12*m**3 - 4*m**2 + 5. Factor v(r).
-4*r*(r - 1)*(7*r - 2)
Let r be -2 - (-1 - 3/1). Find u, given that r*u**3 - 2*u**3 + u - u**3 = 0.
-1, 0, 1
Let u(n) = n**3 + 8*n**2 - 20*n + 2. Let h be u(-10). Let y be (1 - (2 - 1))/h. Factor -2/3*t + y*t**2 + 2/3*t**3 + 0.
2*t*(t - 1)*(t + 1)/3
Let z be 8 + ((-3)/3 - -2). Factor -2*a**5 - z*a**3 + 2 - 10*a + 7*a**4 - 9*a**3 + 20*a**2 - 2*a**3 + 3*a**4.
-2*(a - 1)**5
Let d(o) be the third derivative of o**11/110880 - o**10/8400 + o**9/1680 - o**8/840 + o**5/30 + 2*o**2. Let u(t) be the third derivative of d(t). Factor u(c).
3*c**2*(c - 2)**3
Let j(v) be the second derivative of -v**6/120 - v**5/20 - v**4/8 - v**3/6 - v**2/8 + 6*v. Factor j(i).
-(i + 1)**4/4
Let f(x) = -2*x**2 - 10*x + 4. Let u(v) = 2*v**2 + 9*v - 3. Let h be 1 - 2 - (-10)/(-2). Suppose 8*n = 13*n + 25. Let p(q) = h*u(q) + n*f(q). Factor p(t).
-2*(t + 1)**2
Let x(v) be the second derivative of -v**5/90 - v**4/18 - v**3/9 - v**2/9 + 6*v. Factor x(r).
-2*(r + 1)**3/9
Let r = 166/3 + -55. Factor 0 - 4/3*j - 8/3*j**2 + j**4 - r*j**3.
j*(j - 2)*(j + 1)*(3*j + 2)/3
Factor 3*i**2 + 0 + 27/4*i**4 + 0*i + 3/2*i**5 + 9*i**3.
3*i**2*(i + 2)**2*(2*i + 1)/4
Let f(w) be the first derivative of 3*w**4/4 - 11*w**3/6 + w**2 - w + 1. Let u(o) be the first derivative of f(o). Determine j, given that u(j) = 0.
2/9, 1
Let v(f) = -f**2 + 1. Let g(k) = 4*k**3 - 24*k**2 + 8*k + 12. Let z(o) = g(o) - 12*v(o). Let z(x) = 0. Calculate x.
0, 1, 2
Factor 8*u**3 - u**4 + 16*u**2 - 32*u - 3*u**4 + 3*u**4 - 3*u**4.
-4*u*(u - 2)**2*(u + 2)
Let y be (-2)/24*5/(-200). Let t(a) be the third derivative of 0*a + 1/60*a**5 + 2*a**2 + y*a**6 + 5/96*a**4 + 0 + 1/12*a**3. Find b, given that t(b) = 0.
-2, -1
Let h(d) be the third derivative of -2*d**7/175 - 4*d**6/75 - 4*d**5/75 + 9*d**2. Factor h(n).
-4*n**2*(n + 2)*(3*n + 2)/5
Solve -3*j**2 - 3/2 - 9/2*j + 3/2*j**5 + 3*j**3 + 9/2*j**4 = 0 for j.
-1, 1
Let c be -1*(-3 + (-3 - -3)). Let -6*t**3 - 2*t**4 + 1 + 3*t**5 - t**4 + 2*t**2 + c*t + 4*t**2 - 4 = 0. Calculate t.
-1, 1
Let b(a) = -a**3 - 17*a**2 + 17*a - 17. Let c be b(-18). Let t(d) be the first derivative of 0*d**3 - d**2 + 1/2*d**4 + c + 1/5*d**5 - d. Factor t(s).
(s - 1)*(s + 1)**3
Let r(n) be the first derivative of n**6/30 - n**4/12 + n - 1. Let b(a) be the first derivative of r(a). Factor b(d).
d**2*(d - 1)*(d + 1)
Let b(f) = 8*f**2 - 16*f - 9. Let x(t) = 2*t**2 - 4*t - 2. Let d(a) = -2*b(a) + 9*x(a). Factor d(l).
2*l*(l - 2)
Let q(l) be the first derivative of l**4/7 + 20*l**3/21 + 2*l**2 + 12*l/7 + 12. Find g such that q(g) = 0.
-3, -1
Let u(r) = -r**3 + 8*r**2 + r + 9. Let m be u(8). Let 3*k**2 + m*k - 3*k**4 + 3*k**3 - 23*k + 3*k**3 = 0. Calculate k.
-1, 0, 1, 2
Let g be 75/18 - (-5)/(-30). Factor 8/15*x**g - 2/15*x + 4/5*x**2 - 6/5*x**3 + 0.
2*x*(x - 1)**2*(4*x - 1)/15
Let t be ((-1)/(-3))/((-1)/(-3)). Suppose 12 = 3*g - g. Factor 3*l**2 - g*l**2 + 4*l**2 - t.
(l - 1)*(l + 1)
Let r be (-12)/2*-2*-1. Let t = 14 + r. Determine l, given that -2/7 - 6/7*l**t + 8/7*l**4 - 10/7*l**3 + 10/7*l = 0.
-1, 1/4, 1
Let b be (-2)/(-6) - (-2)/3. Suppose 5 = v - b. Factor 24*d**3 - 24*d**2 - v*d**4 - 1 - 1 + 12*d - 4*d**3.
-2*(d - 1)**3*(3*d - 1)
Suppose 0 = -17*r + 9*r. Factor 0 - 1/3*p**3 - 1/3*p**2 + r*p.
-p**2*(p + 1)/3
Let o = -8 - -9. Let x be (-56)/(-32)*(-1 + 7). Determine r, given that -x*r**2 - 5/2*r**4 - o + 17/2*r**3 + 11/2*r = 0.
2/5, 1
Let o = -497/3 + 167. Factor c**4 + 8/3*c**3 + o - 4*c - c**2.
(c - 1)*(c + 2)**2*(3*c - 1)/3
Factor -12*t + 2 + 2*t**2 + t**2 + 3 + 4.
3*(t - 3)*(t - 1)
Solve 6 + 2/3*b**2 + 4*b = 0 for b.
-3
Suppose 4 = 5*l - 11. Let c(x) be the first derivative of 0*x - 1/12*x**l + 2 + 1/8*x**2. Determine t so that c(t) = 0.
0, 1
Let c(f) be the second derivative of -f**6/180 + f**5/60 + f**4/72 - f**3/18 + 15*f. What is q in c(q) = 0?
-1, 0, 1, 2
Let x(w) be the second derivative of -5*w**4/4 - 6*w**3 - 6*w**2 + 6*w. Find l, given that x(l) = 0.
-2, -2/5
Let a(c) be the first derivative of -c**7/168 + c**5/80 + 3*c + 4. Let r(v) be the first derivative of a(v). Factor r(j).
-j**3*(j - 1)*(j + 1)/4
Let i(g) be the first derivative of 0*g**2 + 2/3*g**3 - 3 - 1/3*g**6 + 0*g - 2/5*g**5 + 1/2*g**4. Solve i(o) = 0 for o.
-1, 0, 1
Let c = 17 - 17. Let m(x) be the first derivative of 1/12*x**4 - 1/3*x**2 + c*x - 1/9*x**3 - 1. Factor m(p).
p*(p - 2)*(p + 1)/3
Suppose r + 31 = 4*j, -2*j + 23 + 45 = -4*r. Let g be (4/(-6))/(r/9). Factor 8/5 - 8/5*q + g*q**2.
2*(q - 2)**2/5
Let x be ((-31)/124)/((-3)/72). Factor x + 2/3*i**2 - 4*i.
2*(i - 3)**2/3
Let r be (-12)/(-10)*(-10)/(-18). Factor 2/3*q**4 + 2*q**3 + r*q + 2*q**2 + 0.
2*q*(q + 1)**3/3
Let r(w) = w**4 - w**3 - w - 1. Let n(o) = -6 - 6*o - 4*o**3 + 0 + 14*o**2 + 7*o**4 - 13*o**2. Let k(u) = n(u) - 6*r(u). Factor k(s).
s**2*(s + 1)**2
Let v(f) be the second derivative of -f**4/12 + 5*f**3/6 - 2*f. Solve v(t) = 0.
0, 5
Let a(r) be the second derivative of -r**6/1080 - r**3/6 - 2*r. Let i(s) be the second derivative of a(s). Suppose i(h) = 0. Calculate h.
0
Let t = 12842 + -642123/50. Let z = 1/25 - t. Solve 1/2*u**4 - u**2 + z*u + 1/2 + 1/2*u**5 - u**3 = 0 for u.
-1, 1
Suppose -2*g + 6 = g. Factor 1 - 3 + 2 + 1 - 3*p + g*p**2.
(p - 1)*(2*p - 1)
Let v(d) be the second derivative of d**4/12 + d**3/6 - 3*d**2 - 3*d + 2. Factor v(p).
(p - 2)*(p + 3)
Factor 13*u**2 + 4*u - 16*u**2 + 7*u**2 - 8.
4*(u - 1)*(u + 2)
Let t(i) be the first derivative of -1/2*i**2 + 2 + i + 1/12*i**3. Solve t(b) = 0 for b.
2
Let a be 16/(-9) + -7 + 9 - 0. Suppose -2 + 0 = -m. Factor 4/9 - 10/9*s + 8/9*s**m - a*s**3.
-2*(s - 2)*(s - 1)**2/9
Factor -3*z**5 - 24*z**4 + 5*z**5 + 12*z - 2*z**5 + 4*z**5 + 48*z**3 - 40*z**2.
4*z*(z - 3)*(z - 1)**3
Suppose -12 = 2*s - 6*s. Let c(d) be the first derivative of 2*d + 1 - 2*d**4 + 4*d**s + 2/5*d**5 - 4*d**2. Let c(z) = 0. Calculate z.
1
Factor -20*w**3 + 8*w - 71*w**2 + 83*w**2 + w**3 - w**3.
-4*w*(w - 1)*(5*w + 2)
Let p(w) be the first derivative of -3*w**5/5 - 3*w**4 - 6*w**3 - 6*w**2 - 3*w - 2. Find v, given that p(v) = 0.
-1
Let t(h) = -4*h - 26. Let g be t(-7). Let c(o) be the first derivative of 1/3*o**g + 4 + 1/12*o**4 + 0*o + 1/3*o**3. Factor c(i).
i*(i + 1)*(i + 2)/3
Let o(a) = -a - 2. Let j be o(-4). Factor -39*t + 17*t - t**j + 16*t - 9.
-(t + 3)**2
Let m(l) be the first derivative of l**7/420 + l**6/270 + l**3 - 2. Let w(g) be the third derivative of m(g). Find r, given that w(r) = 0.
-2/3, 0
Let u(v) be the second derivative of v**6/120 - v**5/40 + v**4/48 + 8*v. Find t, given that u(t) = 0.
0, 1
Let c(j) be the second derivative of j**6/30 + 2*j**5/5 + 3*j**4/2 - 27*j**2/2 - 33*j. Factor c(i).
(i - 1)*(i + 3)**3
Let t(a) be the first derivative of a**4/22 + 4*a**3/33 + a**2/11 + 13. Find y such that t(y) = 0.
-1, 0
Let h be 136/340 + (-16)/(-10). Factor 2/9*r**h + 2/9 - 4/9*r.
2*(r - 1)**2/9
Let s be (-30)/(-14) + (2/14)/(-1). Factor -2/3*q**s - 4/3*q + 0.
-2*q*(q + 2)/3
Suppose -3*i + 2*b - 2 = 0, -3*i = 4*b - 23 + 1. Suppose 5*f = -2*g - 16, f - 2*f = -2*g + 8. Factor z**g + 5*z**2 - 5*z**i.
z**2
Suppose -5*t - 143 + 398 = 0. Factor 8*w**2 - 24*w**3 + 3*w**4 - t - 4 + 46*w**2 - 26.
3*(w - 3)**3*(w + 1)
Suppose 5*m - m + 15 = 5*x, 2*m + 4*x = 12. Let z be (10/(-4))/(3/(-6)). Let m*j**2 + 0*j**4 - 1/2*j**3 + 0 + 0*j + 1/2*j**z = 0. Calculate j.
-1, 0, 1
Let -20*u**2 - u**2 + 4*u**2 + 12*u**3 + 6*u - 4*u**2 + 3 = 0. What is u?
-1/4, 1
Suppose 3/5*x**2 + 9/5 - 3/5*x**3 + 3*x = 0. What is x?
-1, 3
Let a = 884/7 - 126. Let r(j) be the second derivative of a*j**2 + 1/21*j**3 - j + 0 - 1/42*j**4. Find l, given that r(l) = 0.
-1, 2
Factor -3*u - 6/5 - 3/5*u**3 - 12/5*u**2.
-3*(u + 1)**2*(u + 2)/5
Let h(a) be the third derivative of -4*a**2 + 0*a**4 - 1/336*a**8 + 1/120*a**6 + 0*a - 1/210*a**7 + 1/60*a**5 + 0 + 0*a**3. Factor h(c).
-c**2*(c - 1)*(c + 1)**2
Suppose -6*o = 76 - 106. Let c(t) be the first derivative of -t - 1/5*t**o + 0*t**2 + 2/3*t**3 + 0*t**4 - 2. Let c(x) = 0. Calculate x.
-1, 1
Suppose -3*w - 12 = -2*o, -o - 2*w + 5*w + 9 = 0. Factor o*d**2 + d**2 + 2*d - d**2 - 1.
(d + 1)*(3*d - 1)
Let b = 5 - 4. Let p be (1 - b)*(4 - 5). Factor p*s**3 + s**3 + 7*s**3 - 2*s**2.
2*s**2*(4*s - 1)
Let w(h) be the second derivative of 2*h**7/105 - 4*h**6/75 + h**5/25 + 5*h. Factor w(y).
4*y