7. Factor b(s).
-2*s*(s - 9)*(s - 1)**2/5
Find x, given that -102*x + 304/3 + 2/3*x**2 = 0.
1, 152
Let s(p) be the second derivative of 9/20*p**5 - 9/2*p**2 + 11/4*p**4 - 33*p + 5/2*p**3 + 0. Find c, given that s(c) = 0.
-3, -1, 1/3
Let x(u) be the third derivative of u**9/80640 - u**8/13440 + 11*u**5/60 - 6*u**2. Let k(f) be the third derivative of x(f). Suppose k(q) = 0. What is q?
0, 2
Let s be (-3)/(6/(-322)) - (-3 + 5). Factor -s - 5*t**2 - 33 - 103 + 50 + 70*t.
-5*(t - 7)**2
Solve -63*j**3 + 1 + 33*j**3 + 13*j**2 + 38 - 3 + 31*j**3 + 40*j = 0 for j.
-9, -2
Let w(v) be the third derivative of -v**8/2240 + v**6/240 + 7*v**4/12 + 4*v**2. Let u(k) be the second derivative of w(k). Solve u(y) = 0 for y.
-1, 0, 1
Let o(x) be the second derivative of -x**5/60 + 2*x**3/9 + 34*x. Find y, given that o(y) = 0.
-2, 0, 2
Solve 32*m**2 - m**3 + m**2 - 31*m - 4*m - 49 - 20*m**2 = 0.
-1, 7
Let a(r) be the third derivative of -39*r**5/20 - 61*r**4/8 - 13*r**3/2 + 6*r**2. Let u(m) = 9*m**2 + 14*m + 3. Let i(l) = 2*a(l) + 27*u(l). Factor i(o).
3*(o + 1)*(3*o + 1)
Let -2*i**3 + 4*i**3 - 5*i**2 - 33*i**4 - 9*i**2 - 2*i + 10*i**2 + 37*i**4 = 0. Calculate i.
-1, -1/2, 0, 1
Let b(x) be the first derivative of -x**5 + 910*x**4 - 331240*x**3 + 60285680*x**2 - 5485996880*x - 288. Factor b(z).
-5*(z - 182)**4
Determine c, given that -128/3*c + 2/3*c**2 + 2048/3 = 0.
32
Let h(x) be the second derivative of 5*x**4/12 + 40*x**3/3 + 70*x**2 + 156*x. Factor h(f).
5*(f + 2)*(f + 14)
Solve 33/5*l + 3/5*l**3 + 21/5*l**2 + 3 = 0.
-5, -1
Let u(v) be the first derivative of -8*v + 4*v**2 - 2*v**4 + 30 + 2/5*v**5 + 2*v**3. Factor u(o).
2*(o - 2)**2*(o - 1)*(o + 1)
What is z in 52*z**3 - 7 - 56*z**3 + 48*z - 57 = 0?
-4, 2
Suppose 13*s = 5*s + 32. Factor -12*n**5 - 6*n**s + n**4 - 15*n**3 - 10*n + 25*n**2 + 17*n**5 + 0*n**4.
5*n*(n - 1)**3*(n + 2)
Let v(o) be the third derivative of o**6/480 + o**5/20 + o**4/2 - 5*o**3/3 - 3*o**2. Let i(k) be the first derivative of v(k). What is w in i(w) = 0?
-4
Let h(a) be the first derivative of a**6/2 + 3*a**5 + 9*a**4/2 - 4*a**3 - 12*a**2 + 238. Factor h(i).
3*i*(i - 1)*(i + 2)**3
Suppose 4 - 2 = -h - 5*g, h = -3*g. Let t be -8 + 4 + h - -1. Determine i, given that t*i + 0 + 1/3*i**3 - 1/3*i**2 = 0.
0, 1
Let g(q) be the first derivative of 2/9*q**6 + 1/2*q**4 + 3/5*q**5 + 0*q + 0*q**2 + 1/9*q**3 + 3. Find r, given that g(r) = 0.
-1, -1/4, 0
Let g(w) be the second derivative of -w**6/360 + w**5/24 - w**4/4 + 11*w**3/6 + 31*w. Let z(c) be the second derivative of g(c). Factor z(u).
-(u - 3)*(u - 2)
Let z be 1 + (-132)/(-9) - 3/(-9). Factor -3*p**2 + 27*p - 10*p**2 + 4 + 7*p**2 - z.
-3*(p - 4)*(2*p - 1)
Let t(l) be the third derivative of -l**5/15 - l**4 - 6*l**3 + 16*l**2 - 5*l. Suppose t(b) = 0. Calculate b.
-3
Factor 16/7*j**2 - 20/7*j - 4/7*j**3 + 8/7.
-4*(j - 2)*(j - 1)**2/7
Let o be (-18)/(-8) - 5/20. Let c(l) = -4*l**2 + 24 + 3*l**o - 1 - 22*l. Let v(b) = -3*b**2 - 87*b + 93. Let i(y) = -15*c(y) + 4*v(y). Factor i(n).
3*(n - 3)**2
Solve 6*g - 3*g + 1539*g**2 - 1542*g**2 = 0 for g.
0, 1
Suppose 2*c - 2*v = -4*v - 38, -5*c = 3*v + 91. Let x be c/(-45) - (3 - 145/45). Factor 0 + 6/5*z**4 + 0*z**3 + x*z - 6/5*z**2 - 3/5*z**5.
-3*z*(z - 1)**3*(z + 1)/5
Factor 294*c - 44513 + 186*c - 2*c**2 + 64*c + 7521.
-2*(c - 136)**2
Let j(f) = 103*f - 6588. Let p be j(64). Factor -3/7*o**p + 0*o + 6/7*o**3 + 0 + 0*o**2.
-3*o**3*(o - 2)/7
Suppose -4*a + 4*t + 40 = 0, 9 = 4*t + 29. Factor a*x**2 + 0*x**5 - 9*x**4 + 3*x**5 - 9*x + 6*x**3 + 3 + x**2.
3*(x - 1)**4*(x + 1)
Let i(u) be the third derivative of 7*u**5/240 - 19*u**4/96 - u**3/4 - u**2 + 4. Solve i(s) = 0 for s.
-2/7, 3
Let q(p) = -p**2 + 9*p + 12. Suppose -3*f + 2 + 28 = 0. Let h be q(f). Find g such that 13*g**h - 10*g**2 - 4 + 4 = 0.
0
Let a be (3 - 2) + (3 - 1). Let l be (a*(1 - 0))/1. Suppose 3 - 2 + l + 3*v + 0 - 7*v**2 = 0. Calculate v.
-4/7, 1
Let p(j) be the third derivative of j**7/1680 + j**6/320 + 20*j**2 - 5*j. Factor p(l).
l**3*(l + 3)/8
Factor 1/4*y**2 + 3/4*y - 5/2.
(y - 2)*(y + 5)/4
Let k(o) be the second derivative of -o**4/36 + o**3/2 + 2*o - 115. Solve k(t) = 0.
0, 9
Let j(v) be the third derivative of -2*v**7/105 - v**6/5 - 8*v**5/15 + v**4 + 6*v**3 - v**2 - 31*v. What is q in j(q) = 0?
-3, -1, 1
Factor -17161/3 - 1/3*c**3 - 5633*c + 87*c**2.
-(c - 131)**2*(c + 1)/3
Let u = -3669/10 + 368. Let j(v) be the first derivative of 12/25*v**5 - 8/15*v**3 + 2 + 3/5*v**6 + 4/5*v**2 + 0*v - u*v**4. Let j(i) = 0. Calculate i.
-1, 0, 2/3
Let h(b) = 11*b**3 - 28*b**2 + 56*b - 39. Let d(m) = -5*m**3 + 14*m**2 - 28*m + 19. Let j(z) = -14*d(z) - 6*h(z). Let j(i) = 0. Calculate i.
1, 2, 4
What is r in -51*r**5 + 25*r**5 + 25*r**5 - 4*r**4 + 0*r**4 = 0?
-4, 0
Let t(a) be the second derivative of 1/2*a**4 - 11/2*a**3 + 20*a + 0 - 3*a**2 + 33/20*a**5. Factor t(x).
3*(x - 1)*(x + 1)*(11*x + 2)
Suppose 2/3*b**2 + 8/3 + 2/9*b**3 - 32/9*b = 0. Calculate b.
-6, 1, 2
Let p be ((-6710)/(-36))/(3/6). Let x = p + -371. Factor 0 + 10/9*c**3 + 8/9*c - 2/9*c**4 - x*c**2.
-2*c*(c - 2)**2*(c - 1)/9
Let m(c) = -c**2 - 13*c - 18. Let a be m(-12). Let q be (3/2)/((-3)/a). Let -s**2 + 30*s**q + 0 - 31*s**3 + s + 1 = 0. What is s?
-1, 1
Let x(k) be the third derivative of -k**5/30 - 27*k**4/4 + 268*k**2. Factor x(w).
-2*w*(w + 81)
Let p(t) = 75*t**3 - 150*t**2 - 41*t - 8. Let w(b) = b**3 + b**2 + b + 1. Let u(a) = p(a) + 6*w(a). Factor u(z).
(z - 2)*(9*z + 1)**2
Let o = -1442/213 - -528/71. Factor o*s**2 + 8/3*s + 0.
2*s*(s + 4)/3
Let p(y) = 2*y**2 - 16*y + 16. Let d(x) = -3*x**2 + 17*x - 15. Let t(b) = 3*d(b) + 4*p(b). Let v be t(-13). Factor 20*c**2 - v*c**2 + c + 1 - 3*c.
(c - 1)**2
Let r(i) = -i**2 + 8*i + 11*i - 15*i. Let u be r(3). Factor -6*l**4 - 6*l**u - 14*l**5 + 12*l**5 - 2*l**2 + 0*l**3.
-2*l**2*(l + 1)**3
Find f, given that 0 + 46/7*f - 2/7*f**2 = 0.
0, 23
Let b(c) be the first derivative of -4*c**5 + 13*c**4 - 16*c**3/3 - 8*c**2 - 72. Factor b(i).
-4*i*(i - 2)*(i - 1)*(5*i + 2)
Let a(q) = 1. Let i(s) be the second derivative of s**3/6 - 5*s. Let m(b) = b**2 - 3*b - 3. Let k(t) = 3*i(t) + m(t). Let x(c) = -4*a(c) - 2*k(c). Factor x(f).
-2*(f - 1)*(f + 1)
Let x be 36/(((-14)/35)/((-8)/30)). Find u such that -7*u - 3 + 1 - 25*u**2 - 8 + x*u**2 = 0.
-5, -2
Suppose -45*k + 49*k = -7*j + 1, -3*k + 3 = 3*j. Find o, given that 8/3 + 10/3*o + 2/3*o**k = 0.
-4, -1
Solve 793*h**4 + 3024*h + 1851*h**3 + 12*h**4 - 243*h**5 + 32*h**4 - 324 - 7497*h**2 = 0 for h.
-3, 2/9, 3
Let p(m) be the third derivative of -8*m**7/105 + m**6/6 - m**5/15 - 63*m**2. Suppose p(u) = 0. What is u?
0, 1/4, 1
Let w be 2/(-4)*-10 - 2. Let o(y) be the first derivative of 0*y**4 + 4*y**2 + 0*y + 4*y**w - 4/5*y**5 - 6. Solve o(p) = 0.
-1, 0, 2
Let w be 14 + 10/4*8/(-10). Suppose 3 = 13*q - w*q. Determine a so that -2*a**2 - 10/7*a**q - 4/7*a + 0 = 0.
-1, -2/5, 0
Let v(i) = i**5 - i**4 + 2*i**3 + i**2 - i + 1. Let y(n) = 2*n**5 - 2*n**4 + 8*n**3 + n**2 - 4*n + 4. Let j(g) = -3*v(g) + y(g). Find b such that j(b) = 0.
-1, 1
Let f = 234/77 + -20/7. Let g be 8/66*(1 + 2). Find s such that 2/11*s**2 + f*s**4 - g*s**3 + 0*s + 0 = 0.
0, 1
Let d = -212 + 211. Let f be -2*(-1)/(-10) - d. Find r, given that -18/5*r**5 - 4/5 + f*r**2 + 0*r**4 - 14/5*r + 32/5*r**3 = 0.
-1, -2/3, -1/3, 1
Solve 0*k**2 + 17*k**2 + 151102 - 151096 + k**4 - 17*k - 7*k**3 = 0 for k.
1, 2, 3
Let s(c) be the third derivative of c**6/600 - 7*c**4/120 + c**3/5 + 88*c**2. Factor s(a).
(a - 2)*(a - 1)*(a + 3)/5
Solve 0 - 12/5*n**4 + 16/5*n**5 + 12/5*n**2 + 0*n - 16/5*n**3 = 0.
-1, 0, 3/4, 1
Suppose 3*f + 10 = 2*f + a, -15 = -3*a. Let o be (-707)/(-35) - (-1)/f. Let o*i**2 + 22*i**3 - 7*i**3 + i**3 - 28*i - 9 + 1 = 0. Calculate i.
-2, -1/4, 1
Determine h, given that -4378*h**3 - 6*h**2 + 4395*h**3 - 8 + 3*h**4 - 20*h + 0*h**2 + 11*h**4 + 3*h**5 = 0.
-2, -1, -2/3, 1
Let w(a) be the third derivative of a**6/960 + 11*a**5/480 + 5*a**4/64 - 9*a**3/16 + a**2 + 175*a. Factor w(t).
(t - 1)*(t + 3)*(t + 9)/8
Let o(s) be the third derivative of 0 + 3*s**2 + 0*s - 4/21*s**3 + 5/84*s**4 - 1/210*s**5. Solve o(z) = 0.
1, 4
Let 15*q**3 + q**2 + 91*q**2 + 62*q**2 - 60*q - 5*q**3 - 39*q**2 = 0. Calculate q.
-12, 0, 1/2
Suppose -4*n = 4*h - 32, 171*h = 176*h + 4*n - 37. Suppose 0*t + 8/9*t**2 +