+ 4*h - 3. Let u(n) = 14*n**4 + 4*n**3 - 14*n**2 - 4*n + 4. Let r(v) = 3*u(v) + 4*w(v). Factor r(i).
-2*i*(i - 1)*(i + 1)*(5*i + 2)
Let t(l) be the third derivative of -l**5/90 + 2*l**4/9 - 4*l**3/3 - 42*l**2. Suppose t(z) = 0. What is z?
2, 6
Let w(a) be the third derivative of a**7/2520 - a**6/540 + a**5/360 - a**3/2 + 2*a**2. Let q(f) be the first derivative of w(f). Let q(c) = 0. What is c?
0, 1
Let t(h) be the second derivative of -h**8/5040 + h**7/1260 - h**5/180 + h**4/72 - h**3/2 - 7*h. Let b(q) be the second derivative of t(q). Factor b(l).
-(l - 1)**3*(l + 1)/3
Suppose -6*g = -13 - 5. Find b such that -2/3*b**g + 2/3*b - 2/3*b**2 + 2/3 = 0.
-1, 1
Let v(x) be the third derivative of -3*x**7/385 - 7*x**6/55 - 83*x**5/165 + 35*x**4/33 - 25*x**3/33 - 36*x**2. Factor v(r).
-2*(r + 5)**2*(3*r - 1)**2/11
Let x = -476 + 1907/4. Solve 3/8*w**2 + x*w**4 - 9/8*w**3 + 0*w + 0 = 0 for w.
0, 1/2, 1
Let c(o) = 3 + 3*o**3 - o**2 - 5 + o - 3*o. Suppose 4*q = -0*q + 28. Let g(y) = -10*y**3 + 4*y**2 + 7*y + 7. Let m(d) = q*c(d) + 2*g(d). Factor m(x).
x**2*(x + 1)
Let g = 11/12 + -2/3. What is w in 0 - g*w**3 - 1/2*w**2 - 1/4*w = 0?
-1, 0
Let q(l) be the first derivative of -l**5/120 + l**4/12 - l**3/3 - 3*l**2/2 - 3. Let d(a) be the second derivative of q(a). Factor d(f).
-(f - 2)**2/2
Let g(f) be the third derivative of -f**8/112 + f**6/20 - f**4/8 - 9*f**2. Factor g(h).
-3*h*(h - 1)**2*(h + 1)**2
Suppose f - 3*f + 4*g = 0, 0 = 4*g - 16. Let r be -4 - (-4)/f*11. Factor 1/2*w**2 - r*w + 1/2*w**4 - 1 + 3/2*w**3.
(w - 1)*(w + 1)**2*(w + 2)/2
Let w(v) be the second derivative of v**4/4 - v**3/2 - 3*v**2 + 10*v. Factor w(u).
3*(u - 2)*(u + 1)
Let r(n) = 4*n - 9. Let h be r(4). Find t, given that 2 - 14*t - 3*t**3 + 4 + 24*t**2 - h*t - 6*t**3 = 0.
2/3, 1
Let -64*f**4 - 12*f**2 + 10*f**3 + 8*f - 4*f**2 + 62*f**4 = 0. Calculate f.
0, 1, 2
Let v(d) be the second derivative of 4*d**7/105 - d**6/75 - 2*d**5/25 + d**4/30 + 11*d. Find f, given that v(f) = 0.
-1, 0, 1/4, 1
Let g(i) be the first derivative of -i**7/14 + i**6/2 - 27*i**5/20 + 7*i**4/4 - i**3 + 6*i + 3. Let z(c) be the first derivative of g(c). Factor z(k).
-3*k*(k - 2)*(k - 1)**3
Factor 0*x + 3*x**2 - 4 - 2*x - x**3 + 4.
-x*(x - 2)*(x - 1)
Factor 0 - 4/9*s + 2/9*s**3 - 2/9*s**2.
2*s*(s - 2)*(s + 1)/9
Let b(i) be the third derivative of 1/28*i**8 + 0 - 3/40*i**6 + 1/20*i**5 - 3*i**2 + 0*i + 0*i**7 + 0*i**4 + 0*i**3. Factor b(m).
3*m**2*(m + 1)*(2*m - 1)**2
Let p(j) be the first derivative of j**6/15 - 2*j**4/3 - 5*j + 3. Let l(u) be the first derivative of p(u). Factor l(b).
2*b**2*(b - 2)*(b + 2)
Let t(b) be the third derivative of -b**5/12 + 5*b**4/24 + 5*b**3/3 - b**2 + 5. Factor t(w).
-5*(w - 2)*(w + 1)
What is i in 6/7 + 111/7*i**2 - 144/7*i**4 - 24/7*i**3 + 51/7*i = 0?
-2/3, -1/4, 1
Let z(l) be the third derivative of -1/630*l**7 + 0 + 0*l + 0*l**6 + 1/60*l**5 - 1/36*l**4 + 0*l**3 + 2*l**2. Factor z(f).
-f*(f - 1)**2*(f + 2)/3
Let r(y) = 35*y - 628. Let f be r(18). Factor -4/5*u**f + 0 + 3/5*u**4 + 0*u**3 + 0*u + 1/5*u**5.
u**2*(u - 1)*(u + 2)**2/5
Let a(o) = 3*o**5 + 81*o**4 + 414*o**3 - 1767*o**2 + 1926*o - 684. Let i(f) = f**2 + f + 1. Let g(n) = a(n) + 9*i(n). Find y, given that g(y) = 0.
-15, 1
Find o, given that -4/5*o + 2/5*o**2 + 0 = 0.
0, 2
Suppose -3*l + 5*t + 25 = 0, -2*t + 2 = -0. Factor -4 - 4*p**2 + p + 2 + l*p**2 - 5*p.
2*(p - 1)*(3*p + 1)
Let h(n) be the first derivative of 0*n + 0*n**2 - 1/5*n**3 + 3/20*n**4 - 5. Solve h(z) = 0.
0, 1
Let o(f) = 16*f**3 - 24*f**2 - 9*f - 7. Let r(y) = 8*y**3 - 12*y**2 - 5*y - 3. Let v(i) = -3*o(i) + 7*r(i). Factor v(p).
4*p*(p - 2)*(2*p + 1)
Let i(c) be the third derivative of -1/140*c**5 - 1/280*c**6 + 0 + 0*c + 0*c**3 + 0*c**4 + 2*c**2. Suppose i(d) = 0. What is d?
-1, 0
Let p be -2 + 1 - -3 - -1. Determine c so that 0*c + 2 + 2*c**p - 4*c + 6*c**3 - 6*c**2 + 0*c + 8*c**4 = 0.
-1, 1/2
Let j(t) be the first derivative of 1/26*t**4 + 0*t - 2 + 1/13*t**2 - 4/39*t**3. Factor j(m).
2*m*(m - 1)**2/13
Let y = 9495 + -47659/5. Let i = 37 + y. Factor -1/5*x + 0 - i*x**2.
-x*(x + 1)/5
Let c = -117 + 117. Factor 0*n - 8/9*n**5 + 0*n**2 - 2/9*n**3 + c - 10/9*n**4.
-2*n**3*(n + 1)*(4*n + 1)/9
Suppose 0 = j + 6 - 9. Let s(d) be the first derivative of 0*d + 0*d**2 + 3 - 1/12*d**j. Factor s(n).
-n**2/4
Let j = 46 - 33. Suppose -j*u = -10*u. Find i, given that -1/2*i**3 + u*i**2 + 0 + 0*i = 0.
0
Let u(l) be the second derivative of -1/6*l**4 + 1/10*l**6 + 1/2*l**3 - 1/2*l**2 + 0 + l - 1/10*l**5 - 1/42*l**7. Factor u(n).
-(n - 1)**4*(n + 1)
Suppose -11*v**3 + 6*v**2 + 12*v - 2*v**4 + 5*v**4 - v**3 - 9 = 0. Calculate v.
-1, 1, 3
Let i(p) be the first derivative of p**4/2 - 4*p**3 + 12*p**2 - 16*p - 5. What is w in i(w) = 0?
2
Let c(x) be the third derivative of -x**6/60 - x**5/30 + x**4/6 - 4*x**2 - 1. Find r such that c(r) = 0.
-2, 0, 1
Suppose 0 = 5*l - 5*q + 10, -4*l - 4*q = -9*q + 12. Suppose -l*x + 20 = 3*x. Let -3*u**2 - 5*u**4 + u + u - 3*u - 3*u**3 + x*u**4 = 0. What is u?
-1, 0
Let l(f) = f**3 + 6*f**2 + 4*f - 2. Let p be l(-5). Let c(h) = -h**3 + 2*h**2 + 4*h. Let g be c(p). Determine r so that 2/7*r + 0 + 4/7*r**2 + 2/7*r**g = 0.
-1, 0
Suppose -2*v = -3*g - 6, -g - 5*v = -4*g - 15. Let r(q) be the third derivative of -1/24*q**3 + g + 0*q + 0*q**4 + 1/240*q**5 + q**2. Solve r(n) = 0.
-1, 1
What is a in 4*a**4 - 4*a**2 - 2*a - 2*a**4 + 2*a**5 + 2*a**4 = 0?
-1, 0, 1
Let q(i) be the first derivative of 4*i**5/5 - 3*i**4 + 4*i**3 - 2*i**2 - 5. Find v such that q(v) = 0.
0, 1
Suppose -i + 2*m + 7 = -0*i, -5*i - 2*m + 23 = 0. Suppose -z + i - 2 = 0. Factor -1/2*k + 0 + 1/2*k**z + k**4 - k**2.
k*(k - 1)*(k + 1)*(2*k + 1)/2
Suppose 2*d - 3*v - 30 = 0, -2*d + 26 = v - 20. Suppose -3*a = -4*j + d, -3*j - 3*a - 3 = -j. Factor u**4 - 1/2*u**5 + 0 - u**2 + 0*u**j + 1/2*u.
-u*(u - 1)**3*(u + 1)/2
Let w(x) = 5*x**2 - x + 4. Let g(z) = 4*z**2 - z + 3. Let u(o) = 4*g(o) - 3*w(o). Factor u(q).
q*(q - 1)
Let n(a) = a**3 + 7*a**2 + 4. Let p be n(-7). Suppose -4*w + 12 = -p. Determine i, given that -i**4 + w*i**4 + 2*i**3 - 5*i**3 = 0.
0, 1
Let v(y) be the first derivative of -4*y**3/15 - 4*y**2 - 20*y + 8. Find r such that v(r) = 0.
-5
Suppose -3*x = 1 - 7. Suppose -m = x*m - 9. Solve a**m + 0 + 1/2*a + 3/2*a**2 = 0 for a.
-1, -1/2, 0
Let h(q) be the first derivative of q**8/4200 + q**7/525 + q**6/180 + q**5/150 - q**3 - 3. Let b(z) be the third derivative of h(z). Factor b(k).
2*k*(k + 1)**2*(k + 2)/5
Let m(t) = -t + 8. Suppose 4*w + 7 = 5*w - r, 0 = -2*w - 3*r - 1. Let x be m(w). Factor -4 + 3*k**x + 3 - 4*k**4 + 2*k**2.
-(k - 1)**2*(k + 1)**2
Factor 8*d - 60*d**3 - 30*d**2 - 62*d - 21*d + 57*d**3.
-3*d*(d + 5)**2
Let b(j) be the first derivative of -j**4/4 - 2*j**3/3 + j**2/2 + 2*j + 7. Find o, given that b(o) = 0.
-2, -1, 1
Let i(f) be the second derivative of f**6/2 + f**5/4 - 25*f**4/12 - 5*f**3/6 + 5*f**2 + 9*f. Find r such that i(r) = 0.
-1, 2/3, 1
Solve 2/5*r**2 - 8/5 - 1/5*r**3 + 4/5*r = 0.
-2, 2
Let i(f) be the second derivative of -2*f**6/15 + 2*f**5/5 + f**4/3 - 4*f**3/3 - 3*f. Factor i(p).
-4*p*(p - 2)*(p - 1)*(p + 1)
Factor -159*x**2 + 8 - 160*x**2 + 309*x**2 + 3*x**3 + 4*x.
(x - 2)**2*(3*x + 2)
Let k(l) be the first derivative of -2*l**5/65 + 2*l**4/13 + 10*l**3/39 + 8. Factor k(c).
-2*c**2*(c - 5)*(c + 1)/13
Let c(d) be the first derivative of -d**5/90 + d**4/54 + d**3/27 - d**2/9 - 2*d - 3. Let g(y) be the first derivative of c(y). Determine x so that g(x) = 0.
-1, 1
Let y = -6 + 7. Let b = 1 + y. Factor -2 - 2 + r**b + 4 - 2*r.
r*(r - 2)
Let x(r) be the first derivative of 3/8*r**4 + 0*r**3 + 3 + 0*r**2 + 0*r. Factor x(n).
3*n**3/2
Let b = -15 - -18. Let o(v) be the second derivative of 0 + 2/15*v**5 + 2*v - 7/18*v**4 + 2/9*v**b + 1/3*v**2. Suppose o(q) = 0. What is q?
-1/4, 1
Let i(a) be the third derivative of 2*a**7/105 + 2*a**6/5 + 18*a**5/5 + 18*a**4 + 54*a**3 - 3*a**2. Determine o so that i(o) = 0.
-3
Let h(g) be the second derivative of -2*g**6/15 - 9*g**5/5 - g. Factor h(m).
-4*m**3*(m + 9)
Let k(j) be the second derivative of 2/9*j**4 - 4*j - 1/30*j**5 + 0*j**2 - 4/9*j**3 + 0. Suppose k(i) = 0. Calculate i.
0, 2
Let m = -6417146/7 - -918408. Let u = 1676 - m. Solve 4/7*j - 8/7*j**4 - 10/7*j**2 - u*j**3 + 0 = 0.
-2, -1, 0, 1/4
Factor 0*k + 