u, given that w(u) = 0.
-1, 0
Let m(w) = -188*w**2 + 18*w - 13. Let p(g) = -94*g**2 + 8*g - 6. Let t(c) = -6*m(c) + 13*p(c). Factor t(s).
-2*s*(47*s + 2)
Factor -4*h**4 - 114*h**3 + 16*h + 28*h**2 + 229*h**3 - 107*h**3.
-4*h*(h - 4)*(h + 1)**2
Let n be (-30)/12*8/(-10). Let y(v) be the first derivative of 2*v**2 + 3*v**n - 4*v**3 + v**2 + v**4 - 3 - 4*v. Factor y(x).
4*(x - 1)**3
Let q(d) = 2*d**3 - 66*d**2 - 178*d - 100. Let p(v) = 3*v**2 + 2*v. Let h(k) = 10*p(k) - q(k). Factor h(f).
-2*(f - 50)*(f + 1)**2
Suppose -4*m - 32 = -12*m. Let y be (-1 - -2)/(m - 2). Find v, given that -y*v**2 + 0*v + 1/2 = 0.
-1, 1
Factor -10*k**3 - 3*k**4 + 56 + 17*k + 3*k**2 + k**4 + k**4 - 36 + 15*k.
-(k - 2)*(k + 1)**2*(k + 10)
Suppose -58*p = -13*p. Factor p - 1/3*a - 1/6*a**2.
-a*(a + 2)/6
Let q(n) be the third derivative of -1/20*n**6 + 0*n**3 + 1/63*n**7 + 0*n - 1/18*n**4 - 1/504*n**8 + 7/90*n**5 + 0 + 31*n**2. Suppose q(v) = 0. Calculate v.
0, 1, 2
Let i(r) = r + 2. Let c(w) = -21*w**3 + 183*w**2 - 363*w - 114. Let y(x) = -c(x) + 3*i(x). Factor y(q).
3*(q - 5)*(q - 4)*(7*q + 2)
Let p be 1/(-2) - (-9)/2. Suppose 0*k + p = 2*k. Let 3*u**2 - 2*u**k - 2*u + 1 + 0 = 0. What is u?
1
Let x(i) = i**5 + i**4 - i**3 - i**2 + i. Let a(m) = -4*m**5 - 18*m**4 + 6*m**3 + 70*m**2 - 6*m. Let n(l) = a(l) + 6*x(l). Factor n(f).
2*f**2*(f - 4)**2*(f + 2)
Let v = -34 + 37. Let i(p) = -7*p**2 + 7. Let a(m) = m**2 - 1. Let d(f) = v*a(f) + i(f). Factor d(t).
-4*(t - 1)*(t + 1)
Let d(p) = -6*p + 40. Let u be d(7). Let l be u/24 + ((-30)/(-8) - 3). Determine o so that 0 - 2/9*o - 2/3*o**3 + l*o**2 + 2/9*o**4 = 0.
0, 1
Let k(s) be the first derivative of -4*s**4 - 4/5*s**5 - 8*s**3 - 8*s**2 - 4*s - 6. Factor k(t).
-4*(t + 1)**4
Let x(g) = -g**4 - g**3. Let a(w) = 5*w**3 - 5*w**2 + 2*w. Suppose b + 4*b - 105 = 0. Let d = 20 - b. Let u(c) = d*x(c) - a(c). Factor u(l).
l*(l - 2)*(l - 1)**2
Suppose 10 = 5*j, -2*y - 5*j = -2*j - 22. Suppose 4*v - y = -2*g - 2*g, -8 = 5*v - 4*g. Determine a so that 2/7*a**2 + 0 + 0*a - 2/7*a**4 + v*a**3 = 0.
-1, 0, 1
Let y be (240/50)/(-8)*(-10)/12. Let f(i) = i**2 - 8*i - 5. Let q be f(9). Solve y*p**2 - 1/2*p**q + 0 - p + p**3 = 0.
-1, 0, 1, 2
Suppose 46*w - 44*w - 4 = 0. Factor 43 - 18 + 4*d - 25 - d**w.
-d*(d - 4)
Let k(o) = -o - 2. Let m be k(-5). Let w(d) be the first derivative of 2/7*d - 5 - 2/21*d**m + 0*d**2. Solve w(b) = 0 for b.
-1, 1
Let o(c) be the second derivative of -c**7/630 - c**6/18 - 5*c**5/6 - 19*c**4/12 - 13*c. Let u(b) be the third derivative of o(b). What is j in u(j) = 0?
-5
Let z = 2381/2737 + -5/391. Factor 36/7*a**2 - z*a + 15/7*a**4 - 6*a**3 - 3/7.
3*(a - 1)**3*(5*a + 1)/7
Let r(i) be the second derivative of 1/147*i**7 + 0*i**3 - 1/21*i**6 - 1/14*i**4 + 0*i**2 + 1/10*i**5 + 0 + 29*i. Factor r(y).
2*y**2*(y - 3)*(y - 1)**2/7
Let b(t) be the third derivative of -10*t**2 - 5/216*t**4 + 0 + 0*t - 1/9*t**3 - 1/540*t**5. Factor b(a).
-(a + 2)*(a + 3)/9
Solve -1/2*a**2 + 0 - 89*a = 0 for a.
-178, 0
Let w(g) be the second derivative of -2*g**7/21 - 31*g**6/90 - 7*g**5/30 + 2*g**4/3 - 4*g**3/3 - 13*g. Let z(l) be the second derivative of w(l). Factor z(f).
-4*(f + 1)*(4*f - 1)*(5*f + 4)
Let l(b) = -10*b**4 + 12*b**2 - 8*b - 2. Let p be (3/18*3)/(2/(-20)). Let v(d) = 10*d**4 + d**3 - 11*d**2 + 9*d + 1. Let z(c) = p*l(c) - 4*v(c). Factor z(j).
2*(j - 1)**2*(j + 1)*(5*j + 3)
Let p(l) be the second derivative of l**5/70 - l**4/14 + 4*l**2/7 + 54*l. Determine b so that p(b) = 0.
-1, 2
Let l(s) be the third derivative of -s**8/252 - 16*s**7/315 - 5*s**6/18 - 38*s**5/45 - 14*s**4/9 - 16*s**3/9 - 27*s**2. Let l(c) = 0. Calculate c.
-2, -1
Suppose -104*l = -101*l - 15. Let 0*o**2 + 0*o**4 + 0 - 3/4*o**3 + 3/8*o + 3/8*o**l = 0. Calculate o.
-1, 0, 1
Let w(l) = l**3 + l**2 - l. Let t(p) = 5*p**4 - 45*p**3 + 40*p**2 + 10*p. Let z(n) = t(n) + 10*w(n). Factor z(v).
5*v**2*(v - 5)*(v - 2)
Find p such that 4/3*p - 2/9*p**4 + 0 - 2/9*p**2 - 8/9*p**3 = 0.
-3, -2, 0, 1
Factor 3/2*w**4 - 1/2*w**5 + 0 + 0*w + 0*w**2 - w**3.
-w**3*(w - 2)*(w - 1)/2
Let y(n) = -2*n**2 + 4*n + 3. Let a be 6/5*30/18. Let m(d) = -d**2 + 0*d**2 + 0*d**2. Let r(c) = a*y(c) - 6*m(c). Determine o, given that r(o) = 0.
-3, -1
Let z(t) be the third derivative of t**6/40 + 3*t**5/4 + 6*t**4 - 32*t**3 + 91*t**2. Solve z(y) = 0.
-8, 1
Let h(j) = 7*j + 128. Let m be h(-18). Let p(d) be the first derivative of -5 - 2/5*d**5 - m*d**4 - 10/3*d**3 - 2*d**2 + 0*d. What is b in p(b) = 0?
-2, -1, 0
Let z be (-12)/(-9)*6 - 4. Let c be (4/(-24))/(z/(-24)). Factor 2*g**3 + 3*g - 4*g**2 - g**3 + 7*g**2 + c.
(g + 1)**3
Let -7*t**2 - 11*t**2 - 10 + 19*t - t**3 + 20*t**2 - 10*t**2 = 0. What is t?
-10, 1
Let o(u) be the third derivative of -1/12*u**6 - 2/3*u**3 - 9*u**2 + 5/12*u**4 + 0 + 1/15*u**5 + 0*u. Factor o(s).
-2*(s - 1)*(s + 1)*(5*s - 2)
Let o(b) be the first derivative of b**4/20 - 11*b**3/15 - 29*b**2/10 + 39*b/5 - 375. Solve o(k) = 0.
-3, 1, 13
Let t(y) = -y**3 - 6*y**2 - 11*y - 14. Let v be t(-5). Factor -4*b**4 - 130*b**2 + v*b**4 + 8*b**4 + 28 + 45*b + 45*b**3 - 8.
5*(b - 1)**2*(b + 4)*(4*b + 1)
Let m be (2/(-8))/(-1) + (-25839)/(-180). Let q = m - 141. Determine u so that -8/15*u + 16/5*u**2 - q*u**3 + 0 - 98/15*u**4 = 0.
-1, 0, 2/7
Let n be (1 - -2 - 11) + 10. Let j(c) be the first derivative of -10 + c**3 + 0*c**n + 0*c - 3/4*c**4. Suppose j(k) = 0. Calculate k.
0, 1
Let r(g) = 137*g - 280*g + 139*g - 2*g**2 - 4. Let f(m) = 4*m**2 + 9*m + 9. Let p = 28 + -19. Let k(h) = p*r(h) + 4*f(h). Determine c, given that k(c) = 0.
0
Suppose 10 = -0*z - 5*z. Let i(q) = 3*q**2 + 8*q - 2. Let u(l) = 4*l**2 + 9*l - 3. Let w(n) = z*u(n) + 3*i(n). Factor w(c).
c*(c + 6)
Let k = 92 - 98. Let p be k/45 - (-104)/105. Factor -p*u**3 + 6/7*u**2 + 0 + 2/7*u**4 - 2/7*u.
2*u*(u - 1)**3/7
Let j(b) = b**4 + 29*b**3 - b**2 - 17*b - 4. Let g(c) = -27*c**3 + 18*c + 3. Let v(i) = -4*g(i) - 3*j(i). Factor v(o).
-3*o*(o - 7)*(o - 1)*(o + 1)
Let j(w) be the second derivative of 15*w + 3/8*w**2 + 0 + 1/12*w**3 - 1/40*w**5 - 1/12*w**4 + 1/120*w**6. Factor j(z).
(z - 3)*(z - 1)*(z + 1)**2/4
Let j(h) be the second derivative of 0*h**2 - 1/12*h**4 - 1/40*h**5 + 18*h + 1/30*h**6 + 0 + 1/8*h**3 - 1/168*h**7. Let j(k) = 0. Calculate k.
-1, 0, 1, 3
Let l be (-31)/(-11) + 8/44. Let d(g) = -g**2 + 11*g + 12. Let h be d(12). Factor -9/8*w**4 + h - 5/8*w**2 + 2*w**l - 1/4*w.
-w*(w - 1)**2*(9*w + 2)/8
Let p be (-3)/((-6)/14)*-1. Let m(u) = u + 11. Let d be m(p). Factor -a**4 - 21*a - 6 - 2*a**d - 27*a**2 - 15*a**3 + 0*a**4.
-3*(a + 1)**3*(a + 2)
Let s be (-3)/(-6)*12 - (1 + 0). Solve -8*m**4 - 6*m**4 - 25*m**2 + 2*m**5 + 7*m**2 + 35*m**3 - s*m**3 = 0.
0, 1, 3
Factor -2/7*s**4 + 24/7*s**2 + 0*s + 0 - 2/7*s**5 + 16/7*s**3.
-2*s**2*(s - 3)*(s + 2)**2/7
Let j(a) be the third derivative of a**5/210 - 13*a**4/84 + 40*a**3/21 + a**2 + 54. Factor j(k).
2*(k - 8)*(k - 5)/7
Let r(q) be the second derivative of -7*q**6/6 + 23*q**5/4 - 45*q**4/4 + 65*q**3/6 - 5*q**2 - 21*q. Factor r(d).
-5*(d - 1)**3*(7*d - 2)
Let s = -1285/6 - -2573/12. Factor 1/2 + 1/4*x**4 - 1/4*x**3 + s*x - 3/4*x**2.
(x - 2)*(x - 1)*(x + 1)**2/4
Factor 49/12*z**3 - 11*z - 7/6*z**2 - 6.
(z - 2)*(7*z + 6)**2/12
Let l be ((140/55)/7)/2. Let p(q) be the first derivative of 2/11*q**3 + l*q + 1/22*q**4 - 6 + 3/11*q**2. Find g such that p(g) = 0.
-1
Let f(k) = -15*k**2 + 195*k + 3. Let a be f(13). Let s(t) be the first derivative of 1/25*t**5 + 0*t + 1/20*t**4 - 3 - 1/15*t**a - 1/10*t**2. Factor s(r).
r*(r - 1)*(r + 1)**2/5
Let c(d) be the first derivative of -d**4/18 - 4*d**3/9 - 80. Find r such that c(r) = 0.
-6, 0
Let i(m) be the first derivative of -m**3/12 + m**2/4 + 3*m/4 + 103. Factor i(u).
-(u - 3)*(u + 1)/4
Let n(b) = 4*b**4 + 28*b**3 + 4*b**2 - 20. Let v(l) = -l**3 + 4 + 0 - 3. Let j = -220 - -200. Let i(w) = j*v(w) - n(w). Factor i(o).
-4*o**2*(o + 1)**2
Let f = -16/8359 + -8484289/50154. Let t = -169 - f. Factor -1/3*w + t + 1/6*w**2.
(w - 1)**2/6
Suppose 4*m - 6*m = -8. Let a = m - 18/5. Determine s so that 2/5*s**3 - 6/5*s**2 + 6/5*s - a = 0.
1
Let q = 17686 - 194534/11. Let -6/11 - q*k - 6/11*k**2 = 0. What is k?
-1
Let b(d) be the first derivative of -d**7/560 + d**6/240 + d**3 - 19. Let t(c) be the third derivative of b(c). Factor t(g).
-3*g**2*(g - 1)/2
