e second derivative of -1/9*r**3 + b - 1/18*r**4 + 0*r**2 + 4*r. Determine k, given that p(k) = 0.
-1, 0
Let u(y) = 13*y**2 + 7*y - 20. Let i(s) = -3*s**2 - 2*s + 5. Let z(w) = 9*i(w) + 2*u(w). Solve z(c) = 0.
-5, 1
Let b(y) be the second derivative of -y**6/30 - 4*y**5/15 - 5*y**4/6 - 4*y**3/3 - y**2/2 + 9*y. Let i(x) be the first derivative of b(x). Factor i(t).
-4*(t + 1)**2*(t + 2)
Let q = 74 - 70. Let k(a) be the second derivative of 0*a**2 + 4*a + 1/4*a**3 + 0 + 1/4*a**q + 3/40*a**5. Determine n, given that k(n) = 0.
-1, 0
Let x be (3 + 6 + -4)*(4 - 5). Let t(k) = -k**3 + 14*k**2 - 10*k - 20. Let j(l) = -l**3 + 13*l**2 - 11*l - 21. Let f(v) = x*j(v) + 4*t(v). Factor f(m).
(m - 5)**2*(m + 1)
Let q = -2 - 2. Let i be 6*1*(-10)/q. Suppose -8*b + 4*b + i*b**2 + 21*b**3 - 2*b = 0. Calculate b.
-1, 0, 2/7
Let u be 280/1092*(-18)/(-10). Suppose -m = 0, m - 8 = -3*g - g. Factor 0 + u*a - 2/13*a**g.
-2*a*(a - 3)/13
Let -2 + 5/4*c - 1/8*c**2 = 0. Calculate c.
2, 8
Let x = -9 + 347. Factor 25*d - 3*d + 104*d**2 + x*d**3 - 14*d.
2*d*(13*d + 2)**2
Let u = -25/403 + 172356/4433. Let x = 39 - u. Factor 0 + x*w**2 + 2/11*w.
2*w*(w + 1)/11
Let d(s) = -s - 1. Let z(m) = -2*m**2 - 28*m - 6. Let u(k) = 12*d(k) - 2*z(k). Find a such that u(a) = 0.
-11, 0
Let u(q) be the first derivative of -q**3/15 + 233*q**2/5 - 54289*q/5 - 569. Suppose u(y) = 0. What is y?
233
Factor 1/4*x**2 - 6*x + 36.
(x - 12)**2/4
Let t(v) be the first derivative of -3*v**4/32 + v**3/2 + 15*v**2/16 + 30. Determine g so that t(g) = 0.
-1, 0, 5
Let f(k) = -k**3 + 58*k**2 - 586*k + 13. Let t be f(13). Factor -8/7*p**2 + 4/7*p**4 - 8/7*p - 2/7*p**5 + 6/7*p**3 + t.
-2*p*(p - 2)**2*(p + 1)**2/7
Let g(l) be the second derivative of 7/11*l**2 + 0 - 1/66*l**4 + 2/11*l**3 - 33*l. Solve g(n) = 0 for n.
-1, 7
Let o = 101834/38181 + -6/12727. Factor o*n + 0 - 1/3*n**5 - 2*n**3 - 5/3*n**4 + 4/3*n**2.
-n*(n - 1)*(n + 2)**3/3
Let k = -364 - -551. Let i = k + -553/3. Factor -i*j - 2/3 + 22/3*j**2 - 4*j**3.
-2*(j - 1)**2*(6*j + 1)/3
Let w(m) be the third derivative of -m**6/360 + m**5/20 + m**4/72 - m**3/2 + 273*m**2. Suppose w(b) = 0. Calculate b.
-1, 1, 9
Suppose -71 = -5*l + 9. Let g = l - 14. Factor -3*q**4 + 2 - 4*q**g + 2*q**4 + 0*q**4 + 3*q**4.
2*(q - 1)**2*(q + 1)**2
Suppose 0 = -30*j - 7*j + 111. Suppose 0*u**2 + 0*u**j + 0*u + 0 - 1/2*u**5 + 3/2*u**4 = 0. What is u?
0, 3
Let v = 101/165 - 2/165. Let b = -2488 + 2490. Find j, given that 0 + v*j - 3/5*j**b + 3/5*j**4 - 3/5*j**3 = 0.
-1, 0, 1
Suppose 4*d = 4*b, -2*b + 2*d - 5 = 5*d. Let j(u) = -u**3 - u**2 - u + 1. Let n(c) = -4*c**3 + c + 3. Let z(x) = b*n(x) + 3*j(x). Suppose z(t) = 0. What is t?
-1, 0, 4
Let l(q) be the third derivative of -q**5/330 + q**4/132 + 10*q**3/11 - 17*q**2 + 5*q. Factor l(g).
-2*(g - 6)*(g + 5)/11
Let s(b) be the third derivative of -b**6/120 - 29*b**5/360 - 7*b**4/48 - b**3/9 - 53*b**2. Factor s(p).
-(p + 4)*(2*p + 1)*(3*p + 1)/6
Let b(x) be the second derivative of -x**6/45 + x**5/10 - x**4/9 + 57*x. Factor b(n).
-2*n**2*(n - 2)*(n - 1)/3
Determine z, given that 0 + z**3 + 8/5*z**2 - 4/5*z = 0.
-2, 0, 2/5
Let b(y) = y**5 - y**4 + 9*y**3 + 13*y**2 + 2*y + 2. Let i(x) = -2*x**5 + 2*x**4 - 9*x**3 - 14*x**2 - x - 3. Let f(k) = 3*b(k) + 2*i(k). Factor f(q).
-q*(q - 4)*(q + 1)**3
Let w(x) be the first derivative of -1/2*x**2 + 0*x - 8 + 0*x**3 - 2/15*x**5 + 1/30*x**6 + 1/6*x**4. Let i(h) be the second derivative of w(h). Factor i(l).
4*l*(l - 1)**2
Let v = 135 + -131. Let c(x) be the first derivative of -1/7*x**3 + 1 - 1/35*x**5 - 3/28*x**v + 0*x - 1/14*x**2. Factor c(g).
-g*(g + 1)**3/7
Let z(k) be the second derivative of -k**6/15 + 27*k**5/10 - 65*k**4/2 + 169*k**3/3 + 20*k. Factor z(d).
-2*d*(d - 13)**2*(d - 1)
Let b(r) be the first derivative of 0*r**2 + 0*r**3 - 4 + 0*r**4 + 0*r + 1/25*r**5. Factor b(i).
i**4/5
Let u(b) = b**3 - 28*b**2 - 23*b + 648. Let w be u(28). Factor 4/3*s**2 + w - 16/3*s.
4*(s - 3)*(s - 1)/3
Let x = 60 + -56. Suppose -12 = -4*j - p, -5*j + x*p = -8 - 7. Factor 3*f**2 + 9/2*f**j - 9/2*f - 3.
3*(f - 1)*(f + 1)*(3*f + 2)/2
Let c(j) be the first derivative of 9*j**5/5 - 21*j**4/2 + 7*j**3 + 6*j**2 - 230. Factor c(s).
3*s*(s - 4)*(s - 1)*(3*s + 1)
Let j(s) = -s**3 - 21*s**2 + 40*s + 3. Let d(u) = 2*u**3 + 64*u**2 - 120*u - 8. Let x(o) = 3*d(o) + 8*j(o). Factor x(r).
-2*r*(r - 10)*(r - 2)
Suppose 0 = -3*w - 17 + 20, -16 = -5*h + 4*w. Let m(o) be the second derivative of -3/20*o**5 + 1/2*o**4 + h*o + 0 + 0*o**3 + 0*o**2. Factor m(d).
-3*d**2*(d - 2)
Let m = -1187/2600 + -1/200. Let c = 1/26 - m. Solve 1/2*t**3 - c*t - 1/2*t**2 + 1/2 = 0.
-1, 1
Let s(k) be the third derivative of 5*k**2 + 1/300*k**5 + 0 + 0*k - 1/40*k**4 + 0*k**3. Factor s(w).
w*(w - 3)/5
Let v(p) = 2*p**3 + 34*p**2 - 2*p - 37. Let b(c) = 4*c**3 + 68*c**2 - 4*c - 75. Let m(o) = -3*b(o) + 7*v(o). Factor m(f).
2*(f - 1)*(f + 1)*(f + 17)
Let y be (-196)/36 - -5 - 93/(-27). Let u(j) be the first derivative of -9 - y*j + 4*j**3 + 9/2*j**2. Factor u(i).
3*(i + 1)*(4*i - 1)
Let l(m) = 15*m**3 + 70*m**2 + 140*m + 85. Let s(d) = -23*d**3 - 105*d**2 - 210*d - 128. Let t(i) = 8*l(i) + 5*s(i). Determine k, given that t(k) = 0.
-4, -2, -1
Let b(o) be the first derivative of -4*o**4/3 + 8*o**3/3 - 3*o**2/2 - 563. What is l in b(l) = 0?
0, 3/4
Let m(a) = -a**3 + 4*a**2 - 19*a + 18. Let s(z) = -2*z**3 + 4*z**2 - 19*z + 20. Let c(j) = -3*m(j) + 2*s(j). Factor c(p).
-(p - 2)*(p - 1)*(p + 7)
Suppose 52 = 14*b - 18. Suppose -16 = -4*w, l + b*w - 27 = -3. Factor 0*d + 0 - 1/4*d**5 + 3/4*d**3 + 1/2*d**2 + 0*d**l.
-d**2*(d - 2)*(d + 1)**2/4
Let m = -1346 - -1346. Let l(h) be the second derivative of h - 16*h**2 + m + 8/3*h**3 - 1/6*h**4. Determine j, given that l(j) = 0.
4
Let f(d) = -3*d**2 - 9*d. Let a(z) = 19 - 19 - z. Let h = 3 + -2. Let q(g) = h*f(g) - 12*a(g). Factor q(x).
-3*x*(x - 1)
Let i(t) = t**2 - t + 1. Let q(k) be the third derivative of k**5/5 + 9*k**4/8 + 39*k**3/2 - 20*k**2. Let s(g) = 9*i(g) - q(g). Factor s(j).
-3*(j + 6)**2
Let h be 4/(-15)*(-5 - 10) - (-6)/(-12). Factor 19/6*j - h*j**2 + 3/2*j**3 - 1/6*j**4 - 1.
-(j - 6)*(j - 1)**3/6
Let k be 1/5 - (-78)/260. Let z(d) be the first derivative of 3 + 4/3*d**3 + k*d**4 - 4/5*d**5 + 0*d - 1/3*d**6 + 0*d**2. Suppose z(w) = 0. Calculate w.
-2, -1, 0, 1
Solve 2*r**2 + 0 - 1/3*r**3 - 8/3*r = 0 for r.
0, 2, 4
Suppose 0 = 3*w + 2*o + 5 - 27, -4*o + 32 = 3*w. Factor -d**3 + w*d**2 - 1482*d**4 + 12*d + 1478*d**4 - 11*d**3.
-4*d*(d - 1)*(d + 1)*(d + 3)
Suppose -127*f = -26*f + 3*f - 208. Solve 0 + 28/5*h - 4/5*h**f = 0.
0, 7
Let z(d) be the first derivative of -d**7/315 - d**6/60 + d**4/9 - 21*d**2/2 - 7. Let j(r) be the second derivative of z(r). Factor j(x).
-2*x*(x - 1)*(x + 2)**2/3
Let w(o) be the first derivative of o**4 + 104*o**3/3 + 280*o**2 - 1568*o + 16. What is y in w(y) = 0?
-14, 2
Let c(k) be the first derivative of k**8/840 - k**7/70 + k**6/15 - 2*k**5/15 - 43*k**3/3 - 18. Let y(j) be the third derivative of c(j). Factor y(n).
2*n*(n - 2)**3
Let m(l) be the second derivative of -3*l + 1/24*l**4 + 0*l**2 + 0 + 0*l**3. Factor m(v).
v**2/2
Let m = 19/26 + -5/78. Let -m*r**2 - 8/3 - 10/3*r = 0. Calculate r.
-4, -1
Let z(l) be the second derivative of l**6/180 + l**5/12 + l**4/3 - 5*l**3/18 - 25*l**2/12 + 2*l - 35. Factor z(g).
(g - 1)*(g + 1)*(g + 5)**2/6
Let s = -12 - -15. Let -4*w**4 + 10*w**4 + 39*w**s + 3 + 45*w**2 + 6*w**4 + 12*w + 9*w = 0. What is w?
-1, -1/4
Let v be ((-20)/(-4))/(0 + 1). Factor -5*y**3 - 2*y + 17*y**2 - 14*y + v - 2 + 1.
-(y - 2)*(y - 1)*(5*y - 2)
Let b(x) be the third derivative of -x**6/200 + 9*x**5/100 - x**4/5 - 77*x**2 - 3. Factor b(w).
-3*w*(w - 8)*(w - 1)/5
Let j(t) be the first derivative of -3/4*t**5 + 15 + 0*t + 1/2*t**3 - 9/16*t**4 + 0*t**2. Suppose j(x) = 0. What is x?
-1, 0, 2/5
Let 1806 + 614 - 334*f**2 + 1980*f + 4*f**4 + 3*f**4 - 90*f**3 + 519*f**2 - 2*f**4 = 0. What is f?
-2, 11
What is v in -8/3*v - 10/3*v**2 + 0 - 2/3*v**3 = 0?
-4, -1, 0
What is p in 40/7 + 118/21*p - 2/21*p**2 = 0?
-1, 60
Let x(v) = v**3 + 6*v**2 + 10*v + 6. Let c be x(-6). Let m be c/(-36)*4/3. Factor 2*j**m + 755*j**3 - 2*j + 2*j - 756*j**3.
-j**2*(j - 2)
Let y be 18/10 - 97/(-485). Let g(j) be the first derivative of 1/9*j**3 - 1/36*j**6 + 1/12*j**4 + 9 - 1/12*j**y - 1