1)*(v + 2)/5
Determine b, given that -1/4*b**3 + 0 - 5/4*b**2 - 3/2*b = 0.
-3, -2, 0
Let q be 3/2*4/(-3). Let b be (-5)/(-3) - q/6. Let -24*z**3 + b*z**2 - z**4 - z**5 + 25*z**3 - z**2 = 0. What is z?
-1, 0, 1
Let m = 177 - 173. Let f(l) be the second derivative of 1/6*l**m - l**2 + 3*l + 0 + 1/10*l**5 - 1/3*l**3. Suppose f(b) = 0. Calculate b.
-1, 1
Suppose -164*t - 160*t + 494*t - 158*t = 0. Factor -2/7*c**3 + 8/7*c + t - 2/7*c**4 + 8/7*c**2.
-2*c*(c - 2)*(c + 1)*(c + 2)/7
Let v(m) = -m**2 - 2*m - 4. Let y be v(2). Let q be ((-3)/y)/((-5)/(-12)). Factor 3/5 - 3/5*x**3 - 3/5*x**2 + q*x.
-3*(x - 1)*(x + 1)**2/5
Let t = 75 + -96. Let y be t/(-9) - (2 + 0 + -3). Factor -y*w**3 - 4/3*w**2 + 10/3*w + 4/3.
-2*(w - 1)*(w + 1)*(5*w + 2)/3
Let a(d) be the first derivative of 1/7*d**3 + 0*d + 1/7*d**2 - 11. Factor a(h).
h*(3*h + 2)/7
Let u be (-3)/5*(-40)/12. Suppose -6*l + u*l + 8 = 0. Solve -4*i**l - 10*i + 5 + 3 + i**2 = 0.
-4, 2/3
Let y(q) be the first derivative of -q**8/1848 - 2*q**7/1155 + q**6/660 + q**5/165 + 5*q**2 - 3. Let j(h) be the second derivative of y(h). Solve j(b) = 0.
-2, -1, 0, 1
Let g(a) = a**5 + a**4 + a**3 - a - 1. Let j(y) = -6*y**5 - 6*y**4 - 8*y**3 - y**2 + 7*y + 7. Let t(f) = 35*g(f) + 5*j(f). Suppose t(b) = 0. What is b?
-1, 0, 1
Let a(w) be the second derivative of -27/5*w**5 + 0 - 9*w + 3*w**4 - 1/2*w**3 + 0*w**2. Factor a(h).
-3*h*(6*h - 1)**2
Factor 0*v**2 - 3/4*v**3 + 3/8*v + 3/8*v**5 + 0*v**4 + 0.
3*v*(v - 1)**2*(v + 1)**2/8
Let k be (-2)/(2/(-3)) - (-4 - -3). Suppose 0 = -0*u + 5*u + k*v + 16, -4*v = 16. Find g such that u*g**2 - 1/4*g**4 - 1/2*g**3 + 1/4 + 1/2*g = 0.
-1, 1
Suppose -m + 6 - 3 = 0. Suppose 2*k - m*v = -8, 5*v - 24 = 12*k - 14*k. Find w, given that 0*w**k + 2/11*w**4 + 0*w + 2/11*w**3 + 0 = 0.
-1, 0
Let m = 403/60 - 97/15. Find o, given that 1/2*o**2 + m*o**3 + 1/4*o + 0 = 0.
-1, 0
Factor 0*d**2 + 4/11*d**3 + 2/11*d**4 + 0*d + 0.
2*d**3*(d + 2)/11
What is q in 128/3*q**3 + 32/3*q**2 + 2/3*q + 0 = 0?
-1/8, 0
Let d be 7/(-20)*(-44)/110. Let o(m) be the second derivative of d*m**5 - 1/15*m**3 + 0 + 0*m**2 - 5*m + 4/75*m**6 + 1/15*m**4. Factor o(z).
2*z*(z + 1)**2*(4*z - 1)/5
Let z(s) be the first derivative of -s**6/40 - s**5/10 + 7*s**2 - 30. Let k(h) be the second derivative of z(h). Factor k(v).
-3*v**2*(v + 2)
Let p(i) = -i**3 + 8*i**2 - 12*i. Let c be p(6). Let q(o) be the first derivative of 1 + c - 6*o + 4*o**3 + o**4 - 6 - 10*o. Factor q(x).
4*(x - 1)*(x + 2)**2
Let k(i) be the third derivative of i**6/120 + i**5/210 - i**4/6 - 4*i**3/21 + 2*i**2 - 3. Solve k(t) = 0.
-2, -2/7, 2
Let y(w) be the third derivative of -w**5/80 - 9*w**4/16 + 19*w**3/8 - w**2 - 65*w. Factor y(i).
-3*(i - 1)*(i + 19)/4
Suppose 0 = -4*r + 13 + 47. Let r - 10*t**2 + 20*t**3 - 21*t - 5 - 8*t**4 + 8 + t**5 = 0. Calculate t.
-1, 1, 2, 3
Let -1/11*x**5 + 0 - 2/11*x**3 + 0*x**2 + 0*x - 3/11*x**4 = 0. Calculate x.
-2, -1, 0
Let a(v) = 4*v**2 - 16*v + 8. Let z(g) = -g**2 + 3*g - 2. Let t(o) = 3*a(o) + 14*z(o). Factor t(m).
-2*(m + 1)*(m + 2)
Let r = -1066 - -2137/2. Determine h so that 15/4*h + 0*h**2 - 5/4*h**3 - r = 0.
-2, 1
Let l = 175472/5 - 35094. Find f, given that l*f**2 + 8/5 + 2*f = 0.
-4, -1
Let s(i) be the first derivative of -2*i**3/9 + 3*i**2 - 16*i/3 + 237. Let s(b) = 0. Calculate b.
1, 8
Let i(n) be the second derivative of n**7/147 - 2*n**6/105 - 4*n**5/35 + 3*n**4/7 - 3*n**3/7 + 54*n. Suppose i(r) = 0. What is r?
-3, 0, 1, 3
Let x be (-11 - (-14 - -7))*(6/(-2) + 2). Let 9/2*g**2 - 2*g + 0 - 3*g**3 + 1/2*g**x = 0. Calculate g.
0, 1, 4
Let a = -2 - -6. Suppose 0 = -a*g - g - 5*h + 55, 5*g + h = 35. Solve 5/2*n**2 + g*n + 2 = 0.
-2, -2/5
Suppose 3 = m - 4*r + 1, 2*m + 4*r = 4. Let l(q) be the first derivative of -3/4*q**2 - 9/4*q - m - 1/12*q**3. Factor l(k).
-(k + 3)**2/4
Let a(o) be the third derivative of -1/15*o**3 - 4*o**2 + 0*o + 1/8*o**4 - 7/75*o**5 + 0. Factor a(i).
-(4*i - 1)*(7*i - 2)/5
Suppose -970 - 3470 = -20*i. Let y = i - 219. Factor -1/4*j + 0 + 1/4*j**4 - 1/4*j**2 + 1/4*j**y.
j*(j - 1)*(j + 1)**2/4
Let k(z) be the first derivative of -z**3/5 - 2*z**2/5 + 73. Factor k(s).
-s*(3*s + 4)/5
Let s(w) be the second derivative of -w**4/3 + 2*w**3/3 + 2*w**2 - 2*w. Let q(f) = -f. Let p(k) = 4*q(k) + s(k). Factor p(d).
-4*(d - 1)*(d + 1)
Let j(p) be the first derivative of p**5 - 10*p**4 - 95*p**3/3 - 25*p**2 - 85. Factor j(s).
5*s*(s - 10)*(s + 1)**2
Let v = 17176 + -17173. Solve 0*h**2 + 0*h**4 + 3/2*h**5 - 3/2*h**v + 0*h + 0 = 0.
-1, 0, 1
Let w = 8094/415 - -8/83. Factor -14/5*g**2 - 686/15 + w*g + 2/15*g**3.
2*(g - 7)**3/15
Let f be 2/8 + (-126)/(-72). Let w(r) be the first derivative of -2*r**2 + 3*r**f + r**3 - r**2 - 8. Factor w(c).
3*c**2
Let p(d) = d**2 - 173*d - 17958. Let o be p(-73). Factor o + 0*h - h**3 - 1/4*h**4 - h**2.
-h**2*(h + 2)**2/4
Let m(w) = 4*w - 26. Let d be m(7). Suppose -v = 5*i - 23, 2*v + 4*i + 2 - 24 = 0. Factor 1/2*x**v + 0 + 1/2*x + x**d.
x*(x + 1)**2/2
Let b(a) be the third derivative of -1/630*a**7 - 1/24*a**4 + 1/9*a**3 - 1/180*a**5 + 0 + 5*a**2 + 0*a + 1/120*a**6. Factor b(o).
-(o - 2)*(o - 1)**2*(o + 1)/3
Let x(o) = o + 23. Let h be x(-21). Factor 16*n + 27*n**2 - 60*n**h - 16 + 29*n**2.
-4*(n - 2)**2
Let l(y) be the second derivative of 0 + 0*y**2 + 1/2*y**6 + 1/7*y**7 + 0*y**3 + 3/5*y**5 - 10*y + 1/4*y**4. Factor l(d).
3*d**2*(d + 1)**2*(2*d + 1)
Let z(o) be the second derivative of -o**5/90 + o**4/72 + o**3/18 - 3*o**2/2 - 7*o. Let p(w) be the first derivative of z(w). Suppose p(v) = 0. What is v?
-1/2, 1
Let h = -66209/7 - -9459. Determine g so that -5*g**4 - h*g - 4/7 + 4/7*g**3 + 39/7*g**2 = 0.
-1, -2/7, 2/5, 1
Factor -1218 - 4*h**2 - 20*h + 6*h**3 - 2*h**3 + 1206.
4*(h - 3)*(h + 1)**2
Let t(a) be the second derivative of 2*a - 22/3*a**3 + 1/4*a**4 - 15/2*a**2 - 3. Suppose t(k) = 0. What is k?
-1/3, 15
Factor -2/5*g**2 + 2 - 8/5*g.
-2*(g - 1)*(g + 5)/5
Let g = -397/11 - -4481/165. Let n = g + 48/5. Determine x, given that -2/3*x**4 + 0*x + 0*x**3 + n*x**2 + 0 = 0.
-1, 0, 1
Let x(o) be the first derivative of -o**6/2 + 3*o**5/5 + 15*o**4/4 - o**3 - 12*o**2 - 12*o + 29. Factor x(g).
-3*(g - 2)**2*(g + 1)**3
Let m(x) be the third derivative of x**6/60 + x**5/6 - 8*x**4/3 + 12*x**3 + x**2 + 6. Determine q, given that m(q) = 0.
-9, 2
Determine s so that -27 + 63*s + 10*s**4 - 59*s + 30*s**3 - 100*s**2 - 3 + 91*s - 5*s**5 = 0.
-3, 1, 2
Let n = -10 + 36. Suppose -29*j + n*j + 18 = 0. What is u in -15*u**2 + 9 + j*u + 2*u - 4*u + 2*u = 0?
-3/5, 1
Factor -27*j + 6*j**3 + 10*j**2 + 18*j**2 - 3*j**5 - 12*j**4 + 8*j**2.
-3*j*(j - 1)**2*(j + 3)**2
Let j(h) be the third derivative of 1/26*h**4 - 3/13*h**3 - 1/390*h**5 + 0 - 6*h**2 + 0*h. Factor j(o).
-2*(o - 3)**2/13
Determine g so that 505 - 4*g**3 + 2*g**3 + 34*g**2 - 505 = 0.
0, 17
Let i(w) be the first derivative of w**7/105 + w**6/20 + w**5/15 + 19*w**2/2 + 13. Let a(u) be the second derivative of i(u). Let a(c) = 0. Calculate c.
-2, -1, 0
Let w(m) be the third derivative of -m**6/240 + 2*m**5/15 - 15*m**4/16 - 27*m**3/2 - 4*m**2 + 69*m. Factor w(h).
-(h - 9)**2*(h + 2)/2
Let s(a) = -8*a**3 + 2*a + 1. Let o be s(-1). Suppose -3*n**2 + 12*n + o*n - 27 - n = 0. Calculate n.
3
Factor -3888/5 - 3/5*o**2 + 216/5*o.
-3*(o - 36)**2/5
Let l(x) be the first derivative of -2*x**5/95 - 27*x**4/38 - 436*x**3/57 - 480*x**2/19 - 576*x/19 - 60. Suppose l(a) = 0. What is a?
-12, -2, -1
Let u(s) be the third derivative of s**5/30 + s**4/4 - 4*s**3/3 + 22*s**2 + 1. Factor u(n).
2*(n - 1)*(n + 4)
Let x = 495 + -425. Suppose 3*b = 3*u - 24 + 9, -2*u + 5*b + 16 = 0. Determine p so that x*p**4 - p**3 - 5*p**2 + 6*p + 11*p**u - 65*p**4 - 16*p = 0.
-2, -1, 0, 1
Let f(z) be the first derivative of -3*z**4/8 - z**3 - 3*z**2/4 - 245. Factor f(b).
-3*b*(b + 1)**2/2
Let r(v) = -v + 6. Let x be r(0). Suppose 4*q = -5*s - 16, x*s = 4*q + s - 24. Factor q - 2*t**2 - 1 - 4*t**4 - 2*t**3 - 3*t**3 - t**5.
-t**2*(t + 1)**2*(t + 2)
Let q(f) be the third derivative of -f**6/480 - f**5/60 + 4*f**2 + 34. Factor q(v).
-v**2*(v + 4)/4
Solve -579*z**3 - 13506*z + 0*z**4 + 324*z**3 - 4335*z**2 - 11059*z - 5*z**4 = 0.
-17, 0
Let j(f) be the third derivative of -f**8/10080 - f**7/1260 - f**6/360 - f**5/180 - f**4/6 + 11*f**2. Let r(b) be the second derivative of j(