he third derivative of -k**6/180 - k**5/20 - k**4/6 + 16*k**3/3 + 10*k**2. Let u(c) be the first derivative of l(c). Factor u(n).
-2*(n + 1)*(n + 2)
Let o = 3817 + -3814. Let 22/7*c - 8/7 + 5/7*c**4 - 17/7*c**2 - 1/7*c**5 - 1/7*c**o = 0. What is c?
-2, 1, 4
Let v(p) = p**3 - 10*p**2 + p - 9. Let u be v(9). Let b = u - -413/5. Factor -b + 6/5*m + 2/5*m**2.
2*(m - 1)*(m + 4)/5
Let -3*g**2 + 2*g - 5*g**2 - 38*g + 10*g**2 - 96 - 5*g**2 = 0. What is g?
-8, -4
Let i(f) be the second derivative of -10*f + 2/9*f**3 + 0 + 2/9*f**4 - 4/3*f**2 - 1/15*f**5. Let i(l) = 0. Calculate l.
-1, 1, 2
Let a(j) = -j**2 + 8*j - 4. Let b be a(7). Suppose -5*k + 5*r = -20, 5*k + 4*r = b*k + 8. Factor 24*l**4 - 12*l**5 + 7*l**3 - 13*l**3 + 3*l**k.
-3*l**3*(l - 2)*(4*l - 1)
Let g(y) be the first derivative of -2*y**6/3 - 4*y**5 + 80*y**3/3 + 32*y**2 + 243. Find x such that g(x) = 0.
-4, -2, -1, 0, 2
Let g be (-8)/(-2*(-1)/(-3)*3). Factor -7*l - 2*l**3 + 3*l - 2*l**2 + 6*l - 2*l**2 + g.
-2*(l - 1)*(l + 1)*(l + 2)
Let r(j) be the second derivative of -j**8/15120 - j**7/1890 + j**6/180 - j**5/54 + 3*j**4/4 - 19*j. Let l(a) be the third derivative of r(a). Factor l(z).
-4*(z - 1)**2*(z + 5)/9
Let r be (-387)/12*((-24)/9 - -2). Let q = -127/6 + r. Solve q*w**3 + 0*w**2 - 2/3 - w = 0.
-1, 2
Factor -9*w**2 + 4 + 34/3*w + 7/6*w**3.
(w - 6)*(w - 2)*(7*w + 2)/6
Let t(k) be the third derivative of k**7/1260 + k**6/108 + 2*k**5/45 + k**4/9 - k**3/3 - 4*k**2. Let f(m) be the first derivative of t(m). Solve f(i) = 0 for i.
-2, -1
Let b(h) = -2*h**3 + h**2 + 2*h - 1. Let g(l) = -8*l**3 + 25*l**2 + 28*l - 5. Let n(r) = 5*b(r) - g(r). Factor n(y).
-2*y*(y + 1)*(y + 9)
Let m be (9/(-17 + 8))/(-6 - 1). Factor -m*y + 0*y**3 + 2/7*y**4 + 0 - 2/7*y**2 + 1/7*y**5.
y*(y - 1)*(y + 1)**3/7
Suppose 96 = 3*u + 3*u. Factor 7*f**3 - 2*f**3 + u*f - 11*f**2 - 9*f**2 + 4*f.
5*f*(f - 2)**2
Let p be 2/20*(-6210)/(-36). Let c = p + -191/12. Find a such that 5/3*a**3 + a**4 - 4/3*a - c*a**2 + 0 = 0.
-2, -2/3, 0, 1
Let w(s) be the first derivative of s**5/40 - s**4/8 - 156. Solve w(p) = 0 for p.
0, 4
Let k(g) = 2*g**3 - 3*g**2 + g. Let w(t) = t**3 - t**2. Suppose a - 5 + 3 = 0. Let b(i) = a*k(i) - 6*w(i). Factor b(u).
-2*u*(u - 1)*(u + 1)
Let t = 23 - 18. Let o(p) be the second derivative of 5/66*p**4 + 6*p + 4/11*p**2 + 0 - 1/110*p**t - 8/33*p**3. Factor o(d).
-2*(d - 2)**2*(d - 1)/11
Let c(b) = 4*b**2 - 46*b - 29. Let j(h) = -h**2 + h - 5. Let q(n) = -2*c(n) - 6*j(n). Factor q(a).
-2*(a - 44)*(a + 1)
Let u(o) be the first derivative of o**6/27 + 8*o**5/45 - o**4/18 - 8*o**3/27 + 96. Determine h so that u(h) = 0.
-4, -1, 0, 1
Suppose 190/3*a**4 + 88/3*a - 16/3 + 626/3*a**3 + 180*a**2 = 0. Calculate a.
-2, -1, -2/5, 2/19
Let j(a) be the second derivative of 8*a**7/189 + 28*a**6/45 + 113*a**5/45 + 223*a**4/54 + 31*a**3/9 + 14*a**2/9 - 164*a + 1. Determine z so that j(z) = 0.
-7, -2, -1/2
Let t(h) = h**2 - h + 4. Let x be t(4). Suppose x*p - 2*p - 10*p + 4*p**2 = 0. What is p?
-1, 0
Suppose -21*z = -122 + 59. Find b such that 0*b**2 + 0*b + 2/7*b**z + 0 + 0*b**4 - 2/7*b**5 = 0.
-1, 0, 1
Let a(h) be the second derivative of 0 - 3/4*h**4 + 9/2*h**2 + 3/20*h**5 - 1/2*h**3 + 26*h. Factor a(c).
3*(c - 3)*(c - 1)*(c + 1)
Let g(x) = -33*x**2 - 7*x - 1. Let h = -30 + 28. Let a(c) be the third derivative of -2*c**5/15 - c**4/12 - 2*c**2. Let m(w) = h*g(w) + 9*a(w). Factor m(l).
-2*(l + 1)*(3*l - 1)
Let i(s) be the first derivative of -s**4/10 + 4*s**3/15 - s**2/5 + 145. Suppose i(b) = 0. What is b?
0, 1
Let w(g) be the second derivative of -g**7/280 - g**6/40 - g**5/20 - 3*g**2/2 - 11*g. Let q(h) be the first derivative of w(h). Factor q(k).
-3*k**2*(k + 2)**2/4
Let o = -123 + 126. Find k such that -k**2 + o*k**4 + 0*k - 4*k**3 - 3*k + 2*k + 3*k = 0.
-2/3, 0, 1
Let y(w) be the first derivative of -5*w**6/6 + 4*w**5 - 64. Determine n so that y(n) = 0.
0, 4
Let k be (-252)/(-9) + 1351/(-49). Solve -k*a**3 + 0*a**2 + 0 + 0*a - 1/7*a**4 = 0 for a.
-3, 0
Let p = -546 - -7681/14. Let x = p - 15/7. Suppose x*o**3 - 3/2*o**2 - 5/2*o - 1 + 1/2*o**4 = 0. Calculate o.
-1, 2
Let l(b) be the second derivative of b**6/90 - 7*b**5/30 + 5*b**4/3 + 5*b**3/6 + 38*b. Let q(t) be the second derivative of l(t). Factor q(s).
4*(s - 5)*(s - 2)
Factor -1/3*l**2 + 4/3*l - 1.
-(l - 3)*(l - 1)/3
Factor -392/3*p - 2/3*p**3 + 0 + 56/3*p**2.
-2*p*(p - 14)**2/3
Let l(c) be the third derivative of -c**7/1470 - c**6/30 - 221*c**5/420 - 169*c**4/84 + c**2 - c. Suppose l(f) = 0. What is f?
-13, -2, 0
Factor 0 + 33/8*r**2 + 3*r.
3*r*(11*r + 8)/8
Let d = 56 + -50. Let l be (-30)/25*(-2 - (-2)/d). Determine w so that -1/4*w**l - 1/4*w + 0 = 0.
-1, 0
Suppose 0 = -2*z + 5*k + 12, 12 = -4*z - 4*k + 8. Let f(q) be the first derivative of -3/4*q**4 - z - 3*q + 3/2*q**2 + q**3. Suppose f(m) = 0. What is m?
-1, 1
Let k(r) be the first derivative of -2*r**5/15 + 5*r**4/3 + 34*r**3/3 + 68*r**2/3 + 56*r/3 + 250. Let k(n) = 0. Calculate n.
-2, -1, 14
Let n(p) = -4*p**2 - 21*p - 53. Let r(o) = o**2 + 5*o + 13. Suppose -93 - 17 = -5*v. Let h(a) = v*r(a) + 6*n(a). Determine d, given that h(d) = 0.
-4
Let g(f) = -4 - 3*f**3 - 4 - 3 - 6*f**3 - 17*f + 4*f**2. Let l(q) = -5*q**3 + 2*q**2 - 9*q - 6. Let p(v) = -6*g(v) + 11*l(v). Let p(u) = 0. What is u?
-3, 0, 1
Let t = -17908 - -89127/5. Let w = t - -83. Factor -z**3 + w - 2/5*z**2 + z.
-(z - 1)*(z + 1)*(5*z + 2)/5
Factor 2 + 2/5*v**2 - 12/5*v.
2*(v - 5)*(v - 1)/5
Let i(f) be the first derivative of f**5/10 - f**4/4 - f**3/6 + f**2/2 + 106. Factor i(p).
p*(p - 2)*(p - 1)*(p + 1)/2
Let k = 7 - 3. Let b(f) = -6*f**4 + 2*f**3 - 4*f**2. Let i(g) = -5*g**3 + 5*g**2 + 28*g**4 + 3*g**2 - 17*g**4. Let u(q) = k*i(q) + 7*b(q). Factor u(x).
2*x**2*(x - 2)*(x - 1)
Let w(g) = g**2 - g - 1. Let z(d) = d**3 - 7*d**2 + 22*d - 18. Let t(b) = 10*w(b) - 5*z(b). Factor t(u).
-5*(u - 4)**2*(u - 1)
Factor 96*h - 2091*h**4 - 21*h**3 - 18*h**2 + 31 + 65 + 2088*h**4.
-3*(h - 2)*(h + 1)*(h + 4)**2
Let z(d) be the third derivative of 0*d**6 + 0*d**3 + 0*d + 0 - 1/945*d**7 + 1/54*d**4 + 1/90*d**5 + 3*d**2. Solve z(f) = 0 for f.
-1, 0, 2
Let b(d) be the third derivative of 1/140*d**7 + 15*d**2 + 0*d + 0*d**5 - 1/4*d**3 - 1/8*d**4 + 1/40*d**6 + 0. Determine w, given that b(w) = 0.
-1, 1
Let s = -4975/13 - -383. What is w in -2/13 + s*w - 2/13*w**2 = 0?
1
Let r = -93 - -102. Suppose -r*z + 19*z = 0. What is v in -9/2*v**3 + z + 3*v**2 + 0*v = 0?
0, 2/3
Suppose 48*t - 26*t = 0. Suppose -2/5*l**2 + 0*l + 1/5*l**4 + t*l**3 + 1/5 = 0. What is l?
-1, 1
Let x(f) be the third derivative of -f**6/40 - f**5/20 + 3*f**4/4 + 19*f**2 + 6. Factor x(v).
-3*v*(v - 2)*(v + 3)
Let h(x) = x**3 + 28*x**2 - 46*x - 491. Let w be h(-29). Factor 8/3 - 4/3*o - 2/3*o**w + 1/3*o**3.
(o - 2)**2*(o + 2)/3
Factor 288*f - 120/7*f**2 + 2/7*f**3 - 896.
2*(f - 28)**2*(f - 4)/7
Let y(u) = -5*u**2 + 3*u + 5. Let f be y(-3). Let g = -146/3 - f. Determine o so that g*o**4 + 1/3*o**5 + 0 - 5/3*o**2 - o**3 - 2/3*o = 0.
-1, 0, 2
Let m(o) be the third derivative of -o**11/388080 - o**10/105840 - o**9/105840 - 2*o**5/15 + o**2. Let b(u) be the third derivative of m(u). Factor b(d).
-2*d**3*(d + 1)*(3*d + 2)/7
Let c(u) be the third derivative of u**7/630 - u**6/12 + 37*u**5/45 + 221*u**4/12 - 1445*u**3/18 + 420*u**2. Factor c(d).
(d - 17)**2*(d - 1)*(d + 5)/3
Find p such that -45*p**3 + 2*p**5 + 144*p**3 - 10*p**2 - 14*p**4 - 77*p**3 = 0.
0, 1, 5
Determine i, given that 0 + 34/5*i**3 + 28/5*i**2 - 16/5*i - 2*i**4 = 0.
-1, 0, 2/5, 4
Let j be -1 - -21 - (-1 - -5). Let c = -12 - -17. Solve 16 - j*a + 24*a**3 + 52*a**2 + c*a**4 + 4*a**4 + 64*a - 5*a**4 = 0.
-2, -1
Let q be (17/2)/(2/(-8)). Let z = 49 + q. Solve 4*a**2 + 7*a**2 + z*a - 3*a**2 - 3*a**2 = 0.
-3, 0
Let n = -629/4 - -158. Let j be (-2)/5*(-19)/(1368/135). Factor 3/4*i**3 - 3/4*i**2 + n*i**4 + 0 - j*i**5 + 0*i.
-3*i**2*(i - 1)**2*(i + 1)/4
Let w be 507/91 - 3/(-7). Suppose -w*n = 2 - 20. Suppose -b**n + 6*b**3 - 4*b**4 - b**3 + 0*b + 4*b**2 - 4*b = 0. Calculate b.
-1, 0, 1
Let w(k) = -2*k + 4*k - 3*k + 5*k. Let q be w(0). Find r, given that 0*r**2 + 1/2*r**4 + 0 + q*r - 1/4*r**5 - 1/4*r**3 = 0.
0, 1
Let z(u) be the third derivative of -u**5/20 - 25*u**4/8 + 13*u**3 - 24*u**2. Factor z(w).
-3*(w - 1)*(w + 26)
Find t, given that 588/5*