(b) = 0. What is b?
0, 1
Let -3*g**2 + 1 - 2*g + 7*g + 4*g**2 - 3*g = 0. What is g?
-1
Let a(b) = -48*b**3 - 15*b**2 + 21*b + 69. Let i(f) = -7*f**3 - 2*f**2 + 3*f + 10. Let k(d) = -4*a(d) + 27*i(d). Let k(c) = 0. Calculate c.
-2, -1, 1
Factor 0*i**3 - 5/3*i + 10/3*i**2 + 5/3*i**5 - 10/3*i**4 + 0.
5*i*(i - 1)**3*(i + 1)/3
Suppose 13/5*v + 2/5 + 11/5*v**2 = 0. What is v?
-1, -2/11
Let d = 5/118 + 221/354. Let d*i**3 + 2/3*i + 0 + 4/3*i**2 = 0. Calculate i.
-1, 0
Let u be 2/(-3) - 16/(-6). Suppose -p**3 + 3*p - 2 - 2*p**3 + u = 0. What is p?
-1, 0, 1
Let l(b) be the third derivative of -4/105*b**7 + 0*b + 1/12*b**4 + 1/10*b**6 - 2*b**2 + 0 + 1/168*b**8 - 2/15*b**5 + 0*b**3. Find z such that l(z) = 0.
0, 1
Factor 3/2*n + 3 - 3/2*n**2.
-3*(n - 2)*(n + 1)/2
Let t(r) be the second derivative of r**6/135 - r**4/18 - 2*r**3/27 + 16*r. Determine a so that t(a) = 0.
-1, 0, 2
Let y(f) be the first derivative of f**4/9 - 2*f**3/27 - 2*f**2/9 + 2*f/9 - 10. Factor y(l).
2*(l - 1)*(l + 1)*(2*l - 1)/9
Let l(c) be the third derivative of -c**6/660 - 4*c**2. Suppose l(h) = 0. What is h?
0
Let y(m) be the second derivative of m**7/4200 + m**6/900 + m**5/600 + 2*m**3/3 + 4*m. Let h(j) be the second derivative of y(j). Find s, given that h(s) = 0.
-1, 0
Let o(k) be the second derivative of -k**8/84 + 2*k**7/35 - k**6/10 + k**5/15 + k**2 + k. Let g(s) be the first derivative of o(s). Factor g(r).
-4*r**2*(r - 1)**3
Let j(q) be the first derivative of 4/13*q - 4 - 7/26*q**4 + 32/39*q**3 - 11/13*q**2. Solve j(l) = 0 for l.
2/7, 1
Determine t so that 2/3*t**4 + 8/9*t + 0 - 10/9*t**3 - 8/9*t**2 = 0.
-1, 0, 2/3, 2
Let d(a) be the first derivative of a**5/10 + a**4/2 + a**3 + a**2 + a + 1. Let p(m) be the first derivative of d(m). Factor p(o).
2*(o + 1)**3
Suppose 0 = -2*q + 7 + 17. Suppose -4*x = 2*y - q, 6 - 22 = -3*x - 5*y. Suppose 6 + 11*h**3 - x*h**3 + 6*h**2 - 18 + 15*h**2 = 0. Calculate h.
-2, -1, 2/3
Let x be (-4)/(-38) - -26*1/114. What is c in -x*c**2 + 1 + 2/3*c = 0?
-1, 3
Let n(c) be the first derivative of c**3/6 + 7*c**2/12 + 2*c/3 - 1. Find w, given that n(w) = 0.
-4/3, -1
Let p(d) be the second derivative of d**6/10 + 3*d**5/5 + 5*d**4/4 + d**3 + 3*d. Factor p(l).
3*l*(l + 1)**2*(l + 2)
Let q be 0/(1*(5 - 2)). Solve 0 - 9*d**2 - 2*d + q + 0*d = 0 for d.
-2/9, 0
Let a be -1 - -1 - (-4 + 1). Factor -2*l**3 - l**a - 3*l + 0*l**3 - 8*l**2 + 2*l**2.
-3*l*(l + 1)**2
Let j(t) be the second derivative of -t**4/12 + t**3/3 - 11*t. Let j(k) = 0. Calculate k.
0, 2
Suppose 4*f + 50 = -4*j - j, -4*j + 1 = -5*f. Let q be (-4 + 3)*(j + 3). Factor 1/4*w - 1/4*w**4 + 1/4*w**2 - 1/4*w**q + 0.
-w*(w - 1)*(w + 1)**2/4
Let b(z) be the second derivative of 0*z**2 + 1/42*z**4 + 0 - 1/21*z**3 + 4*z. Factor b(l).
2*l*(l - 1)/7
Factor -8 + 4*c - 1/2*c**2.
-(c - 4)**2/2
Let v be (-6)/(0 + 0 - 2). Suppose -v*z + 14 = 2. Determine w so that -w**4 - w**z + w**4 = 0.
0
Let f(w) be the first derivative of 1 + 0*w - 1/6*w**3 - 1/20*w**5 + 0*w**2 - 3/16*w**4. Suppose f(k) = 0. What is k?
-2, -1, 0
Let n = 48 - 48. Let 0*k**2 + n*k**3 - 2/5*k**4 + 0 + 0*k - 2/5*k**5 = 0. Calculate k.
-1, 0
Let w(x) = 4*x + 6. Let f be w(5). Let a = f - 18. Suppose g + a*g**3 - g - 12*g**3 + 2*g**4 = 0. Calculate g.
0, 2
Let x(r) be the first derivative of -8*r**6/9 - 16*r**5/5 - 13*r**4/3 - 8*r**3/3 - 2*r**2/3 - 3. Factor x(p).
-4*p*(p + 1)**2*(2*p + 1)**2/3
Let i be (-2)/8 - (-10)/8. Let c be 2/((1 - -1)/2). Solve -3*d**3 - 4*d - 6*d**2 - d**4 + d**3 - i - c*d**3 = 0 for d.
-1
Let q = -248 - -505/2. Let n(o) be the first derivative of -3*o**2 - 1 + 6*o**3 + 2/3*o - q*o**4. Factor n(g).
-2*(3*g - 1)**3/3
Let g(h) = -2*h**4 - 16*h**3 - 9*h**2 + 77*h - 47. Let a(u) = -6*u**4 - 48*u**3 - 26*u**2 + 230*u - 140. Let q(l) = -3*a(l) + 10*g(l). Factor q(s).
-2*(s - 1)**2*(s + 5)**2
Let w(p) be the first derivative of p**8/5880 + p**7/2940 - p**6/1260 - p**5/420 - 4*p**3/3 + 2. Let j(v) be the third derivative of w(v). Factor j(o).
2*o*(o - 1)*(o + 1)**2/7
Let v(p) be the first derivative of p**4/4 - 8*p**3/3 + 9*p**2/2 - 10*p + 2. Let h be v(7). Find s, given that -2*s**2 - 3*s + 7*s + 4 + h - s**3 = 0.
-2, 2
Factor 1/4 + 1/4*w**3 - 1/4*w**2 - 1/4*w.
(w - 1)**2*(w + 1)/4
Let j be 2/4*-1 + 215/430. Let 1/2*f**4 + 0*f - 1/2*f**2 + j + 0*f**3 = 0. What is f?
-1, 0, 1
Suppose -2 = -2*k, 5*v - 56 = v - 4*k. Let o = v - 7. Let 2*a**2 - 2*a**2 + 2*a**2 - 5*a**2 - 3 - o*a = 0. Calculate a.
-1
Let m be 15/(-3) - 5/((-35)/63). Factor -3/7*b**m - 3/7*b**2 + 0 - 6/7*b**3 + 0*b.
-3*b**2*(b + 1)**2/7
Let v = 1364768/7 + -195368. Let w = v + 402. Suppose -6/7*x**2 - 2/7*x**3 - 2/7 - w*x = 0. Calculate x.
-1
Let j be 2/8 + 24/96. Factor -j*u**2 + 1/2*u + 0.
-u*(u - 1)/2
Let s = 81/8 - 69/8. Factor -3*h**2 + s*h**4 + 0*h + 3/2*h**3 + 0.
3*h**2*(h - 1)*(h + 2)/2
Let k be (-3)/(3/(-2) + 0). Suppose -i - 7 = 5*w, k*w = -w - 6. Factor -v**3 + 4*v**i - 4 - v**3 - 6*v.
2*(v - 2)*(v + 1)**2
Let p(x) be the second derivative of 1/4*x**4 + 0 + 3/2*x**3 - 3/2*x**2 - 9/20*x**5 - 6*x. Determine g so that p(g) = 0.
-1, 1/3, 1
Let h(q) be the second derivative of q**4/60 - 2*q**3/15 + 2*q**2/5 - q. Factor h(m).
(m - 2)**2/5
Suppose 30 = 13*w - 3*w. Suppose 0*b**2 + 0*b + 1/3*b**w - 1/3*b**4 + 0 = 0. What is b?
0, 1
Let t(b) = -13*b**3 - 17*b**2 - 13*b. Let m(c) = -3*c**3 - 4*c**2 - 3*c. Let i(p) = 9*m(p) - 2*t(p). What is y in i(y) = 0?
-1, 0
Let y(w) be the first derivative of 2*w**6/3 - 16*w**5/5 + 2*w**4 + 16*w**3/3 - 6*w**2 + 2. Find o such that y(o) = 0.
-1, 0, 1, 3
Suppose -1 = 2*i - 5. Factor 3 - 2*s**2 - 9 + 8*s - i.
-2*(s - 2)**2
Factor -1/3*b**4 - 1/3 + 4/3*b**3 + 4/3*b - 2*b**2.
-(b - 1)**4/3
Let k(b) be the third derivative of -b**8/1680 - b**7/150 - 2*b**6/75 - 2*b**5/75 + 2*b**4/15 + 8*b**3/15 - 8*b**2. Determine t, given that k(t) = 0.
-2, 1
Let z be (27/18)/((-2112)/(-146)). Let g = z - -5/64. Factor -4/11*i**4 - 2/11*i + 0*i**3 + g*i**5 + 0 + 4/11*i**2.
2*i*(i - 1)**3*(i + 1)/11
Let d = 59 - 231/4. Let i(q) be the first derivative of 8/3*q**3 - 2*q + d*q**4 + 1/2*q**2 + 3. What is n in i(n) = 0?
-1, 2/5
Let w(p) be the first derivative of p**4/14 + 4*p**3/7 + 9*p**2/7 + 6. Factor w(b).
2*b*(b + 3)**2/7
Determine a so that 5*a - 10*a**2 - a**4 + 0*a**4 + 11*a**4 - 11*a**5 + 6*a**5 = 0.
-1, 0, 1
Suppose 3*r - 2*q = 8, -4*q - 1 - 15 = -2*r. Let g(k) be the third derivative of 1/60*k**5 + r*k - 1/40*k**6 - k**2 - 2/9*k**3 + 1/9*k**4 + 0. Factor g(c).
-(c + 1)*(3*c - 2)**2/3
Let p(l) = -3*l**2 + 3*l + 3. Let d(w) be the second derivative of -w**5/20 + w**4/3 - w**3/2 - w**2 - 3*w. Let k(f) = 3*d(f) + 2*p(f). Factor k(z).
-3*z*(z - 1)**2
Let x(s) = -s**3 - 8*s**2 + 5*s + 4. Let q be x(-9). Solve q*u + 22*u**2 - 30*u**5 + 32*u**2 - 3 - 10*u**3 - 62*u**4 + 11 = 0.
-1, -2/3, -2/5, 1
Let t be (2/3)/((-8)/(-24)). Determine z, given that z**t - 12*z + 15*z - 2 + 4 = 0.
-2, -1
Let g(h) be the third derivative of h**6/240 - h**5/60 + h**4/48 - 4*h**2. Factor g(z).
z*(z - 1)**2/2
Let d(f) be the first derivative of -2*f**3/51 + 2*f**2/17 + 6*f/17 + 5. Let d(n) = 0. Calculate n.
-1, 3
Suppose f = v + 7, f = -3*f - 2*v + 40. Let j be ((-3)/f + -1)*-3. Find n such that -4*n + n + n**2 + j*n = 0.
-1, 0
Let t(k) be the third derivative of k**8/448 + k**7/80 + k**6/40 + k**5/80 - k**4/32 - k**3/16 - 8*k**2. Determine n, given that t(n) = 0.
-1, 1/2
Let o be -3 - 0 - 75/(-15). Determine v so that 2*v**2 + 1 + v - 3*v - v**o + 0 = 0.
1
Let i(q) be the third derivative of 1/3*q**3 - 4*q**2 + 1/20*q**5 + 0 - 1/120*q**6 + 0*q - 1/210*q**7 + 5/24*q**4. Suppose i(k) = 0. What is k?
-1, 2
Let y(q) be the first derivative of 3*q**5/5 + 3*q**4 + 2*q**3 - 6*q**2 - 9*q + 18. Factor y(z).
3*(z - 1)*(z + 1)**2*(z + 3)
Let c(a) be the first derivative of -a**4/16 - a**3/12 + a**2/4 + 15. Let c(y) = 0. What is y?
-2, 0, 1
Let x = -207 + 209. Factor 1/6*v**x - 1/3*v**3 + 1/6*v**4 + 0*v + 0.
v**2*(v - 1)**2/6
Let t(m) be the third derivative of -m**9/30240 + m**8/10080 + m**5/20 + m**2. Let k(l) be the third derivative of t(l). Factor k(p).
-2*p**2*(p - 1)
Let y(p) be the first derivative of -5*p**7/84 + p**6/30 + p**5/8 - p**4/12 - p - 1. Let f(a) be the first derivative of y(a). Find d such that f(d) = 0.
-1, 0, 2/5, 1
Suppose 2*r - 4*r = -6. Let d be (r/(-2)