164. Suppose 51*u = c*u - 6. Factor -1/3*w**u + 1/3*w**4 + 2/3 - w**2 + 1/3*w.
(w - 2)*(w - 1)*(w + 1)**2/3
Let v = 2955 + -8833/3. Factor 16/3*m - v - 2/3*m**2.
-2*(m - 4)**2/3
Let i(y) be the first derivative of 0*y + 25 + 1/7*y**3 - 3/14*y**2. Factor i(k).
3*k*(k - 1)/7
Let x = -317/3 - -107. Let o = 43/21 + -5/7. What is i in -4/3 - x*i**3 + o*i**2 + 4/3*i = 0?
-1, 1
Factor 230050*h**2 - 6*h**3 + 3*h**3 + 486 - 229990*h**2 - 351*h.
-3*(h - 9)**2*(h - 2)
Suppose -4*n + 4 + 16 = 0. Let y(b) = -2*b**3 + 5*b**2 + 6*b - 9. Let a(h) = h - 1. Let l(p) = n*y(p) - 35*a(p). Factor l(j).
-5*(j - 2)*(j - 1)*(2*j + 1)
Let b(d) be the third derivative of -d**8/21 - 26*d**7/35 + 109*d**6/60 - 2*d**5/5 - 11*d**4/12 - 8*d**2 - 2. Let b(w) = 0. What is w?
-11, -1/4, 0, 1/2, 1
Let u(l) be the second derivative of -l**7/210 + 6*l**6/25 + 77*l**5/50 + 59*l**4/15 + 53*l**3/10 + 4*l**2 - 268*l. Factor u(g).
-(g - 40)*(g + 1)**4/5
Find q such that 38/5*q + 2/5*q**2 + 68/5 = 0.
-17, -2
Let n = 16 - 8. Suppose 2*d + n = 2*x, x + 3*d - 12 = -2*x. Factor 1 - x*p + 7/4*p**2.
(p - 2)*(7*p - 2)/4
Let z(w) = -9*w**2 + w - 4. Let t(v) = -4*v**2 - 2. Suppose 3*u + g - 26 = -3, 2*u - 4*g - 6 = 0. Let n(f) = u*t(f) - 3*z(f). Factor n(r).
-(r + 1)*(r + 2)
Let l = -359 - -359. Let m(y) be the second derivative of l*y**3 + 0*y**2 - 6*y - 1/8*y**4 + 0 + 3/40*y**5. Suppose m(a) = 0. Calculate a.
0, 1
Let t be 2160/(-320)*2/(-27). Factor -t*i + 1/2 + 1/2*i**3 - 1/2*i**2.
(i - 1)**2*(i + 1)/2
Let t(g) = g**2 - 2*g. Let x(s) = 3*s**2 - 45*s + 38. Let a(m) = -4*t(m) + x(m). Factor a(b).
-(b - 1)*(b + 38)
Suppose 0 = -4*o + 5*b + 1 - 4, -2*o + 2*b = 2. Let k be (-1 - o) + (7 + -4)/6. Factor 0 + 3*w**4 + 0*w**3 - 3*w**2 - k*w + 3/2*w**5.
3*w*(w - 1)*(w + 1)**3/2
Factor -4*p**2 + 153 + 39 + 3568*p - 3560*p.
-4*(p - 8)*(p + 6)
Let y(s) be the third derivative of 0 - 5/24*s**4 + 0*s + 1/24*s**6 + 0*s**5 - 10*s**2 + 0*s**3. Suppose y(u) = 0. Calculate u.
-1, 0, 1
Let a(l) = 17 + 2*l**2 - l + 3*l - 37*l. Let k be a(17). Factor -4/3*f**3 + 0 + k*f + 2/3*f**4 + 2/3*f**2.
2*f**2*(f - 1)**2/3
Let y(t) be the third derivative of t**5/15 + 4*t**4/3 + 10*t**3 - 123*t**2. Solve y(s) = 0 for s.
-5, -3
Suppose -40*y**3 + 49*y**3 - y**2 - 3*y**5 - 5*y**2 = 0. What is y?
-2, 0, 1
Let q be (-1)/(-7) - 204/(-1904). What is p in -q - 1/4*p**3 - 3/4*p**2 - 3/4*p = 0?
-1
Let f(w) be the second derivative of 2*w**6/15 - 4*w**5/5 - 6*w**4 - 40*w**3/3 - 14*w**2 - w + 39. Find k such that f(k) = 0.
-1, 7
Let d = 2 - -13. Suppose -t - h - 9 = -3*t, 2*t - d = 3*h. Let 0*a**t - 1/2*a**4 + 0*a + 0 + 0*a**2 = 0. What is a?
0
Factor -8*f**2 + 2/3*f**3 + 44/3 + 6*f.
2*(f - 11)*(f - 2)*(f + 1)/3
Suppose 0*r = 9*r - 540. Let t = -117/2 + r. Factor -t - 3/4*x**2 - 9/4*x.
-3*(x + 1)*(x + 2)/4
What is g in 4/5*g**5 + 1632/5*g - 2116/5*g**2 + 1196/5*g**3 - 464/5 - 252/5*g**4 = 0?
1, 2, 58
Let b(w) = 2*w**4 - 22*w**3 - 12*w**2 + 12*w. Let q(i) = i**4 - i**3 + i**2 + 3*i. Let p(l) = -b(l) + 4*q(l). What is z in p(z) = 0?
-8, -1, 0
Determine l, given that 1/4*l - 1/4*l**3 + 23/4*l**2 - 23/4 = 0.
-1, 1, 23
Let r(z) = -1 + 174*z - 176*z + 11 + 0. Let d be r(4). Factor -8/5*k**5 + 0*k**d + 0*k + 0 - 2/5*k**3 - 2*k**4.
-2*k**3*(k + 1)*(4*k + 1)/5
Let p be (((-51)/14 - -4) + (-1)/(-7))*0. What is b in 0*b - 10/3*b**3 - 2/3*b**5 + p - 8/3*b**4 - 4/3*b**2 = 0?
-2, -1, 0
Let c(i) = -i**2 - 14*i + 25. Let r be c(-11). Let s = -56 + r. Factor 0 + 1/6*v**s - 1/3*v + 1/6*v**3.
v*(v - 1)*(v + 2)/6
Suppose -4*d + d - 24 = 0. Let a be 20/30 + d/(-6). Suppose -2/5*u**4 + 0*u**a - 4/5*u**3 + 2/5 + 4/5*u = 0. Calculate u.
-1, 1
Let z = 6362 + -6362. Factor -16/9*c**3 - 4/9*c**4 - 16/9*c**2 + z*c + 0.
-4*c**2*(c + 2)**2/9
Let z(n) = -8*n**3 - 5*n**2 - n + 5. Let p be z(-4). Factor -3*j**2 - p + 3*j + 441.
-3*j*(j - 1)
Let r be 16/10 + (-36)/(-90). Let y(o) be the first derivative of -1/3*o + r - 1/3*o**2 - 1/9*o**3. Factor y(u).
-(u + 1)**2/3
Let u be -2 + 6 + (4 - 6). Suppose -m**4 - u*m**3 + 2*m**4 + m**2 + 0*m**4 = 0. What is m?
0, 1
Let y(s) be the third derivative of s**7/105 + s**6/4 + 29*s**5/15 + 7*s**4 + 40*s**3/3 - 388*s**2. Find z, given that y(z) = 0.
-10, -2, -1
Let l(v) = -v**4 + v**3 + 4*v**2 + 8*v + 3. Let h(o) = o**4 - 3*o**3 - 5*o**2 - 9*o - 4. Let b(k) = -3*h(k) - 4*l(k). Factor b(n).
n*(n - 1)*(n + 1)*(n + 5)
Suppose 0 = 14*s + 30*s. Let c(v) be the second derivative of 1/6*v**4 + v**2 + s - 2*v + 2/3*v**3. Find b such that c(b) = 0.
-1
Let i(c) be the third derivative of -c**5/690 - 3*c**4/92 - 8*c**3/69 + 307*c**2. Factor i(z).
-2*(z + 1)*(z + 8)/23
Let h(g) be the third derivative of g**8/840 - g**6/75 + g**5/75 + g**4/20 - 2*g**3/15 + 167*g**2. Let h(u) = 0. Calculate u.
-2, -1, 1
Let v(p) = -2*p**2 + 2*p + 1. Let c(y) = -39*y**2 + 78*y + 114. Let h(x) = c(x) - 18*v(x). Let h(u) = 0. Calculate u.
-2, 16
Let w(v) be the third derivative of -v**8/672 - 3*v**7/35 - 179*v**6/120 - 51*v**5/10 - 289*v**4/48 - 379*v**2 + 1. Factor w(h).
-h*(h + 1)**2*(h + 17)**2/2
Let j(k) be the first derivative of -605/3*k**3 - 110*k**2 - 20*k + 2. Factor j(d).
-5*(11*d + 2)**2
Let q = 4727 + -4725. Factor 0*o + 1/6*o**5 - 1/6*o**3 + 1/3*o**4 - 1/3*o**q + 0.
o**2*(o - 1)*(o + 1)*(o + 2)/6
Let h(y) be the second derivative of -y**4/12 + 7*y**3/6 - 11*y + 5. Factor h(k).
-k*(k - 7)
Suppose -60*b = -68*b + 16. Let x(z) be the second derivative of -1/10*z**4 + 0 - 1/50*z**5 - 2/15*z**3 + b*z + 0*z**2. Factor x(p).
-2*p*(p + 1)*(p + 2)/5
Let d(y) = -32. Let j(b) = b - 1. Let o(f) = -d(f) + 4*j(f). Let g be o(-7). Factor 2/3*x**2 + 0 + 2*x**3 + g*x.
2*x**2*(3*x + 1)/3
Suppose 25*d - 24 = 22*d. Factor -3*x**3 - 6 + 9*x**2 - d + 2.
-3*(x - 2)**2*(x + 1)
Let w(v) = v + 13. Let m be w(-9). Let f(r) be the second derivative of -2/3*r**m + 1/10*r**5 - 2*r**2 + 2*r + 5/3*r**3 + 0. Find i such that f(i) = 0.
1, 2
Let d = -326 + 1957/6. Let g(r) be the first derivative of d*r**6 + 1/2*r**4 + r - 3/2*r**2 + 2/3*r**3 - 3/5*r**5 - 7. Factor g(q).
(q - 1)**4*(q + 1)
Let l be ((-30)/75)/(42/(-30) + (-4)/(-20)). Factor 5/3*k + l*k**2 + 2.
(k + 2)*(k + 3)/3
Suppose -34*x = -54*x + 40. Determine n so that -2/9*n**2 - 4/3*n - x = 0.
-3
Let n be (-3 + 5 - -3)*(-106)/(-10). Determine d so that -14*d**5 - 16*d**4 + n - 352*d**2 - 96*d - 28*d**4 + 11 - 64*d**4 - 304*d**3 = 0.
-2, 2/7
Suppose -12*u + 99 = -3*u. Suppose 0*y - u*y = 0. Factor y*f - 4/3 + 1/3*f**3 + f**2.
(f - 1)*(f + 2)**2/3
Let o(h) be the first derivative of 1/12*h**2 - 1/24*h**4 + 4 + 1/10*h**5 - 1/6*h**3 + 0*h. Factor o(t).
t*(t - 1)*(t + 1)*(3*t - 1)/6
Suppose -5*j + 75 = -0*j. Suppose -15 + j - 5*a**2 = 0. What is a?
0
Let m be (-16)/(-12)*234/104. Suppose 3/4*f + 3/4*f**2 + 1/4*f**m + 1/4 = 0. Calculate f.
-1
Let k be 6/10 + 1008/(-180). Let p be -2 - -3 - k/100*-4. Let -1/5 - p*w - 3/5*w**2 = 0. Calculate w.
-1, -1/3
Let p(t) = 4*t**5 + 10*t**4 - 20*t**3 + 12*t**2 + 6*t. Let k(n) = -n**5 - n**3 - 2*n. Let j(f) = -12*k(f) - 4*p(f). Solve j(l) = 0 for l.
-12, 0, 1
Let k(t) be the second derivative of t**4/2 - 29*t**3/4 + 21*t**2/4 - 14*t - 4. Solve k(c) = 0.
1/4, 7
Let y(p) be the first derivative of -5*p**8/672 - 11*p**7/336 + 7*p**6/90 - p**5/20 + 11*p**3/3 - 10. Let v(z) be the third derivative of y(z). Factor v(g).
-g*(g + 3)*(5*g - 2)**2/2
Let 54/5*c + 729/5 + 1/5*c**2 = 0. What is c?
-27
Let t(u) = -u**2 - 431*u - 2128. Let m be t(-5). Let -12*h - 15/2*h**m - 3/2*h**3 - 6 = 0. Calculate h.
-2, -1
Let f = 20 - 0. Suppose u + 12 = f. Factor 3*v - u - 3*v**3 - 3*v**2 + 9*v**2 + 2.
-3*(v - 2)*(v - 1)*(v + 1)
Suppose -2*x + 3*d - 75 = 0, 4*x = -d - 92 - 93. Let v be 6/10 + (-6)/x*-3. What is f in 0 - v*f**4 - 3/5*f**3 + 1/5*f**2 + 2/5*f + 1/5*f**5 = 0?
-1, 0, 1, 2
Suppose j + 4*n + 14 = 0, -j = -4*j + 5*n + 26. Solve 2/3*o + 0*o**j + 0 - 2/3*o**3 = 0.
-1, 0, 1
Factor -9/5*f + 0 + 24/5*f**2 + 9/5*f**3.
3*f*(f + 3)*(3*f - 1)/5
Let g(y) be the third derivative of 0*y - 5/42*y**5 - 17*y**2 - 4/21*y**3 + 0 + 5/21*y**4. Suppose g(j) = 0. What is j?
2/5
Let z = -4 + 9. Suppose -z*y + y = -5*p - 76, -5*p - 6 = y. Factor 22*n + y*n**3 - 10*n - 12 + n**3 + 39*n**2.
3*(n + 1)*(n + 2)*(5*n - 2)
Let a(j) be the third derivative of 0 - 2*j**2 + 0*j - 1/1176*j**8 + 1/420*j**6 - 1/245*j**7 + 1/30*j**5 + 0*j**4 