3). Let p = 1 - s. Factor -4*c - 7*c**2 + 11*c**2 + 4*c - p*c - 2*c**3.
-2*c*(c - 1)**2
Let d be 330/132*4/35. Find g such that 0 - 2/7*g**5 - d*g**2 + 0*g - 6/7*g**4 - 6/7*g**3 = 0.
-1, 0
Let n(f) be the first derivative of -3*f**4 + 13*f**3 - 5. Let j = 35 - 20. Let c(k) = -3*k**3 + 10*k**2. Let w(r) = j*c(r) - 4*n(r). Factor w(x).
3*x**2*(x - 2)
Let c(a) be the third derivative of -a**6/6 - a**5/5 + 3*a**4 + 32*a**3/3 + 8*a**2 + 2. Determine p so that c(p) = 0.
-8/5, -1, 2
Let m(w) be the third derivative of -w**7/120 - 17*w**6/160 - 7*w**5/20 - 5*w**4/24 - 567*w**2. Factor m(u).
-u*(u + 2)*(u + 5)*(7*u + 2)/4
Let z = 777/265 + 39/106. Let t(a) be the first derivative of 45*a**3 - 243/4*a**2 - 1/4*a**6 + 81/2*a + 5 + z*a**5 - 69/4*a**4. Factor t(b).
-3*(b - 3)**3*(b - 1)**2/2
Suppose -7*h = -5 - 9. Let y(p) = 3*p**2 + p. Let u(k) = k**2 + 1. Let a(o) = h*u(o) - y(o). Factor a(t).
-(t - 1)*(t + 2)
Factor 10/9*g**2 + 2/9*g**4 + 0 + 0*g + 1/9*g**5 - 13/9*g**3.
g**2*(g - 2)*(g - 1)*(g + 5)/9
Let f = 34 - 28. Let u be f*(-8)/128 - 14/(-16). Factor -1/2*a + 0 + u*a**3 + 0*a**2.
a*(a - 1)*(a + 1)/2
Let f be (2/6)/(9/2349). Let i = -43 + f. Factor 44*s + 4*s**3 + 4*s**4 - i*s.
4*s**3*(s + 1)
Let l be (-122)/4*(3 - (-35)/(-10)). Let h = -301/20 + l. Factor 1/5*g**2 - 2/5*g + h*g**3 + 0.
g*(g - 1)*(g + 2)/5
Let w(p) = 5*p**2 + 34*p - 61. Let c(r) = 2*r**2 + r - 1. Let g(y) = -6*c(y) + 2*w(y). Find s, given that g(s) = 0.
2, 29
Let z be (-6)/(-66) - (-320)/110. Let p(d) be the second derivative of -1/6*d**z - 1/10*d**5 - 8*d + 0*d**2 + 0 + 1/4*d**4. Factor p(j).
-j*(j - 1)*(2*j - 1)
Let k be 0 - ((-8)/10 + 0). Suppose -4*g = -9*g. Factor k*j**2 - 1/5*j**3 + g - 3/5*j.
-j*(j - 3)*(j - 1)/5
Let x(d) be the first derivative of 2*d**3/51 + 15*d**2/17 - 32*d/17 - 57. Factor x(q).
2*(q - 1)*(q + 16)/17
Let w(h) be the first derivative of 0*h**2 - 5/4*h**4 - 5/3*h**3 + 0*h + 13. Factor w(x).
-5*x**2*(x + 1)
Let u(z) be the third derivative of -z**4 - z**5 - 9/20*z**6 + 0*z + 0*z**3 + 19*z**2 + 0 - 1/10*z**7 - 1/112*z**8. Suppose u(y) = 0. Calculate y.
-2, -1, 0
Let r(l) = 3*l**3 + 14*l**2 - 8*l. Let a(w) = 4*w**3 + 14*w**2 - 8*w. Let x(k) = -6*a(k) + 7*r(k). Let x(q) = 0. Calculate q.
0, 2/3, 4
Determine v so that 27/2*v**4 - 3*v**2 - 21/2 - 3/2*v**5 + 45/2*v - 21*v**3 = 0.
-1, 1, 7
Let v(d) = 2*d**2 + 1. Let c(u) = -u**4 - 4*u**3 + 2*u**2 + 3. Let m(x) = c(x) - 3*v(x). Factor m(j).
-j**2*(j + 2)**2
Factor -2/3*m**4 - 32/21*m**3 - 8/7*m**2 + 0 + 0*m - 2/21*m**5.
-2*m**2*(m + 2)**2*(m + 3)/21
Let t = 25 + -31. Let w(j) = -64*j**3 + 55*j**2 - 10*j. Let v(l) = -65*l**3 + 55*l**2 - 10*l. Let k(i) = t*v(i) + 5*w(i). Factor k(y).
5*y*(2*y - 1)*(7*y - 2)
Let l(d) = -5*d**3 - 186*d**2 - 4608*d + 3. Let x(g) = -4*g**3 - 188*g**2 - 4608*g + 2. Let t(i) = 4*l(i) - 6*x(i). Find f such that t(f) = 0.
-48, 0
Let g(d) be the second derivative of -d**5/40 + 9*d**4/16 - 23*d**2/2 + 10*d. Let f(r) be the first derivative of g(r). Solve f(v) = 0 for v.
0, 9
Let q(s) = -5*s**3 + 23*s**2 - 45*s + 29. Let l(b) = -16*b**3 - 119*b + 68 + 16 + 70*b**2 - 16*b + 4. Let o(f) = -2*l(f) + 7*q(f). Find t such that o(t) = 0.
1, 3
Let m(u) be the first derivative of 1/44*u**4 - 1/33*u**3 + 0*u + 1/55*u**5 - 26 - 1/22*u**2. Factor m(d).
d*(d - 1)*(d + 1)**2/11
Let a be 74/12 - 12/8. Factor 46/3*n**2 + a*n**3 + 8/3 + 40/3*n.
2*(n + 1)*(n + 2)*(7*n + 2)/3
Let g be ((-3)/9)/(4/108*-3). Let p be (-2)/14 - ((-15)/7)/5. Suppose -6/7*q + 0 - p*q**g - 8/7*q**2 = 0. Calculate q.
-3, -1, 0
Find y such that 4/5*y - 22/5*y**4 + 6*y**3 + 6/5*y**5 - 18/5*y**2 + 0 = 0.
0, 2/3, 1
Let s = -111 + 111. Let m(y) be the first derivative of -2/5*y**5 - 2 + s*y + 2/3*y**3 + 2*y**2 - y**4. Find x such that m(x) = 0.
-2, -1, 0, 1
Let l(i) be the first derivative of 4 + 5/3*i**3 + 5*i - 5*i**2. Factor l(n).
5*(n - 1)**2
Suppose -3*c = -4*s + 4 + 8, -4*s + 12 = -13*c. Find h such that c + 2/17*h - 2/17*h**2 = 0.
0, 1
Let z(n) = 3*n + 41. Let f be z(-14). Let d be (-14)/(-98) + f/(14/(-26)). What is u in -2 - d*u - 1/2*u**2 = 0?
-2
Factor 198/7*l**2 + 0 + 0*l + 3/7*l**3.
3*l**2*(l + 66)/7
Let y(x) be the first derivative of -8*x**5/5 - 17*x**4/2 - 16*x**3/3 + 23*x**2 + 12*x - 56. Suppose y(v) = 0. What is v?
-3, -2, -1/4, 1
Factor -36/7 - 6/7*q + 2/7*q**2.
2*(q - 6)*(q + 3)/7
Let o be 9070/(-14) - 88/(-22). Let g = o + 645. Factor 6/7 + 2/7*x**2 - g*x.
2*(x - 3)*(x - 1)/7
Let k be (-875)/(-250) - (1 + (-2)/(-4)). Let w(r) be the first derivative of 0*r**k + 2/27*r**3 + 7 + 1/18*r**4 + 0*r. Find m, given that w(m) = 0.
-1, 0
Determine z so that 5/6*z**3 - 1/6*z**4 - 4/3*z + 0 - 1/3*z**2 = 0.
-1, 0, 2, 4
Let t be (1 - 10) + (5 + -49)/(-4). Find n such that -32/9*n**t + 0 - 128/9*n - 2/9*n**3 = 0.
-8, 0
Find t, given that -35*t**2 + 5*t**3 + 117*t - 117*t = 0.
0, 7
Let l(v) be the third derivative of -v**5/360 - 23*v**4/9 - 8464*v**3/9 - 14*v**2 + 13. What is a in l(a) = 0?
-184
Determine n so that 0*n**2 + 0 + 0*n + 3/5*n**5 + 0*n**4 - 12/5*n**3 = 0.
-2, 0, 2
Let x be -1 + 1/((-21)/(-27)). Suppose n + v + 4 = 0, 0 = 2*n - 21*v + 19*v - 8. Factor n*w + 8/7*w**5 + 0*w**2 + 0*w**3 + 0 + x*w**4.
2*w**4*(4*w + 1)/7
Let j = -51 - -33. Let i = j + 22. Factor 10*u**i - 11*u**5 - 6*u**5 + 13*u**5 - 8*u**3 + 2*u**2.
-2*u**2*(u - 1)**2*(2*u - 1)
Let x(r) be the third derivative of -r**6/120 - r**5/30 + r**4/8 + 885*r**2. Factor x(n).
-n*(n - 1)*(n + 3)
Let f = 31 - 29. Factor 40 + 0*v**f + 4*v - 23 - 19 - 2*v**2.
-2*(v - 1)**2
Suppose 0 = 23*v - 90*v. Factor v*a**2 - 2/3*a**4 + 2/3 - 4/3*a + 4/3*a**3.
-2*(a - 1)**3*(a + 1)/3
Suppose -460*d + 465*d - 20 = 0. Let c(i) be the first derivative of 3*i**3 - 1 + 3*i**2 + 3/4*i**d + 0*i. Factor c(v).
3*v*(v + 1)*(v + 2)
Let m(x) be the first derivative of -3/2*x**3 + 6 - 3/8*x**4 + 3/4*x**2 + 3/10*x**5 + 3*x. Factor m(c).
3*(c - 2)*(c - 1)*(c + 1)**2/2
Determine f, given that 12/5*f**2 - 14/5*f**3 + 2/5*f**5 + 0*f**4 + 0 + 0*f = 0.
-3, 0, 1, 2
Let i(m) be the second derivative of 3*m**7/14 - m**6/10 + 14*m. Let i(h) = 0. What is h?
0, 1/3
Solve 2 - 9/4*n**5 + 23/4*n**3 - 3*n**4 + 27/2*n**2 + 9*n = 0 for n.
-1, -2/3, 2
Let b(s) be the first derivative of 15*s**4/4 - 65*s**3/6 + 10*s**2 + 20*s + 4. Let k(l) be the first derivative of b(l). Factor k(w).
5*(w - 1)*(9*w - 4)
Let o(l) = -2*l - 28. Let v = -25 - -10. Let k be o(v). Solve 1/4*d**k + 1/2*d + 0 = 0.
-2, 0
Let d be (26/(-5))/((-64)/(-38)). Let m = d - -75/16. Factor -2*z**2 + 16/5*z + m.
-2*(z - 2)*(5*z + 2)/5
Let t be -3 - 4*3/12. Let c be 5/(5/t) - -10. Factor -7 + 13 - c - i**3 + 2*i**2 - i.
-i*(i - 1)**2
Let 0 + 1/3*b**2 + 1/3*b = 0. What is b?
-1, 0
Let x(a) be the second derivative of -a**6/40 + 9*a**5/40 - 3*a**4/4 + a**3 - 8*a + 8. Suppose x(o) = 0. Calculate o.
0, 2
Let j = 1258 + -1248. Let l(c) be the third derivative of -1/24*c**4 + 0*c**3 - j*c**2 + 0*c + 1/15*c**5 + 1/24*c**6 + 0. Factor l(i).
i*(i + 1)*(5*i - 1)
Suppose -6*o + 7*o = 2. Factor -5*p - 65 - p**o + 75 - 4*p**2.
-5*(p - 1)*(p + 2)
Factor -2/21*n**3 + 4/3 - 10/21*n - 16/21*n**2.
-2*(n - 1)*(n + 2)*(n + 7)/21
Let d(y) be the third derivative of -2/135*y**5 + 1/180*y**6 - 1/27*y**4 - 1/1512*y**8 + 0*y - 2*y**2 + 0*y**3 + 0 + 2/945*y**7. Factor d(p).
-2*p*(p - 2)**2*(p + 1)**2/9
Factor -109*a**2 + 40*a + 325*a**2 - 110*a**2 - 111*a**2 + 34 - 5*a**3 + 26.
-5*(a - 3)*(a + 2)**2
Let u be -1*(-12)/(-176)*168/(-63). Suppose -4*q + 2*p = -5 + 1, -q = 3*p + 6. Find w such that 0 + 2/11*w**2 + 0*w + q*w**3 - u*w**4 = 0.
-1, 0, 1
Let i(d) be the first derivative of -d**6/30 + 3*d**5/25 + 3*d**4/20 - 7*d**3/15 - 3*d**2/5 + 33. Let i(j) = 0. Calculate j.
-1, 0, 2, 3
Let a be (-2 - 0)/(2/(-6)*2). Let r(i) be the second derivative of 0 + 0*i**2 - 3/25*i**5 - 1/75*i**6 - 8/15*i**3 - a*i - 2/5*i**4. Solve r(l) = 0.
-2, 0
Let t = 2206 - 2206. Let b(q) be the first derivative of 0*q - 10 + 0*q**3 + t*q**2 - 1/42*q**4. What is v in b(v) = 0?
0
Suppose q - 67 = -15. Suppose 4*m = -0*m + q. Factor m*c**3 - 5*c**3 + c**4 - 32 - 32*c + c**4.
2*(c - 2)*(c + 2)**3
Let w(c) = -3*c**4 + c**3 + 3*c**2 - 3*c. Let r(o) = 25*o**4 - 8*o**3 - 24*o**2 + 23*o + 1. Let x(z) = 6*r(z) + 51*w(z). Determine i, given that x(i) = 0.
-2, 1
Let i(m) = -7*m - 9. Let d be i(-3). Solve 3 - 3 + d*y**4 