- 8. Let o be j(11). Let z(h) be the second derivative of -1/36*h**4 + 0 + 1/6*h**2 + 0*h**3 + o*h. Factor z(u).
-(u - 1)*(u + 1)/3
Let l = 4 + 0. Suppose 0 = 4*w + 4, -l*a = -8*a + 5*w + 5. Factor 8/11*q**3 + a*q + 0 + 2/11*q**4 + 8/11*q**2.
2*q**2*(q + 2)**2/11
Find f such that -15/4 - 3*f + 3/4*f**2 = 0.
-1, 5
Let z(o) = 11*o**5 + 11*o**4 + 8*o**3 + 5*o**2 + 5. Let x(w) = 16*w**5 + 17*w**4 + 12*w**3 + 7*w**2 + 7. Let y(n) = -5*x(n) + 7*z(n). Factor y(m).
-m**3*(m + 2)*(3*m + 2)
Let j = -1422 - -9970/7. Find r such that 2/7*r**4 - j*r**3 + 48/7*r**2 - 64/7*r + 32/7 = 0.
2
Find y, given that -1/4*y**4 + 1/4*y**3 + y**2 + 0 - y = 0.
-2, 0, 1, 2
Let -6/5 - 24*g**2 + 30*g**3 + 21/5*g**5 + 9*g - 18*g**4 = 0. Calculate g.
2/7, 1
Find o such that -2/17*o**2 - 6/17*o + 0 = 0.
-3, 0
Let x = 5 + -4. Suppose -5*s + 24 = -x. Factor 10*u**2 + 10*u**3 + 5*u + 0*u**5 - u**5 + 1 + 2*u**5 + s*u**4.
(u + 1)**5
Let l(j) = -19*j**3 - 32*j**2 - 23*j - 10. Let a(n) = 37*n**3 + 65*n**2 + 47*n + 19. Let m(v) = 4*a(v) + 7*l(v). Factor m(y).
3*(y + 1)**2*(5*y + 2)
Let i = 79/54 - -1/27. Factor -3/2*v + 3 - i*v**2.
-3*(v - 1)*(v + 2)/2
Let k = -28/5 - -61/10. Factor -k*x**3 + 1/2 + 1/2*x - 1/2*x**2.
-(x - 1)*(x + 1)**2/2
Let c(z) = -z**3 - z**2 + 2. Let f be c(0). Let t be 8/9*(-9)/(-12). Solve 0*h + t*h**3 + 0 - 2/3*h**4 + 2/3*h**f - 2/3*h**5 = 0 for h.
-1, 0, 1
Let t be (4 + -2)/((-3)/(-6)). What is g in -4*g**5 - t*g + 7*g**5 + 2*g**3 + 9*g**4 - 5*g + 4*g**3 - 3 - 6*g**2 = 0?
-1, 1
Let s = 5 + -1. What is m in -m**4 + m**5 - 2*m**4 - m**2 + s*m**3 - 5*m**3 + 4*m**3 = 0?
0, 1
Let z(a) be the second derivative of a**4/36 - a**3/9 - 4*a**2/3 + 44*a. Factor z(d).
(d - 4)*(d + 2)/3
Suppose 0 = -4*m + 3*i + 20, -8 + 4 = -4*m - i. Find c, given that 4*c**3 + 4*c**3 + 6*c**m - c**3 - 4*c**3 = 0.
-2, 0
Factor -3*o**2 + 0*o**4 + 5*o**2 - o**5 + o + 0*o**4 - 2*o**4.
-o*(o - 1)*(o + 1)**3
Let w(b) be the second derivative of -1/105*b**7 + 2/75*b**6 + 0*b**5 + 1/15*b**3 - 5*b + 0 + 0*b**2 - 1/15*b**4. Determine c so that w(c) = 0.
-1, 0, 1
Let c(y) = -4*y**3 - 20*y**2 - 16. Let x(g) = g**3 + 4*g**2 + 3. Let a(s) = 3*c(s) + 16*x(s). Suppose a(l) = 0. What is l?
-1, 0
Suppose -2*z - 4 = 4*g, -5*z = -z - 4*g - 16. Factor 2/7*b**3 + 0*b**z - 2/7*b**5 + 0 + 0*b**4 + 0*b.
-2*b**3*(b - 1)*(b + 1)/7
Let b(k) = -k**3 + 11*k**2 - 9*k - 10. Let j be b(10). Let -4*v + 4 + 30*v + 14*v**2 + 18*v**3 + 26*v**2 + j*v**2 = 0. Calculate v.
-1, -2/9
Let m = 49003/11 - 4451. Let k = 148/33 - m. Factor g - k*g**2 - 2/3*g**3 - 1/3*g**5 - 1/3 + g**4.
-(g - 1)**4*(g + 1)/3
Let h(o) be the second derivative of 0 + 0*o**2 - 2/5*o**5 + 1/14*o**7 + 1/30*o**6 - 4*o + 0*o**3 + 1/3*o**4. Solve h(s) = 0.
-2, 0, 2/3, 1
Let a(f) be the second derivative of -3*f**5/16 - 3*f**4/4 - 9*f**3/8 - 3*f**2/4 - 3*f. Suppose a(h) = 0. Calculate h.
-1, -2/5
Let d(s) = -s**2 + 2*s + 2. Let z be d(2). Suppose 4*u**4 + 0 + 0*u**z + 2*u**2 + u - 7*u**3 + 0 = 0. What is u?
-1/4, 0, 1
Let a(d) = -d**3 - 3*d**2 + 7*d + 14. Let b be a(-4). Determine g, given that -6/5*g + 2/5*g**b + 4/5 = 0.
1, 2
Let w(j) be the second derivative of 0*j**3 + 0*j**2 + 0 + j - 1/135*j**6 + 1/54*j**4 - 1/90*j**5 + 1/189*j**7. What is z in w(z) = 0?
-1, 0, 1
Let i(o) = -o**4 + o - 1. Let z(m) = 12*m**4 + 12*m**3 - 18*m**2 - 3*m + 12. Let f(d) = 15*i(d) + z(d). Determine l, given that f(l) = 0.
1
Suppose 2*y = -2*y + 12. Let f be 52/12 + 2/y. Let t(c) = -2*c**3 - 4*c**2 + 3*c + 5. Let g(k) = -k - 1. Let r(w) = f*g(w) + t(w). Determine m so that r(m) = 0.
-1, 0
Let s be -3*16/12 + 1 + 4. Let z(g) be the first derivative of 5/3*g**3 + 3/2*g**2 - 4/5*g**5 + s - g - 3/4*g**4. Determine m so that z(m) = 0.
-1, 1/4, 1
Let k(w) be the second derivative of w**6/6 - 3*w**5/2 + 55*w**4/12 - 5*w**3 - 24*w. Suppose k(g) = 0. Calculate g.
0, 1, 2, 3
Let d = -23 - -25. Solve -11*h + 8*h - 4*h**2 + d*h**3 + 5*h = 0.
0, 1
Let u(s) = 4*s**4 - 4*s**3 + 4*s**2. Let n(d) = d**3 - d**2. Let c = 11 + -12. Let w(f) = c*u(f) - 4*n(f). Solve w(v) = 0.
0
Let s be ((-51)/952*4)/((-6)/8). Suppose -3/7*a - 1/7*a**4 + s + 3/7*a**3 - 1/7*a**2 = 0. Calculate a.
-1, 1, 2
Let p be 56/(-16)*2*1/(-28). Factor 1/4*l**2 - p*l**3 + 0*l + 0.
-l**2*(l - 1)/4
Let k(x) be the third derivative of -x**8/168 + 2*x**7/735 + 3*x**2. Factor k(b).
-2*b**4*(7*b - 2)/7
Let g(d) = -8*d**3 + 11*d**2 + 9. Let r(o) = o**3 - o**2 - 1. Let i(n) = -2*g(n) - 18*r(n). Factor i(u).
-2*u**2*(u + 2)
Let w(r) = -r - 1. Let o(b) = b**2 + 4*b + 5. Let q(a) = a + 5. Let x be q(-4). Let m(v) = x*o(v) + 5*w(v). Factor m(k).
k*(k - 1)
Let d(a) be the third derivative of 0 + 1/30*a**5 - 1/3*a**3 + 0*a**4 + 0*a - 2*a**2. Factor d(s).
2*(s - 1)*(s + 1)
What is n in 2 + 2 + 0 + 0*n**2 - 4*n**2 + 2*n - 2*n**3 = 0?
-2, -1, 1
What is c in 10*c**2 + c + 13*c**4 - 23*c**4 - 5*c**5 + 2*c + 2*c = 0?
-1, 0, 1
Suppose 2*g - 3 = 1. Let y be (-5 - -3)/g + 3. Factor 0*j + 1/4*j**3 + 0 + 1/4*j**y.
j**2*(j + 1)/4
Let u be 26/(-169) - (-36)/65. Let p(l) be the first derivative of 2 - 3/5*l**2 + u*l**3 - 1/10*l**4 + 2/5*l. Factor p(x).
-2*(x - 1)**3/5
Let n(u) = 48*u**3 - 48*u**2 - 69*u + 27. Let l(s) = 7*s**3 - 7*s**2 - 10*s + 4. Let v(k) = -27*l(k) + 4*n(k). Let v(q) = 0. What is q?
-1, 0, 2
What is z in -6 - 8*z + 11*z - 6*z + 3*z**2 = 0?
-1, 2
Let w(z) = -6*z + 26. Let p be w(4). Find c, given that c - 1 - 1/4*c**p = 0.
2
Let -288*z - 36*z**2 - 3/2*z**3 - 768 = 0. What is z?
-8
Let u(j) be the first derivative of 4/5*j**3 + 7 + 0*j - 9/20*j**4 - 3/10*j**2. Factor u(z).
-3*z*(z - 1)*(3*z - 1)/5
Let p(w) = -2*w - 6. Suppose 3*b - 4*g + 16 = 0, 2*b - 2*g + 14 = -b. Let t be p(b). Solve 0*v + 0 + 1/3*v**3 - 1/3*v**t = 0 for v.
0, 1
Let k be 2*(-3)/36*(10 - 16). Factor 1/2*v**4 + 5/2*v**3 + k + 9/2*v**2 + 7/2*v.
(v + 1)**3*(v + 2)/2
Suppose 0 = 8*c + 20 + 28. Let l be -2 - c/9*3. What is h in -1/2*h**2 + 1/2*h + l = 0?
0, 1
Let j(d) be the first derivative of 1/10*d**5 + 5/6*d**3 - 3 + 0*d + 1/2*d**4 + 1/2*d**2. Determine g, given that j(g) = 0.
-2, -1, 0
Suppose 3*n + 54 = 6*n - 3*c, 5*c = -2*n + 22. Factor z**3 + 8 - n*z + 0*z**3 - 3*z**3 + 10*z**2.
-2*(z - 2)**2*(z - 1)
Let i = -2/363 + 367/726. Factor 15/4*t**3 + 13/4*t - 13/2*t**2 - i.
(t - 1)*(3*t - 1)*(5*t - 2)/4
Determine x so that -6 - 15*x**2 - 20*x - 4*x - 6 - 3*x**3 = 0.
-2, -1
Let a(m) be the third derivative of 0*m + 0*m**4 + 1/150*m**5 + 0 - 8*m**2 + 0*m**3. Factor a(j).
2*j**2/5
Suppose f - 5 + 2 = 0. Find t, given that 2/9*t**f - 2/9*t**2 + 2/9*t**4 + 0 - 2/9*t**5 + 0*t = 0.
-1, 0, 1
Let f = 6 - 6. Let n(c) be the second derivative of 2*c + 1/15*c**6 + 5/63*c**7 - 1/6*c**4 + f*c**2 + 0 - 7/30*c**5 + 2/9*c**3. Solve n(s) = 0 for s.
-1, 0, 2/5, 1
Let m(c) be the third derivative of -c**8/504 + 7*c**6/180 - c**5/15 - 50*c**2. What is z in m(z) = 0?
-3, 0, 1, 2
Let n(m) = 10*m**3 + m**2 + 7*m + 7. Let x(v) be the second derivative of -9*v**5/20 - v**3 - 3*v**2 + 5*v. Let o(p) = -6*n(p) - 7*x(p). Solve o(l) = 0 for l.
0, 2
Let i = 680 - 2039/3. What is x in 1/3*x - 2/3 + i*x**2 = 0?
-2, 1
Let m be (-16)/(-12) + 28/6. Factor 10 + 12*g - 18 + 2*g**2 - m*g**2.
-4*(g - 2)*(g - 1)
Let j = 3 + 0. Let h be (2/(-6))/(6/(-36)*1). Solve 2/9*w**j + 2/9*w**h + 0*w + 0 = 0.
-1, 0
Let q(m) be the third derivative of m**7/70 + 3*m**6/40 - 3*m**5/10 - 7*m**4/2 - 12*m**3 - 13*m**2. Factor q(i).
3*(i - 3)*(i + 2)**3
Let -14/11*q**4 + 0*q - 4/11*q**2 - 18/11*q**3 + 0 = 0. Calculate q.
-1, -2/7, 0
Let g(f) = f**3 - 7*f**2 + 5*f + 8. Let t be g(6). Let y be (-14)/(-2) - 6/t. Find j, given that -21/5*j**5 + 57/5*j**y + 3/5*j**2 + 6/5*j - 9*j**3 + 0 = 0.
-2/7, 0, 1
Let f(t) be the first derivative of -t**6/24 - t**5/10 + t**4/8 + t**3/3 - t**2/8 - t/2 - 2. Solve f(g) = 0 for g.
-2, -1, 1
Let u be 5/(-15)*9 + 3. Factor 0*j**2 + u*j + 6/7*j**4 + 0 - 2/7*j**5 - 4/7*j**3.
-2*j**3*(j - 2)*(j - 1)/7
Let r = -153/10 - -144/5. Factor r + 9*l + 3/2*l**2.
3*(l + 3)**2/2
Suppose 2*c - 3*w = 27, -4*c - 3*w = w - 24. Suppose 16*d + 2*d**5 - 4*d**5 + 4*d**5 - 10*d**3 - 2*d**2 - c + 1 + 2*d**4 = 0. Calculate d.
-2, 1
Let g(x) = -5 + 1 - 6 + 1 - 2*x. Let w be g(-6). Factor -7/3*n**5 + 2/3*n**2 + 0 + 0*n + 16/3*n**4 - 11/3*n**w.
-n**2*(n - 1)**2*(7*n - 2)/3
Suppose 5 = -4*y + 13. Suppose -3*p = 5*a - 23, 0*p = 5*p +