9). Let h be ((-44)/(-132))/((-2)/(-18)). Find p, given that -p - 12*p**2 + 3*p + 6*p + p + k*p**h = 0.
0, 1, 3
Factor -6*g**3 - 28*g**3 + 2*g**4 - g**5 + 33*g**3.
-g**3*(g - 1)**2
Let r(m) = -m**3 + 7*m**2 - 42*m + 299. Let t be r(7). Factor -2/5*a**2 - 2/5 + 4/5*a**4 - 1/5*a**t + a - 4/5*a**3.
-(a - 2)*(a - 1)**3*(a + 1)/5
Let o(v) be the first derivative of v**4 - 4*v**2 - 4/3*v**3 + 0*v - 14. What is m in o(m) = 0?
-1, 0, 2
Suppose -6*x + 0 = 6. Let a(g) = -10*g**3 - 14*g**2 - 18*g + 36. Let r(q) = q**3 - q**2 + q. Let h(j) = x*a(j) - 6*r(j). Determine c, given that h(c) = 0.
-3, 1
Suppose 2*g + 120 - 126 = 0. Let t = 97/630 + -1/90. Determine l, given that -1/7*l**g + 1/7*l**4 + 0 - t*l**2 + 1/7*l = 0.
-1, 0, 1
Let i(p) be the third derivative of -p**5/270 + 5*p**4/108 - 56*p**2 + p. Factor i(l).
-2*l*(l - 5)/9
Let a = 13 + -7. Let o(t) = -15*t**4 + 21*t**3 - 5*t + 12*t**4 - 5*t**3 + 7. Let b(z) = z**4 - 5*z**3 + 2*z - 2. Let m(f) = a*o(f) + 21*b(f). Factor m(w).
3*w*(w - 2)**2*(w + 1)
Let d(h) = -4*h**3 - 13*h**2 - 23*h - 14. Let t(g) = 4*g**3 + 12*g**2 + 24*g + 16. Let w(v) = -4*d(v) - 3*t(v). Determine b so that w(b) = 0.
-2, -1
Let k(j) = -2*j**3 + 19*j**2 - 16*j - 67. Let c(h) = 2*h**3 - 20*h**2 + 16*h + 74. Let v(r) = 5*c(r) + 6*k(r). Factor v(m).
-2*(m - 4)**2*(m + 1)
Let o(l) be the third derivative of l**8/504 - 2*l**7/315 - l**6/45 + l**5/45 + l**4/12 + 209*l**2. Solve o(m) = 0.
-1, 0, 1, 3
Let y(c) be the first derivative of c**4 + 52*c**3 + 150*c**2 + 148*c + 332. Determine x so that y(x) = 0.
-37, -1
Suppose 107 - 11*a - 6*a**2 - 83 + 2*a**3 + a**3 - a = 0. What is a?
-2, 2
Let i(j) be the first derivative of -2 - 8/7*j - 4/35*j**5 + 2*j**2 - 12/7*j**3 + 5/7*j**4. Find m such that i(m) = 0.
1, 2
Let w(q) be the third derivative of -11*q**2 + 0*q**5 - 2/105*q**7 + 0*q + 0*q**4 - 1/15*q**6 + 0*q**3 + 0 + 1/84*q**8. Factor w(n).
4*n**3*(n - 2)*(n + 1)
Let t(n) = -6*n - 16. Let c be t(-7). Suppose -3*w + 161 = c. Let -5*v**3 - 15*v + w*v - 10*v**2 - 15*v = 0. What is v?
-3, 0, 1
Let a(w) be the first derivative of 6*w**5/5 - 15*w**4/8 - 7*w**3/2 + 3*w**2/2 + 107. Solve a(b) = 0.
-1, 0, 1/4, 2
Factor -21*o**2 - 3*o**3 - 1379 + 1379.
-3*o**2*(o + 7)
Factor -6 - 4*k - 1/2*k**2.
-(k + 2)*(k + 6)/2
Let j(o) = -5*o**3 + 5*o**2. Let r(z) be the second derivative of 1/2*z**4 + 0*z**3 - 1/4*z**5 + 0 - 5*z + 0*z**2. Let p(s) = 4*j(s) - 3*r(s). Factor p(l).
-l**2*(5*l - 2)
Suppose 0 + 16/7*f**2 - 16/7*f + 4/7*f**5 + 12/7*f**3 - 16/7*f**4 = 0. Calculate f.
-1, 0, 1, 2
Let v(n) be the second derivative of 0 + 1/8*n**4 - 1/4*n**3 - 3/2*n**2 - 13*n. Solve v(j) = 0.
-1, 2
Let o(c) = -2*c + 28. Let u be -3*2*(-6 - -4). Let b be o(u). Factor -8/9*h**3 + 4/9*h - 2/9 - 8/9*h**b + 2/3*h**2.
-2*(h + 1)**2*(2*h - 1)**2/9
Let m(r) be the third derivative of -1/840*r**7 - 5*r**2 + 1/192*r**4 + 0*r**3 + 0*r + 1/240*r**5 + 0*r**6 - 1/2688*r**8 + 0. Factor m(n).
-n*(n - 1)*(n + 1)**3/8
Suppose k**2 + 0 + 0*k + 1/3*k**4 - 4/3*k**3 = 0. Calculate k.
0, 1, 3
Factor 35*q**2 + 2*q**4 - 6*q**3 + 47*q - 49*q - 29*q**2.
2*q*(q - 1)**3
Suppose 46*r + 8*r = -277 + 277. Suppose 0 + 4/5*f**2 + r*f - 2/5*f**3 = 0. Calculate f.
0, 2
Let z(u) be the third derivative of -u**6/960 - 7*u**5/240 - 11*u**4/192 + 13*u**3/24 - 527*u**2. Factor z(v).
-(v - 1)*(v + 2)*(v + 13)/8
Let u(h) be the first derivative of h**5 - 30*h**4 - 395*h**3/3 - 135*h**2 - 389. Solve u(o) = 0 for o.
-2, -1, 0, 27
Determine t, given that -4/5*t**2 + 336/5*t - 7056/5 = 0.
42
Factor 10*p**2 + 2*p + 45 + 3*p + 10*p + 33*p - 7*p**2.
3*(p + 1)*(p + 15)
Let y(o) = -o**4 - o**3 - o**2 + o - 1. Let b(x) = 4*x**4 + 20*x**3 + 81*x**2 + 29*x - 125. Let f(u) = -4*b(u) - 12*y(u). Factor f(c).
-4*(c - 1)*(c + 2)*(c + 8)**2
Let p = 199 + -198. Let w(f) = 8*f**2 + 3 + 5 + 8*f + 6. Let k(h) = h**2 + h + 1. Let t(y) = p*w(y) - 10*k(y). Factor t(u).
-2*(u - 1)*(u + 2)
Let v(t) be the first derivative of t**6/1260 + t**5/210 + 5*t**3 - 15. Let q(x) be the third derivative of v(x). Find o such that q(o) = 0.
-2, 0
Factor 4232/19 + 2/19*f**3 + 186/19*f**2 + 4416/19*f.
2*(f + 1)*(f + 46)**2/19
Let x(r) be the second derivative of r**4/42 + 13*r**3/21 - 30*r**2/7 - 129*r. Find b such that x(b) = 0.
-15, 2
Let r(h) be the third derivative of h**7/4200 - h**5/600 + 5*h**3/6 - 2*h**2. Let v(c) be the first derivative of r(c). Factor v(s).
s*(s - 1)*(s + 1)/5
Suppose -4*y = 5*t - 13, -2*t + 5 = 3. Factor -9/7*s + 2/7*s**y - 5/7.
(s - 5)*(2*s + 1)/7
Suppose -7 = 4*a - 3*x, 5*x = 14*a - 13*a + 23. Find k, given that 2/13*k**5 + 0 - 4/13*k**4 + 2/13*k**3 + 0*k + 0*k**a = 0.
0, 1
Suppose 17 = 2*p - h + 4, -4*h - 8 = 3*p. What is q in 3*q**p + q**2 - 135 - 3*q**3 - q**5 + 135 = 0?
0, 1
Factor 10/7*b**2 - 2/7*b**4 + 0*b + 0 + 8/7*b**3.
-2*b**2*(b - 5)*(b + 1)/7
Let t be -1*((-3)/6 - 83/2). Let o = t - 40. Determine z, given that 0 - 4/11*z - 2/11*z**o = 0.
-2, 0
Factor 95*w**4 - 530*w**3 + 1715 + 242*w**2 - 5*w**5 + 325*w**2 + 2695*w - 217*w**2.
-5*(w - 7)**3*(w + 1)**2
Suppose 19 + 15 = 2*g - 3*v, -4*g - 5*v + 90 = 0. Let y = 23 - g. Factor -j**3 - 2*j**4 + 7*j**3 - j**3 + 3*j**y - 10*j**2 + 4*j.
-2*j*(j - 2)*(j - 1)**2
Let 3*p + 17 - 7*p**2 - 446*p**3 - 14*p**2 + 443*p**3 + 4 = 0. What is p?
-7, -1, 1
Let a(h) = 6*h + 25. Let w be a(16). Let b = w + -113. Let 1/2*d**5 + b*d - 25/2*d**2 - 2 - 7/2*d**4 + 19/2*d**3 = 0. What is d?
1, 2
Let i(s) be the first derivative of 5*s**7/14 + s**6/2 + s**5/5 - 6*s**2 - 12. Let f(g) be the second derivative of i(g). What is u in f(u) = 0?
-2/5, 0
Let a(k) be the second derivative of 11*k - 4/15*k**6 + 6/5*k**5 + 1/3*k**3 + 0 + 7/6*k**4 + 0*k**2 - 16/21*k**7. Solve a(s) = 0 for s.
-1/2, -1/4, 0, 1
Let s(o) be the third derivative of o**10/90720 - o**8/12096 - 11*o**5/30 - 44*o**2. Let d(w) be the third derivative of s(w). Factor d(c).
5*c**2*(c - 1)*(c + 1)/3
Suppose -2*v = 5*i - 7, -3*v + 5*i + 0 = 2. Let n be (-8 + 4)*v/(-10). Factor 2/5*j**2 - n*j + 0.
2*j*(j - 1)/5
Let t(h) be the second derivative of h**7/84 + 2*h**6/15 + h**5/2 + 2*h**4/3 - 7*h - 1. Factor t(p).
p**2*(p + 2)**2*(p + 4)/2
Let j = 23 + -46. Let t = j + 25. Let 4*k**3 - k**3 + k**5 + 4*k**4 - t*k**3 - 2*k**4 = 0. What is k?
-1, 0
Suppose -2*l = l - 9. Let y(s) = s**2 - 7*s + 8. Let p be y(6). Factor -r**l + 13*r**3 + r + r + 8*r**4 + p*r**5 + 8*r**2.
2*r*(r + 1)**4
Let u(n) be the third derivative of -13/51*n**4 + 7/51*n**5 + 2*n + 0 + 49/1020*n**6 + 8/51*n**3 + 8*n**2. Factor u(q).
2*(q + 2)*(7*q - 2)**2/17
Factor 4 - 1/3*o**2 - 11/3*o.
-(o - 1)*(o + 12)/3
Let l = 32/39 - 4/195. Let i = 270756/5 - 54151. Factor -2*z**2 + 2/5 + 8/5*z**4 - i*z - l*z**3 + z**5.
(z - 1)*(z + 1)**3*(5*z - 2)/5
Let u(x) = x**2 + 26*x - 54. Let v be u(-28). Solve 10*i**v - 9*i**2 - 9*i**3 - 3*i**2 = 0 for i.
-2/9, 0
Let t(p) be the first derivative of 4*p + p**2 - 1/2*p**4 + 1 - 4/3*p**3. Suppose t(r) = 0. What is r?
-2, -1, 1
Let t be 4/(-2) - (-7 - 4). Suppose 4*c - 25 = -t. Suppose -c*f + 3*f**5 + 100*f**3 - 92*f**3 - 7*f**5 = 0. What is f?
-1, 0, 1
Suppose 0 + 0*w - 1/2*w**4 + 1/4*w**5 + 0*w**2 + 1/4*w**3 = 0. What is w?
0, 1
Factor -19*w - 1156 - 4*w**2 - 9*w - 108*w.
-4*(w + 17)**2
Let d(s) = 3*s**3 - 36*s**2 + 67*s - 22. Let h(p) = -6*p**3 + 72*p**2 - 135*p + 42. Let b(q) = -9*d(q) - 4*h(q). Factor b(k).
-3*(k - 10)*(k - 1)**2
Let n be (-5)/(-35)*(-826)/(-590). Factor -3/5*j + 4/5 - n*j**2.
-(j - 1)*(j + 4)/5
Let d(u) be the second derivative of -5*u**4/96 + 7*u**3/24 + 3*u**2/16 - 67*u. Factor d(r).
-(r - 3)*(5*r + 1)/8
Let h(r) be the first derivative of r**7/525 + r**6/300 - r**5/150 - r**4/60 + 6*r**2 + 2. Let g(f) be the second derivative of h(f). Factor g(c).
2*c*(c - 1)*(c + 1)**2/5
Suppose 5*a - 12 = a. Let u(i) = 2*i**2 - i + 1. Let r be u(1). Factor -3 - c**r + 3 + 2*c**2 + a*c.
c*(c + 3)
Let p(h) = h**2 + 17*h - 2. Let z be p(4). Let s = -79 + z. Let -81/7*r**2 - 6/7 + 39/7*r + 69/7*r**3 - s*r**4 = 0. What is r?
2/7, 1
Let p(j) = 20*j - 180. Let d be p(9). Let u(x) be the second derivative of 0*x**2 - 1/4*x**4 + d*x**3 - 3*x + 0. Factor u(y).
-3*y**2
Let w(d) be the second derivative of -d**5/40 + d**4/24 + 3*d**3/4 - 9*d**2/4 - 125*d. Let w(k) = 0. What is k?
-3, 1, 3
Let u(t) be the first derivative of t**4/14 - 4*t**3 + 81*