y - 8 = -2*y. Suppose 9*a**4 - 4*a**4 + 4*a + 2*a**y - 12*a**2 - 9*a**3 = 0. Calculate a.
-1, 0, 2/7, 2
Let b(a) be the third derivative of -a**5/140 + a**4/28 + 3*a**3/14 + 3*a**2. Factor b(g).
-3*(g - 3)*(g + 1)/7
Factor -5*u**2 - 5*u**3 - 61 + 5*u + 35 + 31.
-5*(u - 1)*(u + 1)**2
Suppose -a - 8 = -3*a. Factor 13*m**2 + 3*m**4 + m**3 - m - 10*m**2 - 1 - 5*m**a + 0*m**3.
-(m - 1)**2*(m + 1)*(2*m + 1)
Let f = 4 + -16/5. Let l be (-7)/((-21)/(-6)) + 36/15. Factor 2/5*a**2 + l - f*a.
2*(a - 1)**2/5
Let k(x) be the third derivative of x**8/112 + x**7/20 + 9*x**6/80 + x**5/8 + x**4/16 - 22*x**2. Find f such that k(f) = 0.
-1, -1/2, 0
Let u(g) be the third derivative of -g**5/300 - g**4/60 - g**3/30 + 6*g**2. Factor u(o).
-(o + 1)**2/5
Let j(s) = -6*s**2 + 2*s**2 - s + 5*s**2 - 3. Let t be j(3). Find r such that 4*r**2 - t*r**2 - 2*r**2 + 2 - r**2 = 0.
-1, 1
Let v(a) be the first derivative of -4/11*a + 2/55*a**5 - 5/11*a**2 + 2 + 1/22*a**4 - 2/11*a**3. What is h in v(h) = 0?
-1, 2
Suppose 8 = -9*o + 13*o. Let v(y) be the first derivative of -3/2*y**4 + 2*y**3 - 3 + 2/5*y**5 + 0*y - y**o. Find j such that v(j) = 0.
0, 1
Factor -58/5*f**2 - 8/5 + 18/5*f**3 + 48/5*f.
2*(f - 2)*(f - 1)*(9*f - 2)/5
Suppose 2/5*q**2 + 0*q + 0 = 0. What is q?
0
Let n(r) be the third derivative of -r**10/2880 - r**9/630 - 11*r**8/4480 - r**7/840 + r**4/6 - 4*r**2. Let p(q) be the second derivative of n(q). Factor p(i).
-3*i**2*(i + 1)**2*(7*i + 2)/2
Let x(i) be the second derivative of -i**7/21 - i**6/5 - 3*i**5/10 - i**4/6 - 16*i. Determine d so that x(d) = 0.
-1, 0
Let f(z) be the third derivative of z**6/1380 - 4*z**5/345 - z**4/276 + 8*z**3/69 + 3*z**2 + 9. Solve f(r) = 0.
-1, 1, 8
Solve 2/3*x**3 + 4/3*x**2 + 0*x + 0 = 0.
-2, 0
Let f(m) be the second derivative of m**6/6 - 5*m**4/4 + 5*m**3/3 - 7*m. Factor f(y).
5*y*(y - 1)**2*(y + 2)
Let n(g) be the third derivative of g**7/105 + g**6/10 + 3*g**5/10 - 30*g**2. Determine u so that n(u) = 0.
-3, 0
Let -16/7*j**2 + 4/7*j**3 + 0 + 16/7*j = 0. Calculate j.
0, 2
Let t = -2 - -7/3. Let g(m) be the second derivative of m + 0 + 1/36*m**4 + t*m**2 - 1/6*m**3. Solve g(c) = 0.
1, 2
Let l be ((-2)/(-4))/((-1)/(-2)). Let i be (-6)/30 - l/(-5). Determine k, given that 0*k**2 + i - 1/4*k**4 - 1/4*k**3 + 0*k = 0.
-1, 0
Let t = -75 + 1651/22. Let z(p) be the first derivative of -2/33*p**3 + t*p**4 + 0*p - 1/33*p**6 - 1 + 0*p**2 + 2/55*p**5. Let z(y) = 0. What is y?
-1, 0, 1
Let q(t) = t**2 - 10*t + 9. Let c be q(1). Factor 1/4*x**5 + 0*x**4 + 0*x**2 - 1/4*x**3 + c*x + 0.
x**3*(x - 1)*(x + 1)/4
Factor 194*x**3 + 20*x**4 + 16*x**5 - 20*x**4 + 8*x - 144*x**4 + 16*x**5 - 72*x**2.
2*x*(x - 2)**2*(4*x - 1)**2
Factor 1/10*u**4 - 9/5 + 1/10*u**2 - 21/10*u + 1/2*u**3.
(u - 2)*(u + 1)*(u + 3)**2/10
Let h(j) = 5*j**2 + 15*j - 20. Let z(t) = 5*t**2 + 15*t - 20. Let g(b) = 5*h(b) - 4*z(b). What is i in g(i) = 0?
-4, 1
Let b(k) be the second derivative of 0 + 3*k - 1/3*k**3 + 1/45*k**6 + 1/10*k**5 - 2/3*k**2 + 1/18*k**4. What is d in b(d) = 0?
-2, -1, 1
Let 1/6*s**5 + 0*s - 1/6*s**3 - 1/6*s**2 + 1/6*s**4 + 0 = 0. Calculate s.
-1, 0, 1
Factor -3/2*f + 1/8*f**2 + 9/2.
(f - 6)**2/8
Let t(i) = -i**5 + 5*i**4 + 23*i**3 + 17*i**2 - 5*i. Let z(o) = -o**5 + 2*o**4 + 11*o**3 + 8*o**2 - 2*o. Let w(c) = -2*t(c) + 5*z(c). What is g in w(g) = 0?
-1, 0, 2
Let m(x) = 2*x**2 + x. Let b be m(-1). Let c be b + 4/(12/9). Suppose s**2 - s**c + 3*s**3 + 2*s**4 - s**3 = 0. Calculate s.
-1, 0
Let y(a) be the second derivative of -a**6/1620 + a**5/108 - a**4/27 - 2*a**3/3 - 7*a. Let k(t) be the second derivative of y(t). Factor k(r).
-2*(r - 4)*(r - 1)/9
Suppose 2*m**5 - 4*m**3 + 2*m**2 - 2*m**3 - 2*m**4 - 2 + 2 + 4*m = 0. Calculate m.
-1, 0, 1, 2
Suppose -y - 1 = -3. Factor 0*r**y + r + 2*r**2 - 4*r + r**2.
3*r*(r - 1)
Let m(i) = -i**3 - i**2 - i + 5. Let h be m(0). Factor 0*d**3 + 6/5*d**4 + 3/5*d - 3/5*d**h - 6/5*d**2 + 0.
-3*d*(d - 1)**3*(d + 1)/5
Let o(b) be the first derivative of -1 + 2*b - 2/3*b**2 - 7/18*b**4 - b**3. Let s(h) be the first derivative of o(h). Solve s(a) = 0 for a.
-1, -2/7
Let t(m) = m**2 - 11*m - 10. Let n be t(12). Factor -4*h**2 - n + 18*h - 3*h**2 - h**2 - 2.
-2*(h - 2)*(4*h - 1)
Let u(t) be the third derivative of 0*t + 0*t**4 + 0 - 2/945*t**7 - 1/1512*t**8 + 1/540*t**6 - 6*t**2 + 1/135*t**5 + 0*t**3. Suppose u(w) = 0. What is w?
-2, -1, 0, 1
Let n = 9 + -5. Factor -3*r**3 + 3*r**n + 0*r + 5*r - 2*r - 9*r**2 + 3 + 3.
3*(r - 2)*(r - 1)*(r + 1)**2
Suppose 0*y = 4*y - 2*k + 36, -4*y - 44 = -4*k. Let u = 10 + y. What is z in 0*z + z**4 - 3*z - u*z**2 + 2*z + z**3 + 2 = 0?
-2, -1, 1
Suppose -3*p = -2*x + 4, 3*x - 6*p + 2*p - 7 = 0. Let b(u) be the first derivative of 1/15*u**x + 2/3*u**2 + 2/3*u**3 + 1/3*u**4 + 1/3*u - 2. Factor b(f).
(f + 1)**4/3
Suppose l + 3*n + 4 + 0 = 0, 5*l - 14 = 2*n. Determine k, given that -8/3 - 2/3*k**l + 8/3*k = 0.
2
Let d = 53 - 794/15. Let p(r) be the second derivative of 0*r**2 + 0 + 2*r + d*r**3 - 1/30*r**4. Determine k so that p(k) = 0.
0, 1
Let y(v) be the second derivative of -v**4/12 + 4*v**3/3 + 6*v. Let a be y(8). Factor 0 + 2/9*t**4 + 2/9*t**3 + a*t**2 + 0*t.
2*t**3*(t + 1)/9
Let c(n) be the second derivative of 7*n**4/18 + 37*n**3/9 + 10*n**2/3 + 24*n. Factor c(j).
2*(j + 5)*(7*j + 2)/3
Factor 2*y - 7*y**4 + 7*y + 9*y - 25*y**2 - 2*y - 4 + y**5 + 19*y**3.
(y - 2)**2*(y - 1)**3
Factor -9/5*f + 3/5*f**2 + 6/5.
3*(f - 2)*(f - 1)/5
Suppose 9*r = -2*r + 33. Let q(n) be the first derivative of 4 + 1/4*n**2 + 1/6*n**r + 0*n. Suppose q(u) = 0. What is u?
-1, 0
Let f = -36 + 38. Factor -1/2*j**f - j - 1/2.
-(j + 1)**2/2
Let x = -8735/96 + 91. Let l(b) be the third derivative of x*b**4 + 1/240*b**5 + 0 - 1/24*b**3 + b**2 - 1/480*b**6 + 0*b. Factor l(f).
-(f - 1)**2*(f + 1)/4
Let -3*a - 22*a**3 + 0*a + 6*a**2 + 19*a**3 = 0. Calculate a.
0, 1
Let v(b) be the second derivative of -5*b**4/18 + 7*b**3/9 - 2*b**2/3 - 24*b. Find o such that v(o) = 0.
2/5, 1
Let y = 255/2 - 1271/10. Suppose -2*a + 0 = -4. Solve 0 + 0*q + 0*q**a - 1/5*q**4 - y*q**3 = 0.
-2, 0
Suppose 4*j - 2*r - 20 = -0*r, 0 = j + 4*r + 13. Let u be -2 + (j/6 - -2). Determine l, given that 1/4*l**4 + 0*l**2 - 1/2*l**3 - 1/4 + u*l = 0.
-1, 1
Let i(w) = -3*w**2 - 15*w. Let h(f) = -3*f**2 - 16*f. Let r(z) = -3*h(z) + 4*i(z). Find m, given that r(m) = 0.
-4, 0
Let b be ((-1)/(-4))/(40/288). Solve -3/5*w**2 - 6/5 + b*w = 0.
1, 2
Suppose -49*p = -48*p. Let h(n) be the third derivative of 1/36*n**4 + 1/504*n**8 + 0 - 1/45*n**5 + p*n + 1/315*n**7 + 1/9*n**3 - 1/90*n**6 + n**2. Factor h(d).
2*(d - 1)**2*(d + 1)**3/3
Let a(k) be the third derivative of 0*k - 7/8*k**4 + 1/112*k**8 + 1/35*k**7 + 0 + 8*k**2 - k**3 - 2/5*k**5 - 1/20*k**6. Factor a(i).
3*(i - 2)*(i + 1)**4
Let n = 2 - 2. Suppose -2*k + 7*k**2 + 9*k**3 - 5*k**4 + n*k**2 + 3*k**2 - 5*k**2 - 7*k**5 = 0. What is k?
-1, 0, 2/7, 1
Let b(v) = -v**2 - 30*v - 45. Let j(w) = 15*w**2 + 420*w + 630. Let z(f) = 55*b(f) + 4*j(f). Factor z(h).
5*(h + 3)**2
Factor -2/7*k + 0 - 3/7*k**2 - 1/7*k**3.
-k*(k + 1)*(k + 2)/7
Let w(a) be the second derivative of a**6/165 - 2*a**5/55 + 7*a. Factor w(q).
2*q**3*(q - 4)/11
Let f(x) = 2 + 4*x**2 + 3 - 11*x**2. Let q(l) = -11*l**2 + 8. Let b(n) = 8*f(n) - 5*q(n). Let b(d) = 0. What is d?
0
Let s(a) = -2*a + 14. Let q be s(6). Find n, given that -1/4*n**q + 0 - 1/4*n = 0.
-1, 0
Let c(w) be the third derivative of -w**6/420 + w**5/105 + w**4/84 - 2*w**3/21 + 2*w**2. Factor c(f).
-2*(f - 2)*(f - 1)*(f + 1)/7
Let u(c) be the second derivative of c**6/195 + c**5/130 - 7*c. Factor u(z).
2*z**3*(z + 1)/13
Let r(f) = -f**3 + 15*f**2 - 13*f - 12. Let d be r(14). Factor -10*j - 2 - 25/2*j**d.
-(5*j + 2)**2/2
Let b = 79 - 74. Let a(s) be the second derivative of 0 - 1/24*s**4 + 0*s**3 + s - 1/80*s**b + 1/120*s**6 + 0*s**2. Factor a(j).
j**2*(j - 2)*(j + 1)/4
Let k = 10 - 7. Suppose 0*s + 0*s**2 - 2/9*s**4 + 2/9*s**k + 0 = 0. Calculate s.
0, 1
Let f be 1/(-3) + (-14)/(-7). Let k = f - 4/3. Factor 2/3*p**2 + 0 - k*p**3 - 1/3*p.
-p*(p - 1)**2/3
Let v(k) = -k - 3. Let s be v(-5). Suppose 2/3 + 1/3*t**s - t = 0. What is t?
1, 2
Find o, given that 0 + 0*o - 6/7*o**3 + 2/7*o**4 + 4/7*o**2 = 0.
0, 1, 2
Factor 20/17 - 18/17*c**2 - 54/17*c.
-2*(3*c - 1)*(3*c + 10)/17
Find m such that 2/3*m**3 + 0 - 8/