 2
Let j(x) be the second derivative of 1/21*x**4 + 0*x**5 - 1/147*x**7 + 0 - 8*x + 0*x**2 + 1/21*x**3 - 2/105*x**6. Factor j(h).
-2*h*(h - 1)*(h + 1)**3/7
Factor -16*v - 16*v**2 + 9436*v**3 - 9440*v**3 + 0*v**2.
-4*v*(v + 2)**2
Let x be 14/4*(-4)/(-7). Factor 5*w**x + 1 + 3 - w**2 - 8*w.
4*(w - 1)**2
Let 72/13 + 2/13*m**3 - 54/13*m - 20/13*m**2 = 0. What is m?
-3, 1, 12
Factor 0 + 1/5*r**2 + 1/5*r - 1/5*r**4 - 1/5*r**3.
-r*(r - 1)*(r + 1)**2/5
Factor 5*g**2 + 0 + g - 35/2*g**4 - 3/4*g**3 + 49/4*g**5.
g*(g - 1)**2*(7*g + 2)**2/4
Let a = -21267 + 21269. Factor 0 + 1/2*z**a - 3/2*z.
z*(z - 3)/2
Let w(x) be the third derivative of 0*x + 1/3*x**4 + 4/3*x**3 + 1/30*x**5 + 2*x**2 + 0. Factor w(z).
2*(z + 2)**2
Let z be (18/(-15))/((-6)/10). Factor -2*l**3 + l**3 - l**3 + 4*l**z + 2*l**4 + 2*l**5 - 6*l**2.
2*l**2*(l - 1)*(l + 1)**2
Suppose -6*y - 11 = 19. Let x = y + 7. Factor p**3 + 6 - 16 + 5*p**x + 7*p + 4 + 9.
(p + 1)**2*(p + 3)
Factor 4/9*v**4 + 20*v + 8 + 44/9*v**3 + 148/9*v**2.
4*(v + 1)**2*(v + 3)*(v + 6)/9
Let -3*l**2 + 6*l**3 - 70*l**4 - 6*l + 73*l**4 - 3*l**2 + 3*l**2 = 0. Calculate l.
-2, -1, 0, 1
Let t = -10 - -12. Let m be 84/t*(-2)/(-6). Let -8*s - 3*s**2 + 0*s**3 + 7*s + 9*s**4 - 6 - m*s + 15*s**3 = 0. Calculate s.
-1, -2/3, 1
Let r(t) be the third derivative of t**7/1680 - 3*t**3 + 44*t**2. Let z(c) be the first derivative of r(c). Factor z(p).
p**3/2
Let n(a) be the third derivative of a**7/280 - 3*a**6/80 + a**5/16 + 2*a**2 - 70*a. Factor n(i).
3*i**2*(i - 5)*(i - 1)/4
Let o be (0 + 0/3)/(2 + 0). Let d be o - (2*-3 + 4). Factor 3/4 - 3/2*x**d + 0*x + 3/4*x**4 + 0*x**3.
3*(x - 1)**2*(x + 1)**2/4
Let b(g) be the second derivative of -7/6*g**4 + 3/4*g**5 + 0*g**2 + 2/3*g**3 + 0 - 5*g - 3/20*g**6. Factor b(r).
-r*(r - 2)*(3*r - 2)**2/2
Factor -17*z**2 + 2*z**2 + 16245 - 783*z + 213*z + 8*z**2 + 12*z**2.
5*(z - 57)**2
Let d(z) be the third derivative of -z**7/6 - 37*z**6/24 - 13*z**5/3 - 5*z**4/2 + 283*z**2. Factor d(m).
-5*m*(m + 2)*(m + 3)*(7*m + 2)
Let h(d) be the third derivative of -d**9/110880 - d**8/18480 - d**7/9240 - 11*d**5/60 + 9*d**2. Let w(t) be the third derivative of h(t). Factor w(s).
-6*s*(s + 1)**2/11
Let n(d) be the first derivative of 25/4*d**6 - 2*d**3 + 0*d + 9*d**4 - 27/2*d**5 + 0*d**2 + 6. Factor n(v).
3*v**2*(v - 1)*(5*v - 2)**2/2
Factor 0*u - 8 + 1/2*u**2.
(u - 4)*(u + 4)/2
Let f(g) be the first derivative of -g**6/2 + 3*g**5 - 27*g**4/4 + 7*g**3 - 3*g**2 + 159. Find n such that f(n) = 0.
0, 1, 2
Let s be ((-1917)/(-36))/(2/8). Let g = s + -210. Factor 4/5 + 24/5*l**2 + 18/5*l + 2*l**g.
2*(l + 1)**2*(5*l + 2)/5
Let p = 815/329 - 9/47. Let y = p + -66/35. Factor -y*v**2 + 2/5 + 0*v.
-2*(v - 1)*(v + 1)/5
Let 32/9*v**4 - 52/9*v**3 + 256/9*v - 128/9 - 104/9*v**2 - 4/9*v**5 = 0. Calculate v.
-2, 1, 4
Let t(v) be the third derivative of -v**6/48 + 59*v**5/12 - 17405*v**4/48 - 57*v**2. Factor t(i).
-5*i*(i - 59)**2/2
Suppose -14 = -2*q - 2*n - 0*n, q = n - 3. Factor -3*k + k**q + 2*k - k.
k*(k - 2)
Let v = 15 + -23. Let j(k) = -k - 1. Let f be j(v). Factor -3*p + p**2 - f*p**2 + 0*p.
-3*p*(2*p + 1)
Let w(a) be the third derivative of a**7/315 - 2*a**5/15 - 4*a**4/9 - 2*a**2 - 59*a. What is x in w(x) = 0?
-2, 0, 4
Let g be (-176)/(-4048)*(-23)/(-5). Find q, given that -g*q**2 + 7/10*q**3 - 7/10*q + 1/5 = 0.
-1, 2/7, 1
Let i(y) be the second derivative of -y**8/168 - y**7/105 - y**2/2 + 11*y. Let m(b) be the first derivative of i(b). Factor m(g).
-2*g**4*(g + 1)
Suppose 0 = 5*q + 5*d - 25, 5*d - 25 + 5 = -4*q. Suppose -4 = 2*b + 5*n, -q*n = -b - 4*n + 5. Suppose -f**2 + 5*f**b + f**2 - 2*f**3 = 0. What is f?
0
Solve 5 - 5 + 38*o + 4*o**2 + 30*o = 0.
-17, 0
Let y(f) be the second derivative of f**4/3 - 58*f**3/3 - 124*f**2 - 732*f. Solve y(r) = 0 for r.
-2, 31
Let g be ((3/1)/(-96))/(3/(-6)). Let n = g - -7/16. Solve 1 - 4*y - 5/4*y**4 + n*y**3 + 15/4*y**2 = 0 for y.
-2, 2/5, 1
Let j(i) = 16*i**4 + 8*i**3 - 11*i**2 - 13*i. Let t = -52 + 47. Let k(a) = 8*a**4 + 4*a**3 - 6*a**2 - 6*a. Let n(u) = t*k(u) + 2*j(u). Let n(o) = 0. What is o?
-1, -1/2, 0, 1
Let o(r) be the second derivative of -r**9/17010 + r**8/30240 + 35*r**4/12 - 33*r. Let h(u) be the third derivative of o(u). Factor h(t).
-2*t**3*(4*t - 1)/9
Let s = -73901/2 - -36953. Determine i so that 1/2*i**2 - s*i + 2 = 0.
1, 4
Suppose 0 = -2*t + 5*b + 18, 0 = -4*t - 2*b - 1 + 13. Let n(c) be the first derivative of -1/16*c**t - 1/6*c**3 - 2 + 0*c + 0*c**2. Factor n(i).
-i**2*(i + 2)/4
Factor 2*z**2 - 1534*z + 1542*z - 7 + 13.
2*(z + 1)*(z + 3)
Let j(r) = -r**4 + r**3 + r + 1. Let u(d) = d**5 - 10*d**4 + 6*d**3 + d**2 + 11*d + 9. Let p(o) = -18*j(o) + 2*u(o). Find l such that p(l) = 0.
-1, 0, 1, 2
Let y(u) = 45*u**3 - 90*u**2 - 80*u + 55. Let a(t) = -5*t**3 + 10*t**2 + 9*t - 6. Let i(d) = -35*a(d) - 4*y(d). What is r in i(r) = 0?
-1, 1, 2
Let a = 14 - 8. Let q be (9 + -7)/(4/a). Let -20*l + 23/2*l**2 - 3/2*l**q - 8 = 0. What is l?
-1/3, 4
Suppose 4*b - 12 = 4. Let f(q) = 3*q**2 - 13*q + 6. Let l be f(b). Solve -1/3*s**4 - 2/3*s**3 - 1/3*s**l + 0*s + 0 = 0.
-1, 0
Let m = 39994/171879 + -16/69. Let u = m - -67243/17437. Let -6/7*p**2 - u*p**3 - 36/7*p**4 + 0 - 15/7*p**5 + 0*p = 0. What is p?
-1, -2/5, 0
Find q such that 32*q**2 + 24*q - 2*q**5 - q**3 + 10294*q**4 + 0 + 0 + 3*q**3 - 10302*q**4 = 0.
-3, -2, -1, 0, 2
Let l(u) = -u**3 + 44*u**2 - u + 46. Let n be l(44). What is k in -12/7 + 4*k - 20/7*k**n + 4/7*k**3 = 0?
1, 3
Let g = 14 + -8. Suppose -x + 3*x - g = 0. Determine y so that -2*y + y**2 + 2*y**3 - y**4 + 3 - x + 0*y = 0.
-1, 0, 1, 2
Factor 696*t + 1296 + 2/9*t**3 + 220/9*t**2.
2*(t + 2)*(t + 54)**2/9
Suppose 4*u - 6*u + 4 = 0. Factor 13474 - 25*w**u - 6*w - 13474 + 9*w**3.
w*(w - 3)*(9*w + 2)
What is y in 1280 - 32*y + 1/5*y**2 = 0?
80
Let o = 105/334 + 532/167. Factor 1/2 - 5/2*a**3 + 11/2*a**2 - o*a.
-(a - 1)**2*(5*a - 1)/2
Let w(g) be the second derivative of g**4/6 + 17*g**3/6 + 15*g**2/2 + g - 32. Factor w(d).
(d + 1)*(2*d + 15)
Let r(g) be the first derivative of -2*g**5/5 + 3*g**4 - 6*g**3 + 4*g**2 + 42. Let r(t) = 0. Calculate t.
0, 1, 4
Let v(b) be the third derivative of -b**6/420 - b**5/210 + b**4/84 + b**3/21 - 3*b**2 - 14*b. Find n such that v(n) = 0.
-1, 1
Let w be 20/330 - (-15)/(-693)*-50. Find o, given that 0 - 10/7*o**2 - 2/7*o**4 - w*o**3 - 4/7*o = 0.
-2, -1, 0
Factor -87*q**2 + 42*q**2 + 40 - 36*q + 41*q**2.
-4*(q - 1)*(q + 10)
Suppose 0*m - 70 = 5*m - 5*v, -2*m - 5*v = 63. Let c = 19 + m. Let c*t**3 + 0*t + 0 - 1/4*t**4 + t**2 = 0. What is t?
-2, 0, 2
Let l(s) = -s**2 + 5 + 0*s - 3*s + 2*s + 0*s. Let y be l(0). Determine z so that -4*z + 5*z - 3*z - 3*z**y + 6 + 6*z**3 - z - 12*z**2 + 6*z**4 = 0.
-1, 1, 2
Let c = -25960/3 + 8654. Solve 2*r + 2/3 + c*r**3 + 2*r**2 = 0.
-1
Let z(u) be the second derivative of -u**5/50 + 37*u**4/15 - 1369*u**3/15 + 402*u. Factor z(k).
-2*k*(k - 37)**2/5
Suppose 4*c + 62 = 3*n, -4*c + 3*c - 75 = -5*n. Solve -n*f**3 + 2*f + 10*f**4 + 2*f**3 + 14*f - 14*f**4 = 0.
-2, 0, 1
Let n(k) be the second derivative of -k**6/6 + 3*k**5/2 - 5*k**4 + 25*k**3/3 - 15*k**2/2 - 83*k + 1. Factor n(p).
-5*(p - 3)*(p - 1)**3
Let h(l) be the first derivative of 375*l**3 + 151*l**2 + 22*l + 55. Let t(y) = 13500*y**2 + 3625*y + 265. Let w(f) = -25*h(f) + 2*t(f). Factor w(a).
-5*(15*a + 2)**2
Let g(n) = 9*n**3 + 667*n**2 - 457*n - 227. Let j(r) = -117*r**3 - 8670*r**2 + 5943*r + 2952. Let o(i) = 27*g(i) + 2*j(i). Factor o(d).
3*(d - 1)*(d + 75)*(3*d + 1)
Let i(n) be the first derivative of -3/20*n**4 - 2 - 81/5*n - 9/5*n**3 - 81/10*n**2. Find d, given that i(d) = 0.
-3
Let r = -1 + 3. Suppose -41*k + 22*k = -228. Determine u so that 27*u**r - 9*u**2 + 3 - u**3 - 3*u**4 + 6*u**4 - 11*u**3 - k*u = 0.
1
Let s be (-75)/(-18) - 3/18. Let v(m) be the second derivative of 3/4*m**2 + 1/8*m**3 - 3/16*m**s + 0 + 3*m. Determine c so that v(c) = 0.
-2/3, 1
Let m(u) = u - 1. Let z be m(9). Factor 0*a**3 - 5*a**2 + 45*a**4 + z*a**5 - 5*a**3 - 3*a**5 - 40*a**4.
5*a**2*(a - 1)*(a + 1)**2
Let m be 164577/140*8/(-9). Let h = m - -1046. Solve 0 - 4/15*i - 2/5*i**4 - 14/15*i**2 - h*i**3 = 0 for i.
-1, -2/3, 0
Let o(f) be the third derivative of -f**3 - 1/30*f**5 + 1/3*f**4 + 0 - 2*f**2 + 0*f. Factor o(b).
-2*(b - 3)*(b - 1)
Let f(t) = 8*t**5 + 748*t**4