**3 + u*o**2 = 0. What is o?
-3, -1, -1/3, 0
Let x = 7/19 + 3/95. Let i be 842/4631 + 2*(-6)/(-55). Factor 0 + i*v**2 - x*v.
2*v*(v - 1)/5
Suppose -18*k - 11 = -16*k + 3*s, 0 = -3*k - 4*s - 14. Suppose 18/7*m**3 - 2*m**4 - 18/7*m + 10/7*m**k + 4/7 = 0. What is m?
-1, 2/7, 1
Let l be 8 - (7 + (-2 - 1)). Let n(g) be the second derivative of -1/30*g**l + 1/50*g**5 - 1/15*g**3 + 1/5*g**2 + 0 - 6*g. Determine c so that n(c) = 0.
-1, 1
Let p(a) be the first derivative of -3/10*a**2 - 1/30*a**3 + 35 + 0*a. Find y such that p(y) = 0.
-6, 0
Let t(p) = -2*p**3 - 12*p**2 - 2*p + 8. Let m(o) = 3*o - 38. Let r be m(10). Let k(f) = f**2 - 1. Let q(a) = r*k(a) - t(a). Solve q(b) = 0.
-1, 0
Let u(n) = n**3 + 16*n**2 + 2*n + 2. Let w be u(-16). Let l = 30 + w. Factor 2 - 36*b**2 - 9 - 28*b - 20*b**3 - 4*b**4 - 1 + l.
-4*(b + 1)**3*(b + 2)
Let s(o) = o**3 - 4*o**2 + o + 1. Let z be s(4). Suppose y = -0*y + z*c - 1, -2*y = -c - 16. Determine i so that y*i**3 + 6*i**2 - 16*i**2 + 4*i**2 = 0.
0, 2/3
Let f be (-60)/(-7 - 1095/(-165)). Let 198*y**3 - 54*y**4 - 75/2 - 543/2*y**2 + f*y = 0. What is y?
5/6, 1
Factor -1/4*s**3 + 45/4*s - 81/4 - 3/4*s**2.
-(s - 3)**2*(s + 9)/4
Let g(v) be the second derivative of v**7/14 + 3*v**6/5 - 6*v**5/5 - 3*v**4/2 + 7*v**3/2 - 163*v. Factor g(b).
3*b*(b - 1)**2*(b + 1)*(b + 7)
Let s(u) = -u**2 + u - 4. Let z be s(-4). Let d be z/(-4) - 0/(-2). Solve -4 + 0 - w**2 + d - w = 0.
-2, 1
Let s = 7 - 5. Factor 24 + 15*c + 2*c**2 + 53*c - 28*c**3 + 14*c**s.
-4*(c - 2)*(c + 1)*(7*c + 3)
Let m(w) be the first derivative of -2*w + 12 - 3*w**2 + 1/3*w**6 - 4/3*w**3 + 6/5*w**5 + w**4. Factor m(u).
2*(u - 1)*(u + 1)**4
Let r(b) = -b**5 + 4*b**4 + b**2 - 13*b + 4. Let y = -36 + 40. Let a(j) = -j**5 + 3*j**4 + j**3 + j**2 - 12*j + 4. Let v(l) = y*r(l) - 5*a(l). Factor v(w).
(w - 1)**3*(w + 2)**2
Let r be (-10*(-5)/(-120)*(-2 - 1))/1. What is k in -5/4*k**4 + 1/2*k + r*k**2 + 0 - 1/2*k**3 = 0?
-1, -2/5, 0, 1
Let x be (3 - (-280)/(-91))*-2. Let u(o) be the second derivative of -7/78*o**4 - 6*o + x*o**2 + 0 + 5/39*o**3. Factor u(r).
-2*(r - 1)*(7*r + 2)/13
Solve -40/7*f**5 - 4*f**2 + 20/7*f - 124/7*f**4 + 8/7 - 124/7*f**3 = 0 for f.
-1, -1/2, 2/5
Suppose 0 = 10*q - 50 - 10. Let b(u) be the second derivative of 1/2*u**2 - 1/6*u**3 + 1/120*u**q + 9*u + 0 + 1/40*u**5 - 1/16*u**4. Factor b(a).
(a - 1)**2*(a + 2)**2/4
Suppose -5*f + 2 - 14 = 2*u, -3*u = 3*f. Let x(p) = -p**2 + 11*p - 13. Let b be x(9). Factor 6*g**b + 5*g**4 - 3*g**u - g**3 - 3*g**3.
2*g**3*(g + 1)*(3*g - 2)
Suppose 4*o = 3*c + 13, -4*c = c - 5. Suppose -o - 266 = -5*u. Find q, given that 648*q**3 + 4 - 1 + 123*q**2 + 201*q**2 + u*q = 0.
-1/6
Let o(p) = p**2 + 2*p - 7. Let i be o(3). Factor -12 + 32*c**3 - 18*c**3 - 9*c**2 - i*c**3 + 3*c**4 - 24*c.
3*(c - 2)*(c + 1)**2*(c + 2)
Factor -40*v + 59*v - 25*v - v**2.
-v*(v + 6)
Let i(o) be the second derivative of -2/15*o**5 + 1/30*o**6 + 4/3*o**3 + 9/2*o**2 - 1/6*o**4 + 0 - 2*o. Let l(h) be the first derivative of i(h). Factor l(g).
4*(g - 2)*(g - 1)*(g + 1)
Factor 0 - 1/5*l**5 + 14/5*l**4 - 324/5*l - 252/5*l**2 - 13/5*l**3.
-l*(l - 9)**2*(l + 2)**2/5
Factor 2 - 4*o**5 - 54*o**3 + 24*o**4 - 41*o + 5*o + 64*o**2 - 2*o**3 + 6.
-4*(o - 2)*(o - 1)**4
Let x(g) be the second derivative of -g**6/6 + g**5/4 + 5*g**4 + 388*g - 1. Factor x(p).
-5*p**2*(p - 4)*(p + 3)
Let o(f) = f**2 + 59*f - 388. Let q be o(6). Solve 1/4*c**q + 0*c - 1/4 = 0 for c.
-1, 1
Let v be 4/30 - (-88)/15. Factor 10*o**2 + v - 16*o + 18*o - 2*o**3 - 16*o.
-2*(o - 3)*(o - 1)**2
Let q be 4*(-2)/24*-2. Let o = 2011 - 18095/9. Solve 2/9 - q*b - 2/3*b**5 + 4/3*b**3 - o*b**2 + 2/9*b**4 = 0.
-1, 1/3, 1
Let v(k) be the second derivative of -11*k + 0 - 2*k**2 + 1/3*k**3 + 1/6*k**4. Factor v(q).
2*(q - 1)*(q + 2)
Let j(y) be the third derivative of -y**7/9240 - y**6/3960 + y**3/6 + 8*y**2. Let c(p) be the first derivative of j(p). Find t, given that c(t) = 0.
-1, 0
Let x(r) be the second derivative of r**5/50 - r**4/15 - r**3/3 + 6*r**2/5 + 87*r. Determine w, given that x(w) = 0.
-2, 1, 3
Let b(x) be the third derivative of x**6/120 - 31*x**5/60 + 85*x**4/8 - 75*x**3/2 + 295*x**2. Factor b(a).
(a - 15)**2*(a - 1)
Let a(m) be the third derivative of -2*m**7/77 + 23*m**6/660 + 17*m**5/330 - 7*m**4/132 - m**3/11 + 86*m**2. Solve a(i) = 0.
-1/2, -1/3, 3/5, 1
Let d(a) be the third derivative of 0 - 1/200*a**6 + 1/40*a**4 - 1/350*a**7 + 0*a - 2*a**2 + 0*a**3 + 1/100*a**5. Suppose d(t) = 0. What is t?
-1, 0, 1
What is o in 1/3*o**4 + 17*o - 1/3*o**2 - 17*o**3 + 0 = 0?
-1, 0, 1, 51
Let s(z) be the third derivative of 0*z + 6*z**2 + 1/24*z**6 + 0 - 5/24*z**4 - 2/21*z**7 + 1/3*z**5 + 0*z**3. Factor s(d).
-5*d*(d - 1)*(d + 1)*(4*d - 1)
Let l(g) = 156*g + 2341. Let p be l(-15). Factor -4/3*i + p + 1/3*i**2.
(i - 3)*(i - 1)/3
Let m(n) be the third derivative of 0*n - 5/24*n**4 + 2/3*n**3 + 22*n**2 + 0 + 1/60*n**5. Find z, given that m(z) = 0.
1, 4
Let g(d) be the third derivative of d**5/180 - d**4/18 - 101*d**2. Solve g(w) = 0 for w.
0, 4
Let t(h) be the third derivative of -3*h**6/32 + 17*h**5/24 - 35*h**4/24 - 5*h**3/3 + 2*h**2. Factor t(k).
-5*(k - 2)**2*(9*k + 2)/4
Let f(m) be the first derivative of -25*m**3/3 + 15*m**2/2 + 40*m - 151. Factor f(w).
-5*(w + 1)*(5*w - 8)
Suppose -30*p - 390 - 5*p**2 + 44*p + 14*p - 90 + 112*p = 0. What is p?
4, 24
Let s(u) be the second derivative of -3*u**5/20 - 27*u**4/4 + 14*u**3 - 6*u - 18. Factor s(z).
-3*z*(z - 1)*(z + 28)
Let w be (-1242)/(-483) - 10/(0 + 5). Factor -5/7*n**3 - 4/7*n + 13/7*n**2 - w.
-(n - 2)*(n - 1)*(5*n + 2)/7
Let t(l) = -l**3 - 3*l**2 + 2*l + 6. Let c be t(-3). Let -2*r - 10*r**2 + 2 + 9*r**2 + 3*r + c*r = 0. Calculate r.
-1, 2
Let v be (11*140/(-90) + 19)/(2/6). Determine a so that 34/3*a**2 + v*a + 2/3 - 17/3*a**3 - 12*a**4 = 0.
-1, -1/4, -2/9, 1
Let l(o) be the first derivative of 3*o**5/25 - o**4/20 - 3*o**3/5 + 9*o**2/10 - 2*o/5 + 49. Factor l(s).
(s - 1)**2*(s + 2)*(3*s - 1)/5
Let k(j) = 3*j**2 - 5*j - 14. Let q(w) = w**2 + 2*w - 5. Let z(y) = -2*y**2 - 3*y + 10. Let p(m) = -7*q(m) - 4*z(m). Let s(v) = -3*k(v) + 8*p(v). Factor s(l).
-(l - 1)*(l + 2)
Let p(v) be the first derivative of -v**5/10 - 15*v**4/8 - 7*v**3/3 - 170. Factor p(h).
-h**2*(h + 1)*(h + 14)/2
Let n = 178 - 174. Suppose -86*t + 88*t = n. Determine l so that 3/4*l - 1/2 - 1/4*l**t = 0.
1, 2
Let b be -7*(-8)/4956*(-18)/(-4). Let t = b - -109/177. Suppose -4/9 - 8/9*u**3 + 4/3*u**2 + t*u**5 - 8/9*u**4 + 2/9*u = 0. What is u?
-1, -2/3, 1
Let c(y) be the first derivative of 1/6*y**6 - 6 + 0*y + 0*y**3 + 0*y**2 + 0*y**4 + 0*y**5. Suppose c(j) = 0. Calculate j.
0
Let p(x) = 14*x**3 + 2*x**2 + 3*x + 5. Let v be p(-2). Let a = v - -105. Determine c so that a - 2/9*c**5 + 0*c**2 - 2/9*c**4 + 0*c**3 + 0*c = 0.
-1, 0
Determine q so that 11*q + 63*q**2 - 63 - 69*q**2 - 18*q + 58*q = 0.
3/2, 7
Let b(k) be the third derivative of k**5/15 + k**4/2 - 80*k**3/3 - 55*k**2 + k. Factor b(j).
4*(j - 5)*(j + 8)
Solve 8/9*c**2 + 2/9*c**5 - 4/9*c**4 - 4/9 + 2/9*c - 4/9*c**3 = 0 for c.
-1, 1, 2
Let d = -92 + 98. Let g be (-1)/(-4)*(14 + -12 + d). Suppose 8/5 + 12/5*f**g - 4*f = 0. Calculate f.
2/3, 1
Let -3*o**2 + 2*o**2 - 164*o - 158*o + 318*o = 0. What is o?
-4, 0
Let d(h) = 1 - 2*h + 0 + h. Let z(f) be the second derivative of f**4/4 + f**3/6 - 2*f**2 - 7*f. Let u(s) = -4*d(s) - z(s). Factor u(m).
-3*m*(m - 1)
Let g(p) = 7*p**2 - 6*p - 75. Let v(z) = 8*z**2 - 4*z - 75. Let w(q) = -3*g(q) + 2*v(q). Let w(u)