 + 16*f - 71. Let i(k) = 21*c(k) - 3*o(k). Factor i(u).
3*(u - 8)**2
Let w(m) be the first derivative of m**4/36 - m**3/18 + m + 3. Let k(o) be the first derivative of w(o). Solve k(s) = 0 for s.
0, 1
Let j(l) = -7*l**3 - 19*l**2 - 20*l - 16. Let a(g) = -8*g**3 - 20*g**2 - 19*g - 17. Let s(z) = -4*a(z) + 5*j(z). Suppose s(r) = 0. What is r?
-2, -1
Let y(r) be the third derivative of r**8/2016 - r**7/420 + r**6/360 - 8*r**2. Factor y(m).
m**3*(m - 2)*(m - 1)/6
Let z = 1 + 1. Let l(g) be the first derivative of -1/4*g**z + 1/12*g**3 + 1/4*g**4 + 0*g + 2 - 3/20*g**5. What is v in l(v) = 0?
-2/3, 0, 1
Suppose -3*s = 2*y - 6*s - 10, 25 = 5*y + 5*s. Factor -22*h**4 + 20*h**4 + 2*h**2 - 2*h**3 - h**5 + 3*h**y.
2*h**2*(h - 1)**2*(h + 1)
Let c = -5 - -35/6. Let v(a) be the second derivative of -1/4*a**4 + c*a**3 + 0 + 1/30*a**6 + 2*a - a**2 - 1/20*a**5. Factor v(s).
(s - 1)**3*(s + 2)
Let n(w) be the second derivative of -w**6/30 - w**5/4 - w**4/4 + 3*w**3/2 + 4*w. Let n(z) = 0. What is z?
-3, 0, 1
Let k be (-1)/(-2)*0/5. Let v(q) be the second derivative of 0*q**3 + 1/189*q**7 - q + 0 - 1/135*q**6 - 1/90*q**5 + k*q**2 + 1/54*q**4. Factor v(n).
2*n**2*(n - 1)**2*(n + 1)/9
Let w(t) = t**4 - 11*t**3 - 17*t**2 + 16*t + 11. Let f(l) = 2*l**4 - 28*l**3 - 42*l**2 + 40*l + 28. Let m(d) = -5*f(d) + 12*w(d). Factor m(z).
2*(z - 1)*(z + 1)*(z + 2)**2
Let f(x) be the third derivative of -x**9/60480 + x**8/10080 + x**7/5040 - x**6/360 - x**5/12 - 8*x**2. Let o(a) be the third derivative of f(a). Factor o(k).
-(k - 2)*(k - 1)*(k + 1)
Let h(l) be the third derivative of l**7/350 - l**6/200 - 9*l**5/200 - l**4/20 - l**3/2 + 2*l**2. Let g(f) be the first derivative of h(f). Factor g(z).
3*(z - 2)*(z + 1)*(4*z + 1)/5
Factor 214*h**3 - 3 + 10*h - h**4 - 5*h**2 - 7*h**2 - 208*h**3.
-(h - 3)*(h - 1)**3
Factor 17*u**4 - 2*u**4 - 7*u**3 - 2*u**3 - u**3 - 5*u**5.
-5*u**3*(u - 2)*(u - 1)
Let v(t) be the first derivative of -t**6/2 - 3*t**5/5 + 6*t**4 + 12*t**3 - 5. Factor v(x).
-3*x**2*(x - 3)*(x + 2)**2
Factor -9*j**2 - 10*j**2 - 3*j**3 - 21*j - 4*j**2 - 9 + 8*j**2.
-3*(j + 1)**2*(j + 3)
Let z = 85/273 + 2/91. Let p(d) be the first derivative of z*d - 2 - 1/9*d**3 - 1/12*d**4 + 1/6*d**2. Factor p(k).
-(k - 1)*(k + 1)**2/3
Suppose -2 + 6 = -3*f - 2*m, 2*f - 19 = 3*m. Find z such that 1/4 + 3*z**3 + 13/4*z**f + z**4 + 3/2*z = 0.
-1, -1/2
Let a(k) be the second derivative of 0*k**4 + 1/8*k**6 + 0 + 0*k**2 - 19/80*k**5 + 1/6*k**3 - 4*k. Solve a(g) = 0.
-2/5, 0, 2/3, 1
Let v(r) be the third derivative of -r**8/6720 - r**7/2520 + r**6/720 + r**5/120 - r**4/24 + r**2. Let i(p) be the second derivative of v(p). Factor i(o).
-(o - 1)*(o + 1)**2
Let r(a) be the second derivative of 5*a**4/12 - 5*a**3/2 - 10*a**2 + 12*a. Solve r(y) = 0.
-1, 4
Let t(q) = -9*q**2 - 90*q - 21. Let w(h) = -h**2 - 9*h - 2. Let i(l) = -2*t(l) + 21*w(l). Factor i(f).
-3*f*(f + 3)
Let l(n) be the second derivative of -n**9/9072 - n**8/5040 + n**7/2520 + n**6/1080 - 7*n**3/6 - 3*n. Let a(f) be the second derivative of l(f). Factor a(u).
-u**2*(u - 1)*(u + 1)**2/3
Let s(l) = 4*l**5 + 19*l**4 + 52*l**3 + 48*l**2 + 11*l. Let m(y) = -2*y**5 - 10*y**4 - 26*y**3 - 24*y**2 - 6*y. Let g(z) = -5*m(z) - 2*s(z). Factor g(x).
2*x*(x + 1)**2*(x + 2)**2
Let c(v) be the third derivative of v**5/120 + v**4/48 - 6*v**2. Factor c(n).
n*(n + 1)/2
Let l(z) be the first derivative of z**8/504 + 17*z**7/1260 + 4*z**6/135 + z**5/45 - z**3 - 1. Let t(y) be the third derivative of l(y). Solve t(p) = 0 for p.
-2, -1, -2/5, 0
Factor -5*b**3 - 4*b**3 + 2*b**3 + 5*b**3 + 2*b.
-2*b*(b - 1)*(b + 1)
Let h(w) be the second derivative of w**4/28 - 5*w**3/14 + 6*w**2/7 - 4*w. Determine o so that h(o) = 0.
1, 4
Let h(y) be the first derivative of -5*y**3/3 - 25*y**2/2 - 6. Find v such that h(v) = 0.
-5, 0
Let p = 9 + -13. Let i be (-10)/15 + p/(-6). Let i*f + 0 + 2/5*f**2 - 2/5*f**3 = 0. What is f?
0, 1
Let y = 0 + 2. Determine x so that 4 - 2*x**2 + 0*x**y - 3 - 2*x + 3*x**2 = 0.
1
Let w(j) be the second derivative of 5*j**7/21 - j**6/5 - j**5/5 + j. Factor w(d).
2*d**3*(d - 1)*(5*d + 2)
Let z be ((-10)/15)/((-24)/9 - 0). Factor 3/2*l**2 - l**3 - l + 1/4*l**4 + z.
(l - 1)**4/4
Let o(c) be the second derivative of c**5/60 + c**4/12 + c**3/9 + 5*c. Determine z, given that o(z) = 0.
-2, -1, 0
Let l(n) be the first derivative of 3/5*n**3 - 3/10*n**2 - 9/20*n**4 + 3/25*n**5 + 0*n - 1. Factor l(y).
3*y*(y - 1)**3/5
Let v = -25 + 27. Let i(g) be the first derivative of 2/7*g - 3 - 2/7*g**v + 2/21*g**3. Suppose i(m) = 0. What is m?
1
Let v(t) be the third derivative of t**6/180 - 2*t**5/45 + 5*t**4/36 - 2*t**3/9 + 9*t**2. Factor v(g).
2*(g - 2)*(g - 1)**2/3
Let t be (60/16)/((-6)/(-8)). Let k(v) be the second derivative of -1/90*v**t + 3*v + 1/18*v**4 - 1/9*v**3 + 0 + 1/9*v**2. Let k(i) = 0. What is i?
1
Solve 39/7*t**3 + 9*t**4 - 6/7*t - 3/7*t**2 + 0 + 27/7*t**5 = 0 for t.
-1, -2/3, 0, 1/3
Let j be (-6)/(-3)*-1 - -1. Let l = j + 1. Factor -1/4*z**2 + l + z**3 + 0*z.
z**2*(4*z - 1)/4
Let q be 42/(-70)*(-5)/2. Solve -q*s + 3/2*s**2 + 0 = 0.
0, 1
Let m be (3/4)/((-6)/(-16)). Suppose j - 6 + m = 0. Factor 7/4*u**5 + 15/4*u**3 + 19/4*u**j + 1/4*u**2 + 0 - 1/2*u.
u*(u + 1)**3*(7*u - 2)/4
Let g(t) be the second derivative of 0*t**2 + 0*t**3 - 1/36*t**4 + 0 + 3*t. Suppose g(p) = 0. Calculate p.
0
Let k(q) be the second derivative of -q**6/210 - q**5/70 - q**4/84 + 19*q. Suppose k(l) = 0. Calculate l.
-1, 0
Let c = -149 + 449/3. Determine q, given that 2*q + 4/3 + c*q**2 = 0.
-2, -1
Let o = -25 - -25. Let d(i) be the second derivative of 1/20*i**5 + 0 - 1/24*i**4 - 1/60*i**6 + 0*i**2 + o*i**3 - 2*i. Find c such that d(c) = 0.
0, 1
Let a(q) be the second derivative of -q**7/42 - q**6/15 + q**4/6 + q**3/6 + 10*q. Factor a(z).
-z*(z - 1)*(z + 1)**3
Let d(p) be the second derivative of p**7/294 + 2*p**6/105 + 3*p**5/140 - p**4/21 - 2*p**3/21 + 13*p. Determine v so that d(v) = 0.
-2, -1, 0, 1
Let r(g) be the third derivative of -g**8/10080 + g**7/1260 - g**6/360 + g**5/12 - 2*g**2. Let q(n) be the third derivative of r(n). Factor q(h).
-2*(h - 1)**2
Suppose 5*j + 4*q + 23 = 0, -7*q + 2*q = -5*j - 50. Let h(v) = v**2 + 8*v + 7. Let x be h(j). Find u, given that 2/5*u + 6/5*u**2 + 6/5*u**3 + 2/5*u**4 + x = 0.
-1, 0
Let y(t) be the second derivative of 0 + 2*t - 1/180*t**6 + 0*t**2 + 1/24*t**4 + 0*t**5 - 1/18*t**3. Factor y(u).
-u*(u - 1)**2*(u + 2)/6
Let -4/3*x**4 - 1/3*x**5 + 0 + 0*x**2 + 0*x - 4/3*x**3 = 0. Calculate x.
-2, 0
Suppose 2*v - 4 = -4*w + v, 2*w - 3*v = 16. Factor 0*s**4 - 7*s**3 + 2*s**3 + 3*s**3 - w*s**4.
-2*s**3*(s + 1)
Find r such that 16/5*r - 2/5*r**2 - 14/5 = 0.
1, 7
Let p(r) be the second derivative of r**6/10 - 3*r**5/20 - r**4/2 - 7*r. Solve p(x) = 0 for x.
-1, 0, 2
Let n(k) be the third derivative of -1/600*k**6 + 7*k**2 + 0*k + 0*k**3 + 0 - 1/300*k**5 + 0*k**4. Factor n(v).
-v**2*(v + 1)/5
Let g(p) = 12. Let a(j) = -12. Let r(m) = 5*a(m) + 4*g(m). Let o(y) = y**2 - 24. Suppose 18 = -5*u - 7. Let l(t) = u*r(t) + 3*o(t). Solve l(x) = 0.
-2, 2
Determine i so that 4*i + 2*i**5 - 12*i**2 + 2*i**4 - 8*i**2 - 6*i**2 + 24*i**2 - 6*i**3 = 0.
-2, -1, 0, 1
Let y(s) be the third derivative of s**5/210 + s**4/42 + 8*s**2. Let y(m) = 0. Calculate m.
-2, 0
Let s(w) be the first derivative of 3*w**4/4 + w**3 - 5*w**2/2 + 2. Let c(a) = a**3 + a**2 - 2*a. Let d(b) = -10*c(b) + 4*s(b). Determine f so that d(f) = 0.
-1, 0
Let j(p) = -5*p - 117. Let s be j(-24). Determine i so that 1/2*i + 1/4*i**s - 3/4*i**5 + 5/4*i**2 + 0 - 5/4*i**4 = 0.
-1, -2/3, 0, 1
Let q(r) = -r**3 - 5*r**2 + 4*r + 4. Let a be q(-5). Let o be 6/(-8)*a/18. Solve 8/3*y + 8/3 + o*y**2 = 0 for y.
-2
Let g = 57/106 + -2/53. Find v, given that -1/2 + v - g*v**2 = 0.
1
Factor b**5 - 3*b**4 - 3*b**4 + 5*b**4 + 0*b**4.
b**4*(b - 1)
Let a(p) be the first derivative of -p**8/5040 + p**6/540 - p**4/72 - p**3/3 + 1. Let m(i) be the third derivative of a(i). Factor m(f).
-(f - 1)**2*(f + 1)**2/3
Let u = 2/33 - -3/11. Let t(i) be the second derivative of 0 - 2*i**2 - u*i**3 + 1/6*i**4 - i. Factor t(f).
2*(f - 2)*(f + 1)
Let z(k) be the first derivative of 10*k**6/3 + 23*k**5 + 105*k**4/2 + 140*k**3/3 + 5*k**2 - 15*k + 42. Factor z(w).
5*(w + 1)**3*(w + 3)*(4*w - 1)
Suppose 0 = -u - 4*u. Factor -2/3*x