v**3 - v**2 - v. Let r(f) = -2*f**4 + 7*f**3 - 3*f**2 - 7*f - 4. Suppose 94 = -5*l + d, -5*l - d + 20 = 106. Let j(w) = l*k(w) + 2*r(w). Factor j(g).
-4*(g - 1)**2*(g + 1)*(g + 2)
Let s = -6753/4 + 1689. Factor 3/2 - s*x - 3/4*x**2.
-3*(x - 1)*(x + 2)/4
Let t(y) = 0*y**2 + 2*y**2 + 5*y**2 - 8*y**2. Let k(h) = 30*h**2 + 15*h + 10. Let p(l) = k(l) + 25*t(l). Find g such that p(g) = 0.
-2, -1
Let l = 182981/69 + -2652. Let p = l + 10/23. Factor p*v**3 + 1/9*v**4 - 1/3*v + 1/9*v**2 - 2/9.
(v - 1)*(v + 1)**2*(v + 2)/9
What is w in -10505 + 10337 + 4*w**3 + 12*w**2 + 20*w**2 + 4*w = 0?
-7, -3, 2
Suppose -2*w + 2*b + 10 = 0, 3*b - 2 = w - 5. Factor v**2 - 19 + 10 - w*v**2 + 14.
-5*(v - 1)*(v + 1)
Let d(v) = -v**3 + 2*v**2 + 6*v + 1. Let z be d(-6). Suppose -4 - 19*s**2 + 4*s**3 + 7*s**2 - z*s + 0*s**3 + 265*s = 0. What is s?
1
Let k be (-9)/(12/(-4)) + 2. What is g in -k*g**5 - 5 - 5*g + 2*g**2 + 12*g**3 - 2*g**3 + 8*g**2 - 5*g**4 = 0?
-1, 1
Solve 12/7*u + 2/7*u**2 - 2 = 0 for u.
-7, 1
Let u(o) = -1821620*o**2 + 13231*o - 24. Let q(j) = -910811*j**2 + 6616*j - 12. Let f(b) = 7*q(b) - 4*u(b). Factor f(i).
3*(551*i - 2)**2
Let t(w) = 2*w**4 + 5*w**3 - 8*w + 4. Let p(u) = 3*u**4 + 6*u**3 - u**2 - 8*u + 4. Let k(q) = -3*p(q) + 4*t(q). Factor k(z).
-(z - 2)*(z - 1)**2*(z + 2)
Let r(o) = 301*o**2 + 1230*o + 44. Let x(z) = -300*z**2 - 1230*z - 45. Let t(p) = 5*r(p) + 4*x(p). What is w in t(w) = 0?
-4, -2/61
Factor -5/3*h**2 + 25/3*h - 10/3*h**3 - 10/3.
-5*(h - 1)*(h + 2)*(2*h - 1)/3
Suppose -2*m + 0*m = -6. Suppose -2*p = -m*p. Let -4 - 10*l - 13*l**3 - 8*l**2 + p*l + 11*l**3 = 0. What is l?
-2, -1
Factor -14*f**3 + 78*f + f**2 + 19*f**3 - 24 - 38*f**2 - 10*f + 6*f.
(f - 4)*(f - 3)*(5*f - 2)
Suppose -4*o = -5*m - 93, -5*m - 6 = -1. Let n = -43/2 + o. Factor 0 + 3/2*z**4 + 0*z - n*z**2 - z**3.
z**2*(z - 1)*(3*z + 1)/2
Factor -40*g**2 + 5/4*g**5 + 80*g + 0 - 15*g**3 + 5*g**4.
5*g*(g - 2)**2*(g + 4)**2/4
Let o be ((-8)/(-6))/((-24)/(-1548)). Let g = o + -83. Factor 0*s**2 + 0*s + 0 + 6/7*s**g + 3/7*s**4.
3*s**3*(s + 2)/7
Factor 132*k + 176*k - 120 - 1590*k**2 + 439*k + 105*k**3 + 245*k**4 + 113*k.
5*(k - 2)*(k + 3)*(7*k - 2)**2
Let m(y) = 8*y**3 - 5*y**2 - 21*y - 18. Let b(n) = -n**3 + n**2. Let t(h) = 5*b(h) + m(h). Let t(i) = 0. Calculate i.
-2, -1, 3
Factor 0 + 4/3*t**5 + 0*t**3 + 0*t + 16/3*t**2 - 4*t**4.
4*t**2*(t - 2)**2*(t + 1)/3
Suppose -2*c = 3*z - 17, 5*c = -0*z + z + 17. Let i(r) be the second derivative of 0*r**4 + 0*r**2 + 0 - r + 1/60*r**5 + 0*r**z. Factor i(d).
d**3/3
Let b(f) be the first derivative of -5*f**2 + 5/4*f**4 + 0*f + 30 + 5/3*f**3. Factor b(v).
5*v*(v - 1)*(v + 2)
Suppose i = 1 + 1. Determine f, given that -f**i + 269*f - 270*f + 0*f**2 = 0.
-1, 0
Suppose -4*i - 9*i = 42*i. Let f(j) be the third derivative of -4*j**2 + 0 + i*j**4 + 0*j**3 - 1/40*j**5 + 0*j. Factor f(c).
-3*c**2/2
Let i(j) = -j**2 - 9*j - 7. Let n be i(-7). Let o = -5 + n. Let f(b) = -39*b**2. Let t(v) = -3*v**2. Let c(m) = o*f(m) - 27*t(m). Factor c(h).
3*h**2
Let g(z) be the second derivative of -z**5/10 - 5*z**4/6 + 6*z**3 + 72*z**2 - 220*z - 1. Factor g(o).
-2*(o - 4)*(o + 3)*(o + 6)
Let a(x) be the first derivative of -6/5*x - 11 + 3/2*x**2 + 3/5*x**3. Find v, given that a(v) = 0.
-2, 1/3
Let c = 178 + -178. Let a(m) be the second derivative of c - 1/18*m**4 - 4/3*m**2 + 2*m + 4/9*m**3. Factor a(q).
-2*(q - 2)**2/3
Let q(o) be the third derivative of -o**6/280 - o**5/70 - o**4/56 + o**2 - 6*o. Factor q(l).
-3*l*(l + 1)**2/7
Let a be (-32*12/(-240))/(70/25). Suppose -4/7*t**2 + 0*t - a*t**3 + 0 = 0. Calculate t.
-1, 0
Let a = -42 + 36. Let b(f) = 19*f**3 + 24*f**2 + 37*f - 13. Let m(y) = 9*y**3 + 12*y**2 + 18*y - 6. Let t(p) = a*b(p) + 13*m(p). Suppose t(z) = 0. Calculate z.
-2, 0
Let m(w) be the third derivative of -w**5/20 - 5*w**4 + 41*w**3/2 + 62*w**2 + 1. Factor m(z).
-3*(z - 1)*(z + 41)
Let x(f) be the third derivative of -1/420*f**6 + 1/105*f**5 + 0 + 0*f + 8*f**2 + 5/84*f**4 - 2/7*f**3. Find m such that x(m) = 0.
-2, 1, 3
Solve -23*n**2 - 609*n + 3*n**4 + 60*n**3 + 9408 + 22*n**2 - 35*n**2 - 425*n - 2326*n = 0.
-14, 4
Let o(f) be the second derivative of f**7/84 + 3*f**6/20 + 7*f**5/40 - 3*f**4/8 - 2*f**3/3 - 6*f + 2. Suppose o(r) = 0. Calculate r.
-8, -1, 0, 1
Suppose -4*o + 177 + 179 = 0. Suppose o*z - 11*z + 10 + 19 + 9*z**2 + 19 = 0. What is z?
-8, -2/3
Let s(c) be the second derivative of c**6/165 + 2*c**5/11 + 3*c**4/11 - 20*c**3/33 - 19*c**2/11 - 33*c - 1. Suppose s(n) = 0. What is n?
-19, -1, 1
Let k be (-1 - 438/(-462))/((-94)/517). Determine y so that -2/7 + k*y**2 + 0*y = 0.
-1, 1
Let f(l) be the third derivative of -7*l**2 - 1/72*l**4 + 0 + 0*l**3 - 1/630*l**7 - 1/120*l**6 + 0*l - 1/60*l**5. Let f(k) = 0. What is k?
-1, 0
Let l(d) = -d**3 + d**2. Let z be ((-10)/3)/2 - 8/24. Let u(f) = 2*f**2 - 6*f + 4. Let s(q) = z*l(q) + u(q). Suppose s(c) = 0. What is c?
-2, 1
Let v = -135/17 - -287/34. Factor v*p + 23/4*p**2 + 0 + 19/4*p**4 + 10*p**3.
p*(p + 1)**2*(19*p + 2)/4
Let r = -448 + 450. Let t(z) be the third derivative of 0*z**3 + 0*z + 0*z**6 + 1/1470*z**7 - r*z**2 + 0 - 1/420*z**5 + 0*z**4. Factor t(d).
d**2*(d - 1)*(d + 1)/7
Let z(l) = -l + 1. Let t be z(-3). Suppose -3*q + 2 = -d, 4*q = -3*d + t + 16. Factor -4*m + 4 - m**q + m**2 - 3*m**2.
-(m + 2)*(3*m - 2)
Let b(n) be the second derivative of 3/70*n**5 + 0 + 0*n**4 + 14*n + 0*n**3 + 0*n**2 - 1/105*n**6. Factor b(z).
-2*z**3*(z - 3)/7
Factor 9*n**2 - 176*n - 60 - 31*n**2 + 8*n**3 - 86*n**2.
4*(n - 15)*(n + 1)*(2*n + 1)
Suppose 3*d - 16 = -2*b, -3*d - b + 0*b + 14 = 0. Factor -4*x**d - 2*x - 2*x + 5*x**2 + 8*x**2 + 4*x**3 - x**2 - 8.
-4*(x - 2)*(x - 1)*(x + 1)**2
Let g(n) be the second derivative of n**4/6 - 2*n**3/3 - 3*n**2 + 40*n + 2. Suppose g(t) = 0. What is t?
-1, 3
Let z(c) be the third derivative of c**8/10080 + c**7/2520 - c**6/180 + 7*c**5/30 - 19*c**2. Let n(s) be the third derivative of z(s). What is b in n(b) = 0?
-2, 1
Let z = -118 + 115. Let b be 6/z - (-14)/6. Determine a, given that 2/3*a**2 - 1/3*a + b*a**3 - 2/3 = 0.
-2, -1, 1
Suppose -4*j + j = 9, -19 = -o + j. Let 4*m**4 + 9*m**4 + 12*m**2 - o*m**4 = 0. Calculate m.
-2, 0, 2
Let o(k) = -29*k**2 + 19*k**2 - 105*k - 64 - 541. Let g(t) = t**2 - t. Let p(j) = -5*g(j) - o(j). Factor p(l).
5*(l + 11)**2
Let i(y) be the second derivative of 46225*y**4/8 - 215*y**3 + 3*y**2 + 552*y. Factor i(t).
3*(215*t - 2)**2/2
Let h be (-931)/(-105) + 4/30. Suppose 0 = -0*b + 4*b + x - h, -24 = -3*b + 5*x. Factor -21/2*n + b - 27/2*n**2.
-3*(n + 1)*(9*n - 2)/2
Let q(x) be the second derivative of x**4/36 + x**3/3 - 7*x**2/6 - 4*x + 14. Solve q(f) = 0.
-7, 1
Suppose -7*f + 2 = -5. Solve 6*o**2 - o**3 + f - 5*o**3 - 4*o + o**4 + 2*o**3 = 0 for o.
1
Factor -g**3 - 2*g**2 + 105*g - 11*g**3 + 7*g**3 + 2*g**3 - 4*g**2.
-3*g*(g - 5)*(g + 7)
Suppose -112*q + 61*q = 153*q - 408. Find p such that 10*p - 5*p**4 + 55*p**q - 45/2*p**3 + 5/2*p**5 - 60 = 0.
-3, -1, 2
Let v = -92918/5 + 18649. Let o = v - 65. Factor 0*d**2 + 1/5*d**5 - o*d**3 + 0 + 1/5*d + 0*d**4.
d*(d - 1)**2*(d + 1)**2/5
Let v(h) be the third derivative of -h**5/20 + 13*h**4 - 1352*h**3 + 2*h**2 - 106*h. Suppose v(n) = 0. What is n?
52
Let v be (-14)/6*(-444)/259. Let i(h) be the first derivative of -2 + 0*h + 2/9*h**3 - 1/12*h**v - 1/6*h**2. Factor i(y).
-y*(y - 1)**2/3
Let g(y) be the second derivative of y**7/126 - y**6/15 + 2*y**5/15 + y**4/18 - y**3/2 + 2*y**2/3 + 428*y. Find n, given that g(n) = 0.
-1, 1, 4
Let b(j) be the third derivative of 0*j + 1/40*j**6 + 9*j**2 - 1/30*j**5 + 0 + 0*j**4 + 1/1344*j**8 - 1/140*j**7 + 0*j**3. Factor b(i).
i**2*(i - 2)**3/4
Let w(h) be the first derivative of 1/16*h**4 + 3/2*h**2 + 1/2*h**3 + 2*h - 2. Factor w(y).
(y + 2)**3/4
Suppose 3*s - 21 = 2*s. Let u(v) = -2*v**2 - v**2 - 5*v**3 + 4*v**2 - 2. Let n(t) = -16*t**3 + 3*t**2 - t - 7. Let k(j) = s*u(j) - 6*n(j). Factor k(q).
-3*q*(q - 1)*(3*q + 2)
Let m(g) = 402*g**2 - 174*g**3 - 42*g**4 + 3 - 9 - 9*g - 477*g**2. Let t(s) = s**4 - s**3 - 1. Let q(y) = m(y) - 6*t(y). Determine p, given that q(p) = 0.
-3, -1/4, 0
Let l(n) = 44*n**5 - 43*n**5 + 0*n**2 - 1 + n**2 + n. Let s(q) = 4*q**5 - 7*q**4 + 18*q**3 - 19*q**2 + 16*q - 6. Let c(j) = -3*l(j) + s(j). Factor c(u).
(u - 3)*(u - 1)**4
Let a be (-3