 7. Let o(d) = d**2 - 1. Let p(z) = 2*z**3 - 12*z**2 + 16*z - 6. Let b(q) = u*o(q) + p(q). Factor b(x).
2*(x - 2)**2*(x - 1)
Factor q**2 - 1/2 + 1/2*q - q**3 + 1/2*q**5 - 1/2*q**4.
(q - 1)**3*(q + 1)**2/2
Let y be 2/3*(-36)/(-8). Suppose -2*t = y*t - 10. Factor -2*g**5 - 2*g**3 + 4*g**4 - 75*g**t + 75*g**2.
-2*g**3*(g - 1)**2
Let z(g) be the second derivative of g**7/2520 + g**6/360 + g**5/120 + 2*g**4/3 - 4*g. Let v(s) be the third derivative of z(s). Determine c so that v(c) = 0.
-1
Let t = 12 + -5. Factor 7 + j - t - j**2.
-j*(j - 1)
Let a(t) be the third derivative of t**6/280 + t**5/35 + 5*t**4/56 + t**3/7 - 4*t**2. Factor a(m).
3*(m + 1)**2*(m + 2)/7
Let a = 152/21 + -20/3. Let 2/7*p**3 + 0 + a*p**2 + 2/7*p = 0. What is p?
-1, 0
Let u = -11/85 - -62/85. Factor -6/5*d + u*d**2 + 3/5.
3*(d - 1)**2/5
Suppose -2*q = 6 - 18. Let n = -6 + q. Find t such that 1/4*t**2 - 1/4*t + n = 0.
0, 1
Let t be (30 - 23) + -3 + (-2)/2. Let c(z) be the third derivative of 0*z**4 + 0*z - 1/40*z**5 - 1/80*z**6 + 0*z**t + 3*z**2 + 0. Factor c(p).
-3*p**2*(p + 1)/2
Let t(w) = 26*w**2 - 48*w + 17. Let x(q) = 27*q**2 - 48*q + 18. Let u(m) = -6*t(m) + 5*x(m). Suppose u(i) = 0. Calculate i.
2/7, 2
Let s(v) be the second derivative of v**6/70 - 9*v**5/140 + 3*v**4/28 - v**3/14 - 9*v. Determine i so that s(i) = 0.
0, 1
Let j(x) be the first derivative of x**6/24 - 3*x**4/16 - x**3/6 + 9. What is t in j(t) = 0?
-1, 0, 2
Let b = 141 + -136. Suppose 1/2*a**b - 1/2*a**4 + 0 + 0*a - 1/2*a**3 + 1/2*a**2 = 0. What is a?
-1, 0, 1
Solve 3/4*l - 3/4*l**3 + 0 + 3/4*l**2 - 3/4*l**4 = 0.
-1, 0, 1
Let h = 64/43 + -3990/2623. Let o = h + 128/183. Let 0 + o*a - 2/3*a**2 = 0. Calculate a.
0, 1
Let q be (1 + 0)/(10/22) - 1. Find g, given that 28/5*g**2 - 24/5*g**4 - 4/5 + 8/5*g**3 + q*g - 14/5*g**5 = 0.
-1, 2/7, 1
Let n(a) be the second derivative of -a**3/6 - 5*a**2/2 + a. Let j be n(-5). Determine o, given that 1/4*o + 0*o**3 + j + 1/2*o**4 - 1/4*o**5 - 1/2*o**2 = 0.
-1, 0, 1
Factor -2/11 - 3/11*j - 1/11*j**2.
-(j + 1)*(j + 2)/11
Let s(k) = -k + 14. Let j be s(8). Let l(d) be the third derivative of 0 - 7/60*d**j + 1/6*d**4 + 1/6*d**5 + 0*d - d**2 + 0*d**3. Factor l(i).
-2*i*(i - 1)*(7*i + 2)
Factor -26/17*i + 44/17*i**2 - 36/17*i**3 - 2/17*i**5 + 14/17*i**4 + 6/17.
-2*(i - 3)*(i - 1)**4/17
Let 9*z - 2*z**2 + 4*z**2 - 6 - 5*z**2 = 0. Calculate z.
1, 2
Let q = -74/57 + 31/19. Find p, given that q*p**3 + 2/3*p + p**2 + 0 = 0.
-2, -1, 0
Suppose 5*b = 10, -d - 4*b + 5 = -2*d. Suppose -4*g + 0*g**2 + 8*g**2 + 2*g**d + 2*g**3 - 2 - g**4 - 5*g**4 = 0. Calculate g.
-1, -1/3, 1
Let h be ((-2)/1 - -2)/(-1). Let w = h + 4. Factor n**5 + 4*n**4 - n**4 - 2*n**3 + 2 + n - n**w - 4*n**2.
(n - 1)**2*(n + 1)**2*(n + 2)
Suppose u**3 - 2*u + 2*u**3 - 6*u + 5*u = 0. Calculate u.
-1, 0, 1
Let r(n) = -n**2 - 10*n + 13. Let y be r(-11). Solve -14*q**2 + 16 + 0*q**2 + 2*q**y - 4*q**3 = 0.
-2, 1
Solve 24*b**4 - 1500*b + 900*b**2 - 240*b**3 + 1875/2 = 0.
5/2
Suppose -5*s + 5*h = -25, 4*s - h - 14 = -3*h. Find o, given that -1/4*o**3 + 0 + 0*o + 0*o**2 - 1/4*o**s = 0.
-1, 0
Let y = 181 - 1989/11. Suppose 2/11*l**3 - 2/11*l - y + 2/11*l**2 = 0. What is l?
-1, 1
Find b, given that 0 + 2/5*b**4 + 0*b - 4/5*b**3 + 2/5*b**2 = 0.
0, 1
Suppose 0 = 2*k - 77 - 133. Let w be (-2)/3 + 100/k. Suppose 8/7*h - 8/7 - w*h**2 = 0. What is h?
2
Let x be (-4)/1 + 2/(-1). Let u(o) = -o**2 - 6*o + 2. Let j be u(x). Factor 1 - 2*f + f**2 - 3*f**j + f.
-(f + 1)*(2*f - 1)
Let o(f) be the first derivative of f**4 - 2*f**2 - 36. Find y such that o(y) = 0.
-1, 0, 1
Let h(v) = 5*v**2 + 55*v + 30. Let r(y) = -y + 1. Let f(n) = h(n) + 20*r(n). Factor f(c).
5*(c + 2)*(c + 5)
Let c be (8/(-26))/((-142)/923). Determine t, given that -1/2*t**3 + 0 + t - 1/2*t**c = 0.
-2, 0, 1
Let r = -11/21 - -307/105. Solve 0 - 8/5*k - 4/5*k**3 - r*k**2 = 0.
-2, -1, 0
Let i(c) be the first derivative of 2 + 0*c**3 + 0*c + 0*c**2 - 1/18*c**4 - 8/45*c**5. Determine x, given that i(x) = 0.
-1/4, 0
Let h(j) be the second derivative of -j**6/2160 - j**5/360 - j**4/144 + j**3/6 + j. Let g(m) be the second derivative of h(m). Factor g(r).
-(r + 1)**2/6
Let y be (5*3/45)/60. Let i(l) be the second derivative of -l - 1/60*l**5 + 0 + 0*l**3 + 0*l**2 - y*l**6 - 1/72*l**4. Factor i(f).
-f**2*(f + 1)**2/6
Factor 20*k**4 - 10*k - 5*k + 9 + 2*k**2 - 4*k**2 + 14*k**3 - 27*k**4 + k**5.
(k - 3)**2*(k - 1)**2*(k + 1)
Let x(v) be the third derivative of v**6/540 + v**5/180 + v**3/2 + 3*v**2. Let s(h) be the first derivative of x(h). Solve s(y) = 0 for y.
-1, 0
Let k(y) be the third derivative of y**7/140 - y**6/80 - y**5/80 - y**3/3 - y**2. Let x(h) be the first derivative of k(h). Suppose x(i) = 0. What is i?
-1/4, 0, 1
Let p(h) be the first derivative of 3/7*h**2 - 3 - 1/14*h**4 + 0*h**3 + 4/7*h. Factor p(w).
-2*(w - 2)*(w + 1)**2/7
Let i(l) be the second derivative of -1/6*l**2 - 5*l + 0 + 7/18*l**3 - 1/6*l**4. Solve i(r) = 0 for r.
1/6, 1
Suppose -3*w + 2*w = 5*b - 5, -5*b + 5 = 2*w. Let j be -2*(-2 + b) + 0. Factor 3*q**4 - 2*q**3 + 2*q**2 - j*q**3 - q**4.
2*q**2*(q - 1)**2
Let a = 16 + -13. Factor -2/7*s + 0 + 16/7*s**a - 4/7*s**2.
2*s*(2*s - 1)*(4*s + 1)/7
Factor -14/3*z - 49/3 - 1/3*z**2.
-(z + 7)**2/3
Let g(u) = -u + 9. Suppose 11*v - 14 = 6*v - 4*m, -5*v + 38 = -2*m. Let c be g(v). Let 4 + 3*r**3 + 6*r - 5*r**3 + 0*r**c = 0. Calculate r.
-1, 2
Let r(p) = -24*p**4 + 25*p**3 - p**2 + 5. Let f(j) = 2*j**3 - 3 - 5*j**3 + 12*j**4 - 9*j**3. Let g(n) = -5*f(n) - 3*r(n). Factor g(q).
3*q**2*(q - 1)*(4*q - 1)
Let z(n) = -n**2 + 2*n - 1. Let t be z(1). Let b = 7/12 + -1/3. Suppose -1/4*i**4 - 1/4*i**3 + t + b*i + 1/4*i**2 = 0. What is i?
-1, 0, 1
Suppose -3*i + i + 4 = 0. Factor 4 - 1 - 3 + i*z**2.
2*z**2
Let l(s) = -s + 4. Let v be l(2). Let k be 2*(1 - v) - -4. Factor -2/3*y**4 - 2/3 - 4/3*y**3 + 4/3*y**k + 2/3*y + 2/3*y**5.
2*(y - 1)**3*(y + 1)**2/3
Let x(w) be the first derivative of 12*w**5/5 + 4*w**4 - 20*w**3/3 - 4*w**2 - 6. Let x(p) = 0. What is p?
-2, -1/3, 0, 1
Suppose 5*i = -5, 0 = 2*f - 4*i + i + 1. Let t(p) = p**2 - 1. Let k be t(f). Let 2*u**2 - 6*u**5 + 2*u - 4*u + 10*u**k - 2*u**4 - 2*u = 0. Calculate u.
-1, 0, 2/3, 1
Suppose 3*u = -5*y + 29, 3*y + 0*y - 3 = 3*u. Factor -14 + y*h**4 + 14 + 8*h**3.
4*h**3*(h + 2)
Let r(f) = -15*f + 17. Let g be r(1). Determine d so that -4/7*d**g - 64/7 - 32/7*d = 0.
-4
Let x(u) be the first derivative of -2 - u**3 - 6*u + 9/2*u**2. Factor x(y).
-3*(y - 2)*(y - 1)
Let q = -73 - -77. Let h(k) be the third derivative of k**2 + 0 + 1/120*k**5 - 1/240*k**6 + 0*k - 1/12*k**3 + 1/48*k**q. Factor h(t).
-(t - 1)**2*(t + 1)/2
Let d(n) be the first derivative of n**6/10 + 5. Factor d(u).
3*u**5/5
Let c(f) be the first derivative of -f**5/240 + f**4/16 - 3*f**3/8 - f**2/2 - 2. Let x(h) be the second derivative of c(h). Suppose x(v) = 0. Calculate v.
3
Let k = 281/6 + -1189/30. Factor -k*c**2 - 2/5*c**4 + 8*c + 14/5*c**3 - 16/5.
-2*(c - 2)**3*(c - 1)/5
Factor 4/5*q**4 + 8/5*q**3 + 0 - 4/5*q**2 - 8/5*q.
4*q*(q - 1)*(q + 1)*(q + 2)/5
Let i = -115/4 - -29. Determine y, given that -i - 1/2*y - 1/4*y**2 = 0.
-1
Let y(p) be the second derivative of 1/18*p**4 + 1/60*p**5 + 1/18*p**3 + 0*p**2 + 0 - 3*p. Let y(v) = 0. Calculate v.
-1, 0
Let m(l) be the first derivative of 4*l**3/3 - 8*l**2 + 16*l + 26. Let m(t) = 0. What is t?
2
Suppose 0 + 0*w - 1/4*w**3 + 1/4*w**2 = 0. Calculate w.
0, 1
Let f(z) be the third derivative of -z**5/90 + z**4/6 - z**3 + 13*z**2. Suppose f(u) = 0. Calculate u.
3
Let f(n) be the first derivative of -1/80*n**5 + 1/24*n**3 - n + 0*n**2 - 1/40*n**6 + 1/16*n**4 - 1. Let v(h) be the first derivative of f(h). Factor v(x).
-x*(x - 1)*(x + 1)*(3*x + 1)/4
Let l(w) = w**3 - 21*w**2 - w + 26. Let n be l(21). Solve -4/7*i**4 + 0*i**2 + 0*i + 0 + 2/7*i**3 + 2/7*i**n = 0 for i.
0, 1
Let r(q) be the first derivative of -q**4/8 + q**3/4 - q**2/8 - 1. What is o in r(o) = 0?
0, 1/2, 1
Suppose 3*l - 3 - 3 = 0. Factor 11*o**4 + l*o**3 - 9*o**4 - 2*o**5 + 0*o**2 - 2*o**2.
-2*o**2*(o - 1)**2*(o + 1)
Suppose -4*o - 2 = -10. Suppose -2*s**o - 2*s + 4*s - 2*s = 0. What is s?
0
Determine l, given that 1/6*l**2 - 2/3*l - 2 = 0.
-2, 6
Suppose 136 = -8*i - 24. Let d = i + 62/3. Factor -2/3*o**4 + 2*o**3 - 2*o**2 + d*o + 0.
-2*o*(o - 1)**3/3
Suppo