48. Suppose 1/2*g**3 + 3*g**2 + p*g + 4 = 0. Calculate g.
-2
Let c(m) = -10*m**2 - m + 2. Let s be c(-2). Let p be s/(-21) - 6/(-21). Factor -2/3 - 1/3*i + i**p.
(i - 1)*(3*i + 2)/3
Let g(t) be the first derivative of -t**3 - 3*t**2/2 + 18*t + 18. Factor g(y).
-3*(y - 2)*(y + 3)
Suppose 0 = -0*q - 2*q + 4. Let o(g) be the first derivative of -1/3*g**3 + 0*g + 1/5*g**5 + 1 - 1/4*g**4 + 1/2*g**q. Determine x so that o(x) = 0.
-1, 0, 1
Let s = 13 + -25/2. Let q(d) = -d + 4. Let p be q(4). Find i, given that s*i**3 - 1/4*i + 0*i**4 + p + 0*i**2 - 1/4*i**5 = 0.
-1, 0, 1
Let y be (-4)/6 - 28/(-6). Suppose -8 - 4 = -4*m. Factor -n**3 - y*n + 0*n**2 + m*n**2 + 3*n - 3*n**4 + 2*n**5.
n*(n - 1)**2*(n + 1)*(2*n - 1)
Let j(l) be the first derivative of -l**8/672 + l**7/210 - l**6/240 - l**2/2 + 1. Let z(a) be the second derivative of j(a). Let z(i) = 0. Calculate i.
0, 1
Let b(j) be the first derivative of -4*j**3/9 + 10*j**2/3 - 49. Factor b(a).
-4*a*(a - 5)/3
Let v be -6 - (288/(-20))/2. Let -2/5*t**5 + v*t**4 - 6/5*t**3 + 0 + 0*t + 2/5*t**2 = 0. Calculate t.
0, 1
Suppose 4*y + 6 = 5*y. Let i(g) be the first derivative of 2 + 1/6*g**3 + 1/8*g**2 + 1/24*g**y - 1/20*g**5 - 1/8*g**4 - 1/4*g. What is r in i(r) = 0?
-1, 1
Let u(q) be the first derivative of q**7/2940 - q**5/420 + q**3/3 - 3. Let p(g) be the third derivative of u(g). Suppose p(w) = 0. Calculate w.
-1, 0, 1
Let i(j) be the first derivative of -j**6/14 + 9*j**4/28 - 2*j**3/7 - 17. Factor i(q).
-3*q**2*(q - 1)**2*(q + 2)/7
Let o(q) be the first derivative of 15*q**3 + 21*q**2/2 - 12*q + 6. Factor o(s).
3*(3*s - 1)*(5*s + 4)
Let s(x) be the first derivative of x**6/90 - x**4/36 + 2*x + 2. Let m(n) be the first derivative of s(n). Determine a so that m(a) = 0.
-1, 0, 1
Suppose -2 = 2*d, -2*s - d + 10 = -3*d. Factor -3 + 6*y**2 - 4*y - 1 + 5 + 0 - s*y**3 + y**4.
(y - 1)**4
Factor -8*t - 68*t**4 - 88*t**2 - 7*t**5 - 4 - 24*t - 112*t**3 - 9*t**5.
-4*(t + 1)**4*(4*t + 1)
Let g(s) be the third derivative of 0*s**3 + 0 + 1/60*s**6 + 1/15*s**5 + 1/12*s**4 + 0*s + s**2. Solve g(p) = 0.
-1, 0
Suppose -10*q**3 + 6 - 2*q**3 + 5*q + 7*q - 20*q**2 + 4*q**4 + 10 = 0. What is q?
-1, 1, 4
Let a(u) be the third derivative of -u**6/600 - u**5/300 + u**4/120 + u**3/30 + u**2. What is n in a(n) = 0?
-1, 1
Let p = -11 + 14. Factor 1 - 2*a + 8*a - 5 + a**3 - p*a**3.
-2*(a - 1)**2*(a + 2)
Let u = 51 + -49. Let 0*j + 2/3*j**4 + 2/3 + 0*j**3 - 4/3*j**u = 0. Calculate j.
-1, 1
Let s(u) be the second derivative of 1/15*u**6 + 0*u**2 - 1/12*u**3 + u + 1/6*u**4 + 0 - 3/20*u**5 - 1/84*u**7. Factor s(b).
-b*(b - 1)**4/2
Let a(t) be the second derivative of t**5/10 - t**4/3 + 11*t. What is n in a(n) = 0?
0, 2
Factor 15*v**2 + 21*v - 42 + 3*v**3 - 40 + 91.
3*(v + 1)**2*(v + 3)
Let j(r) = 2*r**2 - 9*r - 3. Let x be j(5). Factor 0*u**x + 0*u + 0 + 1/2*u**3.
u**3/2
Let k(l) be the third derivative of -l**7/10080 + l**6/1440 - l**5/480 - l**4/24 + l**2. Let s(v) be the second derivative of k(v). Factor s(j).
-(j - 1)**2/4
Let d(h) be the first derivative of 3*h**4/32 + h**3/4 - 3*h**2/4 - 3*h - 10. Solve d(l) = 0.
-2, 2
Suppose -3*u = 2*n + 4, 3*u - 2*n = 5*u + 4. Let o be ((-24)/(-15))/2 - 0. Find h, given that o*h**3 - 2/5*h**4 + 0*h**2 + u + 0*h = 0.
0, 2
Let w = 55/14 - 24/7. Let h(v) be the second derivative of -1/10*v**5 - 1/12*v**4 + 0*v**6 + 1/4*v**3 + w*v**2 + 1/84*v**7 + v + 0. Factor h(d).
(d - 2)*(d - 1)*(d + 1)**3/2
Solve -6*o**2 - 6*o - 6*o**3 + 0 + 4*o**3 - 2 = 0.
-1
Let u(g) be the third derivative of g**9/1512 + g**8/840 - g**7/420 - g**6/180 - g**3/3 - 4*g**2. Let k(p) be the first derivative of u(p). Factor k(j).
2*j**2*(j - 1)*(j + 1)**2
Let n(s) be the third derivative of -3*s**2 - 1/20*s**4 - 1/100*s**5 + 0*s + 0 + 0*s**3. Let n(l) = 0. What is l?
-2, 0
Let v(d) be the third derivative of -d**7/945 + d**5/54 - 4*d**3/27 + 11*d**2. Suppose v(g) = 0. Calculate g.
-2, -1, 1, 2
Suppose 15 = w + 2*l, 0*w - 4*w = l - 25. Solve -w*i + 2*i - i + 2 + 2*i**2 = 0.
1
Let t be (13 - 13)/(2*(-2 - -1)). Factor -2/5*v**3 + 0*v**2 + t + 2/5*v.
-2*v*(v - 1)*(v + 1)/5
Let j(r) be the third derivative of r**6/900 - r**5/450 - r**4/45 + 4*r**3/45 - 13*r**2. Let j(t) = 0. What is t?
-2, 1, 2
Let q(r) be the second derivative of -r**6/30 + r**5/20 + r**4/24 - 5*r**2/2 - 4*r. Let l(i) be the first derivative of q(i). Factor l(v).
-v*(v - 1)*(4*v + 1)
Let o(g) be the second derivative of -g**5/90 - g**4/18 + g**2 + 4*g. Let c(m) be the first derivative of o(m). Determine u, given that c(u) = 0.
-2, 0
Let y(f) = 3*f**4 + 6*f**3 - 3*f + 3. Let u(a) = -4*a - 2*a**2 + 3*a**4 + 16*a**3 + 4 - 10*a**3 + a**2. Let i(z) = -3*u(z) + 4*y(z). Solve i(o) = 0.
-1, 0
Let r(d) be the first derivative of 2*d**5/25 + d**4/5 + 2*d**3/15 + 10. Find p such that r(p) = 0.
-1, 0
Let g be (-4)/((-4)/(-3)) + 4 + 2. Factor -3/2*l**g - 1/2*l + 0 - 1/2*l**4 - 3/2*l**2.
-l*(l + 1)**3/2
Let y = 1 + 4. Factor i + 10*i**5 - 6*i**3 + 7*i**2 - y*i - 2*i**4 + 3*i**2 - 8*i**5.
2*i*(i - 1)**3*(i + 2)
Let k be (1 - 3)/((-6)/6). Suppose 0 = 3*z + 2*j - 4, 16 = 5*z - k*j + 4. Solve -40/3*q + 6*q**3 - 4*q**z - 16/3 = 0 for q.
-2/3, 2
Let o(f) = 2*f**2 + 50*f + 3. Let m be o(-25). Let x(u) be the first derivative of -1 + 0*u - 3*u**4 + 8/3*u**m + 8/5*u**5 - u**2 - 1/3*u**6. Factor x(j).
-2*j*(j - 1)**4
Factor -3*w**2 + 0 + 9/2*w + 1/2*w**3.
w*(w - 3)**2/2
Let n be (-5)/(-20)*(10 + -4). Suppose -19 = -4*i - 7. What is m in i*m + 0 - n*m**2 = 0?
0, 2
Let g = 84 + -84. Determine a so that -1/4*a**3 + g + 1/4*a**2 + 0*a = 0.
0, 1
Let u(t) = -t**3 + t + 1. Let v(h) = 6*h**3 - 3*h**2 - 5*h - 1. Let a(w) = -5*u(w) - v(w). Let a(q) = 0. What is q?
-1, 2
Suppose -f = -w, 0 = 13*w - 11*w + 5*f - 21. Determine u, given that u**w + 1/3 + 7/3*u**2 + 5/3*u = 0.
-1, -1/3
Let q = -7 - -113/16. Let a(x) be the second derivative of -q*x**4 + 0 + 1/2*x**3 - 3/2*x**2 + 2*x. Determine u so that a(u) = 0.
2
Suppose 0 = 4*c + c - 20. Determine d so that -3*d - 6*d**2 + 0 - d + c*d**2 - 2 = 0.
-1
Let c(z) be the first derivative of 3/8*z**4 - 5 + 0*z - 3/4*z**2 - 3/10*z**5 + 1/2*z**3. Solve c(g) = 0 for g.
-1, 0, 1
Let u(h) be the third derivative of -10*h**2 + 1/540*h**6 + 5/108*h**4 - 2/135*h**5 + 0 - 2/27*h**3 + 0*h. What is k in u(k) = 0?
1, 2
Suppose -53*a - 86 - 11*a + 16*a**3 + 4*a**4 + 22 = 0. What is a?
-2, 2
Let k(q) be the first derivative of 2*q**3/15 - 2*q/5 + 6. Factor k(y).
2*(y - 1)*(y + 1)/5
Let m(f) be the first derivative of f**5/180 - f**4/72 - 2*f**2 - 2. Let y(x) be the second derivative of m(x). Suppose y(s) = 0. What is s?
0, 1
Let n(w) be the first derivative of w**8/336 + w**7/210 - w**6/40 - w**5/12 - w**4/12 + 5*w**2/2 - 4. Let m(l) be the second derivative of n(l). Factor m(f).
f*(f - 2)*(f + 1)**3
Let h(o) be the third derivative of o**7/42 - o**5/4 - 5*o**4/12 - 6*o**2. Factor h(a).
5*a*(a - 2)*(a + 1)**2
Let g(c) be the second derivative of -1/180*c**5 + 0*c**3 - 3/2*c**2 + 0 + 0*c**4 - c. Let r(p) be the first derivative of g(p). Solve r(y) = 0.
0
Determine d so that 2/3*d**4 + 0*d - 2/3*d**5 + 0 - 8/3*d**2 + 8/3*d**3 = 0.
-2, 0, 1, 2
Let r(j) be the first derivative of -j**7/140 - 3*j**6/80 + j**5/40 + 3*j**4/16 + 2*j**2 - 1. Let o(n) be the second derivative of r(n). Factor o(k).
-3*k*(k - 1)*(k + 1)*(k + 3)/2
Let s(z) be the third derivative of z**7/105 - z**6/60 + 6*z**2. Factor s(t).
2*t**3*(t - 1)
Let u(a) = -3*a**4 + 4*a**3 - 6*a**2 + 4*a + 5. Let y(b) = 2*b**4 - 3*b**3 + 5*b**2 - 3*b - 4. Let f(q) = 3*u(q) + 4*y(q). Factor f(h).
-(h - 1)**2*(h + 1)**2
Let r(a) be the first derivative of -a**7/525 - a**6/300 + a**5/150 + a**4/60 - 2*a**2 - 3. Let v(i) be the second derivative of r(i). Solve v(h) = 0 for h.
-1, 0, 1
Let k = 0 + 3. Suppose 5*u**4 - 2*u**4 - k*u**2 + 2*u**3 + u**3 - 3*u**5 = 0. What is u?
-1, 0, 1
Let h(p) = -2*p - 7. Let c be h(-5). Suppose -6*x**3 - 2 + 6*x + 0*x**3 + 5*x**2 - c*x**2 = 0. Calculate x.
-1, 1/3, 1
Let x(a) be the second derivative of 2*a**6/3 - a**5/4 - a - 8. Solve x(p) = 0 for p.
0, 1/4
Let a(b) be the third derivative of b**7/280 - b**6/160 - b**5/16 - 3*b**4/32 - 32*b**2. Let a(i) = 0. Calculate i.
-1, 0, 3
Let u = 173 + -24219/140. Let l(r) be the third derivative of 0*r**4 + 0*r**3 + 1/147*r**7 - 1/105*r**5 - r**2 + 0 - 