Let l(a) be the second derivative of a**4/66 - 2*a**3/33 + a**2/11 + 4*a. Factor l(v).
2*(v - 1)**2/11
What is y in 0 + 0*y + 4/5*y**2 + 8/5*y**3 + 4/5*y**4 = 0?
-1, 0
Let n be 2/(52/(-20) + 3). Suppose 2*k + 11 = n*q, -3*k + 0*q = q - 9. Let 0*u + 2/7*u**3 + 0*u**k + 4/7*u**4 + 0 + 2/7*u**5 = 0. Calculate u.
-1, 0
Find x, given that 4*x**3 + 7*x**2 + 0*x**3 - 11*x**2 = 0.
0, 1
Let z = -23 + 25. Suppose -z*q = -13 + 9. Suppose -q*o**5 - 2/5*o**2 - 18/5*o**3 + 4/5*o + 26/5*o**4 + 0 = 0. Calculate o.
-2/5, 0, 1
Let x be 23/3 + 1/3. Suppose x*n = 7*n. Suppose n + 4/9*w - 14/9*w**3 - 10/9*w**2 = 0. What is w?
-1, 0, 2/7
Let y(a) be the first derivative of 4*a - 20*a**2 + 7 + 100/3*a**3. Suppose y(w) = 0. Calculate w.
1/5
Suppose 12*y - 17*y = 0. Factor o**2 + 0 - o**4 + y*o**3 + 1/2*o - 1/2*o**5.
-o*(o - 1)*(o + 1)**3/2
Let p(i) be the second derivative of -i**4/54 + 4*i**3/27 - i**2/3 - 22*i. Factor p(k).
-2*(k - 3)*(k - 1)/9
Let i = -1/3128 - -155619/3128. Let j = -923/20 + i. Factor -12/5*y + 3/5 - 12/5*y**3 + 3/5*y**4 + j*y**2.
3*(y - 1)**4/5
Let o(z) = -3*z**4 - 3*z**3 - 2. Let r(d) = -5*d**4 - 6*d**3 - d**2 - 5. Suppose -4*w - 5 = 3. Let t(v) = w*r(v) + 5*o(v). Determine h so that t(h) = 0.
-1, 0, 2/5
Let k be (-3)/(39/2) - (-1722)/546. Solve 0*w + 8/5*w**k - 8/5*w**2 + 0 - 2/5*w**4 = 0 for w.
0, 2
Let b(q) be the first derivative of -2/9*q**4 + 1/6*q**2 + 1/9*q**3 + 2 + q. Let h(g) be the first derivative of b(g). Determine i, given that h(i) = 0.
-1/4, 1/2
Let l be ((-18)/120)/(2/(-8)). Factor 3/5 + l*b**2 + 6/5*b.
3*(b + 1)**2/5
Suppose -24 = -2*f - 4*f. What is w in -3*w**2 + f - 4*w + w**2 + 3 - 1 = 0?
-3, 1
Let v(t) be the second derivative of 0*t**3 + t + 0 + 0*t**2 - 1/36*t**4 + 1/60*t**5. Factor v(q).
q**2*(q - 1)/3
Let s = 62 + -103. Let r = 44 + s. Suppose 4/5*a**2 + 0 - 2/5*a**r - 2/5*a = 0. Calculate a.
0, 1
Let g be -1 - (-14)/12*1. Let n(v) be the first derivative of 0*v - 1 + g*v**3 - 1/8*v**4 + 0*v**2. Factor n(q).
-q**2*(q - 1)/2
Let m(v) be the third derivative of 3*v**7/665 - 4*v**6/285 + v**5/114 + v**4/114 - 2*v**2. Factor m(y).
2*y*(y - 1)**2*(9*y + 2)/19
Let h(f) = -f**2 + 0*f - f**3 + 3*f**3 - 7*f - f. Let w(c) = -22*c + 7*c + 2*c**3 + c**3 - 3*c**2. Let y(l) = 9*h(l) - 5*w(l). Find p such that y(p) = 0.
-1, 0
Let m(d) = 10*d**3 + 4*d**2 + 2*d - 4. Let v(o) = 11*o**3 + 4*o**2 + 3*o - 5. Let y(t) = 5*m(t) - 4*v(t). Let y(s) = 0. Calculate s.
-1, 0, 1/3
Let u(b) = b**2 - 5*b - 9. Let w be u(8). Factor -11*j + 3*j + w*j**2 - 3*j**2 + 0*j**4 + 48*j**3 + 28*j**4.
4*j*(j + 1)**2*(7*j - 2)
Let o be 5 + 0 + 10 + 40/(-4). Solve 2/5*i**4 - 2/5*i**o + 0 - 2/5*i**2 + 0*i + 2/5*i**3 = 0 for i.
-1, 0, 1
Let n(t) be the second derivative of -t**5/180 - t**4/72 + t**3/9 - 3*t**2/2 + 4*t. Let k(y) be the first derivative of n(y). Determine r so that k(r) = 0.
-2, 1
Let k(t) = -2*t**2 - t - 4. Let p(w) = 1 + 0*w**2 + w**2 + 0. Suppose 5*y - 5*h = 15, -5*y + 4*y = 4*h + 7. Let g(j) = y*k(j) + 4*p(j). Factor g(c).
c*(2*c - 1)
Let z = 4 + -2. Let p(c) be the third derivative of z*c**2 + 1/60*c**5 + 0*c + 2/3*c**3 + 0 + 1/6*c**4. Solve p(h) = 0.
-2
Let b(h) be the third derivative of 1/6*h**4 + 1/210*h**7 + 4*h**2 - 1/20*h**5 + 2/3*h**3 - 1/60*h**6 + 0*h + 0. Factor b(g).
(g - 2)**2*(g + 1)**2
Let h(c) = -5*c**3 + 11*c**2 - 10*c + 4. Let w(j) = -j**2 + 1. Let b(l) = -h(l) + 4*w(l). Factor b(q).
5*q*(q - 2)*(q - 1)
Let x(o) be the first derivative of -o**8/9240 + o**7/4620 + 2*o**3/3 - 3. Let p(y) be the third derivative of x(y). Solve p(k) = 0.
0, 1
Let j(b) be the third derivative of 0*b - 2*b**2 + 1/72*b**4 + 0*b**3 + 0 - 1/180*b**5. Factor j(q).
-q*(q - 1)/3
Let i(j) = -j - 2. Let l be i(-2). Let g(s) be the third derivative of 0*s**3 + 0*s + 2*s**2 + 0 + 1/480*s**6 + 0*s**5 + l*s**4 - 1/840*s**7. Factor g(z).
-z**3*(z - 1)/4
Let t(j) be the third derivative of -6/5*j**5 + 8*j**2 - 1/2*j**3 + 0*j + 2/5*j**6 + 0 + 9/8*j**4. Factor t(z).
3*(z - 1)*(4*z - 1)**2
Let -1/4*d**2 + 1/2*d - 1/4*d**3 + 0 = 0. Calculate d.
-2, 0, 1
Suppose -5*z = -3*z + 5*l - 22, l - 14 = -2*z. Let s be 13/z - (-2)/(-12). Determine x, given that 1/2*x**3 + 0*x**s + 0 - 1/4*x + 0*x**4 - 1/4*x**5 = 0.
-1, 0, 1
Let o(a) be the second derivative of a**6/1260 - a**4/84 - a**3/6 - 3*a. Let h(k) be the second derivative of o(k). Solve h(b) = 0.
-1, 1
Factor 0 - d + 7/4*d**2 - 3/4*d**3.
-d*(d - 1)*(3*d - 4)/4
Let h(s) be the third derivative of -s**8/1680 + s**7/1050 + s**6/300 - s**5/150 - s**4/120 + s**3/30 - 6*s**2. Suppose h(x) = 0. Calculate x.
-1, 1
Factor 6*j**2 + 3*j + 2*j**3 + 4*j - 3*j.
2*j*(j + 1)*(j + 2)
Let g = 366 - 4020/11. Determine y so that 2/11*y**3 + g*y**2 + 0 + 4/11*y = 0.
-2, -1, 0
Let b(f) be the first derivative of 4*f**5/5 + 2*f**4 + 4*f**3/3 + 25. Factor b(v).
4*v**2*(v + 1)**2
Let g(v) = -v**3 + 4*v**2 - v. Let m be g(3). Let o = 8 - m. Factor -4*w + 4*w - 2*w + o*w**2.
2*w*(w - 1)
Let a be (8/3 - -1) + -3. Suppose -1/3*b**3 + 0*b + 0 + a*b**2 = 0. Calculate b.
0, 2
Let i be -6*(-24)/(-18)*2/(-6). Factor -i*y**5 + 0 - 10*y**3 + 14/3*y**2 + 26/3*y**4 - 2/3*y.
-2*y*(y - 1)**3*(4*y - 1)/3
Let c(n) = -n**2 + 9*n - 1. Let k(x) = 2*x. Let r(o) = 2*c(o) - 11*k(o). Find d, given that r(d) = 0.
-1
Let r(m) be the third derivative of 0 + 0*m + 0*m**4 + 5*m**2 - 1/210*m**7 + 0*m**6 + 1/30*m**5 - 1/6*m**3. Suppose r(v) = 0. What is v?
-1, 1
Factor 5*p**4 - 337*p**2 + 6*p**3 - 5*p + 332*p**2 - p**3.
5*p*(p - 1)*(p + 1)**2
Let w(i) be the second derivative of -i**6/15 - i**5/5 + 7*i**4/6 - 4*i**3/3 - 16*i. Determine j, given that w(j) = 0.
-4, 0, 1
Suppose -5*j = 2*x + 10, -4*j + j = 5*x + 6. Let f be j/(-5) + (-4)/(-15). Factor 7/3*d - 7/3*d**3 + 2/3 - f*d**2.
-(d - 1)*(d + 1)*(7*d + 2)/3
Let k(q) be the third derivative of -q**5/30 - 5*q**4/12 + 17*q**2. Solve k(v) = 0 for v.
-5, 0
Let p(n) be the third derivative of n**6/24 + n**5/3 - 55*n**4/24 + 5*n**3 + 17*n**2. Determine l, given that p(l) = 0.
-6, 1
Suppose 2*m + h - 6 = 0, 0*m - 5*m + 30 = -5*h. Solve 1/2*a**2 + 1/2*a**m - a**3 + 0*a + 0 = 0.
0, 1
Let f be 48/(-384) + (-74)/(-80). Solve -4/5*l - 8/5*l**2 + 0 + 0*l**3 + 8/5*l**4 + f*l**5 = 0.
-1, 0, 1
Factor 0 - 4/9*v**2 + 22/9*v**4 - 2*v**3 + 0*v.
2*v**2*(v - 1)*(11*v + 2)/9
Let u(p) = -p**2 + 19*p + 2. Let l be u(19). Let 4/5*k**4 + 0*k**3 + 0 - 4/5*k**l + 2/5*k - 2/5*k**5 = 0. What is k?
-1, 0, 1
Let j(w) be the second derivative of -16*w**2 + 8/3*w**3 + 0 - 1/6*w**4 - w. Factor j(d).
-2*(d - 4)**2
Factor -16/3*u - 32/3 + 20/3*u**3 + 4/3*u**4 + 8*u**2.
4*(u - 1)*(u + 2)**3/3
Suppose 11*m = 8*m + i + 3, -3*m + 9 = -3*i. Solve 0*t + 8/5*t**3 - 2/5*t**4 + 2/5*t**2 + m - 8/5*t**5 = 0 for t.
-1, -1/4, 0, 1
Let h(v) = -v**3 - 4*v**2 - v. Let k be h(-4). Suppose 3*y + 3*q + 7 = 8*y, 0 = 2*y + k*q - 8. Factor -4/7*u**4 + 4/7*u**y + 2/7*u + 0*u**3 + 0 - 2/7*u**5.
-2*u*(u - 1)*(u + 1)**3/7
Suppose 0 = -r + u + 5, 2*u = r + 4*r - 16. Determine v so that r - 4*v**2 + 0*v**4 - v**4 + 3*v**4 = 0.
-1, 1
Let o(m) be the second derivative of 0*m**2 + m - 1/3*m**3 + 1/10*m**5 - 1/3*m**4 + 0 + 1/6*m**6. Let r(x) = -x**2. Let v(p) = -o(p) - r(p). Factor v(u).
-u*(u - 1)*(u + 1)*(5*u + 2)
Let s be 6/(-4) - 102/(-68). Solve -2/3*z**5 + 4/3*z**4 + s*z**2 + 0 + 0*z - 2/3*z**3 = 0 for z.
0, 1
Let d(n) be the third derivative of -2*n**7/735 - n**6/105 + n**5/105 + n**4/21 + 5*n**2. Factor d(i).
-4*i*(i - 1)*(i + 1)*(i + 2)/7
Factor -9*v**2 - 71*v + 149*v + 3*v**3 - 72*v.
3*v*(v - 2)*(v - 1)
Let c = -2 - -4. Factor -1 - c*h - h**2 - 3 - 2*h + 0.
-(h + 2)**2
Let x(h) be the second derivative of 8*h - 1/12*h**4 + 0 - 1/20*h**5 - 3/2*h**2 + 5/6*h**3. Factor x(c).
-(c - 1)**2*(c + 3)
Let u(w) be the first derivative of -48/7*w - 1/7*w**3 - 9 - 12/7*w**2. Find o such that u(o) = 0.
-4
Let l(d) = -d**2 - 16*d - 26. Let r be l(-14). Let 0 + 0*s + 0*s**3 - 4/3*s**5 + 2*s**4 - 2/3*s**r = 0. What is s?
-1/2, 0, 1
Factor -f**4 + 3*f**3 - 3*f - 1 - 1/4*f**2.
-(f - 2)**2*(2*f + 1)**2/4
Let i(a) be the second derivative of a**6/180 - a**5/60 + a**4/72 + 2*a. Factor i(l).
l**2*(l - 1)**2/6
Let u be (-54)/(-12) + 3/2. Let b = u - 6. Factor 4/7*i + 2/7*i**2 + b.
2*i*(i + 2)/7
Let v(f) be the second derivative of 0*f**2 - 7*f + 0 + 0*f**5 + 1/12*f**4 + 0*f**3 - 1/30*f**6. Let v(r) = 0.