**3 + 23*l**3 + h*l**2 + 2*l**2.
3*l**2*(l + 2)
Suppose -144 = 2*z - 144. Let k(c) be the second derivative of z + 0*c**3 + 1/2*c**4 + 0*c**2 - 2*c - 3/20*c**5. Factor k(a).
-3*a**2*(a - 2)
Factor 66/19*a - 8/19*a**2 - 16/19.
-2*(a - 8)*(4*a - 1)/19
Factor 0 - 3/7*w**2 + 2/7*w + 1/7*w**3.
w*(w - 2)*(w - 1)/7
Let -19*g**3 + 6*g**5 - 32*g**3 - 440*g**2 + 392*g**2 + 93*g**4 = 0. What is g?
-16, -1/2, 0, 1
Let x(l) be the first derivative of l**6/30 + 43*l**5/25 - 91*l**4/20 - 43*l**3/15 + 9*l**2 + 489. What is q in x(q) = 0?
-45, -1, 0, 1, 2
Let b(r) be the second derivative of 2*r**6/15 + 7*r**5/5 + 11*r**4/3 + 10*r**3/3 + 16*r + 2. Determine v so that b(v) = 0.
-5, -1, 0
Let h = -1336 - -10693/8. Suppose h*o**2 + 0 - 1/8*o**3 - 1/2*o = 0. Calculate o.
0, 1, 4
Let n(q) = q**3 - q**2 - q. Let h(p) = -12*p**3 + 32*p**2 - 40*p + 32. Let v(g) = h(g) + 8*n(g). Factor v(o).
-4*(o - 2)**3
Suppose 2*r + 7*k - 10 = 2*k, 4*r - 44 = 2*k. Suppose -22 - 36*w + 5*w**2 - r - 2*w**2 + 140 = 0. Calculate w.
6
Suppose g = c - 4, g + 0 - 2 = -c. Factor 141*s + 29*s**c + 3*s**5 + 306*s**2 + 181*s**3 + 6*s**5 + 30 - 54*s**2 + 78*s**4.
3*(s + 1)**3*(s + 5)*(3*s + 2)
Let o(s) be the second derivative of 8/3*s**3 + 1/6*s**4 + 0*s**2 + 57*s + 0. Factor o(l).
2*l*(l + 8)
Let p(o) = 16*o**4 - 2*o - 17*o**4 + o**5 + 3*o. Let t(i) = 10*i**5 - 14*i**4 + 2*i**3 + 2*i**2 + 12*i. Let x(q) = -12*p(q) + t(q). Factor x(r).
-2*r**2*(r - 1)*(r + 1)**2
Let c be (4 + 0)*(-3)/(-3). Let x be ((-3 + c)/(-2))/(-1 + 0). Solve -x - o - 1/2*o**2 = 0 for o.
-1
Let x(p) be the first derivative of p**3/3 - 5*p**2 + 9*p + 95. Factor x(t).
(t - 9)*(t - 1)
Let r(d) be the third derivative of -d**6/60 + d**5/20 + d**4/8 + d**3/2 - 2*d**2. Let g be r(-2). Factor 0*l**2 + g*l**3 + 0*l**2 + l**5 - 23*l**3 + 3*l**4.
l**3*(l + 1)*(l + 2)
Let i(h) be the first derivative of -1/9*h**3 + 1/4*h**2 - 1/24*h**4 + 0*h - 2. Factor i(x).
-x*(x - 1)*(x + 3)/6
Let t(g) be the second derivative of g**7/42 + g**6/24 - 3*g**2/2 + 2*g. Let l(k) be the first derivative of t(k). Factor l(w).
5*w**3*(w + 1)
Let c(p) be the third derivative of -p**5/120 - 5*p**4/16 - 7*p**3/6 - 4*p**2 - 15. Factor c(q).
-(q + 1)*(q + 14)/2
Let z be 10*3/(-6)*3. Let d = z + 19. Find p such that -6*p**2 - d*p**3 + 3 + 8*p**2 - 3 + 4*p - 2*p**4 = 0.
-2, -1, 0, 1
Let z(j) = 3*j**3 - 86*j**2 - 308*j + 996. Let g(a) = 8*a**3 - 171*a**2 - 618*a + 1991. Let h(r) = -4*g(r) + 9*z(r). Find p, given that h(p) = 0.
-10, 2
Suppose 8*n = n + 14. Let w = n + -4/5. Solve 0 + 2/5*s - w*s**3 - 4/5*s**2 = 0.
-1, 0, 1/3
Let l(n) = -23*n**3 + 21*n**2 - n + 3. Let i(j) = -66*j**3 + 62*j**2 - 4*j + 8. Let u(y) = -3*i(y) + 8*l(y). Suppose u(t) = 0. Calculate t.
0, 2/7, 1
Let f be 78/126 + (-4)/12. Factor -1/7*l**2 + 0 + 2/7*l**3 + 1/7*l**4 - f*l.
l*(l - 1)*(l + 1)*(l + 2)/7
Let n(s) be the third derivative of s**7/1260 - s**6/270 + s**5/180 - 13*s**3/6 - 8*s**2. Let g(b) be the first derivative of n(b). Factor g(z).
2*z*(z - 1)**2/3
Let l(m) be the second derivative of 4*m - 1/2*m**4 + 4*m**2 + 5/3*m**3 + 0. Let k(o) = o**2 - o - 1. Let r(u) = -8*k(u) - l(u). Determine s so that r(s) = 0.
-1, 0
Let q(a) be the second derivative of -a**7/14 - 3*a**6/2 - 36*a**5/5 + 16*a**4 - 5*a + 4. Factor q(g).
-3*g**2*(g - 1)*(g + 8)**2
Let f(i) = -i**2 + 24*i - 63. Let p be f(3). Let q(l) be the third derivative of 0*l + 1/90*l**5 + 0*l**3 + 7*l**2 - 1/18*l**4 + p. Factor q(w).
2*w*(w - 2)/3
Let v be (-3 + 9)/((-12)/54). Let f be (-12)/v + 2/9. Find m, given that f*m**3 - 2/3*m + 2/3 - 2/3*m**2 = 0.
-1, 1
Let b(m) be the second derivative of 3*m**5/140 - m**4/14 - 41*m**3/14 + 9*m**2 + 212*m. Determine a so that b(a) = 0.
-6, 1, 7
Let h(c) be the first derivative of -4*c**2 + 0*c - 16/3*c**3 + 5/2*c**4 - 27. Factor h(w).
2*w*(w - 2)*(5*w + 2)
Let v(u) be the first derivative of -2*u**6/3 + 44*u**5/5 - 43*u**4 + 292*u**3/3 - 112*u**2 + 64*u - 132. Determine a, given that v(a) = 0.
1, 4
Let z(m) be the first derivative of m**6/240 - m**5/20 + m**4/4 + 12*m**3 + 11. Let n(r) be the third derivative of z(r). Factor n(i).
3*(i - 2)**2/2
Let q(s) = -7*s**3 - 15*s**2. Let y(m) = 20*m**3 + 46*m**2. Let x(l) = 14*q(l) + 5*y(l). Find a, given that x(a) = 0.
-10, 0
Let h(g) be the third derivative of g**7/945 + g**6/135 + g**5/90 - g**4/27 - 4*g**3/27 + 14*g**2 + 4*g. Factor h(f).
2*(f - 1)*(f + 1)*(f + 2)**2/9
Let u(z) be the second derivative of 11/60*z**5 - 5/2*z**2 + 3*z + 0 + 13/24*z**4 + 1/3*z**3. Let l(k) be the first derivative of u(k). Solve l(x) = 0.
-1, -2/11
Let u(g) = -32*g**2 - 38*g - 32. Let h(n) = 7*n**2 + 8*n + 6. Let d(v) = 28*h(v) + 6*u(v). Determine w, given that d(w) = 0.
-2, 3
Suppose -2*u = 19*r - 24*r - 6, 3*u - r = 22. Let h(t) be the first derivative of 2/3*t**3 + u*t + 4*t**2 + 11. Determine k, given that h(k) = 0.
-2
Let o(t) be the second derivative of t**4/12 - t**2 + 3*t. Let v be o(-2). Factor -4*d + 3 + v - 5 + 2*d**2.
2*d*(d - 2)
Let n(s) be the second derivative of -s**4/20 + s**3/5 + 9*s**2/10 + 7*s + 1. Factor n(p).
-3*(p - 3)*(p + 1)/5
Let x(o) = -o**3 - o**2 + o. Let w(p) = -p**3 - p**2 - 2*p - 4. Let s(u) = w(u) - 2*x(u). Solve s(c) = 0.
-2, -1, 2
Let f(z) be the first derivative of -z**5/120 + z**4/24 + z**3/36 - z**2/4 - 20*z + 20. Let d(b) be the first derivative of f(b). Factor d(o).
-(o - 3)*(o - 1)*(o + 1)/6
Solve 41*x**2 - 67 + 29*x**2 - 5*x**5 + 10*x**4 + 195*x + 55*x**4 - 190*x**3 - 57 - 11 = 0.
-1, 1, 3, 9
Let x(k) be the third derivative of k**7/1365 + k**6/130 - 201*k**2. Solve x(m) = 0 for m.
-6, 0
Let g(f) = -f**2 - 9*f + 4. Let v be g(-7). Let q be -4 + 1 + 58/v. Factor -q*n**2 - 2/9*n**4 + 0 - 4/9*n**3 + 0*n.
-2*n**2*(n + 1)**2/9
Let n = -1012197/7 + 144335. Let z = n + 265. Factor z*b + 0 + 3/7*b**2 - 3/7*b**3 - 3/7*b**4.
-3*b*(b - 1)*(b + 1)**2/7
Let s be ((-5)/(-2))/(-31 - 6152/(-192)). Factor -18/5*h - s - 6/5*h**2.
-6*(h + 1)*(h + 2)/5
Suppose 51 - 51 + 40*h**3 + 25*h + 30*h**2 - 20*h = 0. What is h?
-1/2, -1/4, 0
Suppose 2*q + 162 + 844 = -5*c, 0 = -2*c + 3*q - 391. Let t = -997/5 - c. Suppose -3/5*v + t*v**3 + 0 + 0*v**2 = 0. What is v?
-1, 0, 1
Let q(x) be the second derivative of -1/18*x**4 - 1/3*x**3 + 0 + 5*x + 4/3*x**2. Suppose q(f) = 0. What is f?
-4, 1
Suppose 0 = -5*w - 5*q + 25, -2*w + 0*q = -2*q - 6. Let r(t) be the second derivative of 0*t**2 + t**3 + 5/4*t**w + 3/5*t**5 + 1/10*t**6 + 0 - t. Factor r(f).
3*f*(f + 1)**2*(f + 2)
Let v(d) = -20*d**3 + 17*d**2 - 37*d + 5. Let y(o) = 6*o**3 - 6*o**2 + 12*o - 2. Let c(m) = -2*v(m) - 7*y(m). Solve c(g) = 0.
1, 2
Factor -30/7*s - 12/7 - 24/7*s**2 - 6/7*s**3.
-6*(s + 1)**2*(s + 2)/7
Suppose 5*j + 0*j - 3*s = 5, -4*s = -3*j + 3. Let n(t) be the first derivative of 0*t - 2/3*t**6 + 0*t**2 - 16/3*t**3 - j + 0*t**4 + 12/5*t**5. Factor n(a).
-4*a**2*(a - 2)**2*(a + 1)
Factor -4*k**2 + 8*k - 23 - 20*k + 23.
-4*k*(k + 3)
Suppose -24/7 - 108/7*q**2 + 93/7*q + 6/7*q**4 + 33/7*q**3 = 0. What is q?
-8, 1/2, 1
Let k(i) be the second derivative of -i**5/210 - i**4/42 - i**3/21 + 19*i**2 - 44*i. Let d(a) be the first derivative of k(a). Find r such that d(r) = 0.
-1
Let i(y) = -2*y - 1. Let h(v) = 5*v**2 + 50*v - 20. Let m(c) = -h(c) - 25*i(c). Factor m(d).
-5*(d - 3)*(d + 3)
Let s be -4*1*5/70*(-21)/3. Factor 0*u**3 + u**s - u**4 + 1/2*u + 0 - 1/2*u**5.
-u*(u - 1)*(u + 1)**3/2
Let f(m) be the third derivative of -m**7/420 + m**6/80 - m**5/40 + m**4/48 + m**2 + 12. Factor f(l).
-l*(l - 1)**3/2
Let p(b) be the third derivative of 1/480*b**6 + 3/560*b**7 + 1/96*b**4 + 0 + 0*b + 35*b**2 + 0*b**3 - 3/160*b**5 - 1/672*b**8. Determine i so that p(i) = 0.
-1, 0, 1/4, 1, 2
Let k be (130/(-30) + 5)/((-20)/(-18)). Factor 6*i**3 - k - 9/5*i - 63/5*i**4 + 18/5*i**2 + 27/5*i**5.
3*(i - 1)**3*(3*i + 1)**2/5
Let q be (2/(-7))/(12/(-42)). Suppose -4*n = -z - 3, -5*z + 5*n + 14 = -q. Factor -z*s + s**4 + s**3 - s**2 - 2*s**2 - 2 + 0.
(s - 2)*(s + 1)**3
Let k be ((2 - 8) + 0)/((-18)/24). Let b = k - 4. Determine l so that 0*l - 2/11*l**2 - 2/11*l**5 + 0 - 6/11*l**b - 6/11*l**3 = 0.
-1, 0
Let p(s) be the third derivative of 4*s**2 + 1/224*s**8 - 1/16*s**4 + 0*s**3 + 0 + 1/20*s**5 + 0*s - 1/70*s**7 + 0*s**6. Solve p(o) = 0.
-1, 0, 1
Let q(v) be the first derivative of 2*v**5/105 - v**4/14 - 8*v**3/7 - 