*(s - 1)*(s + 1)**2
Let t(z) be the first derivative of 13/2*z**4 + 2/3*z**6 - 3*z**2 - 10 + 18/5*z**5 + 10/3*z**3 - 4*z. Factor t(p).
2*(p + 1)**3*(p + 2)*(2*p - 1)
Determine q, given that 16/25*q + 2/25*q**4 - 2/5*q**3 + 4/25*q**2 + 0 = 0.
-1, 0, 2, 4
Let q(o) = -10*o**3 + 26*o**2 - 104*o + 72. Let w(t) = -6*t**3 + 17*t**2 - 69*t + 48. Let s(l) = 5*q(l) - 8*w(l). Solve s(x) = 0 for x.
-6, 1, 2
Let x be (-5100)/(-1428) + 10/(-25) + 6/(-35). Find q, given that -q**2 + 0 - 1/2*q**5 + q**4 + 0*q**x + 1/2*q = 0.
-1, 0, 1
Let h be (-3731)/(-1638) + (-4)/(-18). Factor 5/2*q + 5 - h*q**2.
-5*(q - 2)*(q + 1)/2
Let y = 14711 - 14711. Factor y*n**2 + 1/11*n**3 - 1/11*n + 0.
n*(n - 1)*(n + 1)/11
Let x(l) be the second derivative of -l**5/10 - 7*l**4/6 - 8*l**3/3 + 16*l**2 - 139*l. Factor x(i).
-2*(i - 1)*(i + 4)**2
Suppose 55 = m + 4*m + p, -m + 3*p = 5. Suppose 2*j - j = -3*u - 2, 0 = 5*j + m. Solve -4/5*w + 2/5*w**3 - 2/5*w**2 + u = 0.
-1, 0, 2
Solve 35*r**2 - 205/3*r + 100/3 - 5/3*r**4 + 5/3*r**3 = 0.
-5, 1, 4
Let q(a) be the second derivative of a**4/3 + 184*a**3/3 + 182*a**2 + 201*a + 2. Factor q(m).
4*(m + 1)*(m + 91)
Suppose 4*a = -5*b + 28, -3*b - 3*a + 14 = -b. Suppose 2*z = b*z - 6. Factor 0 + z*q**2 - 36*q**3 + 0 + 33*q**3.
-3*q**2*(q - 1)
Let q(d) be the third derivative of d**8/840 + 3*d**7/175 + 13*d**6/150 + 2*d**5/15 - 2*d**4/5 - 32*d**3/15 + 102*d**2 + d. Let q(o) = 0. Calculate o.
-4, -2, 1
Let u(b) = 6*b**3 - 414*b**2 - 14283*b + 27. Let t(n) = n**3 + 3. Let x(l) = -9*t(l) + u(l). Factor x(z).
-3*z*(z + 69)**2
Let f = 85 - 81. Determine p, given that -9*p**4 + p**2 - 5*p**4 - 5*p**2 + 18*p**f = 0.
-1, 0, 1
Let c be 1389/(-180) - 14/168. Let n = c - -11. Factor n*m**2 + 0 - 2*m**3 + 8/5*m.
-2*m*(m - 2)*(5*m + 2)/5
Factor 30 + 11*j**2 + 15 - j**3 - 18*j - 21*j.
-(j - 5)*(j - 3)**2
Let o be (-3)/(-6) - 591/(-6). Let h be 6/(-4) - o/(-22). Factor -2*z**5 - 2*z**h - 4 - 4*z**4 + 4.
-2*z**3*(z + 1)**2
Suppose 0 = v + 3*v - 16. Suppose 16 = 2*n - 4*l, n - 5*l - 65 = -4*n. Factor z**2 - v*z - z**2 + 16 + 4*z**3 - n + 2*z**4.
2*(z - 1)*(z + 1)**3
Let k(l) be the third derivative of -l**7/35 - l**6/6 + 11*l**5/30 + 5*l**4/6 - 8*l**3/3 + 7*l**2 + 17. Solve k(m) = 0.
-4, -1, 2/3, 1
Suppose -4*a = -5*t + 17, a = 3*a - t + 1. Suppose 0 = -a*x + 3*x + c - 1, -c + 16 = 4*x. Factor 0*p**2 + 0*p**3 + 0 + 0*p - 2/7*p**4 + 2/7*p**x.
2*p**4*(p - 1)/7
Factor -9/2*l - 3 - 3/2*l**2.
-3*(l + 1)*(l + 2)/2
Find a, given that 8*a**3 - 60*a + 8*a**2 - 5*a**3 + 0*a - 144 + a**3 = 0.
-3, 4
Let q(u) = -2*u**3 + 11*u**2 - 9*u. Let r(b) = -3*b**3 + 17*b**2 - 14*b. Let k(a) = -8*q(a) + 5*r(a). Factor k(o).
o*(o - 2)*(o - 1)
Let d(z) = -z**3 - 5*z**2 - 7*z - 4. Let v be d(-4). Factor -64*x**3 - 11*x**2 + v + 12*x**4 + 31*x**2 - 8.
4*x**2*(x - 5)*(3*x - 1)
Let x(n) be the first derivative of n**5 - 55*n**4/4 - 5*n**3/3 + 55*n**2/2 - 33. Factor x(m).
5*m*(m - 11)*(m - 1)*(m + 1)
Suppose 41*x - 21*x - 49 = 11. Determine a so that 4/3*a**x + 8/9*a + 0 - 20/9*a**2 = 0.
0, 2/3, 1
Let t(h) = -13*h**3 - 191*h**2 - 269*h + 77. Let a(u) = 27*u**3 + 381*u**2 + 539*u - 155. Let b(g) = 3*a(g) + 5*t(g). Factor b(y).
4*(y + 2)*(y + 10)*(4*y - 1)
Let s(n) be the third derivative of -n**6/900 - n**5/100 - n**4/30 - n**3/6 - 6*n**2. Let i(r) be the first derivative of s(r). Solve i(z) = 0 for z.
-2, -1
Suppose -24 = -2*n - 2*n. Suppose i - 9 + n = 0. Suppose -2/3 + 2/3*t - 2/3*t**i + 2/3*t**2 = 0. What is t?
-1, 1
Let a(y) be the third derivative of y**10/181440 - y**9/45360 + y**8/40320 - 25*y**4/24 + 21*y**2. Let q(b) be the second derivative of a(b). Factor q(r).
r**3*(r - 1)**2/6
Let n(f) = -f + 21. Let c be n(11). Factor -17*t**2 + c*t**2 + 9*t**2 - 8.
2*(t - 2)*(t + 2)
Let s = -174 + 179. Let d(b) be the second derivative of 0*b**2 + 1/2*b**4 - 3/20*b**s + 4*b + 0 + 0*b**3. Determine w, given that d(w) = 0.
0, 2
Let o(i) be the third derivative of -2*i**2 - 1/8*i**3 - 1/240*i**5 + 46 - 5/96*i**4 + 1/480*i**6 + 0*i. Determine p, given that o(p) = 0.
-1, 3
Let -15/2*w**5 - 21*w + 435/2*w**2 + 597/2*w**3 - 48 + 201/2*w**4 = 0. What is w?
-1, 2/5, 16
Let p be (-4*20/(-1040))/((-1)/(-4)). Factor 2/13*o**3 - p + 4/13*o**2 - 2/13*o.
2*(o - 1)*(o + 1)*(o + 2)/13
Let y be (320/224)/(1 + (-9)/14). Factor -10/3*t**2 + 32/9*t**y + 0 - 2*t + 16/9*t**3.
2*t*(t - 1)*(4*t + 3)**2/9
Let y be 488/(-60) + 12/90 + (20 - 10). Factor -38/11*n + 6/11 + 12/11*n**y.
2*(n - 3)*(6*n - 1)/11
Let x(o) = o**2 + 1. Let q be 9/6*-2*1/3. Let d(b) = -6*b**2 + 4. Let v(t) = q*d(t) - 4*x(t). Find f, given that v(f) = 0.
-2, 2
Let n = 156 - 60. Let w = -478/5 + n. Factor w*b**2 + 0 + 0*b + 2/5*b**5 + 6/5*b**3 + 6/5*b**4.
2*b**2*(b + 1)**3/5
Let f(v) = v**2 - 5*v + 11. Let k be f(5). Suppose 4*z + 3 = k. Let -2/5*w**z + 0 - 2/5*w = 0. Calculate w.
-1, 0
Let j(l) = -l**2 + 15*l - 7. Let z be j(12). Let k = 32 - z. Determine o so that k*o**2 - 6 - 2*o**2 + 2 = 0.
-2, 2
Suppose 0 = -3*y - 3*f + 276, 454 = 5*y - f + 4*f. Solve y*z**3 + 19 + 5 - 92*z**3 + 18*z**2 - 36*z = 0.
2
Let k(w) be the first derivative of -w**6/6 + w**5 - 5*w**4/4 - 5*w**3/3 + 3*w**2 + 238. What is c in k(c) = 0?
-1, 0, 1, 2, 3
Let c(g) be the first derivative of g**4/18 - 26*g**3/27 + 56*g**2/9 - 160*g/9 + 268. Factor c(r).
2*(r - 5)*(r - 4)**2/9
Let i = -8 - -5. Let m = 3 - i. Factor -3*s**3 + 2 + m*s**2 - 15*s**2 + 4 + 6.
-3*(s - 1)*(s + 2)**2
Let v be (-2)/(-4) - 1/4. Let b = -1/5 + 7/10. Let b*x - 1/4*x**2 - v = 0. Calculate x.
1
Let q(v) = v**2 - 1 - 6 + 5 - 9*v. Let j(k) be the third derivative of k**5/20 - 19*k**4/24 - 5*k**3/6 - 2*k**2. Let a(h) = -4*j(h) + 9*q(h). Factor a(w).
-(w + 2)*(3*w - 1)
Let x be (27/(-15) - -2)*1335/6. Let v = 45 - x. Factor -2*q + 2 + v*q**2.
(q - 2)**2/2
Let 0*r**2 + 1 - 5*r**3 - 3/2*r**5 + 5/2*r - 5*r**4 = 0. Calculate r.
-1, 2/3
Let b(m) = -m**4 - m**3 - m. Let i(p) = -2*p**2 - 8*p + 0*p**2 + 17*p**4 - 19*p**4. Suppose 4*c + 21 = 5. Let z(h) = c*b(h) + i(h). Factor z(q).
2*q*(q - 1)*(q + 1)*(q + 2)
Let r(u) be the second derivative of -3/70*u**5 - 2 - 9*u + 3/7*u**3 - 1/7*u**4 + 0*u**2. Find a, given that r(a) = 0.
-3, 0, 1
Let q(f) be the second derivative of -1/900*f**6 - 1/15*f**4 + 0 - 3*f - 11/6*f**3 + 0*f**2 - 1/60*f**5. Let d(z) be the second derivative of q(z). Factor d(m).
-2*(m + 1)*(m + 4)/5
Let y = -1/14446 - -4954987/130014. Suppose -1/9*u**3 - y - 49/3*u - 7/3*u**2 = 0. Calculate u.
-7
Suppose -q = 1, -5*j - 2*q - 13 = 79. Let u be 9/14*(-24)/j. Solve 0 + 0*a**2 - 4/7*a**3 - u*a**4 + 0*a = 0.
-2/3, 0
Factor 7*z - 3 - z - 12*z - 2*z**2 + 1 + 2*z.
-2*(z + 1)**2
Factor -42*l**2 - 2*l**3 - 686 + 32*l - 349*l + 23*l.
-2*(l + 7)**3
Let k(y) be the first derivative of 0*y**2 + 1/12*y**6 - 4 + 0*y**4 + 0*y - 1/10*y**5 + 0*y**3. Factor k(p).
p**4*(p - 1)/2
Let s(f) be the third derivative of -f**7/630 + f**5/30 - f**4/2 + 9*f**2. Let q(d) be the second derivative of s(d). Find u, given that q(u) = 0.
-1, 1
Let s be 5/2*(-16)/(-5). Suppose -v + s = 3*v. Suppose -3*f**3 + 0*f**5 - 3*f**4 - f**2 + 0*f**v - 2*f**5 + f**5 = 0. Calculate f.
-1, 0
Solve -32/9*z**2 - 2/3*z**3 + 2/9*z**4 - 8/3*z + 0 = 0 for z.
-2, -1, 0, 6
Let x(k) be the second derivative of k**7/63 - 7*k**6/45 - k**5/10 + 23*k**4/18 - 14*k**3/9 + k + 346. Find o such that x(o) = 0.
-2, 0, 1, 7
Let a = -7524 + 37622/5. Let 2/5*q + 0 + a*q**2 = 0. Calculate q.
-1, 0
Determine b, given that 32/5 + 2/5*b**3 + 16/5*b**2 + 8*b = 0.
-4, -2
Suppose 8*g = 4*g. Find k, given that -4*k + 3*k - 12*k**2 - 2*k + g*k = 0.
-1/4, 0
Suppose 208 = -93*t + 97*t. Factor 0 - t*x**2 + 8 + 38*x - 4*x + 10*x.
-4*(x - 1)*(13*x + 2)
Suppose 62 = 21*j + 20. Let z(s) be the third derivative of -1/9*s**4 + 1/90*s**5 + 0 - 2*s**j + 1/3*s**3 + 0*s. Suppose z(w) = 0. What is w?
1, 3
Let k = -8/33 + 35/99. Let a(o) be the third derivative of 0 - 1/8*o**4 - 7/180*o**5 - k*o**3 + 0*o + 3*o**2. Factor a(z).
-(z + 1)*(7*z + 2)/3
Let f = -214 - -214. Let i(w) be the second derivative of -1/21*w**3 - 2/7*w**2 + f + 1/42*w**4 - 3*w. Factor i(m).
2*(m - 2)*(m + 1)/7
Let m be ((-40)/(-7 - -2) - 3) + -9 + 6. Factor -4/3*z**4 - 12 - 32*z - 32/3*z**3 - 88/3*z**m.
-4*(z + 1)**2*(z + 3)**2/3
Let u(m) = -2*m**2 + 53*m - 281. Let c be u(19). Suppose 7/3*w**2 + 2/3*w + 5/3*w**c + 1/3*w**5 + 