3*b**2 + 11. Factor l(d).
3*d*(d + 2)
Let k = 2021/9 + -1122/5. Let y(f) be the second derivative of 0*f**2 + 0 - 11/18*f**4 + 8/15*f**5 + 2/9*f**3 - 2*f - k*f**6. Factor y(v).
-2*v*(v - 1)**2*(7*v - 2)/3
Let g(d) = -8*d**2 - 17*d + 28. Let v(i) = 15*i**2 + 35*i - 55. Let h(s) = -5*g(s) - 3*v(s). Determine m, given that h(m) = 0.
-5, 1
Let o(m) = -m + 7. Let z be o(4). Solve 18*p**2 - z*p + 8 - 5*p - 16*p**2 = 0.
2
Let h(v) = 81*v - 4. Let o be h(-5). Let b = o - -2879/7. Solve 6/7*y**3 - b*y**2 + 2*y - 4/7 = 0 for y.
2/3, 1
Let q be (-3)/(-12) + (-77)/420. Let p(d) be the second derivative of 0*d**2 + 1/50*d**5 + q*d**3 + 1/15*d**4 + 2*d + 0. Factor p(k).
2*k*(k + 1)**2/5
Let b(g) be the third derivative of g**6/24 - 11*g**5/180 + g**4/36 + 2*g**2. Suppose b(h) = 0. Calculate h.
0, 1/3, 2/5
Let y(z) be the second derivative of 3*z**5/80 + z**4/8 + 5*z. Solve y(i) = 0 for i.
-2, 0
Suppose -2*n + 0*u = -3*u - 4, u = 0. Factor 0*f**n + 1/3*f**3 + 1/3*f**4 + 0 + 0*f.
f**3*(f + 1)/3
Factor 27*d**2 - 51*d**2 + 28*d**2 - 24*d.
4*d*(d - 6)
Suppose -2*a = -7*a - h, -4*h = 0. Let n(j) be the second derivative of -1/15*j**5 + 1/30*j**6 - 1/36*j**4 + 1/9*j**3 + 0*j**2 + j + a. Factor n(i).
i*(i - 1)**2*(3*i + 2)/3
Suppose -20*m**3 - 16*m**2 + 44*m - 234 + 210 + 64*m**2 = 0. What is m?
-1, 2/5, 3
Let b(g) be the third derivative of -g**7/1785 + g**5/510 - 5*g**2. Factor b(p).
-2*p**2*(p - 1)*(p + 1)/17
Suppose 58 = 2*n - 3*a, n + 3*n + a - 102 = 0. Let k = 80/3 - n. Factor -2*s - 2/3*s**3 + k + 2*s**2.
-2*(s - 1)**3/3
Let o(u) be the second derivative of u**7/280 + u**6/40 + 3*u**5/40 + u**4/8 + u**3/6 - 3*u. Let t(a) be the second derivative of o(a). Factor t(s).
3*(s + 1)**3
Let l(z) = -z**3 + 3*z**2 + 12*z - 7. Let v be l(5). Suppose -5*q - 4*x - 6 = -0, -x = 4*q - 4. Factor h**2 + 2*h**4 - 7*h**2 + 2*h**q - 2*h**v + 0*h**3.
2*h**2*(h - 2)*(h + 1)
Let c = -187 - -3743/20. Let l(z) be the second derivative of 2*z + c*z**5 + 1/12*z**4 + 1/42*z**7 + 0*z**2 + 0*z**3 + 1/10*z**6 + 0. Factor l(q).
q**2*(q + 1)**3
Let f(g) be the first derivative of 4*g**5/5 + g**4 - 4*g**3/3 - 2*g**2 - 25. What is r in f(r) = 0?
-1, 0, 1
Let s = 1481/1065 + 2/213. Determine v so that -7/5*v + 23/5*v**3 + 1/5 - 8/5*v**4 + s*v**2 - 16/5*v**5 = 0.
-1, 1/4, 1
Factor 0*h**2 - 3/4*h**4 + 0*h + 0 - 1/4*h**3.
-h**3*(3*h + 1)/4
Let r(b) be the second derivative of -b**7/2520 - b**6/360 + b**4/18 - b**3/3 - 2*b. Let x(z) be the second derivative of r(z). Factor x(u).
-(u - 1)*(u + 2)**2/3
Factor -n**3 + 4*n**2 - 5*n**2 - 3*n**3 - 15*n**2 - 16*n.
-4*n*(n + 2)**2
Factor -2/21*q**4 - 128/21 + 8/21*q**3 + 8/7*q**2 - 64/21*q.
-2*(q - 4)**2*(q + 2)**2/21
Let q = 1 - -1. Factor 5*l**3 - l**q + 2*l**3 - 9*l + 4*l**2 - l**3.
3*l*(l - 1)*(2*l + 3)
Let q(f) be the second derivative of -f**7/1680 + f**6/360 - f**5/240 - 2*f**3/3 + 3*f. Let d(h) be the second derivative of q(h). Factor d(s).
-s*(s - 1)**2/2
Let h(l) be the third derivative of 1/20*l**4 + 0*l - 1/840*l**8 + 0 - 1/15*l**3 - 1/150*l**6 - 1/75*l**5 + 4*l**2 + 1/175*l**7. Factor h(r).
-2*(r - 1)**4*(r + 1)/5
Let c be ((-21)/6 + 0)*(-96)/168. Let -1/4*w - 1/4*w**c + 0 = 0. What is w?
-1, 0
Suppose 12 = 5*z + 3*t, -5*z - t = -2*t + 4. Let a = -20/9 - -136/45. Factor 0 - a*p**4 + 1/5*p**2 + 3/5*p**3 + z*p.
-p**2*(p - 1)*(4*p + 1)/5
Suppose 8*t - 10 = 3*t. Let o(b) be the first derivative of 1/5*b**5 + 2 + 1/4*b**4 - 1/3*b**3 + 0*b - 1/2*b**t. Factor o(a).
a*(a - 1)*(a + 1)**2
Let v be -1 - -1 - (0 - 8). Suppose -v*d = 3*l - 3*d + 10, 0 = l - 2*d - 4. Factor -4/7*t**2 + l + 0*t - 6/7*t**3 - 2/7*t**4.
-2*t**2*(t + 1)*(t + 2)/7
Let z(a) be the first derivative of -a**6/1620 + a**5/540 - a**3 + 3. Let s(r) be the third derivative of z(r). Suppose s(m) = 0. Calculate m.
0, 1
Let -10*j**5 + 24*j**5 + 10*j**5 - 10*j**2 + 2*j**4 - 8*j - 66*j**3 + 58*j**2 = 0. What is j?
-2, 0, 1/4, 2/3, 1
Let x(i) be the second derivative of 1/14*i**4 - 1/210*i**5 + 2*i + 0 - 3/7*i**3 - 2*i**2. Let j(o) be the first derivative of x(o). Let j(g) = 0. What is g?
3
Let k(i) be the third derivative of -i**9/15120 + i**8/5040 + i**7/630 + i**5/15 - 2*i**2. Let y(x) be the third derivative of k(x). Let y(d) = 0. Calculate d.
-1, 0, 2
Factor 0 + 0*j + 3*j**4 - 3/2*j**3 - 3/2*j**2.
3*j**2*(j - 1)*(2*j + 1)/2
Let w(g) = -2*g**2 - 36*g. Let m be w(-18). Suppose -3*l**4 + m + 0*l + 7/3*l**5 + 2/3*l**3 + 0*l**2 = 0. What is l?
0, 2/7, 1
Let k = -214 - -216. Factor -2/3 + 1/3*q**4 + 1/3*q**3 - 5/3*q - q**k.
(q - 2)*(q + 1)**3/3
Let q be -1 - -1*((-3)/(-2))/1. Factor 1/2 + q*j**2 - j.
(j - 1)**2/2
Suppose -2*n + 0*n = 5*l - 344, 2*l = -3*n + 131. Let -3*v - 8 - 5*v + 0*v + l*v**2 = 0. What is v?
-2/7, 2/5
Solve -2*m**3 - 18*m + 9*m**2 + 27/2 + 1/6*m**4 = 0.
3
Let r be -4*3/(3/10). Let y be (16/r)/(4/(-5)). Suppose -7/4*v**5 + 0 + 5/4*v**4 - y*v + 9/4*v**3 - 5/4*v**2 = 0. What is v?
-1, -2/7, 0, 1
Let f(d) be the first derivative of -8*d**6 + 28*d**5/5 - d**4 + 2. Factor f(o).
-4*o**3*(3*o - 1)*(4*o - 1)
Let c(s) be the first derivative of -2*s**5/15 - s**4/3 - 2*s**3/9 + 2. Solve c(m) = 0 for m.
-1, 0
Factor 2*l + 98 + 89 - 4*l**2 + 4*l - 183.
-2*(l - 2)*(2*l + 1)
Let x = -283 + 593/2. Factor -x - 9*r - 3/2*r**2.
-3*(r + 3)**2/2
Let z = -186 - -560/3. What is n in -2/9*n**3 + z*n**2 + 0 - 4/9*n = 0?
0, 1, 2
Let d = -13 + 20. Let v(a) be the second derivative of 0 - 1/20*a**5 + 0*a**2 + 1/42*a**d + 0*a**4 + 0*a**6 + a + 0*a**3. Factor v(j).
j**3*(j - 1)*(j + 1)
Let n = -36 - -110/3. Determine u so that 0 - n*u + 2/3*u**2 = 0.
0, 1
Suppose 7*a - 10 = 2*a. Find c such that 4*c**4 + 8*c**3 + c**4 + 4*c**a - 3*c**4 + 4*c**2 = 0.
-2, 0
Let i(t) = -4*t**2 + 5*t - 3. Let v(w) = -3*w**2 + 5*w - 4. Let u(h) = 2*i(h) - 3*v(h). Factor u(f).
(f - 3)*(f - 2)
Let u(i) be the second derivative of 8*i**6/15 + 13*i**5/5 + i**4 - 32*i**3/3 - 8*i**2 - 18*i. Factor u(b).
4*(b - 1)*(b + 2)**2*(4*b + 1)
Suppose -4*v - v**4 + 4*v**4 + 34*v**3 + 0*v**2 - 30*v**5 - v**4 - 2*v**2 = 0. What is v?
-1, -1/3, 0, 2/5, 1
Let p(v) = -v**2 - v - 3. Let q(h) be the third derivative of h**5/15 + h**4/6 + 13*h**3/6 - h**2. Let w(j) = 26*p(j) + 6*q(j). Factor w(i).
-2*i*(i + 1)
Let j(n) be the first derivative of -n**4/4 + 7*n**3/3 + 9*n**2/2 - 8*n - 7. Let g be j(8). Factor 3/2*h**5 + 0*h**4 + 0*h**2 + g + 3/2*h - 3*h**3.
3*h*(h - 1)**2*(h + 1)**2/2
Let m(s) be the second derivative of -s**4/3 - s**3/3 + s**2 + 8*s. Suppose m(v) = 0. Calculate v.
-1, 1/2
Factor -12*b + 2*b**2 - 8*b**2 + 24 - 234*b**3 + 237*b**3.
3*(b - 2)**2*(b + 2)
Suppose 5*x - 3*y = 39, -5*y - 10 - 35 = -5*x. Solve -2*b - 2 + x*b - 2*b**2 + 16*b**2 + 8*b**3 = 0 for b.
-1, 1/4
Let q be (28/56)/(2/12). Determine v so that 0 - 1/5*v**5 + 1/5*v - 2/5*v**2 + 2/5*v**4 + 0*v**q = 0.
-1, 0, 1
Determine m so that 4/7*m + 8/7*m**3 + 0 - 10/7*m**2 - 2/7*m**4 = 0.
0, 1, 2
Suppose 9 = 4*z - z. Let d(c) be the first derivative of 2*c + 2*c**2 + 2/3*c**z - 1. Factor d(b).
2*(b + 1)**2
Let l(c) = -5*c**2 - 2*c + 4. Let i(u) = -6*u**2 - 2*u + 5. Suppose 17 = 3*t + 2. Let g(n) = t*l(n) - 4*i(n). Find r such that g(r) = 0.
-2, 0
Let n(s) be the second derivative of s**6/270 - s**5/45 - s**4/6 + 3*s**3/2 + 4*s. Let u(p) be the second derivative of n(p). Determine r, given that u(r) = 0.
-1, 3
Let p = -72 + 325. Factor 1 - p*l**3 - 96*l - 330*l**2 - 37*l**3 - 9 + 48*l**3.
-2*(l + 1)*(11*l + 2)**2
Let c be 0 - (1 - 2)/24. Let q(n) be the third derivative of n**2 - c*n**4 + 0 - 1/60*n**5 + 0*n + 0*n**3. Factor q(t).
-t*(t + 1)
Solve 0 - 2/15*f**3 + 4/15*f - 2/15*f**2 = 0.
-2, 0, 1
Let g be 1*(-2 + 10/4). Let v(t) be the first derivative of -1/3*t**3 + 2*t - g*t**2 + 1. Factor v(f).
-(f - 1)*(f + 2)
Let q be 5/(-7) - (-6)/(-21). Let v be (-9*1)/3*q. Factor -3*a - a**2 + 0 - a**v + 1 + 4*a**2.
-(a - 1)**3
Let a(q) be the third derivative of q**8/168 - q**7/210 - q**6/20 + 7*q**5/60 - q**4/12 - 6*q**2. Find y, given that a(y) = 0.
-2, 0, 1/2, 1
Let w(y) be the third derivative of -y**8/1680 - y**7/1050 + y**6/100 + y**5/75 - y**4/15 - 30*y**2. Determine p so that w(p) = 0.
-2, 0, 1, 2
Let a(c) = c**2 - c + 1. Let n(j) = 4*j**2 + 18*j + 5. Let w(m) = 3*a(m) + 3*n(m). Let w(t) = 0. Calculate t.
-3, -2/5
Let j(n) be the first derivative of -2/11*n**2 - 4 + 2/11*n + 2/