- 4. Suppose v(b) = 0. Calculate b.
23
Let x(o) = -o**2 - 8*o - 1. Let q(f) = -2*f**2 - 15*f - 3. Let b(d) = -d + 8. Let s be b(8). Let l be (s + -3)*3/(-3). Let a(c) = l*q(c) - 5*x(c). Factor a(k).
-(k + 1)*(k + 4)
Find x, given that -6/5*x**2 + 0 + 2/5*x**3 + 4/5*x = 0.
0, 1, 2
Let n be (-40)/(-60) + 68/6. Factor -4*h - 5*h**2 - n + h**2 + 12.
-4*h*(h + 1)
Factor 32 - 1/4*d**2 + 127/4*d.
-(d - 128)*(d + 1)/4
Let x(g) be the second derivative of g**4/20 + 13*g**3/2 + 96*g**2/5 + 53*g. Find h such that x(h) = 0.
-64, -1
Determine b, given that -2/5*b**3 - 2/5*b**4 + 2/5*b**2 + 0 + 2/5*b = 0.
-1, 0, 1
Let n be -1 - 15*3/(-27). Solve 6*d**4 + n - 4/3*d**2 + 8*d**3 - 8/3*d = 0 for d.
-1, 1/3
Let y(m) = 4*m**4 + 6*m**3 + 16*m**2 - 6*m - 8. Let p(j) = 11*j**4 + 17*j**3 + 46*j**2 - 17*j - 23. Let l(a) = -6*p(a) + 17*y(a). Suppose l(s) = 0. Calculate s.
-1, 1
Suppose -2*f = -5*f + 12. Let a = 7 - f. Factor 3*l - l - l**a - l - 1 + l**2 + 0*l.
-(l - 1)**2*(l + 1)
Determine a so that 1/7*a**3 + 9*a**2 + 961/7 + 1023/7*a = 0.
-31, -1
Let r be ((-21)/(-49))/(15/140). Factor -1/2*w + 0*w**2 - 1/2*w**5 + w**3 + 0 + 0*w**r.
-w*(w - 1)**2*(w + 1)**2/2
Let i be 42/9*1/(-6)*-3. Factor i*z**2 + 3*z**3 + 5/3*z**4 + 0 + 1/3*z**5 + 2/3*z.
z*(z + 1)**3*(z + 2)/3
Factor -123/5*k + 3/5*k**3 - 57/5*k**2 - 63/5.
3*(k - 21)*(k + 1)**2/5
Let h(q) = -19*q**2 - 5*q + 1. Let v be 8 + (-8)/((-4)/(-1)). Let t(a) = 9*a**2 + 3*a. Let b(c) = v*h(c) + 13*t(c). Solve b(f) = 0.
-2, -1
Let h be (-18)/(-1) - (14 - 13). Find u such that -20*u**5 + 22*u**2 + h*u**3 - u**4 + 6*u**2 + 8*u - 5*u**3 - 27*u**4 = 0.
-1, -2/5, 0, 1
Factor 0*t + 0 - 13/6*t**2 + 1/6*t**3.
t**2*(t - 13)/6
Let h(q) be the first derivative of 6/7*q - 6 - 2/7*q**2 - 2/21*q**3. Factor h(y).
-2*(y - 1)*(y + 3)/7
Let l be (-2)/24 + (-3)/(-9). Let b(d) be the second derivative of 0*d**5 + 0*d**3 + 0*d**2 + 5*d - 1/10*d**6 + 0 + l*d**4. Suppose b(h) = 0. Calculate h.
-1, 0, 1
Suppose 5*s + 93 = 93. Factor -1/2*g**2 + 1/2 + s*g.
-(g - 1)*(g + 1)/2
Let r(c) = -c**3 - 2*c. Let o(y) = -y**3 - 5*y**2 + 28*y + 20. Let s(n) = o(n) + 4*r(n). Factor s(w).
-5*(w - 2)*(w + 1)*(w + 2)
Let y(l) be the third derivative of l**7/840 + l**6/120 + l**5/48 + l**4/48 + 33*l**2. Let y(f) = 0. Calculate f.
-2, -1, 0
Factor 10*c**3 + 61*c + 113*c**2 - 30 + 6 - 81*c**2 - 2*c**3 - 5*c**3.
(c + 3)*(c + 8)*(3*c - 1)
Factor 279/2*p**2 - 36 - 219/2*p + 6*p**3.
3*(p - 1)*(p + 24)*(4*p + 1)/2
Let q(h) be the first derivative of 3/16*h**2 - 9 - 1/8*h + 1/32*h**4 - 1/8*h**3. Suppose q(p) = 0. What is p?
1
Let x(h) be the first derivative of 4*h**4 - 10*h**3 - 2*h**2 - 78. Factor x(k).
2*k*(k - 2)*(8*k + 1)
Let z be (-2)/4 - (-82)/36. Let v = 19/9 - z. Find l, given that -v*l**3 + 1/3*l**4 + 0*l**2 + 0*l + 0 = 0.
0, 1
Suppose -10*k**2 + 14*k - 10*k**2 + 12*k + 35*k**2 + 169 - 14*k**2 = 0. Calculate k.
-13
Let i(r) = 3*r**3 - 37*r**2 + 30*r + 82. Let j(k) = 14*k**3 - 186*k**2 + 145*k + 411. Let s(q) = -11*i(q) + 2*j(q). Find v such that s(v) = 0.
-1, 4
Let f(p) be the third derivative of -p**9/60480 + p**7/3360 - p**6/1440 - 7*p**4/12 + 27*p**2. Let i(z) be the second derivative of f(z). What is h in i(h) = 0?
-2, 0, 1
Let v(c) be the first derivative of 5*c**3 - 55*c**2 - 80*c + 56. Factor v(a).
5*(a - 8)*(3*a + 2)
Let m(j) be the second derivative of 13*j**4/9 + 16*j**3/3 - 8*j**2/3 - 374*j. Factor m(v).
4*(v + 2)*(13*v - 2)/3
Let l = 1154 - 173099/150. Let y(o) be the third derivative of 2/15*o**3 - 7/120*o**4 - 9*o**2 + 0 + l*o**5 + 0*o + 1/600*o**6. Determine x so that y(x) = 0.
-4, 1
Let b be (-8)/6*(-21)/56. Let o(q) be the second derivative of -q**3 + 2*q + 0 - q**2 - b*q**4 - 1/10*q**5. Solve o(v) = 0.
-1
Let l(p) be the second derivative of -25*p**4/2 + 23*p**3/2 + 81*p**2/2 - 16*p. Let n(x) = -15*x**2 + 7*x + 8. Let z(u) = -2*l(u) + 21*n(u). Factor z(j).
-3*(j - 1)*(5*j + 2)
Suppose 160*h - 112 = -29 + 77. Solve -h - 25*x**3 - 7/2*x**5 - 15*x**4 - 15/2*x - 20*x**2 = 0.
-1, -2/7
Let w(p) = -p**3 - 6*p**2 - p - 4. Let f be w(-6). Suppose -2*l - 4*g = 3 - 7, 3*l - f*g = -2. Factor 6/7*o**2 + 2*o**4 - 4/7*o + l + 24/7*o**3.
2*o*(o + 1)**2*(7*o - 2)/7
Let f(g) = -2*g**2 + 5*g + 6. Let a(r) = -r**2 + 6*r + 5. Let o(z) = -3*a(z) + 2*f(z). Let p be o(-7). Factor 2 - 4*t - 3 + p*t**2 + 1.
4*t*(t - 1)
Find b such that -b**2 + 62*b - 18 - 70 + 73 - 946 = 0.
31
Let s(p) be the third derivative of 0 - 3*p**2 + 0*p + 1/10*p**5 + 0*p**3 - 3/8*p**4 + 1/40*p**6. Factor s(m).
3*m*(m - 1)*(m + 3)
Suppose m = 3*m + 3*q - 10, -q - 8 = -5*m. Suppose -4*x**3 - 12390 + 12390 + 4*x**m = 0. Calculate x.
0, 1
Factor 24 + 15*j + 3/2*j**2.
3*(j + 2)*(j + 8)/2
Let r(p) be the second derivative of p**6/25 - 97*p**5/150 + 149*p**4/90 - 43*p**3/45 - 6*p**2/5 - 27*p + 2. Determine a, given that r(a) = 0.
-2/9, 1, 9
Let w = -30 - -45. Let h be (-8)/(-12)*(5 - -1). Factor 7*n**h - 2 + n**4 - w*n**3 + 3*n - 1 + 9*n**2 - 2*n**4.
3*(n - 1)**3*(2*n + 1)
Let h be (6/(-4))/(33/(-44)). Let 6*z**h + 88 + 18*z**2 - 16 + 2*z**3 + 96*z + 56 = 0. Calculate z.
-4
Let d(w) be the first derivative of -w**6/60 + 3*w**5/20 - w**4/2 + 2*w**3/3 - 6*w - 1. Let a(r) be the first derivative of d(r). What is y in a(y) = 0?
0, 2
Suppose w - 15 - 6 = 2*g, -3*g - 36 = -3*w. Factor 0 + 1/4*s**4 + 0*s + 1/4*s**2 - 1/2*s**w.
s**2*(s - 1)**2/4
Let t(u) be the second derivative of -u**8/140 - u**7/35 - 3*u**6/80 - u**5/40 + 13*u**4/6 + 17*u. Let a(q) be the third derivative of t(q). Factor a(g).
-3*(g + 1)*(4*g + 1)**2
Let q(s) be the first derivative of 2*s**3 + 1/2*s**4 + 0*s**2 - 8*s + 3. Let q(j) = 0. Calculate j.
-2, 1
Let q(h) be the first derivative of -2*h**3/7 - 16*h**2/7 + 24*h/7 + 75. Factor q(d).
-2*(d + 6)*(3*d - 2)/7
Let b = 163 + -160. Let z(u) be the first derivative of b - 1/2*u**4 - 2/5*u**5 + 2/3*u**3 + 1/3*u**6 + 0*u**2 + 0*u. Solve z(p) = 0 for p.
-1, 0, 1
Let o(t) = t - 3. Let c be o(5). Suppose -4*v = 20, p + v = -3*p + 19. Suppose 3*l + 6*l**2 - 7*l + c*l + p*l = 0. Calculate l.
-2/3, 0
Let l(f) be the third derivative of f**9/12096 - 11*f**5/60 + 7*f**2. Let w(o) be the third derivative of l(o). Factor w(z).
5*z**3
Suppose 4*r - 16 = i, -8 = -2*r - 10*i + 5*i. Let h be r/15*(-4 - (-88)/4). Factor -9/5*v**3 - h*v**2 - 9/5*v + 6/5.
-3*(v + 1)*(v + 2)*(3*v - 1)/5
Let b be (5 - 23)/((-6)/(-4)). Let a = -10 - b. Determine z, given that -9 + 4*z + 10*z**3 - 11 + 3*z**2 - 44*z + 5*z**4 - 18*z**a = 0.
-2, -1, 2
Let a(v) be the first derivative of v**4/4 - 185. Factor a(q).
q**3
Let s be 18/60*(-8)/(-36). Let g(v) be the second derivative of 1/3*v**4 - 4*v**3 - 9*v**2 + 2/5*v**5 + 8*v + 0 - s*v**6. Determine k so that g(k) = 0.
-1, 3
Let b(p) = 13*p**2 - 286*p + 3743. Let c(h) = 4*h**2 - 96*h + 1248. Let u(y) = 2*b(y) - 7*c(y). Solve u(m) = 0.
25
Suppose -3*p - 3*u = 0, -8*p + 3*p + 2*u + 28 = 0. Factor -3*t**3 - t**4 + t**3 + p*t**3 - 3*t**3.
-t**3*(t + 1)
Solve -72*j**5 - 62*j**4 - 3626*j**2 + 70*j**5 - 637*j**3 - 6860*j - 77*j**3 = 0 for j.
-10, -7, 0
Suppose v + 22 = 3*v + 2*p, 5*p - 35 = -3*v. Let l be 812/20 + (-6)/v. Let 16*z - 4*z**3 - l + 40 = 0. Calculate z.
-2, 0, 2
Factor -5*z**3 - 5*z**3 + 22*z - 15 + 3*z + 5*z**3 - 5*z**2.
-5*(z - 1)**2*(z + 3)
Let p(m) = -m**2 - 10*m - 17. Suppose -15*r = 62 + 43. Let i be p(r). Factor -4/5*j**2 + 2/5*j**3 + 2/5*j**i + 0 + 0*j.
2*j**2*(j - 1)*(j + 2)/5
Let w(i) be the second derivative of -i**7/70 - i**6/45 + i**5/30 + 5*i**3/3 - 7*i. Let q(y) be the second derivative of w(y). Suppose q(x) = 0. What is x?
-1, 0, 1/3
Let b be (-4)/14 - 23/(-7). Let t be 1 - (-5 - (-1 + -2)). Factor 6*a**2 - 4*a**t + 13*a - 10*a + a**b + 0 - 6.
-3*(a - 2)*(a - 1)*(a + 1)
Suppose 2*b = -2*m - 58, 0*b + 129 = -5*b + 3*m. Let d be (2/9)/((-3)/b). Solve -2/5*x**d - 2/5 - 4/5*x = 0.
-1
Suppose 219*v = 1135 - 259. Find z, given that 0*z + 0 - 4/3*z**v - 4*z**2 - 16/3*z**3 = 0.
-3, -1, 0
Let b(f) be the second derivative of -f**4/6 - 26*f**3/3 - 48*f**2 - 650*f. Solve b(q) = 0.
-24, -2
Factor 1/3*r**2 + 0 + 1/6*r**3 + 0*r.
r**2*(r + 2)/6
Let o(x) be the third derivative of 31*x**2 + 0*x - 1/48*x**4 - 1/840*x**7 - 1/120*x**6 - 1/48*x**5 + 0*x**3 + 0. Factor o(u).
-u*(u + 1)**2*(u + 2)/4
Let h(w) be the third derivative of 1/60*w**8 + 4/15*w**4 - w**2 + 0 + 0*w + 4/15