/14). Let y(k) be the second derivative of -1/18*k**q + 0 + 0*k**2 - 1/27*k**3 - 1/45*k**5 + k. Suppose y(p) = 0. Calculate p.
-1, -1/2, 0
Let z = -315 - -316. Factor -2*n + z - 7/4*n**2 + 5/4*n**3.
(n - 2)*(n + 1)*(5*n - 2)/4
Suppose -5*b = r - 17, 4*b + 4*r = 3*b + 11. Let q(o) = o**3 + 8*o**2 + 5*o - 10. Let f be q(-7). Factor 8*k**4 - 5*k**f - k + k**b - 3*k**2 + 0*k**2.
k*(k - 1)*(k + 1)*(3*k + 1)
Let t = 2638/11 + -240. Let o = 19/44 + t. Factor 3/4*f**3 - 1/4*f**2 - 3/4*f + o.
(f - 1)*(f + 1)*(3*f - 1)/4
Let z(r) be the first derivative of r**6/27 - 2*r**5/15 + r**4/6 - 2*r**3/27 - 17. Find d, given that z(d) = 0.
0, 1
Let t(n) = 6*n**2 + 5*n - 5. Let j(c) = 3*c**2 + 3*c - 3. Let p(r) = 5*j(r) - 3*t(r). Factor p(f).
-3*f**2
Let m = -2 - -2. Let j be 2 + -4 - (-5 + m). Factor -z**4 - 4*z + 2*z**2 + 2*z + 2*z**j - z**4.
-2*z*(z - 1)**2*(z + 1)
Let t = -47 + 145/3. Solve 0 + 0*r + r**3 + 1/3*r**2 - t*r**4 = 0 for r.
-1/4, 0, 1
Let h(q) be the third derivative of -q**8/25200 - q**7/6300 + q**5/12 - 3*q**2. Let d(t) be the third derivative of h(t). Factor d(f).
-4*f*(f + 1)/5
Let r(g) be the third derivative of -1/12*g**4 + 0*g**3 + 4*g**2 + 1/30*g**5 + 0 + 0*g. Factor r(z).
2*z*(z - 1)
Let o(j) be the second derivative of -2*j**6/15 + 3*j**5/5 - j**4/3 - 2*j**3 + 4*j**2 - 18*j. Factor o(y).
-4*(y - 2)*(y - 1)**2*(y + 1)
Let r be (-1)/(-3) + (-35)/(-21). Suppose -6 = -b + r*k, 0 = 2*k + 4 - 0. Factor -4*t**2 - 28*t + 4*t**3 - 5*t**3 - b + 23*t.
-(t + 1)**2*(t + 2)
Let c(w) be the second derivative of 1/45*w**6 + 1/18*w**3 - w - 1/126*w**7 + 0*w**5 + 0 + 0*w**2 - 1/18*w**4. Factor c(u).
-u*(u - 1)**3*(u + 1)/3
Solve 0 - 2/9*k**4 - 4/9*k**2 + 0*k + 2/3*k**3 = 0.
0, 1, 2
Let s = -5 + 5. Let a be (s - -1)/((-10)/(-20)). Solve 2/3 + a*j**2 - 2*j - 2/3*j**3 = 0.
1
Let w be ((-1)/(-2))/((-110)/(-12)). Let n = 577/495 - w. Factor -10/9*u + 2/9 - 20/9*u**3 - 2/9*u**5 + n*u**4 + 20/9*u**2.
-2*(u - 1)**5/9
Let m(c) = -c. Let n(k) = k**2 - 8*k + 1. Let u(j) = -6*m(j) + n(j). Determine w so that u(w) = 0.
1
Let x(q) be the third derivative of -q**8/294 - 2*q**7/735 + q**6/35 + q**5/15 + q**4/21 + 10*q**2. Determine b so that x(b) = 0.
-1, -1/2, 0, 2
Let r be 5/(-4)*(5 - (-462)/(-90)). Let p(w) be the second derivative of -w + 0*w**3 + 0*w**2 + 1/15*w**6 - r*w**4 + 0*w**5 + 0. Factor p(x).
2*x**2*(x - 1)*(x + 1)
Let r = -1/51 - -107/255. Let c(l) be the second derivative of 3*l + 0*l**4 + r*l**2 - 1/5*l**3 + 1/50*l**5 + 0. Factor c(t).
2*(t - 1)**2*(t + 2)/5
Let x(z) be the second derivative of z**2 - 2*z + 0*z**3 + 0 + 1/300*z**6 - 1/525*z**7 + 0*z**4 + 0*z**5. Let c(t) be the first derivative of x(t). Factor c(f).
-2*f**3*(f - 1)/5
Let m be 10/(-6) - -1 - 901/(-159). What is k in -3/2*k**4 - 1/2*k**m + 0*k - 1/2*k**2 + 0 - 3/2*k**3 = 0?
-1, 0
Let f = 25/4 - 117/20. Factor 0 + 2/5*x - f*x**2.
-2*x*(x - 1)/5
Determine u, given that -2/5*u**3 + 2/5*u**2 - 2/5 + 2/5*u = 0.
-1, 1
Let q(j) = 5*j**3 - 3*j - 1. Let m(l) = -4*l**3 + 4*l + 2. Let y(r) = -3*m(r) - 2*q(r). Suppose y(x) = 0. What is x?
-1, 2
Factor -8/5 + 4/5*u**3 + 8/5*u**2 - 4/5*u.
4*(u - 1)*(u + 1)*(u + 2)/5
Let c(z) be the second derivative of 3*z**5/80 - 3*z**4/16 + z**3/4 - 16*z. Factor c(y).
3*y*(y - 2)*(y - 1)/4
Factor -2/5 - 14/15*c + 4/3*c**2.
2*(c - 1)*(10*c + 3)/15
Let t = -8 + 7. Let v be t/(-18) - 2/(-12). Let 0 + 2/9*f**2 + v*f = 0. What is f?
-1, 0
Let q be 1/2*15 + 310/(-62). Factor 1 + 2*v**2 + q*v + 1/2*v**3.
(v + 1)**2*(v + 2)/2
Let y be (-2 - 8)/2 + -2. Let i be y/2*6/(-42). Factor 0 - i*q - 1/2*q**2.
-q*(q + 1)/2
Solve -2/3 + 5/3*p - 4/3*p**2 + 1/3*p**3 = 0 for p.
1, 2
Let g(n) be the first derivative of -n**6/27 + n**4/9 - n**2/9 + 6. Factor g(p).
-2*p*(p - 1)**2*(p + 1)**2/9
Factor -2/3*r + 4/3*r**4 + 0*r**3 - 4/3*r**2 + 2/3*r**5 + 0.
2*r*(r - 1)*(r + 1)**3/3
Let a(v) be the second derivative of -1/20*v**5 + 2*v + 0*v**2 - 2/3*v**3 - 1/3*v**4 + 0. Factor a(i).
-i*(i + 2)**2
Let c(s) = s**4 + 1. Let a(b) = 12*b**4 - 2*b**3 + 4*b**2 + 14. Let k(y) = 2*a(y) - 28*c(y). Find p such that k(p) = 0.
-2, 0, 1
Let i(v) = -3*v**2 - 11*v**4 + 4*v**4 + 6*v + 4*v**2 - 6. Let j(k) = -8*k**4 + k**2 + 7*k - 7. Let n(h) = 7*i(h) - 6*j(h). Factor n(b).
-b**2*(b - 1)*(b + 1)
Let z(u) be the second derivative of u**9/15120 - u**8/2240 + u**7/1260 + u**4/3 + 2*u. Let o(f) be the third derivative of z(f). Let o(w) = 0. Calculate w.
0, 1, 2
Let k be -9 - -8 - (-2 + -6)/2. Let u(b) be the second derivative of 1/24*b**4 - 3*b + 0*b**k + 0 - 1/40*b**5 + 0*b**2. Suppose u(y) = 0. What is y?
0, 1
Suppose 0 = -2*z + 3 + 5. Find k, given that -2*k**4 - 2*k**2 - 10*k + 10*k + z*k**3 = 0.
0, 1
Factor -28*n**3 - 5*n + 0*n**2 + 3*n**4 - n + 34*n**3 - 12*n**2 + 9.
3*(n - 1)**2*(n + 1)*(n + 3)
Let h(f) be the second derivative of -f**7/35 + f**6/50 + 3*f**5/100 + 2*f. Factor h(v).
-3*v**3*(v - 1)*(2*v + 1)/5
Factor 2/9*u**5 + 4/9*u**2 - 1/3*u**4 + 0*u - 1/9 - 2/9*u**3.
(u - 1)**3*(u + 1)*(2*u + 1)/9
Let f(d) = 20*d**2 + 6*d + 2. Suppose 5*n + 15 + 10 = 0. Let s(i) = 7*i**2 + 2*i + 1. Let g(y) = n*f(y) + 14*s(y). Let g(m) = 0. What is m?
-2, 1
Let z(w) be the third derivative of 0*w + 0 - 9/20*w**5 - 8/35*w**7 + 13/8*w**4 - w**6 - w**3 - 4*w**2. Solve z(d) = 0.
-2, -1, 1/4
Let u = -1 + 4. Let k(x) be the second derivative of -1/4*x**2 + 1/60*x**6 + 1/20*x**5 + 0 - 1/6*x**3 + 0*x**4 + u*x. Find t such that k(t) = 0.
-1, 1
Let t be -2 - (-9 + (-6)/(-3)). Factor -n + 2*n + 1 + t*n**2 + n - 4*n**2.
(n + 1)**2
Let k(u) be the second derivative of u**6/180 - u**5/30 + 2*u**3/3 - 4*u. Let l(b) be the second derivative of k(b). Determine g, given that l(g) = 0.
0, 2
Let u(m) be the first derivative of -7*m**5/110 - 5*m**4/66 + 2*m**3/33 + 3*m + 2. Let t(d) be the first derivative of u(d). Factor t(i).
-2*i*(i + 1)*(7*i - 2)/11
Suppose -6*c + 3 = -5*c. Let k(y) be the first derivative of -1/2*y**4 + 4/21*y**c + 0*y**2 + 0*y - 1. Factor k(g).
-2*g**2*(7*g - 2)/7
Let p be 140/8*24/(-10). Let d be (8/p)/((-2)/3). Solve -6/7*i - 2/7 - 6/7*i**2 - d*i**3 = 0.
-1
Let y be 3366/(-56) + (-4)/16. Let c = y + 123/2. Factor -6/7*v**3 - 2/7*v + c*v**2 + 0.
-2*v*(v - 1)*(3*v - 1)/7
Let a be (-12)/(-10) - 3/15. Let s be 8 + 2 + (4 - 4). Suppose 22*g**3 - 2*g**3 + 5*g**4 + a - s*g**2 - 20*g**4 + 4*g**5 = 0. Calculate g.
-1/4, 1
Let o(n) be the first derivative of n**6/2 - 9*n**5/5 + 3*n**4/2 + 2*n**3 - 9*n**2/2 + 3*n + 17. Factor o(a).
3*(a - 1)**4*(a + 1)
Let d be 3/12 - (-3)/(-12). Suppose 0*a - a + 8 = d. What is v in 5*v**2 + a*v**4 - 10*v**3 - v - 2*v**5 + v - v**2 = 0?
0, 1, 2
Let g(y) be the second derivative of -17/42*y**4 - 16/21*y**3 + 0 - 4/7*y**2 - 1/14*y**5 + 4*y. Factor g(q).
-2*(q + 1)*(q + 2)*(5*q + 2)/7
Let 22*p**2 - 35*p**2 + p**4 - 4*p**3 + p**3 + 15*p**2 = 0. What is p?
0, 1, 2
Let a be (-12)/42 + (-760)/(-2709). Let w = a - -88/387. Let 4/9*r**3 + 0 + 2/9*r**4 + 0*r + w*r**2 = 0. Calculate r.
-1, 0
Let s be (5 - (-145)/(-25))/(6/(-5)). Determine o so that 0 + 1/3*o**5 + 0*o + s*o**4 - 1/3*o**3 - 2/3*o**2 = 0.
-2, -1, 0, 1
Let q(a) = -a**4 + a**3 - a**2 + a. Let u(v) = 2*v**3 - 2*v. Let d(r) = 2*q(r) + u(r). Determine b, given that d(b) = 0.
0, 1
Let o = -161122 + 14500777/90. Let j = o - -27/10. Find y such that 2/9*y**2 + 0 - j*y = 0.
0, 2
Suppose 2*v - m - 3 = v, 4*v - 17 = 5*m. Let b = 6 + v. Factor 2 + 1 + 4*c**3 + 4*c - 6*c**2 - b - c**4.
-(c - 1)**4
Let j = 144 - 716/5. Solve 0*i**3 - 2/5*i**4 + 6/5*i**2 + j*i + 0 = 0 for i.
-1, 0, 2
Let t(f) be the third derivative of 7*f**5/720 - 11*f**4/72 + f**3/6 + 19*f**2. Find y such that t(y) = 0.
2/7, 6
Suppose -k = 2*k - 21. Let s = -5 + k. Factor 1 + 20*f**s + 3 - 22*f + 12*f**2 - 14*f**3.
-2*(f - 1)**2*(7*f - 2)
Suppose s + 3*n = -2*s - 12, 0 = s - 3*n - 16. Factor 0*b - b + 5*b**2 + b**3 + s - 2*b**2 - 4*b**2.
(b - 1)**2*(b + 1)
Let i(c) be the first derivative of -c**5/120 + c**4/48 - 2*c**2 + 5. Let n(p) be the second derivative of i(p). Factor n(b).
-b*(b - 1)/2
Let p(l) be the third derivative of 1/70*l**7 + 7/40*l**6 - l**3 + 0 + 6*l**2 - 1/56*l**8 + 1/20*l**5 - 5/8*l**4 + 0*l. Let p(q) = 0. Calculate q.
-1, -1/2, 1, 2
Let u(d) = -d**2 + 5*d + 6. Let f be u(6). Let z be (-3 - -1) + f + 4. Let 7*h**z + h**4 + 2*h**4 + h**5 + 2*h**4 + 9*h**3 - 11*h + 13*h =