*l**2. Let o(w) be the first derivative of b(w). What is k in o(k) = 0?
-1, 1
Let p(a) be the second derivative of -1/30*a**6 - 2/15*a**5 + 0*a**3 + 0*a**4 - 11*a + 0 - 9/2*a**2. Let l(d) be the first derivative of p(d). Solve l(q) = 0.
-2, 0
Suppose -1/5*f**4 + 4/5*f**3 - 4/5*f**2 + 0 + 0*f = 0. Calculate f.
0, 2
Suppose -10*b - 6 = -11*b - 4*m, -13 = -5*b - 3*m. Let p(a) be the first derivative of -4 - 1/4*a - 1/5*a**5 - 5/4*a**3 - 7/8*a**b - 13/16*a**4. Solve p(i) = 0.
-1, -1/4
Let w(v) be the first derivative of 5*v**3/3 - 205*v**2 - 840*v - 414. Factor w(o).
5*(o - 84)*(o + 2)
Let x(q) = q**2 + q - 1. Let h(c) = 5*c**2 + 6*c - 6. Let n be (5/2)/((-6)/(-24)). Suppose 0 = -5*j + n - 40. Let k(y) = j*x(y) + h(y). Factor k(a).
-a**2
Let a(o) = 2*o**3 - 2*o**2 + 2*o + 2. Let k(j) = 13*j**3 - 5*j**2 - 64*j + 34. Let t(p) = 10*a(p) - 2*k(p). Factor t(f).
-2*(f - 4)*(f + 6)*(3*f - 1)
Let i(l) be the third derivative of 0 + 0*l**3 - 3*l**2 + 0*l**4 + 1/90*l**5 + 0*l. Factor i(q).
2*q**2/3
Suppose 2*x + 3*y - 5 = 0, 4*x + 5*y - 12 - 1 = 0. Factor -2*k**2 + 4*k + 7 - x.
-2*k*(k - 2)
Let s(p) = -p**3 - p**2 + 1. Let w(r) = -2*r**3 + 38*r**2 - 48*r + 6. Let i(d) = -6*s(d) + w(d). Factor i(c).
4*c*(c - 1)*(c + 12)
Factor 0 - 2/5*t**2 - 4/15*t + 2/15*t**4 + 0*t**3.
2*t*(t - 2)*(t + 1)**2/15
Let r be (-795)/(-20) - (-4)/16. Let z be ((-4)/10)/((-104)/r). Factor 14/13*w**2 + 0 - 6/13*w - 10/13*w**3 + z*w**4.
2*w*(w - 3)*(w - 1)**2/13
Factor -1/2 - 19/6*i**2 + 4/3*i**3 + 7/3*i.
(i - 1)**2*(8*i - 3)/6
Let k(c) be the second derivative of c**8/20160 - c**7/3780 + c**6/2160 + 3*c**4/4 + 11*c. Let n(w) be the third derivative of k(w). Let n(p) = 0. What is p?
0, 1
Suppose 5*s + 3*b + 12 = 0, -11*s = -6*s + 4*b + 11. Let j be -5 - (s + (-1165)/20). Suppose -3/4*c**3 - j*c + 375/4 + 45/4*c**2 = 0. Calculate c.
5
Let z(q) be the third derivative of -q**7/525 - 7*q**6/150 + 17*q**5/150 + q**4/2 - 236*q**2 - 1. Let z(y) = 0. What is y?
-15, -1, 0, 2
Let s = -9/4 + 143/60. Let h(q) be the first derivative of -s*q**3 + 1 - 1/5*q**2 + 0*q. Factor h(r).
-2*r*(r + 1)/5
Let k(j) be the third derivative of -j**9/35280 + j**8/1960 + 3*j**4/4 + 25*j**2. Let u(f) be the second derivative of k(f). Suppose u(v) = 0. Calculate v.
0, 8
Let g be -19*(-24)/1368 + (-3)/9. Factor g - 2/15*r + 2/15*r**4 + 2/15*r**3 - 2/15*r**2.
2*r*(r - 1)*(r + 1)**2/15
Let i(u) be the second derivative of -u**4/84 + 2*u**3/21 - 3*u**2/14 + 29*u. Factor i(r).
-(r - 3)*(r - 1)/7
Determine b so that 0 - b**2 - 1/3*b**4 - b**3 - 1/3*b = 0.
-1, 0
Let i(s) be the third derivative of -5*s**8/48 + 20*s**7/21 - 3*s**6 + 8*s**5/3 + 10*s**4/3 + 6*s**2 + 16. Factor i(n).
-5*n*(n - 2)**3*(7*n + 2)
Let -81*l - 10*l + 37*l - 51*l + 5*l**2 + 450 = 0. Calculate l.
6, 15
Let w(b) = -7 - b - b**2 - 5*b**3 + 4*b**3 + 10. Let d be w(0). Factor -n + n**2 + d*n**2 - 5*n**2.
-n*(n + 1)
Let x(z) = 21 - 22 + 10*z - 10*z - z**2. Let o(i) = 2*i**2 + 22*i + 8. Let t(n) = -o(n) + 4*x(n). Factor t(f).
-2*(f + 3)*(3*f + 2)
Let f(p) be the second derivative of p**5/20 + p**4/4 - 3*p**3/2 + 5*p**2/2 + 15*p - 6. Factor f(a).
(a - 1)**2*(a + 5)
Let n(s) = -7*s**3 - 19*s**2 + 118*s - 131. Let t(w) = -76*w**3 - 208*w**2 + 1296*w - 1440. Let r(m) = -32*n(m) + 3*t(m). Let r(u) = 0. What is u?
-8, 2
Let n = -17/7 - -439/175. Let d(s) be the first derivative of -n*s**5 - 6 + 1/30*s**6 + 0*s**2 + 0*s**3 + 1/20*s**4 + 0*s. Factor d(f).
f**3*(f - 1)**2/5
Let u(x) be the third derivative of -x**6/40 - 3*x**5/10 + 15*x**4/8 - 4*x**3 + 108*x**2. Let u(i) = 0. What is i?
-8, 1
Let j(v) be the first derivative of -v**6/480 + v**5/120 - v**4/96 - 7*v**2 + 4. Let q(m) be the second derivative of j(m). Factor q(r).
-r*(r - 1)**2/4
Let x be 0/((-9)/(27/(-6))). Suppose 0 = -5*z - x*z + 25. Factor -2*h**2 + z - 4 + 15 - 2*h**2.
-4*(h - 2)*(h + 2)
Let j(s) be the first derivative of -2*s**5/55 + 3*s**4/11 - 16*s**3/33 - 93. Solve j(f) = 0.
0, 2, 4
Let h(v) be the third derivative of 0 - 3/2*v**3 - 3/20*v**5 + 0*v - 31*v**2 - 5/4*v**4. Factor h(o).
-3*(o + 3)*(3*o + 1)
Let q(i) be the third derivative of -i**6/660 + 17*i**5/330 - 31*i**4/132 + 5*i**3/11 - 17*i**2. Suppose q(k) = 0. Calculate k.
1, 15
Let g = 7 - 3. Let v = 11 - 6. Find z, given that z - z - v*z**2 + 3*z**2 - g*z = 0.
-2, 0
Let s be ((-8)/(-10))/(6/(-240)*-8). Factor -2*y - 28*y**2 - 7*y**s - 2*y**3 + 16*y**2 - 16*y**3 - y**4.
-2*y*(y + 1)**2*(4*y + 1)
Let s = 440 + -438. Let a(l) be the first derivative of 4/3*l**3 + 0*l + 0*l**s - 8/5*l**5 + 4 - l**4. Suppose a(q) = 0. Calculate q.
-1, 0, 1/2
Let j(b) be the second derivative of 4/5*b**3 + 1/20*b**4 + 24/5*b**2 - 4*b + 0. Find c such that j(c) = 0.
-4
Let n(v) be the second derivative of 3*v**7/14 + 2*v**6/5 - 6*v**5/5 - 9*v**4/2 - 11*v**3/2 - 3*v**2 + 17*v. Let n(k) = 0. What is k?
-1, -1/3, 2
Let o(x) be the first derivative of -x**5 - 15*x**4 - 75*x**3 - 125*x**2 + 61. Factor o(c).
-5*c*(c + 2)*(c + 5)**2
Let o(s) be the third derivative of s**7/56 + 11*s**6/20 + 129*s**5/80 - 1243*s**4/16 + 121*s**3 + 639*s**2. Determine c so that o(c) = 0.
-11, 2/5, 4
Suppose 249 - 229 = 10*k. Factor -2*c + 1/2*c**2 + k.
(c - 2)**2/2
Let j(u) be the third derivative of u**7/5880 - u**6/210 + 2*u**5/35 - 5*u**4/8 - u**2. Let o(r) be the second derivative of j(r). Factor o(g).
3*(g - 4)**2/7
Let g(r) be the first derivative of -r**4/6 + 8*r**3/9 - r**2 + 198. Factor g(w).
-2*w*(w - 3)*(w - 1)/3
Suppose 6*d - 35 = 25. Suppose 0 = 20*f - 10*f - d. Factor -1/4*p**2 - p - f.
-(p + 2)**2/4
Let y be (-9252)/72 + (-1)/2*2. Let p = -2797/22 - y. Determine l so that 40/11*l + 12/11*l**2 - 16/11 - 10/11*l**4 - p*l**3 = 0.
-2, 2/5, 1
Let o(k) = -34*k**2 + 40*k - 20. Let n(c) = 7*c**2 - 8*c + 4. Suppose 5*i = 5*u, 2*u = 2*i - u - 3. Let d(s) = i*o(s) - 14*n(s). Factor d(a).
4*(a - 1)**2
Let r(p) = -2*p + 1 + 5*p - 1 - 4. Let j be r(3). Factor -2*s + 5 + 10*s**2 - 2*s**2 - 2*s**5 + 8*s**4 - 12*s**3 - j.
-2*s*(s - 1)**4
Solve -84 - 4 - 6*f**2 - 52*f + 2*f**2 + 19 + 21 = 0 for f.
-12, -1
Let s(a) be the second derivative of 3*a**5/20 - a**4 - 5*a**3/2 + 2*a - 29. Factor s(o).
3*o*(o - 5)*(o + 1)
Let l(f) = 11*f**3 - 95*f**2 + 175*f - 91. Let q(p) = 21*p**3 - 190*p**2 + 350*p - 181. Let w(z) = 11*l(z) - 6*q(z). Factor w(s).
-5*(s - 17)*(s - 1)**2
Suppose -16 - 130 = -73*d. Let p(b) be the third derivative of 0*b - 1/33*b**3 + 1/44*b**4 - 1/165*b**5 + 0 - 3*b**d. Solve p(u) = 0.
1/2, 1
Let b(r) = 3*r**3 + r**2 - 3*r + 3. Let q be b(1). Let o(m) be the first derivative of 0*m + 0*m**3 + 0*m**5 + 1/6*m**2 - 5 + 1/18*m**6 - 1/6*m**q. Factor o(s).
s*(s - 1)**2*(s + 1)**2/3
Let r be (-69)/(-12) + 6/(-8). Factor m**2 + 2*m**3 + 0*m**5 + m**5 - 4*m**3 + r*m**3 + 3*m**4.
m**2*(m + 1)**3
Let c(r) be the first derivative of -4*r**5/5 + 6*r**4 - 20*r**3/3 - 48*r**2 + 144*r + 170. Factor c(x).
-4*(x - 3)**2*(x - 2)*(x + 2)
Factor -4/5*h**2 + 32/5*h - 48/5.
-4*(h - 6)*(h - 2)/5
Let i(m) be the second derivative of 5*m**7/6 - 5*m**6/6 - 65*m**5/4 - 475*m**4/12 - 125*m**3/3 - 20*m**2 - 19*m. Determine u so that i(u) = 0.
-1, -2/7, 4
Factor 7*m**2 - 260 - 50*m + m**2 - m**2 - 2*m**2 - 115.
5*(m - 15)*(m + 5)
Let t(d) be the second derivative of 0 - 43*d + 1/6*d**3 + 0*d**4 + 1/42*d**7 + 0*d**6 - 1/10*d**5 + 0*d**2. Find x, given that t(x) = 0.
-1, 0, 1
Let x(h) be the third derivative of -h**5/330 + h**4/132 + 2*h**3/11 - 2*h**2 + h. Factor x(c).
-2*(c - 3)*(c + 2)/11
Let -1/5*h**4 + 11/5*h**2 + 2*h**3 + 0*h + 0 = 0. What is h?
-1, 0, 11
Let y = 498 - 495. Let t(n) be the first derivative of 9/5*n**5 - 1 + 3/4*n**4 + 0*n - 3*n**3 - y*n**2 + 1/2*n**6. Factor t(m).
3*m*(m - 1)*(m + 1)**2*(m + 2)
Let y(g) be the first derivative of -6*g**6/7 - 4*g**5/5 + 11*g**4/7 + 4*g**3/3 - 4*g**2/7 + 150. Solve y(o) = 0.
-1, 0, 2/9, 1
Let x(z) = z**2 - 6*z - 3. Let o be x(7). Factor 4*l**3 + 6*l - 11*l + l**2 + o + l - 5*l**2.
4*(l - 1)**2*(l + 1)
Suppose -9*j**2 - 21/2*j + 3/2*j**3 + 0 = 0. Calculate j.
-1, 0, 7
Let l be 2 + (16 - 0/(-4)). Let n = l + -15. Factor -4*r**2 + 17*r**3 + 4*r + 18*r**3 - 39*r**n + 4*r**4.
4*r*(r - 1)**2*(r + 1)
Suppose -4*l + 4*q + 8 = 0, 130*l - 132*l = -17*q + 41. Factor 1/2*z + 0 - 5/3*z**2 + 2*z**3 - z**4 + 1/6*z**l.
z*(z - 3)*(z - 1)**3/6
Let o = -21 + 26. Facto