 + 8*m**5/5 - 5*m**4 - 8*m**3 + 3. Factor r(s).
4*s**2*(s - 2)*(s + 1)*(s + 3)
Let q(u) = 15*u**2 + 39*u - 18. Let b(p) = -30*p**2 - 78*p + 36. Let g(y) = -3*b(y) - 5*q(y). Factor g(m).
3*(m + 3)*(5*m - 2)
Suppose 3*d**2 + 7/3*d + 1/3*d**4 + 5/3*d**3 + 2/3 = 0. What is d?
-2, -1
Let l(s) = -3*s**4 - 6*s**3 - 2*s**2 + 4*s + 5. Let w(j) = 3*j**4 + 6*j**3 + 3*j**2 - 3*j - 6. Let z(v) = -3*l(v) - 2*w(v). Factor z(d).
3*(d - 1)*(d + 1)**3
Suppose -5*h + 2*g + 13 = 0, -4*g - 4 = -3*h + 1. Suppose -p + h*p = 10. Factor -27*d**3 + 12*d**4 - 3*d**p + 6*d**2 + 8*d**2 - 3*d - 2*d**2 + 9*d**3.
-3*d*(d - 1)**4
Let i(f) = f**3 + 24*f**2 + 2*f + 50. Let w be i(-24). Factor 0 + 1/2*h**w + 1/2*h.
h*(h + 1)/2
Factor 0*m**2 - 1 - 2*m - 3 + 6*m**2.
2*(m - 1)*(3*m + 2)
Let h(j) be the first derivative of 4/9*j + 2/27*j**3 - 2 - 1/3*j**2. Find m, given that h(m) = 0.
1, 2
Let u(y) be the second derivative of 1/180*y**5 + 0 - y**2 - 1/72*y**4 - 1/9*y**3 - 2*y. Let w(q) be the first derivative of u(q). Factor w(j).
(j - 2)*(j + 1)/3
Let l(p) be the second derivative of p**6/24 + 7*p**5/20 + 13*p**4/48 - 5*p**3/12 - 11*p. Determine k so that l(k) = 0.
-5, -1, 0, 2/5
Factor -1/8*n**3 + 1/2*n**2 + 0 + 0*n.
-n**2*(n - 4)/8
Let f(a) be the second derivative of -a**4/6 + 2*a**3/3 + 3*a. Find b such that f(b) = 0.
0, 2
Factor 12/7*b**5 + 0 + 4/7*b**2 + 0*b + 4/7*b**3 - 20/7*b**4.
4*b**2*(b - 1)**2*(3*b + 1)/7
Suppose -4 - 7 = -4*h + q, 6 = -2*q. Factor -3*k**3 + 5*k**4 - k**3 - h*k**4 + k**4.
4*k**3*(k - 1)
Let p = -94 + 178. What is c in -97*c**3 + 460*c**3 + 12*c + 48*c**2 + p*c**2 = 0?
-2/11, 0
Factor -6 - 200/3*c**2 - 40*c.
-2*(10*c + 3)**2/3
Let o(r) be the third derivative of -r**7/1260 + r**5/360 - 28*r**2. What is d in o(d) = 0?
-1, 0, 1
Let a(r) be the second derivative of r**6/30 - r**5/40 - r**4/4 - r**3/12 + r**2/2 - 3*r. Suppose a(m) = 0. What is m?
-1, 1/2, 2
Let d be (-2)/14*14/(-60). Let z(c) be the second derivative of 0 - 1/100*c**5 - 1/30*c**4 - 2*c - d*c**3 + 0*c**2. Suppose z(j) = 0. What is j?
-1, 0
Let f be (-14)/(-4410)*-7 - (-4)/18. Factor f - 2/5*i + 1/5*i**2.
(i - 1)**2/5
Let o(t) = t**2 + t - 2. Let g be (-9)/((3/(-2))/(-1)). Let u(m) = 3*m**2 + 4*m - 7. Let v(r) = g*u(r) + 21*o(r). Suppose v(q) = 0. What is q?
0, 1
Let o(a) be the second derivative of -a**6/2700 + a**5/450 - a**3/6 - a. Let y(m) be the second derivative of o(m). Factor y(l).
-2*l*(l - 2)/15
Suppose -8/7*n - 162/7*n**3 - 72/7*n**2 + 0 = 0. What is n?
-2/9, 0
Let r(y) be the first derivative of -5*y**3/3 - 16. Determine m, given that r(m) = 0.
0
Let q = 14 + -10. Suppose -q*r - 8 = -36. Let l(d) = -8*d**2 - 5*d - 1. Let z(h) = -7*h**2 - 4*h - 1. Let c(i) = r*z(i) - 6*l(i). What is m in c(m) = 0?
1
Let k be (-8)/(-54)*(-2)/16*-12. Factor 2/9 + 4/9*u + k*u**2.
2*(u + 1)**2/9
Suppose 5*o - 4*o = 0. Let x(l) be the third derivative of 1/60*l**5 - 1/6*l**4 + l**2 + 2/3*l**3 + o + 0*l. Factor x(s).
(s - 2)**2
Let l = -65 - -68. Let -1/5*s + 1/5*s**4 + 0 + 3/5*s**2 - 3/5*s**l = 0. What is s?
0, 1
Factor 0*n**2 + 0*n**4 + 1/2*n**3 - 1/4*n + 0 - 1/4*n**5.
-n*(n - 1)**2*(n + 1)**2/4
Let h = -88 + 177/2. Determine w, given that w + 1/2*w**2 + h = 0.
-1
Let k(h) = -5*h**2 - 8 - 2*h - 5*h + 2. Let d(p) = -p**2 - p - 1. Let u(z) = 6*d(z) - k(z). Factor u(q).
-q*(q - 1)
Let q(i) = -4*i**3 - 8*i**2 + 3*i + 3. Let t(g) = -4*g**3 - 8*g**2 + 2*g + 2. Let y(c) = 2*q(c) - 3*t(c). Factor y(n).
4*n**2*(n + 2)
Let m(h) be the first derivative of -h**6/540 + 2*h**5/135 - 5*h**4/108 + 2*h**3/27 + h**2 - 1. Let j(t) be the second derivative of m(t). Factor j(d).
-2*(d - 2)*(d - 1)**2/9
Let i = -48 + 50. Find o, given that -4/7*o + 2/7 + 2/7*o**i = 0.
1
Factor -2/3 - 8/3*f**2 + f**3 + 7/3*f.
(f - 1)**2*(3*f - 2)/3
Suppose -13*s + s = 0. Factor -2/3*p + s*p**2 + 2/3*p**3 + 0.
2*p*(p - 1)*(p + 1)/3
Let s(k) be the first derivative of 1/2*k + k**3 + 1/2*k**4 + 1/10*k**5 + 2 + k**2. Determine z, given that s(z) = 0.
-1
Let j(b) be the second derivative of 1/120*b**6 + 3*b + 0*b**2 + 0 + 1/80*b**5 + 0*b**3 - 1/48*b**4 - 1/168*b**7. Solve j(z) = 0 for z.
-1, 0, 1
Let y(h) = h**2 + 8*h - 5. Let d(w) = 94*w + 6 - 103*w + 2*w**2 - 4*w**2. Let o(z) = -4*d(z) - 5*y(z). Factor o(g).
(g - 1)*(3*g - 1)
Factor -2/19*f**3 - 2/19*f + 0 + 4/19*f**2.
-2*f*(f - 1)**2/19
Let l(g) be the first derivative of 1/10*g**4 - 1/5*g**2 - 2/15*g**3 - 1 + 2/5*g. Factor l(x).
2*(x - 1)**2*(x + 1)/5
Let c = 67 + -65. Let g = -107 + 967/9. Find v such that -2/9*v**4 - 10/9*v**3 - 14/9*v - g - c*v**2 = 0.
-2, -1
Let g be ((99/12 - 3) + -5)*12. Factor -3/5*v**g + 0*v**2 + 0 + 0*v.
-3*v**3/5
Let o(t) be the first derivative of t**2 + 1/120*t**5 + 1 + 0*t**3 + 0*t - 1/96*t**4 - 1/480*t**6. Let c(y) be the second derivative of o(y). Factor c(s).
-s*(s - 1)**2/4
Let s(m) be the first derivative of m**9/3024 + m**8/420 + m**7/210 + 2*m**3/3 - 4. Let f(g) be the third derivative of s(g). Factor f(r).
r**3*(r + 2)**2
Let k(x) = x**3 + x**2 + x - 1. Let u(i) = -8*i**3 - 12*i**2 + 2*i + 2. Let y(l) = -4*k(l) - 2*u(l). Find m, given that y(m) = 0.
-2, 0, 1/3
Solve 18*h**4 - h**3 - 7*h**3 - 14*h**4 = 0.
0, 2
Let s(k) be the second derivative of 3*k**7/14 + 19*k**6/15 + 53*k**5/20 + 7*k**4/3 + 2*k**3/3 - 46*k. Solve s(w) = 0.
-2, -1, -2/9, 0
Determine m, given that -32 + 60 + 20*m + 2*m**2 + 22 = 0.
-5
Let w(j) = 2*j**2 - 11*j + 5. Let a(d) = -5*d**2 - 7 - 5 + 1 + 6*d + 17*d. Let x(c) = -6*a(c) - 13*w(c). Factor x(o).
(o + 1)*(4*o + 1)
Let k(m) be the first derivative of -m**6/27 + 8*m**5/45 - m**4/3 + 8*m**3/27 - m**2/9 - 5. Find h, given that k(h) = 0.
0, 1
Let q be 0 - -2 - (-2 - 0). Factor -3*p**4 + p**q - 2*p**4 + 2*p**4 + 2*p**3.
-2*p**3*(p - 1)
Let y(m) be the first derivative of m**5/30 + m**4/18 - 5*m**3/9 + m**2 - 4*m - 7. Let q(t) be the first derivative of y(t). Factor q(j).
2*(j - 1)**2*(j + 3)/3
Let u(p) = p**3 + 6*p**2 + 4*p - 6. Let r be u(-2). Solve 4/5 + 2/5*h**3 + r*h + 8/5*h**2 = 0 for h.
-2, -1
Suppose 7 = 5*n + 2*s, -13 = 3*s - 1. Factor 6*x**5 - 14*x**4 + 6*x**n + 0*x**4 - 2*x**2 - 4*x**3 + 8*x**3.
2*x**2*(x - 1)**2*(3*x - 1)
Let c(h) = -h**2 - 5*h - 3. Let l be c(-2). Suppose -26*b**4 - 3*b**3 - 10*b**5 + 12*b**4 + 0*b**l + 14*b**2 + 4*b + 9*b**3 = 0. What is b?
-1, -2/5, 0, 1
Let u = -90 - -30. Let v be (-64)/u + (-2)/5. Factor 2/3 - 2/3*p**2 + v*p**3 - 2/3*p.
2*(p - 1)**2*(p + 1)/3
Let z(u) be the third derivative of u**9/1890 - u**8/1120 - u**7/1260 + u**4/24 - 2*u**2. Let x(b) be the second derivative of z(b). Let x(g) = 0. What is g?
-1/4, 0, 1
Let a(x) be the third derivative of x**8/100800 - x**7/6300 + x**6/900 + x**5/20 + x**2. Let v(q) be the third derivative of a(q). Solve v(b) = 0.
2
Let s(a) = a**2 + 8*a + 7. Let y be s(-5). Let m be y/(-2)*8/80. Find g, given that -24/5*g + m*g**2 + 24/5*g**3 + 8/5 + 8/5*g**4 = 0.
-2, 1/2
Let c(b) be the first derivative of 3*b**5/20 + 3*b**4/16 - b**3/4 - 3*b**2/8 - 1. Factor c(s).
3*s*(s - 1)*(s + 1)**2/4
Let i be ((-24)/(-9))/(-4)*(-24)/32. Factor 0*q - 1/4*q**3 + i*q**2 - 1/2*q**4 + 0 + 1/4*q**5.
q**2*(q - 2)*(q - 1)*(q + 1)/4
Let y(i) be the second derivative of 6*i + 0*i**2 + 0 - 1/3*i**4 + 0*i**3. Find f, given that y(f) = 0.
0
Let n(k) be the second derivative of k**7/1260 + k**6/120 + k**5/30 + k**4/6 + k. Let c(r) be the third derivative of n(r). Determine d, given that c(d) = 0.
-2, -1
Let j(q) be the second derivative of -4*q + 0*q**2 - 1/10*q**6 + 1/4*q**4 - 1/14*q**7 + 0 + 3/20*q**5 + 0*q**3. Suppose j(d) = 0. Calculate d.
-1, 0, 1
Let r be ((-1)/3)/((-2)/(-6)). Let p be r/2 + 2/4. Factor 1/2*s**2 - s**3 + 0 + p*s + 1/2*s**4.
s**2*(s - 1)**2/2
Suppose -3*n + 5*n = -2*a + 14, -a + 3 = -n. Let g = 5/2 - n. Factor 0 + 0*j + g*j**3 - 1/2*j**2.
j**2*(j - 1)/2
Let z(i) be the third derivative of -i**7/8820 + i**6/840 - i**5/210 - 11*i**4/24 + 7*i**2. Let a(l) be the second derivative of z(l). Solve a(y) = 0 for y.
1, 2
Let n = -83 - -89. Let h(t) be the third derivative of 3*t**2 + 0*t - 7/30*t**5 - 1/6*t**4 + 0 + 0*t**3 - 1/12*t**n. Factor h(b).
-2*b*(b + 1)*(5*b + 2)
Let m(x) be the second derivative of x**5/130 + 2*x**4/39 + x**3/13 + 2*x. Factor m(l).
2*l*(l + 1)*(l + 3)/13
Let p be (-42)/(-126) - 1*2/6. Suppose 0 - 1/4*k**4 - 1/2*k**3 + p*k + 0*k**2 = 0. What is k?
-2