- 1)**2
Let w(i) = i**2 + i + 1. Suppose 0 = 2*y + 5*a + 2, -y - 3 = 2*y + 4*a. Let o(d) = -d**3 - 4*d**2 - 3*d - 3. Let p(h) = y*o(h) - 3*w(h). Factor p(c).
c**2*(c + 1)
Let z be 0*(20/(-12) - -2). Let l(b) be the second derivative of 0 - 1/80*b**5 + z*b**2 + 0*b**4 + 1/24*b**3 - 2*b. Factor l(g).
-g*(g - 1)*(g + 1)/4
Let d(u) be the second derivative of 1/12*u**3 - 1/16*u**4 + 1/40*u**6 + 0*u**2 + 5*u + 5/168*u**7 - 7/80*u**5 + 0. Let d(o) = 0. What is o?
-1, 0, 2/5, 1
Let u(q) = -q**2 + q + 3. Let o be u(0). Let s be ((-4)/o)/(-2) + 0. Let 4/3*r**2 - 2/3*r**3 - s*r + 0 = 0. Calculate r.
0, 1
Let r(p) be the third derivative of 2/45*p**5 - 7*p**2 + 0*p**3 + 2/315*p**7 + 0*p**4 + 0 + 0*p + 1/30*p**6. Factor r(a).
4*a**2*(a + 1)*(a + 2)/3
Let i(r) be the second derivative of r**5/20 + r**4/4 + r**3/3 + 11*r. Solve i(w) = 0.
-2, -1, 0
Let i(m) be the first derivative of 0*m**2 + 1/12*m**4 + 0*m + 1 + 0*m**3. Suppose i(q) = 0. Calculate q.
0
Let v be 32/(-56) - (-54)/21. Let n(p) be the second derivative of -1/2*p**v + 0 + 0*p**3 + 1/12*p**4 + p. Factor n(h).
(h - 1)*(h + 1)
Suppose -6 = -2*l, -c - 3*l - 3 = 3*c. Let q be -4*((-4)/1 - c). Factor 2/3*t**3 + 2/3*t**q + 0 + 0*t**2 + 0*t.
2*t**3*(t + 1)/3
Let d(u) be the second derivative of -u**7/147 + 8*u**6/105 - 3*u**5/10 + 3*u**4/7 + 61*u. Factor d(m).
-2*m**2*(m - 3)**2*(m - 2)/7
Factor -2*y**2 - 2/9*y**3 - 6 - 6*y.
-2*(y + 3)**3/9
Let r(c) = -c**5 - c**4 - c + 1. Let m(p) = 6*p**4 - 4*p**3 - 16*p**2 + 10. Let x(l) = -m(l) + 2*r(l). Find z such that x(z) = 0.
-4, -1, 1
Let y(n) be the second derivative of 0 - 5/42*n**4 + 4/35*n**5 + 1/35*n**6 - 2/147*n**7 - 4/7*n**3 - 4/7*n**2 + 3*n. Suppose y(q) = 0. What is q?
-1, -1/2, 2
Suppose 3*g = -1 + 4. Let p(u) = u**2 + 5*u - 2. Let c(d) = -d + 1. Let t(v) = g*p(v) + 3*c(v). Solve t(k) = 0.
-1
Suppose -13*v - 193 = -219. Suppose -6/19*b**v - 4/19*b + 0*b**3 + 0 + 2/19*b**4 = 0. Calculate b.
-1, 0, 2
Let w be (7/((-21)/(-24)))/2. Let i(y) be the second derivative of 0*y**w + 0 - 1/30*y**6 - 2*y + 1/2*y**2 - 1/3*y**3 + 1/10*y**5. Factor i(n).
-(n - 1)**3*(n + 1)
Let m(q) be the first derivative of -2*q**3/15 - 7*q**2/5 + 16*q/5 + 40. Let m(h) = 0. What is h?
-8, 1
Let u(p) be the third derivative of -2/25*p**5 + 4*p**2 - 1/15*p**4 + 4/175*p**7 - 1/120*p**8 + 0 + 0*p**3 + 11/300*p**6 + 0*p. Find b such that u(b) = 0.
-1, -2/7, 0, 1, 2
Let z(x) be the second derivative of 0*x**2 - 1/60*x**4 + 3*x + 1/15*x**3 + 0. Factor z(d).
-d*(d - 2)/5
Suppose 179*z - 182*z = -9. Let r = 32/55 - 2/11. Factor 0 - 8/5*q + 8/5*q**2 - r*q**z.
-2*q*(q - 2)**2/5
Let l be -2 + (-1)/(-1) + 3. Suppose 7*o - 3*o - o**l + 0*o - 2*o = 0. What is o?
0, 2
Let q = 2 - 0. Suppose -4*b + 5*u = 2, -3*u + 13 = q*b + 3. Solve c**2 + 5 + b*c - 5 = 0.
-2, 0
Suppose 2*y + 25 = j - 3*y, -4*y = j + 20. Factor 0 - 2/3*v**2 + j*v.
-2*v**2/3
Let c = -6/11 + 40/33. Let v(x) be the first derivative of 0*x**2 + c*x + 2 - 2/9*x**3. Factor v(j).
-2*(j - 1)*(j + 1)/3
Let u(a) = 7*a**2 - 7*a - 9. Let t(o) = 34*o**2 - 36*o - 44. Let h(p) = -6*t(p) + 28*u(p). Factor h(j).
-4*(j - 3)*(2*j + 1)
Suppose -8*v = -3*v - 10. Let u be v/9 - (-16)/9. Let u*y**2 + 10*y**5 + 14*y**3 + 16*y**4 - 3*y**5 - 3*y**3 = 0. What is y?
-1, -2/7, 0
Let c(i) be the third derivative of i**8/12 - 6*i**7/35 + i**6/15 - 6*i**2. Factor c(r).
4*r**3*(r - 1)*(7*r - 2)
Factor 3/2*p - 1/4*p**2 - 9/4.
-(p - 3)**2/4
Suppose 7*o = -3*c + 2*o, -2*c = 4*o. Let w be (-144)/(-63) - (c - -2). Let 0*d - 2/7*d**2 - w*d**3 + 0 = 0. Calculate d.
-1, 0
Let f(o) be the first derivative of o**4/14 - 2*o**3/7 - 4*o**2/7 + 24. Let f(d) = 0. Calculate d.
-1, 0, 4
Factor 3*x**3 + 48*x**4 - 50*x**4 - x**3.
-2*x**3*(x - 1)
Suppose -3*d - 4 = -x, -d + 0 = 2*x - 1. Let u be (0 - 0)/x + 0. Solve 0*n**4 + u*n - 3*n**2 + n + 3*n**3 - n**4 = 0 for n.
0, 1
Let b(y) = 7*y**2 + 11*y - 15. Let t(h) = 3*h**2 + 6*h - 7. Let k(c) = -2*b(c) + 5*t(c). Let d(z) = z**2 + 17*z - 11. Let i(g) = -4*d(g) + 9*k(g). Factor i(o).
(o + 1)*(5*o - 1)
Let u(t) be the second derivative of 9*t**5/20 + 2*t**4 + 7*t**3/2 + 3*t**2 - 24*t. Determine g so that u(g) = 0.
-1, -2/3
Let u(m) be the third derivative of 0 + 0*m**4 - 1/720*m**6 + 1/2*m**3 + 4*m**2 + 0*m**5 + 0*m. Let x(h) be the first derivative of u(h). Factor x(n).
-n**2/2
Let g(f) be the third derivative of -f**5/300 - f**4/15 - 7*f**3/30 - 47*f**2. Solve g(k) = 0.
-7, -1
Let b be (-81)/(-12) - 3/(-12). Factor 3*q**5 + 3*q + 9*q**4 + 3*q**4 + 18*q**3 - b*q**4 + 12*q**2 + 7*q**4.
3*q*(q + 1)**4
Let o = 2/23 - -32/161. Let b = -474/7 - -68. Factor 0*s**3 + 0 - b*s**5 + 4/7*s**4 + o*s - 4/7*s**2.
-2*s*(s - 1)**3*(s + 1)/7
Let w = -1/138 - -187/414. Let r(j) be the first derivative of 2/15*j**5 + 2/3*j + 0*j**2 + 0*j**4 + 3 - w*j**3. Let r(s) = 0. Calculate s.
-1, 1
Let y be 1/((-4)/(12/(-1))). Factor -y - o**2 + 1 + o + 2.
-o*(o - 1)
Let d be 0 - -4 - (0 + 0). Let n(l) be the first derivative of -1 + 1/2*l**d - 2/3*l**3 - 2*l**2 + 0*l. Solve n(c) = 0.
-1, 0, 2
Let i(p) be the second derivative of 1/60*p**5 + 1/36*p**4 + 0 - 1/18*p**3 - 1/6*p**2 + 2*p. Factor i(l).
(l - 1)*(l + 1)**2/3
Let k = -13 - -8. Let n(s) = s**2 + 16*s - 16. Let p(h) = h. Let b(a) = 12*a + 8. Let m(d) = b(d) - 20*p(d). Let v(l) = k*m(l) - 2*n(l). Solve v(q) = 0.
2
Let i be (-7)/(7/(-4)) + 102/(-27). Factor -i*x**3 + 2/9*x**4 + 2/9*x + 0 - 2/9*x**2.
2*x*(x - 1)**2*(x + 1)/9
Suppose 16/9*y**2 + 0 - 98/9*y**5 + 140/9*y**4 + 104/9*y**3 + 0*y = 0. What is y?
-2/7, 0, 2
Let j = 55 + -219/4. Let n(i) be the first derivative of -i + 1/6*i**3 - j*i**2 - 1. Factor n(f).
(f - 2)*(f + 1)/2
Let r(c) be the first derivative of c**6/540 - c**5/45 + c**4/9 - 4*c**3/3 - 1. Let x(v) be the third derivative of r(v). Find l such that x(l) = 0.
2
Let s = 26 - 18. Let i(q) = -q**2 + 10*q - 14. Let w be i(s). Factor -2/7*n**w + 12/7*n - 18/7.
-2*(n - 3)**2/7
Let y(u) be the first derivative of 4/9*u**3 + u**2 + 4 + 0*u - 1/6*u**4. Solve y(g) = 0.
-1, 0, 3
Let 6/5*x - 2/5*x**2 - 4/5 = 0. What is x?
1, 2
Let m(x) = 6*x**3 - 3*x**2 - 5. Let r(f) = f**3 - f**2 - 1. Let h(v) = -m(v) + 5*r(v). Solve h(y) = 0 for y.
-2, 0
Let y(x) be the first derivative of 5*x**6/6 + 3*x**5/5 - 27*x**4/4 + 25*x**3/3 - 3*x**2 + 43. Factor y(f).
f*(f - 1)**2*(f + 3)*(5*f - 2)
Factor 0 + 2/9*t - 2/9*t**3 + 0*t**2.
-2*t*(t - 1)*(t + 1)/9
Factor -8*i**3 + i**5 + 16 - 24*i**2 - 16/3*i + 7/3*i**4.
(i - 3)*(i + 2)**3*(3*i - 2)/3
Let m(j) = 13*j + 78. Let z be m(-6). Let -4/5 + 6/5*a - 2/5*a**3 + z*a**2 = 0. What is a?
-2, 1
Let w(x) be the third derivative of 0*x**3 - 2*x**2 - 1/20*x**6 + 1/168*x**8 - 2/105*x**7 + 0 + 2/15*x**5 + 1/3*x**4 + 0*x. Factor w(b).
2*b*(b - 2)**2*(b + 1)**2
Let j(a) be the first derivative of 1/12*a**4 + 0*a + 0*a**2 + 2 - 1/9*a**3. Factor j(x).
x**2*(x - 1)/3
Determine a, given that 8*a + a**2 + 0*a**4 - 8*a**3 + 3*a**2 - 5*a**4 + a**4 = 0.
-2, -1, 0, 1
Let n = 7 + -5. Factor -a**2 - 6*a + a**2 + 4*a**2 - 5*a**n - 9.
-(a + 3)**2
Suppose 4*h - 8 = -5*x + 10, -10 = -5*x. Let l(i) be the second derivative of 0 - 1/15*i**3 + i - 2/5*i**h + 1/30*i**4. Factor l(v).
2*(v - 2)*(v + 1)/5
Let z(f) be the third derivative of f**4/24 - f**3/3 + 3*f**2. Let b be z(4). Determine i so that 0*i**3 - b*i**3 - i**2 + 0*i**2 - i**2 = 0.
-1, 0
Factor 12*v**3 - 6*v**3 - 15*v**2 + 10*v - v**3.
5*v*(v - 2)*(v - 1)
Let h(j) = -j**2 + j**3 + 9*j**3 + 6*j**3 - 17*j**3. Let a be h(0). What is v in a + 2/3*v**2 + 0*v = 0?
0
Factor -2/13*m**2 + 2/13 + 0*m.
-2*(m - 1)*(m + 1)/13
Let k(p) be the first derivative of -p**6/9 + 2*p**5/15 + p**4/3 - 9. Factor k(r).
-2*r**3*(r - 2)*(r + 1)/3
Solve -2/5*q**3 - 4/5*q**2 + 0 + 6/5*q = 0.
-3, 0, 1
Let t(v) be the third derivative of 0*v**3 - 9*v**2 - 7/15*v**5 - 1/3*v**4 + 0 + 0*v + 2/35*v**7 - 1/15*v**6. Suppose t(u) = 0. What is u?
-1, -1/3, 0, 2
Find h such that 6/13*h**2 + 0 + 0*h**3 - 2/13*h**4 + 4/13*h = 0.
-1, 0, 2
Let z(a) be the first derivative of -2*a**3/27 - a**2/3 + 15. Determine x so that z(x) = 0.
-3, 0
Suppose -2*f + 2*i - 42 = 2*f, -2*f - 26 = -2*i. Let d = f + 8. Solve d*y + 1/4*y**2 - 1/4 = 0 for y.
-1, 1
Let d(l) = -4*l - 1. Suppose 0 = 3*z + 2 + 1. Let f be d(z). What is o in 4*o**2 - f*o**2 - 3*o**2 = 0?
0
Let f(a) be the second derivative of -a*