3)
Let k(j) be the first derivative of 4*j**3/3 + 8*j**2 + 12*j + 7. Let k(l) = 0. Calculate l.
-3, -1
Let l(y) = -y**4 - y**2 - 1. Let b(t) = 6*t**4 - 10*t**3 - 8*t**2 - 8*t + 8. Let r(c) = b(c) + 8*l(c). Factor r(u).
-2*u*(u + 1)*(u + 2)**2
Let c = 2230/117 + -320/13. Let w = 62/9 + c. What is m in w*m + 0 + 2*m**2 + 2/3*m**3 = 0?
-2, -1, 0
Let n = 25 + 20. Let d be ((-6)/n)/(7/(-21)). Factor 0 + 0*q - d*q**4 + 2/5*q**2 + 0*q**3.
-2*q**2*(q - 1)*(q + 1)/5
Suppose 2*r + l + 4 = -3*l, 4*l + 12 = 2*r. Let a = -2 + r. Factor 0 + 0*k**4 + 1/5*k**3 + a*k**2 + 0*k - 1/5*k**5.
-k**3*(k - 1)*(k + 1)/5
Let z(q) = q**3 + q**2 + 2*q - 2. Let a be z(1). Let v be 0/(a/((-6)/9)). Let 0*m + v*m**2 - 1/3*m**3 - 1/3*m**4 + 0 = 0. Calculate m.
-1, 0
Let n = 1 + 2. Let g(d) be the first derivative of -1/2*d**2 - 1/6*d**n + 3/5*d**5 + 7/8*d**4 + 0*d - 1. Determine t, given that g(t) = 0.
-1, -2/3, 0, 1/2
Let p(j) be the second derivative of j**6/50 - 9*j**5/50 + j**4/20 + 12*j**3/5 + 24*j**2/5 - 12*j. Factor p(d).
3*(d - 4)**2*(d + 1)**2/5
Let l(j) = -63*j**3 + j - 1. Let v be l(1). Let q be ((-24)/v)/(1/15). Factor -66/7*b**2 - 8/7 + 40/7*b**3 + q*b - 8/7*b**4.
-2*(b - 2)**2*(2*b - 1)**2/7
Let s be (4/8)/((-1)/(-6)). Let p(z) be the first derivative of -1/14*z**4 + 0*z - 4/21*z**s + 2 - 1/7*z**2. Factor p(q).
-2*q*(q + 1)**2/7
Let c(p) be the first derivative of 49*p**8/1200 + 7*p**7/100 + 7*p**6/150 + p**5/75 + p**3/3 - 2. Let n(d) be the third derivative of c(d). Factor n(a).
a*(7*a + 2)**3/5
Let c(m) be the first derivative of m**4/20 - m**2/10 - 5. Factor c(z).
z*(z - 1)*(z + 1)/5
Let u(x) be the first derivative of 1 + 0*x + 2/45*x**5 + 1/18*x**4 - 2/27*x**3 - 1/9*x**2. Factor u(t).
2*t*(t - 1)*(t + 1)**2/9
Determine q so that -2/3*q**3 + 0 - 2/3*q**4 - 2/9*q**5 - 2/9*q**2 + 0*q = 0.
-1, 0
Suppose 2*r = -22 + 30. Let j be ((-8)/(-10))/((-2)/(-10)). Factor -j - 2*u**2 - 3*u - r*u + 4*u - 3*u.
-2*(u + 1)*(u + 2)
Let b(r) be the first derivative of -r**4/16 + r**3/4 - 3*r**2/8 + r/4 + 15. Let b(p) = 0. What is p?
1
Suppose -2*y + 7 + 0 = -3*a, y - 3*a + 1 = 0. Let s be 144/90*2/y. What is b in 0*b**3 + 2/5*b**5 - 4/5*b**4 - s*b + 0 + 4/5*b**2 = 0?
-1, 0, 1
Let w(d) be the second derivative of d**7/14 - 7*d**6/10 + 9*d**5/4 - 9*d**4/4 + 14*d. Factor w(m).
3*m**2*(m - 3)**2*(m - 1)
Let d(m) be the third derivative of m**6/60 + 4*m**5/15 + 4*m**4/3 - 12*m**2. Suppose d(s) = 0. Calculate s.
-4, 0
Let j(z) be the third derivative of z**7/840 - z**5/40 + z**4/12 + z**3/6 + 2*z**2. Let r(i) be the first derivative of j(i). Factor r(m).
(m - 1)**2*(m + 2)
Let x(t) be the second derivative of 1/120*t**6 - 1/40*t**5 - 1/8*t**2 + 0 + 1/12*t**3 - 3*t + 0*t**4. Find k such that x(k) = 0.
-1, 1
Suppose 0 = -4*h + 20, c + 2*h = 5*c - 6. Factor -d + 7*d**2 + 0*d - 5*d - 10*d + c.
(d - 2)*(7*d - 2)
Let n(c) be the third derivative of -c**5/90 + c**4/36 + 10*c**2. Factor n(i).
-2*i*(i - 1)/3
Let u = -89/1860 + 2/31. Let g(v) be the third derivative of 0*v + v**2 - 1/6*v**4 + 0 + u*v**5 + 1/2*v**3. Let g(w) = 0. Calculate w.
1, 3
Let l(y) = 2*y**2 - y - 1. Let x(t) = -42*t**2 + 34*t + 22. Let w(g) = -44*l(g) - 2*x(g). Factor w(s).
-4*s*(s + 6)
Suppose 5*f + 0*f = 50. Let a be ((-4)/3)/(f/(-6)). Let -2/5*n**2 + 0 - 2/5*n**4 - a*n**3 + 0*n = 0. Calculate n.
-1, 0
Let v(r) be the second derivative of r**7/525 - r**6/100 + r**5/50 - r**4/60 + r**2 - 2*r. Let f(t) be the first derivative of v(t). Solve f(d) = 0 for d.
0, 1
Let g(k) be the second derivative of -k**7/42 + k**6/10 - 3*k**5/20 + k**4/12 + 6*k. Determine r, given that g(r) = 0.
0, 1
Find i such that 0*i + 1/5*i**2 + 0 = 0.
0
Let p(t) be the first derivative of -2*t**3/3 - t**2/2 - 2*t + 11. Let x(b) = 2 + 1 + 2*b + 2*b**2 - 1. Let z(a) = 2*p(a) + 3*x(a). Find y, given that z(y) = 0.
-1
Suppose -f - 5*r + 28 = 0, 3*f - r = f + 1. Let x(q) = -3*q**2 + 3*q + 6. Let n(z) = 2*z**2 - z - 3. Let c(i) = f*x(i) + 5*n(i). Solve c(l) = 0 for l.
-3, -1
Let h(x) be the second derivative of x**5/5 + x**4 + 2*x**3 + 2*x**2 + 12*x. Factor h(g).
4*(g + 1)**3
Factor 4*c**2 + c**2 + 4*c**3 + 3*c**2 - 4*c**2 - 8*c.
4*c*(c - 1)*(c + 2)
Let d(s) be the third derivative of s**8/13440 + s**7/1260 + s**6/288 + s**5/120 - 5*s**4/24 - s**2. Let g(t) be the second derivative of d(t). Factor g(k).
(k + 1)**2*(k + 2)/2
Let f(g) = g**4 + 17*g**3 + 7*g**2 - 17*g - 12. Let y(k) = -2*k**4 - 52*k**3 - 20*k**2 + 52*k + 36. Let x(r) = 7*f(r) + 2*y(r). Find s such that x(s) = 0.
-4, -1, 1
Let 2/5*g**2 + 2/5*g - 2/5*g**4 + 0 - 2/5*g**3 = 0. Calculate g.
-1, 0, 1
Let h(r) = -8*r**3 + 5*r**2 + 5*r. Let i(n) = -55*n**3 + 35*n**2 + 35*n. Let g(o) = 15*h(o) - 2*i(o). What is q in g(q) = 0?
-1/2, 0, 1
Let x(n) be the third derivative of n**7/840 - n**5/120 + n**3/24 + 2*n**2 - 12*n. Factor x(h).
(h - 1)**2*(h + 1)**2/4
Let v be (-63)/486*(-1)/7. Let z(w) be the second derivative of v*w**4 + 0*w**2 - w + 1/27*w**3 + 0. Solve z(a) = 0.
-1, 0
Factor -5/4*a**5 + 0*a**2 + 0 - 15/4*a**4 + 0*a - 5/2*a**3.
-5*a**3*(a + 1)*(a + 2)/4
Let i = -3493/5 - -701. Let -8/5*p + 2/5*p**4 + i*p**2 - 8/5*p**3 + 2/5 = 0. Calculate p.
1
Let y be (-2)/(-8) + (-3)/(24/(-14)). Determine r, given that 2/5*r**4 + 4/5*r**3 + 0*r + 0 + 2/5*r**y = 0.
-1, 0
Let k = -9/26 + 123/130. Solve -1/5*p**3 + p - 1/5*p**2 - k = 0 for p.
-3, 1
Let u = 61/24 - 1/24. Suppose 2*a - 4 - u*a**3 + 3*a**2 + 1/2*a**4 = 0. What is a?
-1, 2
Let k be 0/2 + (-30)/(-40). Factor k - 3/4*i**2 + 0*i.
-3*(i - 1)*(i + 1)/4
Let h be (-4 - 1)/((-32)/336). Let f = h - 51. Factor -3/2*i**2 + 0*i + 0 - f*i**5 - 9/2*i**3 - 9/2*i**4.
-3*i**2*(i + 1)**3/2
Let 5/3*w**5 + 10*w**4 + 5*w + 0 + 50/3*w**2 + 20*w**3 = 0. What is w?
-3, -1, 0
Let h(g) = 3*g - 4. Let i be h(3). Suppose 0 = n + 4*p - 4 - 8, -2*n - i*p + 18 = 0. Solve 0*w + 1/2*w**2 + 0 + 32*w**5 + 24*w**n + 6*w**3 = 0 for w.
-1/4, 0
Let l(x) be the third derivative of -x**8/84 + 8*x**7/105 - x**6/6 + 2*x**5/15 - 14*x**2. Factor l(b).
-4*b**2*(b - 2)*(b - 1)**2
Let g(y) = -y**3 - 7*y**2 + 5*y + 35. Let t be g(-7). Find j, given that t*j**3 + 0 + 0*j - 2/5*j**2 + 2/5*j**4 = 0.
-1, 0, 1
Let y(n) = 22*n**2 - 60*n + 17. Let t(j) = 265*j**2 - 720*j + 205. Let k(l) = 3*t(l) - 35*y(l). Factor k(p).
5*(p - 2)*(5*p - 2)
Factor -30*l - 90 - 5/2*l**2.
-5*(l + 6)**2/2
Solve 0*p + 0 + 1/4*p**4 + 0*p**3 + 0*p**2 = 0 for p.
0
Let s(y) be the second derivative of y**6/20 + y**5/20 - y**4/24 - 37*y. Solve s(a) = 0.
-1, 0, 1/3
Determine c so that -c + 2*c**3 - 11*c + 8 + 2*c**3 = 0.
-2, 1
Let u(g) be the third derivative of -7*g**2 + 0*g**5 - 1/560*g**8 + 0 + 0*g**3 + 1/100*g**6 + 0*g - 1/40*g**4 + 0*g**7. Solve u(j) = 0.
-1, 0, 1
Let i(p) = 7*p**3 - p**2 + p - 1. Let v be i(1). Let s be (v/(-8))/((-2)/1296). Factor -87*u + s*u**2 - 729*u**3 - 70*u + 8 + 49*u.
-(9*u - 2)**3
Let v(l) be the second derivative of -l**7/21 + 16*l**6/105 - 11*l**5/70 + l**4/21 + 12*l. Factor v(b).
-2*b**2*(b - 1)**2*(7*b - 2)/7
Let a(o) = -12*o**2 - 51*o - 66. Let z(i) = i**2 + 4*i + 5. Let n(u) = 2*a(u) + 27*z(u). Factor n(t).
3*(t + 1)**2
Let b = 13 - 8. Determine p, given that 0*p**2 + b + 6*p**2 - 9 - 10*p = 0.
-1/3, 2
Let d(u) be the third derivative of -u**6/120 - u**5/30 + u**4/24 + u**3/3 - 10*u**2. Factor d(s).
-(s - 1)*(s + 1)*(s + 2)
Let b = -14 + 16. Find l such that -4 - b*l**2 + 4 + 5*l**2 = 0.
0
Let h = -80 - -78. Let o be 2 + 0 + -2 + 1. Let z(u) = u**3 + 1. Let l(a) = -a**5 + 3*a**3 + 2. Let d(i) = h*z(i) + o*l(i). Factor d(b).
-b**3*(b - 1)*(b + 1)
Solve 0 - 2*y**4 + 0*y - 2*y**3 - 2/3*y**2 - 2/3*y**5 = 0.
-1, 0
Let t be (6/42 - 0) + (-2)/(-2). Find j, given that 10/7*j**4 - 2/7*j**5 - 2/7*j**2 + 16/7*j - 2*j**3 - t = 0.
-1, 1, 2
Let x be -12*(5 + (-16)/3). Suppose -4/7*m**3 - 8/7 + 8/7*m + 6/7*m**2 - 2/7*m**x = 0. What is m?
-2, 1
Let d(a) = -3*a**3 + a. Let h be d(-1). Factor -5*i + 5*i + 4*i**h - 2*i**3.
-2*i**2*(i - 2)
Let w = -2/459 + 10112/3213. Let l = -266 + 1866/7. Suppose -l - w*c**3 + 6/7*c**4 - 2/7*c + 22/7*c**2 = 0. What is c?
-1/3, 1, 2
Let t(u) = 2*u**2 - 2*u - 1. Let a be t(2). Find j such that -j**2 - j + j - j**4 + 2*j**a = 0.
0, 1
Let a = 127 + -253/2. Factor -2*g - a*g**4 - 1/2 - 3*g**2 - 2*g**3.
-(g + 1)**4/2
Factor 6/7*c**3 + 2/7*c**4 - 10/7*c**2 + 0 + 4/7*c - 2/7*c**5.
-