- 1)
Factor -4/7*x + 6/7*x**2 - 2/7*x**4 + 0*x**3 + 0.
-2*x*(x - 1)**2*(x + 2)/7
Suppose -3*w = -f - 17, 4 = -2*w + 14. Let o be 10/6 + f/(-6). Factor -4*l**o + 2*l + 2*l**2 + 0*l**2.
-2*l*(l - 1)
Find o such that -2/9*o**4 - 4/9*o**2 - 8/9*o + 8/9*o**3 + 2/3 = 0.
-1, 1, 3
Let v(b) be the second derivative of 1/40*b**5 + 0*b**4 - 1/12*b**3 + 0 + 0*b**2 + 5*b. Suppose v(g) = 0. What is g?
-1, 0, 1
Let k(f) = 4*f - 2. Let x be k(2). Find j such that -6*j**3 - 8*j**5 - j**5 + 7*j**5 + 2*j**2 + x*j**4 = 0.
0, 1
Let b(h) be the first derivative of 0*h + 38*h**5 + 8*h**2 + 25/3*h**6 + 104/3*h**3 + 57*h**4 + 4. Suppose b(o) = 0. Calculate o.
-2, -1, -2/5, 0
Let m be 7 - (-1 + (0 - -3)). Find f such that 4*f**3 + 6*f**2 + 2 + 0*f - 2*f**m + 2*f**4 - 2*f - 10*f**2 = 0.
-1, 1
Factor 1/3*c + 0*c**2 - 1/3*c**3 + 0.
-c*(c - 1)*(c + 1)/3
Let a(y) be the second derivative of y**10/211680 - y**8/23520 + y**6/5040 - y**4/3 + 9*y. Let r(x) be the third derivative of a(x). Factor r(l).
l*(l - 1)**2*(l + 1)**2/7
Let x(n) be the first derivative of n**6/3 + 14*n**5/5 + 19*n**4/2 + 50*n**3/3 + 16*n**2 + 8*n + 2. Determine l, given that x(l) = 0.
-2, -1
Let n(v) be the first derivative of 0*v**4 + 0*v**2 + 1/60*v**5 + 2*v - 1/18*v**3 + 1. Let f(z) be the first derivative of n(z). Factor f(o).
o*(o - 1)*(o + 1)/3
Suppose 3 - 7 = r. Let b be (-18)/r*2/3. Factor -2*d**5 - 4*d**3 + 5*d**3 + b*d**5 - 2*d**4.
d**3*(d - 1)**2
Factor -3/7 + 3/7*x**2 - 12/7*x**3 + 12/7*x.
-3*(x - 1)*(x + 1)*(4*x - 1)/7
Let l(w) be the first derivative of -w**3/5 + 6*w**2/5 - 9*w/5 - 2. Find q such that l(q) = 0.
1, 3
Let p(q) be the second derivative of 1/12*q**4 - 1/6*q**3 - 5*q + 0*q**2 + 0. Suppose p(r) = 0. Calculate r.
0, 1
Let o(u) be the third derivative of -u**8/210 - u**7/175 + 13*u**6/300 + 17*u**5/150 + u**4/20 - 2*u**3/15 + 19*u**2. Suppose o(q) = 0. Calculate q.
-1, 1/4, 2
Let f = -4 - -6. Let n(i) be the second derivative of -1/60*i**6 + 1/24*i**4 + i + 1/40*i**5 + 0 + 0*i**f - 1/12*i**3. Factor n(k).
-k*(k - 1)**2*(k + 1)/2
Let n = -6 + 10. Suppose -5*u + 0 = -5*j + 5, -4*j = 2*u - 22. Factor -4*l + 4*l**j - 2*l + 0 + 6*l**3 - 3 - l**n.
3*(l - 1)*(l + 1)**3
Let s(j) be the second derivative of 9*j**7/70 + 2*j**6/5 + j**5/4 - j**4/4 - j**2 + 3*j. Let u(c) be the first derivative of s(c). Find w, given that u(w) = 0.
-1, 0, 2/9
Let z be (-38)/8 - (10/2 + -10). Factor 3/4*o + z - 3/4*o**3 + o**4 - 5/4*o**2.
(o - 1)**2*(o + 1)*(4*o + 1)/4
Let h(a) be the second derivative of a**10/105840 - a**9/26460 + a**8/23520 + 5*a**4/12 - 4*a. Let p(x) be the third derivative of h(x). Factor p(g).
2*g**3*(g - 1)**2/7
Let s(p) = -p**2 + 13*p - 20. Let j be s(11). Let z = -40 - -121/3. Determine o, given that 1/2*o - z - 1/6*o**j = 0.
1, 2
Let q(p) be the second derivative of p**6/45 + p**5/15 - p**4/6 - 8*p**3/9 - 4*p**2/3 - 11*p. Factor q(w).
2*(w - 2)*(w + 1)**2*(w + 2)/3
Let u = 10 - 1. Suppose 4*x - 21 + u = 4*a, 5*x = 3*a + 19. Factor 2/9*t**3 + 4/9*t**a + 0*t + 0.
2*t**2*(t + 2)/9
Let m(q) be the third derivative of -3*q**5/20 - q**4/8 + q**3 - 10*q**2 - q. Factor m(h).
-3*(h + 1)*(3*h - 2)
Let v(a) be the third derivative of -a**6/120 + a**4/24 - 18*a**2. Let v(p) = 0. Calculate p.
-1, 0, 1
Suppose -3*z - 3*l - 11 + 35 = 0, 5*l = -3*z + 34. Suppose -a = 3*h - 19 - 11, 3*a + 30 = z*h. Factor -5*r + 4*r**3 + 4*r**2 + 0*r**2 + h*r**3 - 4 - 9*r.
2*(r - 1)*(r + 1)*(7*r + 2)
Let t(g) = -g**2 + 9*g - 17. Let x = -19 - -28. Let u = 5 + -3. Let j(q) = -2*q + 4. Let f(o) = u*t(o) + x*j(o). Factor f(w).
-2*(w - 1)*(w + 1)
Factor 0 - 1/2*r - 1/4*r**4 + 1/4*r**2 + 1/2*r**3.
-r*(r - 2)*(r - 1)*(r + 1)/4
Factor -1/4*h - 1/4*h**2 + 0.
-h*(h + 1)/4
Factor -6/7*i - 2/7 - 4/7*i**2.
-2*(i + 1)*(2*i + 1)/7
Let h = 10 - 7. Factor 3*r**3 + 3*r**h - r**4 - 5*r**3.
-r**3*(r - 1)
Let p(o) be the second derivative of o**7/126 - o**6/30 + o**5/30 + o**4/18 - o**3/6 + o**2/6 + 3*o. Solve p(j) = 0 for j.
-1, 1
Let i(j) be the third derivative of -j**6/180 - j**5/120 + j**4/24 + j**3/6 + 2*j**2. Let u(r) be the first derivative of i(r). Factor u(y).
-(y + 1)*(2*y - 1)
Let a(v) be the third derivative of -v**5/90 + v**4/36 - 4*v**2. Factor a(c).
-2*c*(c - 1)/3
Suppose 3*v = 5*v. Let h(m) be the third derivative of 0*m**4 + 1/9*m**3 + v + 0*m + 2*m**2 - 1/90*m**5. Factor h(z).
-2*(z - 1)*(z + 1)/3
Let p(r) be the first derivative of r**3/3 + 2*r**2 + 3*r + 7. Suppose p(z) = 0. What is z?
-3, -1
Let f be (-63)/14*8/(-18). Factor 4/5*h + 2/5*h**f + 0.
2*h*(h + 2)/5
Factor 4/3 + 23/6*l + 5/6*l**3 + 7/2*l**2 - 1/6*l**4.
-(l - 8)*(l + 1)**3/6
Let t(b) be the first derivative of 2*b**6/3 - 4*b**4 + 8*b**3/3 + 6*b**2 - 8*b - 4. Factor t(d).
4*(d - 1)**3*(d + 1)*(d + 2)
Let c(k) = 7 + k**2 - 2 - 3 - 2*k. Let r be c(2). Factor -2*q - 8*q**r - 14/3*q**3 + 4/3.
-2*(q + 1)**2*(7*q - 2)/3
Let x be (-6)/7*(-11 - -4). Let a be ((-16)/x)/((-2)/3). Find b, given that -4*b**2 - 2*b**5 + a*b**4 + 2*b**4 + 2*b - 2*b**4 = 0.
-1, 0, 1
Let u be (1/18)/((-2)/(-4)). Let s(f) be the second derivative of u*f**3 + 0 + 0*f**2 - 1/18*f**4 + 1/45*f**6 - 1/30*f**5 - 2*f. Factor s(m).
2*m*(m - 1)**2*(m + 1)/3
Let n = 1 + 1. Let y(b) be the second derivative of 3/20*b**5 + 0*b**4 + 0*b**2 - 1/15*b**6 + 0 - 1/6*b**3 + n*b. Factor y(u).
-u*(u - 1)**2*(2*u + 1)
Let m(f) be the second derivative of -2*f**2 + 1/12*f**4 + 0 + 0*f**3 + 3*f. What is p in m(p) = 0?
-2, 2
Suppose -27 = 5*b - 3*u - 0, -5*b - 19 = -u. Let j be (4/b)/((-16)/24). Let 0*x - 2/3 + 2/3*x**j = 0. What is x?
-1, 1
Factor 4/7*l**2 + 4/7 - 10/7*l.
2*(l - 2)*(2*l - 1)/7
Let m(f) = f**3 + 3*f**2 - 6*f - 6. Let h be m(-4). Factor -2*y**h + 2*y - 2 + 5*y**2 - 2 - 9*y**3 + 6*y.
-(y + 1)*(3*y - 2)**2
Let x(j) be the first derivative of 3*j**5/5 + 3*j**4/2 + j**3 + 64. Let x(w) = 0. Calculate w.
-1, 0
Let v be (-4)/6*15/(-2400). Let y(j) be the third derivative of 1/420*j**7 + 0*j**4 + 3*j**2 + 0*j**3 + 0*j + 0 - v*j**6 + 0*j**5. Factor y(l).
l**3*(l - 1)/2
Let r be (-2)/3 + 8/6. Suppose -4*z - 3 = -11. Determine x, given that r + x + 1/3*x**z = 0.
-2, -1
Solve 6*s + s**4 - 10*s**2 + 3*s**5 - 75*s**3 + 9*s**4 + 73*s**3 - 7*s**5 = 0.
-1, 0, 1, 3/2
Let o(y) be the second derivative of -1/3*y**3 - 7*y + 0*y**2 + 0 - 1/2*y**4. Factor o(p).
-2*p*(3*p + 1)
Let z = 24 - 16. Let d be (z/(-10))/(42/(-15)). Determine x, given that 0 - d*x**2 - 2/7*x = 0.
-1, 0
Let u(c) = c**3 + 3*c**2 - 11*c - 6. Let w be u(-5). Let k be (-7 + w + 4)/(-14). Determine l, given that -2/7 - 4/7*l - k*l**2 = 0.
-1
Suppose 8 = -3*k + 7*k. Factor 1/3*w**5 + 1/3 + 5/3*w + 10/3*w**3 + 10/3*w**k + 5/3*w**4.
(w + 1)**5/3
Determine g so that 107 - 39 - 5*g**2 - 8 - 5*g = 0.
-4, 3
Let u(t) be the third derivative of 1/12*t**4 - 3*t**2 + 1/180*t**6 + 0 + 0*t + 1/9*t**3 + 1/30*t**5. Factor u(i).
2*(i + 1)**3/3
Let n(l) = -4*l - 1. Let q be n(-1). Suppose -z - 19 = -4*o, 2*o - 2*z = -3*z + 5. What is f in 2/3*f**5 + 0 - 5/6*f**q + 1/6*f - 1/2*f**2 + 1/2*f**o = 0?
-1, 0, 1/4, 1
Suppose -9/5*g**2 - 6/5*g - 1/5 - 4/5*g**3 = 0. Calculate g.
-1, -1/4
Suppose 5/3*d**2 + 0 + 10/3*d**3 - 5/3*d**4 - 10/3*d = 0. What is d?
-1, 0, 1, 2
Let u(y) = 2*y - 6. Let z be u(5). Factor -z*a**2 + 4*a**2 + 3*a**3 - 6*a**3.
-3*a**3
Factor -3*z**3 + 6*z**3 - 4*z**4 - 3*z**3 + 12*z**2 - 8*z.
-4*z*(z - 1)**2*(z + 2)
Suppose -5*v - 4 = -v - 4*o, 0 = 3*v + 5*o - 21. Let a(z) be the second derivative of 1/36*z**4 + v*z + 0*z**2 + 0 - 1/9*z**3. Solve a(m) = 0 for m.
0, 2
Determine j, given that 0 + 2/7*j**4 + 0*j + 2/7*j**2 - 4/7*j**3 = 0.
0, 1
Let a(j) = 11*j**2 + j + 4. Let q be 7/1 - (5 - 7). Let i = q - 6. Let c(l) = 5*l**2 + l + 2. Let k(f) = i*a(f) - 7*c(f). Factor k(m).
-2*(m + 1)**2
Let v(g) be the second derivative of -g**6/45 + g**5/15 + g**4/18 - 2*g**3/9 + 5*g. Determine o so that v(o) = 0.
-1, 0, 1, 2
Let w(l) be the second derivative of l**7/231 - l**6/165 - l**5/110 + l**4/66 - 23*l. Factor w(x).
2*x**2*(x - 1)**2*(x + 1)/11
Let g(t) = t - 2. Let w be g(4). Determine b, given that -b**3 + 0*b + 0*b**3 - 3*b - 2*b**2 + w*b = 0.
-1, 0
Let t(g) be the third derivative of 0*g + 0 + 0*g**3 + 0*g**5 + 1/420*g**6 - 1/735*g**7 - 3*g**2 + 0*g**4. Factor t(p).
-2*p**3*(p - 1)/7
Let f = 90 + -88. Let z = 7 - 4. Factor -8/5 - 16/5*p - 2/5*p**z - f*p**2.
-2*(p