(j). Solve s(p) = 0 for p.
0, 2
Let v(p) be the first derivative of 54*p**3/17 + 234*p**2/17 + 338*p/17 - 761. Determine z so that v(z) = 0.
-13/9
Let s be (7 - 7)/(-2 - -1). Suppose -4*v + 5*c + 17 = s, 0 = -3*v - 0*v + 3*c + 12. Find i, given that -17*i + 9*i + 6 + 6*i**v - 14*i**2 - 6*i = 0.
-1, 1/3, 3
Suppose -28 = 61*b - 333. Solve -8/3*q**3 + 4/3*q + 0 + 4/3*q**b + 0*q**4 + 0*q**2 = 0 for q.
-1, 0, 1
Let m(h) be the third derivative of 0*h**3 + 0*h + 1/110*h**5 + 42*h**2 + 1/33*h**4 + 0 + 1/1320*h**6. Let m(r) = 0. What is r?
-4, -2, 0
Let a(f) be the second derivative of f**4/78 - 86*f**3/13 + 16641*f**2/13 - 4*f - 48. Let a(g) = 0. Calculate g.
129
Let w be (2/(-3)*(-55 + 58))/(-6). Determine i so that -4*i - 2/3*i**2 + w*i**4 + 4/3*i**3 + 3 = 0.
-3, 1
Factor 56/5 - 56/5*s**2 + 2/5*s**3 - 2/5*s.
2*(s - 28)*(s - 1)*(s + 1)/5
Let c(p) = 5*p**3 - 15*p**2 + 21*p. Let b(d) = d**3 - 3*d**2 + 4*d. Let f(z) = -z**3 - z**2 + 4*z + 1. Let y be f(-4). Let v(g) = y*b(g) - 6*c(g). Factor v(t).
3*t*(t - 2)*(t - 1)
Let c be (15/9)/(4 - 33/9). Suppose 5*n = v + 1, 2*n - 4*v = v + c. Factor 0*z**3 + 0*z**2 + 2/7*z**4 + n*z + 2/7*z**5 + 0.
2*z**4*(z + 1)/7
Determine l so that -50*l + 0 - 80*l**2 - 2/5*l**5 - 32/5*l**4 - 36*l**3 = 0.
-5, -1, 0
Let x = -170 - -173. Let m(v) be the third derivative of 0 + 0*v - 1/270*v**5 + v**2 + 0*v**x + 1/54*v**4. Factor m(u).
-2*u*(u - 2)/9
Find t, given that -8*t**3 - 224825 - 10608*t - 828*t**2 + 227529 - 8*t**3 = 0.
-26, 1/4
Let n = -36946 - -258642/7. Determine l, given that 100/7 + n*l + 1/7*l**2 = 0.
-10
Factor 23*g - 42*g**2 + 28*g**3 + 98*g**2 + 4*g**4 + 9*g.
4*g*(g + 1)*(g + 2)*(g + 4)
Let o = -44 - -48. Find p, given that 6*p**3 - 9 + 4*p**3 + 9 + 5*p**o = 0.
-2, 0
Let h = -249/37 + 821/111. Suppose 4*b = 2*b. Factor h*r**3 + 0 + 2/3*r**4 - 4/3*r**2 + b*r.
2*r**2*(r - 1)*(r + 2)/3
Factor -1672*w**2 - 5841*w**3 + 11681*w**3 - 5836*w**3 + 174724*w.
4*w*(w - 209)**2
Factor -32*o + 8 - 68*o**2 - 60*o**2 + 32*o**2 - 34*o**2.
-2*(5*o + 2)*(13*o - 2)
Let n = -116 - -289. Let s = 521/3 - n. Factor -s*j**3 + 0*j**2 + 2/3*j + 0.
-2*j*(j - 1)*(j + 1)/3
Suppose 2*l = 3*u - 68, -3*l = 4*u - 2*l - 76. Factor 23*h**3 - 5*h**5 - h - 20*h**4 - u*h**2 - 4*h - 53*h**3.
-5*h*(h + 1)**4
Factor -1664*s - 2/3*s**3 + 3072 + 196/3*s**2.
-2*(s - 48)**2*(s - 2)/3
Let i(s) be the first derivative of 4*s**5/5 - 8*s**3 - 16*s**2 - 12*s - 455. Suppose i(y) = 0. What is y?
-1, 3
Determine x so that 1/11*x**4 + x - 21/11*x**2 + 9/11*x**3 + 0 = 0.
-11, 0, 1
Suppose 3*k = -0*k + b + 14, 0 = -5*b + 5. Suppose 13 = k*w - 7. Factor 1/4*x**2 - 1/4*x**w - 1/4*x + 0 + 1/4*x**3.
-x*(x - 1)**2*(x + 1)/4
Determine y, given that -2*y**3 - 53 + 1 - 20*y**2 - 8 - 62*y = 0.
-5, -3, -2
Suppose -62*o - 73*o - 51*o = -372. What is a in 1/3*a**3 + 0 + 1/3*a - 2/3*a**o = 0?
0, 1
Let a be 7 + 465/(-62) - (-7 + -1). Let a*r**2 + 49/2 + 63/2*r + 1/2*r**3 = 0. Calculate r.
-7, -1
Let n = 23702/11 - 2152. Determine r so that n*r**2 - 18/11*r + 0 - 6/11*r**3 - 6/11*r**4 = 0.
-3, 0, 1
Let n(s) be the second derivative of s**4/102 - 8*s**3/51 - 20*s**2/17 - 3*s - 6. Let n(r) = 0. Calculate r.
-2, 10
Let o be (2522/(-195) + 13)/(6/9). Factor 1/10*m**2 + 0 + o*m**3 - 1/5*m.
m*(m - 1)*(m + 2)/10
Let p(m) be the second derivative of -2*m**5/5 + 17*m**4/6 - 16*m**3/3 + 3*m**2 - 8*m. Factor p(o).
-2*(o - 3)*(o - 1)*(4*o - 1)
Let -7074*o - 44*o**2 + o**3 - 11*o**3 + 7058*o = 0. What is o?
-4, -2/5, 0
Suppose -72*z = -61 - 83. Determine a so that 3*a + 3/4*a**z + 9/4 = 0.
-3, -1
Factor -7*q**5 - q**2 + 337*q**3 - 334*q**3 + 6*q**5 + q**4 - 2*q.
-q*(q - 2)*(q - 1)*(q + 1)**2
Suppose -61 + 15 = u + 2*d, 0 = d. Let n = 50 + u. Factor -1/4 - k**3 - 3/2*k**2 - 1/4*k**n - k.
-(k + 1)**4/4
Factor 0*r - 3/2*r**4 + 0*r**2 + r**3 + 0 + 1/2*r**5.
r**3*(r - 2)*(r - 1)/2
Suppose 0 = -7*v + 5*v + 10. Suppose v - 9 = -2*j. Factor -30*q**2 - 3*q**3 - j*q**3 + 4*q**3 + q**4 + 28*q**2.
q**2*(q - 2)*(q + 1)
Let h(n) = n**3 + 4*n**2 + 5*n + 4. Let m be h(-2). Factor 19*t**2 + 4 + 4*t - 2 - 17*t**m.
2*(t + 1)**2
Solve 25/4*t**2 - 6 - 1/4*t**4 + 5/2*t - 5/2*t**3 = 0 for t.
-12, -1, 1, 2
Let d(c) be the second derivative of c**6/240 + c**5/40 - c**3/3 + 5*c**2 - 7*c. Let s(i) be the first derivative of d(i). Find j such that s(j) = 0.
-2, 1
Let j(o) = -4*o**3 - 116*o**2 - 644*o - 1200. Let w(y) = 4*y**3 + 122*y**2 + 645*y + 1200. Let k(f) = 5*j(f) + 4*w(f). Factor k(p).
-4*(p + 3)*(p + 10)**2
Let y be 0*(1 - -1)/(-4). Suppose -c - h + 4 = y, 4*c - 4*h - 16 = -h. Factor 4*a + 4*a**3 - 18 + c*a + 10*a**2 - 2*a - 2*a**3.
2*(a - 1)*(a + 3)**2
Let y(p) = -192*p**4 + 144*p**3 - 35*p**2 - 16*p. Let m(o) = 64*o**4 - 48*o**3 + 12*o**2 + 6*o. Let w(i) = 8*m(i) + 3*y(i). Factor w(l).
-l**2*(8*l - 3)**2
Let m(z) = 4*z**2 - 9*z - 43. Let w(c) = -15*c**2 + 38*c + 169. Let h(v) = 22*m(v) + 6*w(v). Factor h(u).
-2*(u - 17)*(u + 2)
Let i(r) = 3*r**3 + 3*r**2 - 2. Let q(z) = 7*z**3 + 7*z**2 + z - 5. Let j(d) = 5*i(d) - 2*q(d). Let j(n) = 0. What is n?
-2, 0, 1
Let d(g) = -g**2 - 7*g. Let w(z) = -z**3 - 8*z**2 - 7. Let s be w(-8). Let n be d(s). Factor -2*v + n + 1 - v**2 - 1.
-v*(v + 2)
Let v(z) = 135*z**2 - 5*z + 5. Let y(k) = -137*k**2 + 6*k - 4. Let a(p) = -4*v(p) - 5*y(p). Solve a(c) = 0.
0, 2/29
Let n(s) be the second derivative of s**7/357 - 13*s**6/255 + 47*s**5/170 - 23*s**4/102 - 16*s**3/17 + 36*s**2/17 - 2*s + 2. Solve n(g) = 0.
-1, 1, 6
Let q(p) = 4*p + 5. Let z be q(-4). Let b(c) = -8*c**2 - 2*c. Let w(d) = -4*d**2 - d. Let r(l) = z*w(l) + 6*b(l). Factor r(i).
-i*(4*i + 1)
Let u(m) be the first derivative of 1/6*m**2 - 1/3*m - 1/6*m**4 - 7 + 2/9*m**3 + 1/18*m**6 - 1/15*m**5. Factor u(y).
(y - 1)**3*(y + 1)**2/3
Suppose 0 = -7*w + 2*w. Suppose -a - 3*h = -46 + 16, w = 3*a + h - 50. Determine x so that -1 - 4 + 0*x**2 - 5 - 5*x**2 + a*x = 0.
1, 2
Let w(r) = -r**2. Suppose 13 = -2*y + 11. Let q = -15 + 0. Let z(x) = 12*x**2 + 6*x. Let d(i) = q*w(i) + y*z(i). Determine s so that d(s) = 0.
0, 2
Solve 25*t**3 - 4*t - 13*t**3 - 10*t**3 + 2*t**2 = 0.
-2, 0, 1
Let c(o) be the first derivative of -o**6/30 - 3*o**5/10 - 3*o**4/4 - 9*o - 5. Let r(k) be the first derivative of c(k). Factor r(t).
-t**2*(t + 3)**2
Determine k, given that 2/3*k**2 + 34/15*k - 8/5 = 0.
-4, 3/5
Factor -2*m**2 - 58 - 16*m + 116 - 58.
-2*m*(m + 8)
Let w(o) be the second derivative of -1/165*o**6 + 0*o**2 + 21*o + 1/110*o**5 + 0 + 1/33*o**4 + 0*o**3. Find l such that w(l) = 0.
-1, 0, 2
Suppose 39 = 17*d - 4*d. Let i(b) be the first derivative of 0*b**4 + 8 + 0*b + 0*b**2 - 1/12*b**d + 1/20*b**5. Factor i(c).
c**2*(c - 1)*(c + 1)/4
Let h(u) = 1. Let l(s) = 3*s**2 - 3*s + 3. Let n be (-4)/(-8) - (-1)/2. Let o(c) = n*l(c) - 3*h(c). Factor o(z).
3*z*(z - 1)
Let v(n) be the first derivative of 0*n**2 + 5/24*n**6 + 1/4*n**5 + 18 - 5/16*n**4 - 5/12*n**3 + 0*n. Factor v(m).
5*m**2*(m - 1)*(m + 1)**2/4
Let t(q) be the second derivative of 23*q + 0*q**2 - 1/70*q**5 + 0 + 4/21*q**3 + 0*q**4. Factor t(n).
-2*n*(n - 2)*(n + 2)/7
Suppose -11/7*t**2 + 0 + 1/7*t**4 - 4/7*t**3 - 6/7*t = 0. What is t?
-1, 0, 6
Let v(w) be the first derivative of 3/16*w**2 + 0*w + 40 + 0*w**5 + 1/16*w**6 + 0*w**3 - 3/16*w**4. Suppose v(h) = 0. Calculate h.
-1, 0, 1
Let u(k) = -5*k + 213. Let j be u(42). Let d(f) be the first derivative of 1/15*f**j - 3 + 0*f**2 + 0*f. Find c such that d(c) = 0.
0
Let s(t) be the third derivative of t**7/630 + 19*t**6/720 + 13*t**5/120 - 35*t**4/144 - 25*t**3/36 - 423*t**2. Solve s(h) = 0.
-5, -1/2, 1
Let v(m) be the second derivative of -289*m**7/84 + 323*m**6/60 - 7*m**5/8 + m**4/24 - 165*m. Determine g so that v(g) = 0.
0, 1/17, 1
Let i be (1/2)/(5/(-30)). Let t be i/6 - 45/(-6). Find n such that 1 + t*n + 2*n**4 + 7*n + 9*n**2 + 7*n**3 - 9*n = 0.
-1, -1/2
Let s be ((-198)/(-77))/((-9)/(-14)). Suppose 5/2*d**5 - d**s - 1 + 2*d**2 - 5*d**3 + 5/2*d = 0. What is d?
-1, 2/5, 1
Let c be 3/((-1)/1 + 2). Suppose -16 - 29*k**3 + 32*k + k**3 - 4*k**c - 20*k**4 + 36*k**2 = 0. What is k?
-2, -1, 2/5, 1
Let y = 2489 + -2487. Factor -3/7 + 60/7*k**y + 3/7*k.
3*(4*k + 1)*(5*k - 1)/7
Let k(p) = 15*p**4 - 95*p**3 + 120*p**2 + 720*p + 5. Let s(d) = 8*d**4 - 47*d**3 + 60*d**2 + 360*d + 3. Let w(a) = 3*k(a) - 5*s(a). Factor w(x).
5*x*(x - 6)**2*(x + 2)
Fac