9. Determine p, given that 12*p**2 + 6*p + 12 - 28 + 2*p**m + 10*p**3 - 14*p = 0.
-2, 1
Let w(g) = g**2 + g + 1. Let i(f) = f + 4. Let z be i(14). Let c(a) = -z - a + 20 + 3*a. Let m(d) = -c(d) + 2*w(d). Factor m(j).
2*j**2
Let s = -53 - -67. Find w, given that 2*w**2 - s*w - 18*w - 12 + 22*w = 0.
-1, 6
Let x(f) = -3*f + 20. Let c be x(6). What is m in 0*m**3 - 2*m**3 + 2*m + 2*m**2 + 0*m**c - 4*m**2 + 2*m**4 = 0?
-1, 0, 1
Let g(c) be the first derivative of c**6/10 + 3*c**5/10 - c**3 - 3*c**2/2 - 10*c + 14. Let a(m) be the first derivative of g(m). Factor a(r).
3*(r - 1)*(r + 1)**3
Factor 7 + 106/5*o + 3/5*o**2.
(o + 35)*(3*o + 1)/5
Let u be (-4)/(-12)*12*11/88. Factor -1/2*w**2 - 1/6*w**4 - 1/6*w + 0 - u*w**3.
-w*(w + 1)**3/6
Let j(l) be the third derivative of l**7/630 - l**5/30 + l**4/9 - 8*l**3/3 - 3*l**2. Let c(w) be the first derivative of j(w). Factor c(f).
4*(f - 1)**2*(f + 2)/3
Let q = 18 - 20. Let y = 5 + q. What is p in -8*p**3 + p**5 + 7*p**y + 0*p**4 - p**2 + p**4 = 0?
-1, 0, 1
Determine c so that -6/17*c**3 - 14/17*c**2 + 16/17 + 4/17*c = 0.
-2, -4/3, 1
Let v(k) be the first derivative of -k**3 - 129*k**2/2 + 132*k - 777. Factor v(t).
-3*(t - 1)*(t + 44)
Let d = -41 + 43. Suppose 2*f**2 - 1 + 3*f**2 - 2*f**d - 2*f**2 = 0. What is f?
-1, 1
Suppose -7 = -2*h - 3. Suppose -9*g + h = -8*g. Factor -5*u**g - 28*u - 3*u**2 - 2 + 26 - 4*u**2.
-4*(u + 3)*(3*u - 2)
Let y(j) be the second derivative of j**4/18 - 17*j**3/9 + 16*j**2/3 - 299*j. Let y(r) = 0. What is r?
1, 16
Let p be (-2)/3 - 682/12. Let h = -571/10 - p. Factor 4/5*c + h*c**2 + 0.
2*c*(c + 2)/5
Let m = 8 + 0. Suppose 0 = -4*f + 8*f - m. Factor -2*l**3 - 2*l**2 - l**4 - 3*l**f + 2*l**4 + 6*l**2.
l**2*(l - 1)**2
Let x(w) be the third derivative of w**7/14 + 11*w**6/24 + w**5 + 5*w**4/6 + 32*w**2 - w. Suppose x(o) = 0. Calculate o.
-2, -1, -2/3, 0
Let o(s) be the first derivative of s**3/7 - 18*s**2/7 + 33*s/7 - 11. What is l in o(l) = 0?
1, 11
Let t = 211 + -211. Let m(q) be the second derivative of 0*q**3 + 6/25*q**5 + 0*q**2 + 3*q - 8/25*q**6 - 1/20*q**4 + t. Factor m(j).
-3*j**2*(4*j - 1)**2/5
Find c such that -9776*c - c**3 - 31624*c + 1275*c**2 + 2*c**3 - 6*c**3 - 360*c**2 - 42320 = 0.
-1, 92
Let q(h) = -7*h**3 + 2*h**2 + h - 5. Let f(m) = -2*m**3 - m**2. Let n(u) = 3*f(u) - q(u). Factor n(k).
(k - 5)*(k - 1)*(k + 1)
Let k(d) be the first derivative of 2*d**5/55 - d**4/22 - 34*d**3/33 + 21*d**2/11 + 72*d/11 - 94. Suppose k(q) = 0. Calculate q.
-4, -1, 3
Let t(p) = -p**3 - 1 - p**4 + 2*p**4 + 0*p**3. Let m(i) = 3*i**3 - 9*i**2 + 6*i + 3. Let g(z) = z - 3. Let r be g(4). Let v(y) = r*m(y) + 3*t(y). Factor v(k).
3*k*(k - 1)**2*(k + 2)
Let p(b) = -b**2 + 18*b + 2. Let m be p(18). Factor -350*q**4 - 24*q**3 + 4*q**5 - 12*q + 350*q**4 - 32*q**m.
4*q*(q - 3)*(q + 1)**3
Let y(l) be the first derivative of l**5/50 + l**4/5 + 3*l**3/5 - 5*l + 8. Let x(b) be the first derivative of y(b). Let x(t) = 0. Calculate t.
-3, 0
Suppose -37*d + 32*d = 170. Let y = d - -176/5. Factor -2/5*g**2 - y - 8/5*g.
-2*(g + 1)*(g + 3)/5
Let c = 4491/2 - 2242. Factor c*w**2 + 2 + 8*w.
(w + 2)*(7*w + 2)/2
Suppose 0 = -15*r - 72*r + 128 + 46. Let -8/7*k + 4/7 + 4/7*k**r = 0. Calculate k.
1
Let k(j) be the first derivative of -10/3*j**3 + 25/8*j**4 + 7/24*j**6 - 1/2*j - 3/2*j**5 + 15/8*j**2 - 39. Factor k(p).
(p - 1)**4*(7*p - 2)/4
Let z(i) be the third derivative of -i**5/90 - 5*i**4/36 + 7*i**2. What is g in z(g) = 0?
-5, 0
Let w be (-42)/8*(-8)/6. Let b(t) be the third derivative of 0*t**3 - 3/28*t**6 - 1/7*t**4 + 5*t**2 + 9/490*t**w + 1/5*t**5 + 0 + 0*t. Factor b(c).
3*c*(c - 2)*(3*c - 2)**2/7
Factor 29/3*l**3 + 0 + 13*l**2 + 5/3*l**4 - 3*l.
l*(l + 3)**2*(5*l - 1)/3
Factor 1/2*w**5 - 7/2*w**3 - 3*w + 0 - 1/2*w**4 + 13/2*w**2.
w*(w - 2)*(w - 1)**2*(w + 3)/2
Let f(m) = m**2 + 2*m - 4. Let x be f(-4). Let l = -307/2 - -154. Determine v, given that -l*v**3 + 1/2*v + 0 - 1/2*v**x + 1/2*v**2 = 0.
-1, 0, 1
Suppose 4*z + 10*k + 104 = 12*k, 2*z + k = -48. Let r be z/(-12) - 6/8. Factor -8/9*o**3 - r*o**2 - 2/9 - 2/9*o**4 - 8/9*o.
-2*(o + 1)**4/9
Let v(o) be the third derivative of -o**5/20 - 3*o**4/8 - o**3 - 2*o**2 - 26*o. Let v(h) = 0. Calculate h.
-2, -1
Let a(t) be the first derivative of -t**4 + 14*t**3/3 - 6*t**2 - 79. Factor a(x).
-2*x*(x - 2)*(2*x - 3)
Let o(j) = -2*j**2 - 9*j + 5. Let z be o(-5). Let n(m) be the first derivative of -1/8*m**2 + z*m + 1/12*m**3 + 7. Factor n(l).
l*(l - 1)/4
Factor -1210/3*a**2 - 200/3 + 50/3*a**3 - 992/3*a.
2*(a - 25)*(5*a + 2)**2/3
Let t = 128 + -126. Suppose -3*n + 4*k - 10 = 0, -t*k + 1 = -7. Factor -4/15 - 8/15*v**n + 6/5*v.
-2*(v - 2)*(4*v - 1)/15
Let p(f) be the third derivative of -f**8/47040 - f**7/3920 - f**6/840 - 2*f**5/15 + 7*f**2. Let j(z) be the third derivative of p(z). Factor j(u).
-3*(u + 1)*(u + 2)/7
Let k(j) = 2*j - 9. Let v be k(7). Factor 62*h**2 - 26*h**2 - 31*h**2 - v.
5*(h - 1)*(h + 1)
Let u be 5/6 + (-6 + -8)/28. Factor u*d**3 - 4/3 + d**2 + 0*d.
(d - 1)*(d + 2)**2/3
Suppose -10*n + 46 = 13*n. Let x = 1/253 + 493/3289. Solve -x*h + 8/13*h**n + 10/13*h**3 + 0 = 0 for h.
-1, 0, 1/5
Let a(l) = 2*l**2 + 8*l - 47. Let r be a(-8). Suppose -3*m + 0*m = i - r, 5*m - 35 = -3*i. Solve 1/3*c**3 - 1/3*c - 1/3*c**m + c**2 - 2/3 = 0 for c.
-1, 1, 2
Suppose -5*c - 4*s + 31 = 0, -285*c - 5*s = -281*c - 32. Factor 0 + 0*r + 2/3*r**4 + 8/3*r**2 - 8/3*r**c.
2*r**2*(r - 2)**2/3
Let o = 1061/12 + -523/6. Factor -10 - o*y**3 + 5/2*y**2 + 5*y.
-5*(y - 2)**2*(y + 2)/4
Let c(u) be the first derivative of 4*u**5/5 - 8*u**4 + 52*u**3/3 - 12*u**2 - 96. Factor c(f).
4*f*(f - 6)*(f - 1)**2
Let l(d) = 20*d**3 + 56*d**2 + 52*d + 16. Let q(h) = h**4 - 39*h**3 - 113*h**2 - 105*h - 32. Let g(r) = -10*l(r) - 4*q(r). Factor g(w).
-4*(w + 1)**3*(w + 8)
Let h(y) be the third derivative of y**5/15 - 2*y**4 + 12*y**2 + 18*y. Solve h(p) = 0 for p.
0, 12
Let f(w) be the second derivative of w**5/40 + 5*w**4/36 + w**3/36 - w**2/2 - 38*w. Factor f(k).
(k + 1)*(k + 3)*(3*k - 2)/6
Let j(d) be the third derivative of 0*d**5 - 2/35*d**7 + 0*d + 0*d**3 + 14*d**2 - 17/180*d**6 + 0 - 5/504*d**8 + 1/9*d**4. Let j(g) = 0. Calculate g.
-2, -1, 0, 2/5
Let t(v) be the third derivative of v**5/120 - v**4/16 - v**3/3 + 104*v**2. Factor t(s).
(s - 4)*(s + 1)/2
Suppose -5*f + 8 = -f + 3*c, f + 5*c = 19. Let p(r) = -20*r**2 - 20*r + 25. Let y(w) = w**2 + w - 1. Let l(j) = f*p(j) - 25*y(j). Find s such that l(s) = 0.
-1, 0
Suppose 0 = -5*y + 36 + 69. Suppose 4*o - 2*i - 12 = 0, 0 = -4*o + i - 7 + y. Solve o*x**5 + x**4 - 3*x**5 - x - 2*x**2 + x**4 = 0 for x.
-1, 0, 1
Let -32*f + 136*f + 194*f - 10*f**2 + 87*f - 190 = 0. What is f?
1/2, 38
Let r be 8/(-96) - (-5 + 98/21). Factor v + r*v**2 + 0.
v*(v + 4)/4
Let u(x) be the third derivative of x**8/6720 - 7*x**5/60 + 10*x**2. Let b(g) be the third derivative of u(g). Find i, given that b(i) = 0.
0
Determine z, given that 136/9*z**2 - 34/9*z**4 + 0 - 8/9*z**5 + 8/3*z**3 + 32/9*z = 0.
-4, -2, -1/4, 0, 2
Let m(f) be the second derivative of f**7/105 + 8*f**6/15 + 101*f**5/10 + 161*f**4/3 - 980*f**3/3 + 2744*f**2/5 + 56*f - 2. Factor m(d).
2*(d - 1)**2*(d + 14)**3/5
Let c be (-5)/(-2)*(6/15 + 66/(-275)). Suppose -s + 3*s + 4*l = 8, l = -s + 2. Factor s*j**3 + 2/5*j**4 + 0*j + c - 4/5*j**2.
2*(j - 1)**2*(j + 1)**2/5
Factor w**3 + 64*w**2 + 3*w**3 + 6*w**4 - 8*w + 3*w - 70*w**2 + w**5.
w*(w - 1)*(w + 1)**2*(w + 5)
Let x(t) be the third derivative of t**6/600 + 3*t**5/100 + t**4/20 - 8*t**3/15 + 145*t**2. Let x(y) = 0. What is y?
-8, -2, 1
Let y(h) be the first derivative of 0*h**2 + 0*h - 22 + 5/4*h**4 + 0*h**3. Find d such that y(d) = 0.
0
Let -99*k**4 + 2312*k - 21*k**5 - 4600*k - 117*k**3 - 21*k**2 + 2306*k = 0. Calculate k.
-3, -1, 0, 2/7
Let g(w) = w**4 + 2*w**3 - w**2 - 2*w. Let o(q) = -3*q**4 - 5*q**3 + 3*q**2 + 5*q. Let c(l) = 5*g(l) + 2*o(l). Factor c(p).
-p**2*(p - 1)*(p + 1)
Let -216/5 - 2/15*q**2 + 24/5*q = 0. Calculate q.
18
Let o(z) be the third derivative of z**5/20 + 7*z**4/2 + 26*z**3 + 727*z**2. Solve o(h) = 0.
-26, -2
Let j(l) be the second derivative of 5*l**6/3 - 7*l**5/8 - 55*l**4/24 - 5*l**3/6 - 6*l - 4. Solve j(g) = 0.
-2/5, -1/4, 0, 1
Suppose 95*z + 33 = 106*z. Let k(f) be the second derivative of -f + 0*f**2 + 0 - 2/9*f**z - 1/18*f**4. 