3. Factor j(p).
2*(p - 1)*(p + 1)
Suppose 8 = j + j. Factor 5*q**3 - 166 + 6*q**2 + 14*q**3 + 166 - 7*q**j.
-q**2*(q - 3)*(7*q + 2)
Let b = -59 + 61. Factor -52*a + 33*a + 27*a + b*a**2.
2*a*(a + 4)
Suppose 246 = -5*m - 44. Let i = 58 + m. Solve 1/4*b + i - 1/4*b**2 = 0 for b.
0, 1
Let i(j) = -4*j + 36. Let d be i(8). Suppose x + 8 = -2*u, 1 = d*x + u - 2. Factor 18/5*l**3 + 12/5*l**x + 0 + 2/5*l.
2*l*(3*l + 1)**2/5
Factor -2/5*l**3 + 4 - 6/5*l - 12/5*l**2.
-2*(l - 1)*(l + 2)*(l + 5)/5
Factor 21*b**2 - 4*b**3 + 150*b + 13*b**3 - 132*b + 12*b**2.
3*b*(b + 3)*(3*b + 2)
Let -63/4*a + 1/4*a**3 - 15/2*a**2 - 8 = 0. What is a?
-1, 32
Let u(s) be the second derivative of -5*s**4/24 + 235*s**3/6 - 11045*s**2/4 + 165*s. Factor u(r).
-5*(r - 47)**2/2
Let j(c) = 5*c**2 - 2. Let b be j(1). Let f(p) = -p**3 - p**2 + p + 1. Let x(y) = y**2 - 1. Let q(s) = b*x(s) + f(s). Find k such that q(k) = 0.
-1, 1, 2
Let f = 16360 + -16358. Factor 21 - 6*u + 3/7*u**f.
3*(u - 7)**2/7
Let j = 18/143 + -2287/19305. Let i(d) be the third derivative of -j*d**6 + 0 + 1/270*d**5 - 5*d**2 + 0*d + 0*d**4 + 1/315*d**7 + 0*d**3. Factor i(u).
2*u**2*(u - 1)*(3*u - 1)/9
Let y be (-3 - -1)/(-8 - (-36)/8). Determine s so that 6/7*s + y + 2/7*s**2 = 0.
-2, -1
Let j(z) be the first derivative of -z**5 - 5*z**4/4 + 20*z**3/3 + 10*z**2 - 5. Solve j(s) = 0 for s.
-2, -1, 0, 2
Let r(u) = u**5 - u**3 + u**2 - u. Let w(z) = 8*z**5 - 11*z**3 + 5*z**2 - 2*z. Let y(d) = -5*r(d) + w(d). Let y(t) = 0. Calculate t.
-1, 0, 1
Let n(h) be the second derivative of -h**6/135 + h**5/45 + 5*h**4/18 - 32*h**3/27 + 16*h**2/9 - 205*h. Determine u, given that n(u) = 0.
-4, 1, 4
Factor -96*k**5 - 46*k**5 + 40*k**4 + 147*k**5.
5*k**4*(k + 8)
Let h(m) be the second derivative of -m**6/240 + m**5/20 + 5*m**3/3 + 9*m. Let v(i) be the second derivative of h(i). Factor v(n).
-3*n*(n - 4)/2
Let a be (-9135)/(-870) - (9 - -1). Factor 0 + 7/4*z**2 - 7/4*z**4 - 1/2*z + a*z**3.
-z*(z - 1)*(z + 1)*(7*z - 2)/4
Let z(k) be the third derivative of -k**5/210 + 2*k**4/7 - 48*k**3/7 + 208*k**2. Factor z(b).
-2*(b - 12)**2/7
Let c(f) be the third derivative of -f**8/16800 - f**7/6300 + 7*f**4/12 + 4*f**2. Let w(k) be the second derivative of c(k). Find b, given that w(b) = 0.
-1, 0
Let y(q) = -2*q - 3. Let f be y(-3). Factor 3*a**3 - 11*a**2 + 0*a**f + 5*a + 4*a + 3*a - 4.
(a - 2)*(a - 1)*(3*a - 2)
Let q be -3 - ((7 - 2) + -16). Factor x**3 - q*x**2 + 7*x**4 + 4*x - 7*x**4 + 0*x + 3*x**4.
x*(x - 1)*(x + 2)*(3*x - 2)
Let r(c) be the second derivative of -c**7/7 + 19*c**6/15 - 33*c**5/10 + 3*c**4/2 + 30*c + 2. Factor r(d).
-2*d**2*(d - 3)**2*(3*d - 1)
Let j be 170/(-340) - 11/(-6). Factor -2/9*t**2 - j*t - 10/9.
-2*(t + 1)*(t + 5)/9
Let d = -95/1628 - -3/37. Let l(k) be the third derivative of 0 - 2/33*k**3 + 1/165*k**5 + 4*k**2 + 0*k + d*k**4. Suppose l(w) = 0. What is w?
-2, 1/2
Suppose 3*p - y - 14 = 0, -3*y + 4*y = p - 4. Let v(m) = -m**3 + 5*m**2 - 2*m + 12. Let w be v(p). Factor -10/7*h + 2/7*h**w + 8/7.
2*(h - 4)*(h - 1)/7
Let v(m) be the second derivative of m**6/15 - 9*m**5/10 + 3*m**4 + 4*m**3/3 - 24*m**2 + m + 56. Solve v(t) = 0.
-1, 2, 6
Let g(m) = -58*m**2 - 2080*m - 108148. Let i(z) = 24*z**2 + 832*z + 43259. Let y(u) = 5*g(u) + 12*i(u). Factor y(r).
-2*(r + 104)**2
Let c(m) be the first derivative of 4*m**5/35 - 32*m**4/7 + 296*m**3/7 + 1088*m**2/7 + 1156*m/7 + 108. Suppose c(b) = 0. What is b?
-1, 17
Let v be 27*(-18)/(-2106)*13. Find g such that 1/4*g - 1/4*g**v + 3/4*g**2 - 3/4 = 0.
-1, 1, 3
Let f = -63 + 66. Let 0*h**2 - 43*h**3 + 18*h + 37*h**3 - f*h**4 + 15*h**2 = 0. What is h?
-3, -1, 0, 2
Let p(v) be the second derivative of v**10/30240 - v**8/6720 - v**4/6 - 11*v. Let t(u) be the third derivative of p(u). Factor t(w).
w**3*(w - 1)*(w + 1)
Suppose 24*k - 3 = 27*k. Let u be ((-8)/(-84))/k*-9. Solve -8/7*v - u - 2/7*v**2 = 0.
-3, -1
Factor 215/9*l + 1/9*l**2 + 0.
l*(l + 215)/9
Suppose -5*x + 79 = -131. Solve -24*h**3 - 2*h**4 - 18*h**3 + 2*h**2 + x*h**3 = 0 for h.
-1, 0, 1
Suppose 5*v + 25*v + 10*v**2 - v**2 - 48 - 12*v**2 = 0. What is v?
2, 8
Let o = -564 + 303. Let r = o - -264. Determine b, given that 0*b**2 - 2/3 + 4/3*b**r - 4/3*b + 2/3*b**4 = 0.
-1, 1
Let b = -1988 - -1991. Factor -3*h**2 - 25 - 1/5*h**b - 15*h.
-(h + 5)**3/5
Let a(q) be the third derivative of -q**5/150 - q**4/20 + 4*q**3/15 - 429*q**2. Factor a(u).
-2*(u - 1)*(u + 4)/5
Let n(f) be the third derivative of f**6/450 + f**5/15 + 3*f**4/10 - 8*f**3/3 - 27*f**2. Let x(s) be the first derivative of n(s). Factor x(u).
4*(u + 1)*(u + 9)/5
Let j = 12538947/13 - 964025. Let f = 510 - j. Factor -8/13*o - 2/13*o**5 + 0 - f*o**2 + 6/13*o**3 + 4/13*o**4.
-2*o*(o - 2)**2*(o + 1)**2/13
Let r be ((-36)/(-70))/((-10)/((-2800)/21)). Factor 24/7*d + r + 3/7*d**2.
3*(d + 4)**2/7
Let h(l) be the third derivative of -l**7/1050 + l**6/200 - l**4/30 + 62*l**2. Factor h(s).
-s*(s - 2)**2*(s + 1)/5
Factor 6/7*q**2 + 2/7*q**4 - 8/7 + 8/7*q**3 - 8/7*q.
2*(q - 1)*(q + 1)*(q + 2)**2/7
Let j(g) be the second derivative of 0 + 15*g - 2*g**3 + 18*g**2 + 1/12*g**4. Determine c so that j(c) = 0.
6
Let z = 1067 + -1057. Let y(h) be the first derivative of -20*h - 5/2*h**4 - 10*h**2 + 25*h**3 - z - 5*h**5. Find x, given that y(x) = 0.
-2, -2/5, 1
Let x(b) be the second derivative of -b**7/14 - 4*b**6/5 - 27*b**5/10 + 27*b**3/2 - b + 3. Suppose x(q) = 0. Calculate q.
-3, 0, 1
Let n(x) be the second derivative of -x**6/2 - 17*x**5/4 + 5*x**4/2 + 224*x. Find q, given that n(q) = 0.
-6, 0, 1/3
Let c be 10/(-20)*(2 - 2). Let i(f) be the second derivative of 1/42*f**4 - 1/105*f**6 + 7*f + 0 - 1/21*f**3 + 1/70*f**5 + c*f**2. Factor i(b).
-2*b*(b - 1)**2*(b + 1)/7
Let u(g) = -g - 4. Let h be u(-4). Suppose h = 2*w - 3*j + 5, -2*w + 13 - 3 = 2*j. Factor -o - w*o - 7 + 3 - o - o**2.
-(o + 2)**2
Let d(l) be the second derivative of l**4/48 + l**3/12 + l**2/8 + 41*l. Find m such that d(m) = 0.
-1
Let x(m) = 32*m**2 + 2*m - 2. Let r be x(1). Let b = r + -27. Let -b*l + l + 4*l + l - l**2 = 0. Calculate l.
0, 1
Let u(v) be the third derivative of 1/480*v**6 + 9/8*v**4 + 3/40*v**5 - 4*v**2 + 9*v**3 + 0 + 2*v. Let u(t) = 0. What is t?
-6
Suppose -48*p = 32*p + 41*p - 363. Determine g so that 1/4 - 1/4*g + 1/4*g**p - 1/4*g**2 = 0.
-1, 1
Let t(c) be the first derivative of c**4/8 + 17*c**3/6 - 29*c**2/2 + 20*c - 310. Factor t(i).
(i - 2)*(i - 1)*(i + 20)/2
Let f = -57 + 55. Let b(o) = -o**2 + o + 6. Let y be b(f). Factor 6*q**3 + 3*q**4 + y + 15/4*q**2 + 3/4*q.
3*q*(q + 1)*(2*q + 1)**2/4
Find r, given that 50*r**2 + 312 + 80 - 48*r**2 - 56*r = 0.
14
Let j be 9660/126 + (1 - 0)/(-3). Let n = j + -75. Factor 2/3 + 2/3*c**2 - n*c.
2*(c - 1)**2/3
Let u = -11015 + 11017. Factor -5/2 + 3*d - 1/2*d**u.
-(d - 5)*(d - 1)/2
Let h = -64166/5 - -12880. Let z(o) be the first derivative of -40*o**2 - 41/2*o**4 - 8*o + 27*o**6 + h*o**5 + 5 - 226/3*o**3. Determine g, given that z(g) = 0.
-1, -2/9, 1
Suppose -2*q - 3*q + 80 = 0. Factor -4*o**2 + 4*o**2 + 2*o - 10*o - q*o**3 - 44*o**2 + 20*o**4.
4*o*(o - 2)*(o + 1)*(5*o + 1)
Let z be (-40)/336*4/(-100). Let r(g) be the third derivative of 0*g**5 - z*g**7 - 4*g**2 + 0*g**6 - 1/336*g**8 + 0*g**3 + 0*g + 0 + 0*g**4. Factor r(q).
-q**4*(q + 1)
Let u(v) be the second derivative of 13*v - 3/5*v**5 - 5/3*v**4 - 4/3*v**3 + 2/15*v**6 + 2/21*v**7 + 0*v**2 + 0. Determine g, given that u(g) = 0.
-1, 0, 2
Let q be (6/(-12))/(1/(-6)). Suppose a = 2*z - 0*a - 5, 0 = -3*a - q. What is v in -z*v**3 - 2*v**2 + 0*v**2 + 2*v**5 + 2*v**4 + 3*v**5 - 3*v**5 = 0?
-1, 0, 1
Factor 42*i**2 + 43904 + 2352*i + 1/4*i**3.
(i + 56)**3/4
Suppose 3*f = -k + 8 - 23, 0 = -5*k + 2*f - 41. Let b = k - -11. Factor 0*g + b*g + g**2 - 3*g**2.
-2*g*(g - 1)
Suppose w + 219 + 245 = -3*o, 133 = -o + 4*w. Let a = o - -155. Factor 1/4*l**a + 1/2 + 3/4*l.
(l + 1)*(l + 2)/4
Let q = -351/196 - -100/49. Factor -q*t**2 + 0 + 1/4*t**3 - 1/2*t.
t*(t - 2)*(t + 1)/4
Let y(s) be the first derivative of 23/2*s**4 - 30*s**3 - 11/5*s**5 + 11 - 27*s + 81/2*s**2 + 1/6*s**6. Factor y(n).
(n - 3)**3*(n - 1)**2
Let l be (2/(-3))/(7/(-21)). Let p(b) be the first derivative of 3/5*b**5 + 3/4*b**4 - 3/2*b**l - 4 + 0*b - b**3. Factor p(h).
3*h*(h - 1)*(h + 1)**2
Let a(r) = 3*r**3 - 6*r**2 + 9*r - 1. Let b(x) = 2*x**3 - 1