- 8/7*k + 6/7 = 0. Calculate k.
1, 3
Let q be (-5573)/(-26) - ((-24)/(-52))/(-3). Let r = -210 + q. Factor 0*y + 3/2*y**3 + r*y**2 + 0.
3*y**2*(y + 3)/2
Suppose -40*k + 43*k = 0. Suppose -3*l - 20 = -4*i - k*i, 0 = -2*l - i + 5. Factor -6/7*g**4 + 0*g**2 + l*g + 4/7*g**3 + 2/7*g**5 + 0.
2*g**3*(g - 2)*(g - 1)/7
Let u be -1*3 - (-3275)/(-25). Let y = u + 537/4. Factor 3/4*i - 3/4*i**3 + 1/2 - y*i**2 - 1/4*i**4.
-(i - 1)*(i + 1)**2*(i + 2)/4
Let c = 3203/2130 - 4/1065. Let t be 4/18 + (-8)/36. Factor t - c*x + 1/2*x**2.
x*(x - 3)/2
Let d(g) be the second derivative of -g**5/40 - g**4/8 + g**3/12 + 3*g**2/4 + g + 18. What is m in d(m) = 0?
-3, -1, 1
Let l(w) be the second derivative of 15*w**5/4 + 65*w**4/2 + 64*w**3 + 48*w**2 + 42*w. Factor l(s).
3*(s + 4)*(5*s + 2)*(5*s + 4)
Factor -2/23*z**4 + 0*z + 6/23*z**3 + 8/23*z**2 + 0.
-2*z**2*(z - 4)*(z + 1)/23
Let q(b) = 7*b**4 - 2*b**3 - 20*b**2 + 2*b + 2. Let m(v) = 15*v**4 - 5*v**3 - 40*v**2 + 5*v + 5. Let s(o) = 2*m(o) - 5*q(o). Factor s(r).
-5*r**2*(r - 2)*(r + 2)
Let g(y) be the second derivative of -y**5/70 - y**4/14 + y**3/21 + 3*y**2/7 + 206*y. Factor g(k).
-2*(k - 1)*(k + 1)*(k + 3)/7
Let k(j) = -j**3 - j + 1. Let w(i) = 20*i**3 - 12*i**2 + 7*i - 21. Let p(l) = -4*k(l) - w(l). Let y(m) be the first derivative of p(m). Solve y(u) = 0.
1/4
Suppose 0 = -g + 2*z - 5, 2*g + 3*z - 27 = -2. Let t(d) be the third derivative of 1/60*d**g + 11*d**2 + 0 + 0*d + 1/3*d**3 - 1/8*d**4. Factor t(k).
(k - 2)*(k - 1)
Let c = 76 + -73. Find p such that -4 - 50*p - 332*p**c - 220*p**4 - 221*p**2 + 13*p**2 - 67*p**5 + 17*p**5 = 0.
-2, -1, -1/5
Solve 24*c**3 + 88*c**2 + c**4 + 103*c**2 + 3*c**4 - 191*c**2 = 0 for c.
-6, 0
Let p(d) = -d**2 + 23*d - 3. Let g be p(6). Let a = g + -197/2. Factor 0 - l**2 + 1/2*l**3 + a*l.
l*(l - 1)**2/2
Find a such that 40*a**2 - 37*a**2 - 43*a + a**3 + 45*a = 0.
-2, -1, 0
Suppose -5*i + 1 = -y, i - 5*y = -18 - 1. Let n be 3 - 0 - (i + -3). Factor v + 2*v**4 - 2*v**2 - n*v**3 - v**5 + 4*v**3 + v**3.
-v*(v - 1)**3*(v + 1)
Suppose 4*y = 2*j + 34, -8*y + 28 = -4*y + 4*j. Let t be -1 + (-9)/3 - (-36)/y. Factor -1/2*v**3 + t*v + 1/2*v**2 - 1/2.
-(v - 1)**2*(v + 1)/2
Let k(a) be the third derivative of a**5/30 - a**4/6 - a**3 - 10*a**2 + 6. Factor k(i).
2*(i - 3)*(i + 1)
Let b(q) be the second derivative of -q**8/1008 + q**7/315 - q**5/90 + q**4/72 - 10*q**2 - 12*q. Let c(j) be the first derivative of b(j). Factor c(y).
-y*(y - 1)**3*(y + 1)/3
Let s(n) be the first derivative of -n**6/180 - n**5/36 + n**4/18 + n**3/6 + 4*n**2 - 3. Let w(o) be the second derivative of s(o). What is b in w(b) = 0?
-3, -1/2, 1
Suppose 3*a = 145 - 28. Let p = a - 35. Factor 3*u + 3/2 + 0*u**2 - 3*u**3 - 3/2*u**p.
-3*(u - 1)*(u + 1)**3/2
Let d(i) be the first derivative of 28 + 0*i**2 + 0*i - 1/44*i**4 + 1/11*i**3. Factor d(c).
-c**2*(c - 3)/11
Let j(p) = -p**3 + 7*p**2 - p + 9. Let x(h) = h**2 + 7. Let a be x(0). Let g be j(a). Factor 2 + 2*y**2 - 6*y + 4*y - g.
2*y*(y - 1)
Let w be 12/(-4) + 26/6. Let o(x) be the second derivative of -14*x + w*x**3 - 7/24*x**4 - x**2 + 0. Factor o(b).
-(b - 2)*(7*b - 2)/2
Let p(u) be the second derivative of 0*u**3 + 1/32*u**4 - 1/80*u**6 + 1/112*u**7 - 3/160*u**5 - 15*u + 0*u**2 + 0. Determine b so that p(b) = 0.
-1, 0, 1
Factor 4*i**5 - 3*i**3 - 5*i**3 - 4*i**3 + 39*i + 10 + 6*i**4 - 5*i**5 + 56*i**2 + 46*i**3.
-(i - 10)*(i + 1)**4
Let s(w) be the second derivative of -1/25*w**5 + 2/15*w**3 + 0 - 1/5*w**4 + 6/5*w**2 + 19*w. Factor s(j).
-4*(j - 1)*(j + 1)*(j + 3)/5
Determine o, given that -3/8*o**2 + 81/8*o - 39/4 = 0.
1, 26
Suppose h + 13 = 5*d + 35, 0 = 3*h - 4*d - 88. Suppose -h = 4*r - 8*r. Factor 22*y**2 + 0*y + 6*y**3 - r*y - 22*y**2 + 2*y**4.
2*y*(y - 1)*(y + 2)**2
Let r(v) be the first derivative of -2*v**5/5 + 2*v**4 + 2*v**3 - 10*v**2 - 16*v + 71. Determine o, given that r(o) = 0.
-1, 2, 4
Suppose -t - 16 = 5*p, -2*p - 5*t = -2*t + 9. Let a(m) = -m**2 - 4*m - 3. Let z be a(p). Factor 1/2*x - 2*x**2 + z.
-x*(4*x - 1)/2
Let f(p) = 3*p**3 + 21*p**2 - 23*p - 3. Let x = 7 + -18. Let n(k) = -7*k**3 - 42*k**2 + 45*k + 5. Let v(i) = x*f(i) - 6*n(i). Let v(s) = 0. Calculate s.
-3, 1/3
Let q(h) be the first derivative of -2*h**3/45 + 2*h**2/3 - 32*h/15 + 179. Let q(t) = 0. What is t?
2, 8
Let a(n) be the second derivative of n**6/90 + n**5/30 - 7*n**4/36 - 4*n**3/9 + 2*n**2 + 66*n - 5. Find f, given that a(f) = 0.
-3, -2, 1, 2
Let a be ((-84)/(-35) + 2/(-5))/3. Let t(c) be the second derivative of 5/24*c**4 - c - a*c**3 + 0 - c**2. Factor t(h).
(h - 2)*(5*h + 2)/2
Factor 3 + 31/2*r - 10*r**3 + 23/2*r**2.
-(r - 2)*(4*r + 1)*(5*r + 3)/2
Let x = -258 - -258. Let g(o) be the third derivative of -1/150*o**5 - 4/15*o**3 - 1/15*o**4 + 6*o**2 + 0 + x*o. Determine c so that g(c) = 0.
-2
Let q = 2880 + -11519/4. Factor 5/4*g - g**2 + q*g**3 - 1/2.
(g - 2)*(g - 1)**2/4
Let q(s) = -7*s**3 - 81*s**2 - 77*s - 3. Let j(a) = -36*a**3 - 404*a**2 - 384*a - 16. Let b(u) = 3*j(u) - 16*q(u). Factor b(o).
4*o*(o + 1)*(o + 20)
Let h(v) be the first derivative of 0*v - 24 - v**2 + 1/6*v**4 + 4/9*v**3. Factor h(b).
2*b*(b - 1)*(b + 3)/3
Let f(x) be the first derivative of -x**6/6 - 3*x**5/4 - 5*x**4/6 + 14*x + 17. Let k(m) be the first derivative of f(m). Determine p so that k(p) = 0.
-2, -1, 0
Let y(g) be the third derivative of g**6/120 + 7*g**5/60 + 5*g**4/8 + 3*g**3/2 - 128*g**2 + 2*g. Factor y(z).
(z + 1)*(z + 3)**2
Let c = 854 - 854. Let w(i) be the third derivative of 0*i + 1/22*i**4 - 3/11*i**3 + c - 1/330*i**5 - 7*i**2. Let w(q) = 0. What is q?
3
Let w(c) = 26*c**3 - 69*c**2 + 79*c - 36. Let f(h) = 77*h**3 - 208*h**2 + 238*h - 107. Let j(u) = -6*f(u) + 17*w(u). Factor j(i).
-5*(i - 2)*(i - 1)*(4*i - 3)
Let v(d) be the first derivative of 2/21*d**3 + 4/7*d + 3/7*d**2 - 9. What is s in v(s) = 0?
-2, -1
Let w(v) be the first derivative of 5 - 1/4*v**2 + 1/6*v**3 + 0*v. Find y, given that w(y) = 0.
0, 1
Let q(g) be the second derivative of 0*g**3 + 0 + 1/16*g**4 - 3/8*g**2 + 12*g. Factor q(d).
3*(d - 1)*(d + 1)/4
Let t be 78/(-10) - (-824)/103. Factor t*a**5 + 0*a**4 + 2/5 + 3/5*a - 4/5*a**3 - 2/5*a**2.
(a - 2)*(a - 1)*(a + 1)**3/5
Let d = -597 + 28657/48. Let n(l) be the second derivative of 0*l**3 + d*l**4 + 1/8*l**5 + 0*l**2 + 0 + 5/24*l**6 - 7*l. Let n(j) = 0. Calculate j.
-1/5, 0
Let d = 2444/77 + -346/11. Factor 0 + 4/7*b + d*b**2.
2*b*(b + 2)/7
Let g(d) = d**2 - 9*d - 1033. Let q be g(37). Factor -5/7*j**2 + 0 + 0*j - 1/7*j**q.
-j**2*(j + 5)/7
Let 0*m**2 + 0*m**2 + 6*m**3 - m**3 - 10*m**2 = 0. What is m?
0, 2
Let m(l) be the first derivative of -l**3/6 + 57*l**2/2 + 115*l/2 - 595. Factor m(h).
-(h - 115)*(h + 1)/2
Suppose 0 = -11*m + 22. Let q be 1 - (-6)/(-96)*4/m. Factor 23/8*s**3 + 1/4 + 27/8*s**2 + 13/8*s + q*s**4.
(s + 1)**3*(7*s + 2)/8
Let i(a) = 2*a + 1. Let u be i(-3). Let b(y) = 2*y + 12. Let p be b(u). Factor 0*k**p + 9*k**2 - 7*k**2.
2*k**2
Let t(m) be the first derivative of m**6/2 + 6*m**5/5 - 9*m**4/2 - 8*m**3 + 15*m**2/2 + 18*m - 673. Let t(l) = 0. Calculate l.
-3, -1, 1, 2
Let q(h) = h**5 - h. Let m(n) = -9*n**5 - 15*n**4 - 5*n**3 + 15*n**2 + 14*n. Let f(t) = t - 10. Let a be f(6). Let g(w) = a*q(w) - m(w). Factor g(o).
5*o*(o - 1)*(o + 1)**2*(o + 2)
Suppose 7*f**2 + 1/6*f**3 - 576 + 48*f = 0. Calculate f.
-24, 6
Solve -1875 - 32*w**4 - 60*w**3 - 1867*w**2 + 1417*w**2 + 29*w**4 - 1500*w = 0 for w.
-5
Let z(l) be the first derivative of l**4/20 - 16*l**3/3 + 160*l**2 + 772. Factor z(h).
h*(h - 40)**2/5
Let v(s) be the third derivative of s**5/255 + 311*s**4/204 - 52*s**3/17 - 35*s**2. Factor v(c).
2*(c + 156)*(2*c - 1)/17
Let k = -40 + 63. Let c = k - 20. Factor -4*a**3 + c*a**2 + a**2 - a**5 - 2*a**4 - 2*a**2 + 5*a**3.
-a**2*(a - 1)*(a + 1)*(a + 2)
Suppose 0*a + 0 + 8/5*a**2 - 2/5*a**4 + 0*a**3 = 0. What is a?
-2, 0, 2
Suppose -3*t - 510 = 5*j, -4*j + t = 5*t + 408. Let l = j + 104. Suppose -3/4*n**l + 5/4*n - 1/2 - 1/4*n**3 + 1/4*n**4 = 0. Calculate n.
-2, 1
Let r(c) = -c**5 + c**4 + 2*c**3 - c**2 + c. Let i(j) = -15*j**5 - 159*j**4 - 54*j**3 + 6*j**2 - 6*j. Let w(g) = i(g) + 6*r(g). Factor w(y).
-3*y**3*(y + 7)*(7*y + 2)
Let k(n) = -n**3 + 9*n**2 + 12. Let j be k(9). Suppose 2*z = 6*z - j. Factor -2*i - 5 + 5 - 2*i**z - 4*i**2.
-2*i*(i + 1)**2
Let l(p) = 27*p**3 +