 of j**8/10080 - j**7/3780 - j**4/6 - 11*j**2. Let w(i) be the second derivative of y(i). Suppose w(v) = 0. What is v?
0, 1
Let q(a) be the second derivative of a**5/160 + 5*a**4/48 + 17*a**3/48 + a**2/2 - 7*a + 2. Factor q(z).
(z + 1)**2*(z + 8)/8
Factor 9 - 21*k**2 + 4*k + 31 - 6*k**3 - 19*k**2 + 2*k**3.
-4*(k - 1)*(k + 1)*(k + 10)
Let w(y) be the first derivative of -y**3 + 18*y**2 + 135*y - 205. Suppose w(b) = 0. What is b?
-3, 15
Let v(t) be the first derivative of -t**4/4 - 19*t**3/3 - 17*t**2 + 304. Determine w so that v(w) = 0.
-17, -2, 0
Factor 117*b**2 + 445 - 3*b**3 - 108*b - 1089*b + 638.
-3*(b - 19)**2*(b - 1)
Factor 0 - 1/4*z**4 + 1/4*z + 1/4*z**2 - 1/4*z**3.
-z*(z - 1)*(z + 1)**2/4
Factor -1/6*m**3 - 38*m + 96 + 14/3*m**2.
-(m - 16)*(m - 6)**2/6
Let f(s) be the first derivative of s**6/135 + s**5/45 - s**4/54 - 2*s**3/27 - 12*s - 13. Let b(j) be the first derivative of f(j). Factor b(l).
2*l*(l - 1)*(l + 1)*(l + 2)/9
Let q = -7 + -20. Let p = q + 55/2. Factor -1/2*a**2 + 1/2*a**3 + 1/2*a**4 - p*a + 0.
a*(a - 1)*(a + 1)**2/2
Let p(y) be the second derivative of y**7/210 + 2*y**6/75 - y**5/100 - y**4/15 + 3*y - 1. Factor p(v).
v**2*(v - 1)*(v + 1)*(v + 4)/5
Let g = 45 + -27. Let r be 4*(-3 + g/4). Suppose -r*l + 1 - 2*l**2 - 10 + 5*l**2 = 0. Calculate l.
-1, 3
Let p(d) = 6*d**2 - 3*d + 2. Let c be ((-2)/10)/(6/(-30)). Let w be p(c). Solve -6*b**3 + 3*b**w + 3*b - 3/2*b**4 + 3*b**2 - 3/2 = 0 for b.
-1, 1/2, 1
Suppose 426 = 8*j + 426. Let c(a) be the second derivative of j*a**2 + 0 + 1/30*a**4 - 10*a - 2/15*a**3. Factor c(n).
2*n*(n - 2)/5
Factor -3 - 3*j**2 + 0*j**2 + 17 - 2 - 10*j + j**2.
-2*(j - 1)*(j + 6)
Let z be 1962/(-5) - 10/25. Let o = z + 394. Factor -3/5*f**5 + 0*f**4 + o*f**3 + 0*f**2 - 3/5*f + 0.
-3*f*(f - 1)**2*(f + 1)**2/5
Let o(y) be the third derivative of -5*y**8/21 - 4*y**7/7 + 55*y**6/24 + 95*y**5/12 + 15*y**4/2 + 10*y**3/3 + y**2 + 15*y. Let o(g) = 0. Calculate g.
-2, -1, -1/4, 2
Let c(m) = -9*m**3 + 28*m**2 - 28*m - 14. Let z(n) = -n**2 - 1. Let u = 17 - 10. Suppose -10*s + u*s = -3. Let h(p) = s*c(p) - 6*z(p). Factor h(q).
-(q - 2)**2*(9*q + 2)
Let l(w) be the second derivative of w**7/294 + 2*w**6/105 - w**5/20 - 5*w**4/42 + 48*w - 1. Factor l(t).
t**2*(t - 2)*(t + 1)*(t + 5)/7
Suppose 245*s**3 - 105*s**2 + 5*s**5 - 34*s**4 - 41*s**4 + 10595*s - 180*s**2 - 10485*s = 0. Calculate s.
0, 1, 2, 11
Let h(f) be the second derivative of 0*f**2 + 20*f - 1/40*f**5 + 0 - 1/12*f**3 - 1/12*f**4. Factor h(g).
-g*(g + 1)**2/2
Let v = 9040/7 + -47146/35. Let u = 56 + v. Factor -u*h**3 - 8/5*h**2 + 0 - 8/5*h.
-2*h*(h + 2)**2/5
Let j(f) = 16*f**2 + 1018*f - 286. Let w(x) = 65*x**2 + 4072*x - 1141. Let q(d) = 18*j(d) - 4*w(d). Factor q(a).
4*(a + 73)*(7*a - 2)
Let c(o) = -5*o**2 - 1188*o - 29417. Let w(d) = -6*d**2 - 1188*d - 29415. Let g(h) = -6*c(h) + 7*w(h). Factor g(a).
-3*(2*a + 99)**2
Let s(q) = 2*q + 1. Let j(g) = g**3 + 10*g**2 + 38*g + 29. Let o(x) = j(x) - 5*s(x). Solve o(b) = 0 for b.
-6, -2
Let p(x) = x**3 + 6*x**2 - 6*x + 9. Suppose a = -1 - 6. Let u be p(a). Solve -u*i**2 - 78*i - i**2 - 3 + 72*i = 0 for i.
-1
Let h(a) = 10*a + 2. Let g be h(-2). Let t be -4 - g/4 - (-3)/2. Factor b + 1/3*b**t + 0.
b*(b + 3)/3
Suppose -17*c = 26*c - 129. Let u(q) be the first derivative of 3/5*q**5 - q**c + q**2 + 9 - 1/2*q**4 + 0*q. Find t, given that u(t) = 0.
-1, 0, 2/3, 1
Factor -48/7*b - 2/7*b**3 - 18/7*b**2 - 32/7.
-2*(b + 1)*(b + 4)**2/7
Let z(j) be the first derivative of 6*j - 2/3*j**3 - 8 + 2*j**2. Factor z(v).
-2*(v - 3)*(v + 1)
Let a = 6620 - 46338/7. Factor 10/7*b - a*b**3 - 6/7*b**2 - 4/7 + 2/7*b**4.
2*(b - 1)**3*(b + 2)/7
Suppose 0 = -2*i - 4*w + 7*w - 13, 0 = 2*w - 2. Let j be (-3 - (-9 - i)) + (-14)/(-10). Find d, given that j + 93/5*d**2 - 72/5*d - 21*d**4 + 72/5*d**3 = 0.
-1, 2/7, 2/5, 1
Let s(t) = 5*t**2 - 9*t - 14. Let c be (0 - (-2 + 61)) + 4. Let w(h) = 70*h**2 - 125*h - 195. Let i(a) = c*s(a) + 4*w(a). Factor i(d).
5*(d - 2)*(d + 1)
Let t be (-448)/4256 - (-2)/19. Let t*f**2 + 4/7*f**3 + 2/7*f**4 - 2/7 - 4/7*f = 0. What is f?
-1, 1
Let h(x) be the first derivative of 1/15*x**5 - 1/54*x**6 + 1/36*x**4 + 2/3*x**2 - 4/9*x + 2 - 11/27*x**3. Find q such that h(q) = 0.
-2, 1, 2
Let p be 2*1/(-42)*-49. Determine f, given that -5/3*f**2 - p*f**4 - 1/3*f**5 - 5*f**3 + 16/3*f + 4 = 0.
-3, -2, -1, 1
Factor -88/3 + 4/3*q**3 + 60*q - 32*q**2.
4*(q - 22)*(q - 1)**2/3
Let h = 1/77 + 74/231. Let s(l) be the third derivative of 3*l**2 + 0*l + 0*l**6 + h*l**3 + 0*l**4 - 1/15*l**5 + 0 + 1/105*l**7. Find g, given that s(g) = 0.
-1, 1
Let n(z) be the third derivative of 7/8*z**4 + 0 + 13*z**2 + 0*z - z**3 - 3/20*z**5. Suppose n(y) = 0. What is y?
1/3, 2
Let n(h) = -h**3 + h + 1. Let c(m) = m**3 + m - 3. Let x(p) = -c(p) - 2*n(p). Let f(l) be the first derivative of x(l). Suppose f(t) = 0. Calculate t.
-1, 1
Factor 0 + 0*u**2 + 0*u - 2/3*u**3.
-2*u**3/3
Determine g, given that 6/5*g**2 - 24/5 + 0*g = 0.
-2, 2
Factor -1633*w**2 - 16 + 1639*w**2 - 12*w + 3*w**3 - w**3.
2*(w - 2)*(w + 1)*(w + 4)
Let k(q) = -q**2 - 54*q - 438. Let l be k(-10). Let t(b) be the first derivative of -2/11*b**3 - 2 + 4/11*b - 5/11*b**l. Factor t(r).
-2*(r + 2)*(3*r - 1)/11
Let -15 + s**2 - 7*s + 2 + 13 = 0. Calculate s.
0, 7
Suppose -50 = -5*d - 5*p, 4*p - 20 = -0*p. Solve -2*s**2 - 498 + d*s**2 - 3*s**4 + 498 = 0.
-1, 0, 1
Let o be -2 + 2 - (-12 + 9). Find i, given that 1/10*i**4 - 1/5*i + 0*i**o - 3/10*i**2 + 0 = 0.
-1, 0, 2
Solve -1/2*u**2 - 39*u - 1521/2 = 0 for u.
-39
Let u(f) be the third derivative of f**9/12096 - f**8/5376 - f**7/1008 + 7*f**4/24 - 2*f**2. Let l(s) be the second derivative of u(s). What is b in l(b) = 0?
-1, 0, 2
Let v = -186/7 + 572/21. Factor -2/3*o**3 + 0*o**2 + v*o + 0.
-2*o*(o - 1)*(o + 1)/3
Let t(q) be the second derivative of q**5/45 - 8*q**4/27 + 40*q**3/27 - 32*q**2/9 + 114*q. Solve t(a) = 0.
2, 4
Let k(f) be the second derivative of -f**7/231 + f**6/165 + f**5/55 - f**4/33 - f**3/33 + f**2/11 - 127*f. Let k(l) = 0. Calculate l.
-1, 1
Let t(w) = 4*w**2 + w - 1. Let u be t(1). Let c(g) = -g**2 - g + 1. Let j(q) = 4*q**2 - 10*q + 16. Let y(r) = u*c(r) + 2*j(r). Factor y(n).
4*(n - 3)**2
Let h(r) be the first derivative of 0*r**2 - 1/6*r**4 + 0*r + 2/5*r**5 - 4/9*r**3 - 10. Factor h(g).
2*g**2*(g - 1)*(3*g + 2)/3
Let y(m) be the second derivative of 1331*m**5/30 + 121*m**4/6 + 11*m**3/3 + m**2/3 - 166*m. Factor y(g).
2*(11*g + 1)**3/3
Let u(a) be the third derivative of 0*a - 5/4*a**4 + 3*a**2 + 0 + 3/2*a**3 + 1/10*a**6 - 9/20*a**5. Factor u(x).
3*(x - 3)*(x + 1)*(4*x - 1)
Let r(f) = -f**3 + 40*f**2 - 71*f - 188. Let g be r(38). Factor 0*u - g*u**2 + 6*u**3 + 0 - 5/2*u**4.
-u**2*(u - 2)*(5*u - 2)/2
Let a be 8/(16/6 + -2). Let y(i) = -21*i + 23 - 23*i**2 - 10 + a*i**2 + 7. Let f(u) = 32*u**2 + 62*u - 60. Let v(r) = 6*f(r) + 17*y(r). Factor v(j).
5*(j - 1)*(j + 4)
Factor -61/2*z**2 - 450 - 1/2*z**3 - 480*z.
-(z + 1)*(z + 30)**2/2
Determine a, given that 29*a**3 - 12*a**4 - 16*a**5 + 96*a - 64 + 156*a**2 + 244*a**2 + 167*a**3 + 36*a + 12*a = 0.
-2, -1, 1/4, 4
Let d(g) be the second derivative of 1/3*g**6 + 5/42*g**7 - 35/6*g**3 - 10/3*g**4 - 1/2*g**5 - 17*g + 0 - 5*g**2. Factor d(c).
5*(c - 2)*(c + 1)**4
Let i(r) be the first derivative of r**6/48 + r**5/10 - r**4/16 - r**3/2 + 9*r**2/16 - 6. Determine q, given that i(q) = 0.
-3, 0, 1
Suppose 420 = -5*y + 5*l, 2*y + 2*l + 252 = -y. Let m = y - -84. Factor 0*o**2 + m*o - 2/3*o**4 - 2/3*o**5 + 0 + 0*o**3.
-2*o**4*(o + 1)/3
Let q(b) = 5*b**2 + 4*b + 12. Let k(f) = -f**2 + f + 1. Let i = -15 + 20. Suppose 0 = i*d + 76 + 24. Let m(u) = d*k(u) - 5*q(u). Factor m(r).
-5*(r + 4)**2
Factor -1/3*y**3 + 4/3 + 1/3*y - 4/3*y**2.
-(y - 1)*(y + 1)*(y + 4)/3
Let q(c) be the first derivative of -c**7/560 + c**6/320 + c**5/40 - c**4/16 - 5*c**2 + 14. Let v(u) be the second derivative of q(u). Factor v(k).
-3*k*(k - 2)*(k - 1)*(k + 2)/8
Let s(q) = 49 + 49*q + 59*q - 70*q + q**2. Let z(c) = -c**2 - 78*c - 99. Let u(w) = 9*s(w) + 4*z(w). Factor u(y).
5*(y + 3)**2
Suppose -10*v**3 + 10*v - 4/3*v**4 + 14/3 - 10/3*v**2 = 0. Calculate v.
-7, -1, -1/2, 1
Suppose -4*j = -12, 0 = -4*r - 2*j - j + 65. Factor r + 2*n**2 + 0*n**2 - 6 - 8*n.
2*(n - 2)**2
Suppose -4*w + 2*w + 6 = 0. Suppose -2*c + w = -