 q**5/24 + 5*q**4/96 - 18*q**2. Factor b(r).
5*r*(r + 1)**2/4
Factor 0*b**3 - 3*b**3 + 4*b**3 - 8 + 12*b - 6*b**2.
(b - 2)**3
Let h(q) be the third derivative of -q**8/420 - q**7/525 + q**6/75 + q**5/75 - q**4/30 - q**3/15 - 8*q**2. Determine d, given that h(d) = 0.
-1, -1/2, 1
Let q(f) be the first derivative of f**3 + 6*f**2 + 12*f - 3. Determine k so that q(k) = 0.
-2
Let j(s) = 6*s**4 + 6*s**3 - 3*s**2 + 3*s + 3. Let p(q) = -7*q**4 - 7*q**3 + 4*q**2 - 4*q - 4. Let r(t) = -4*j(t) - 3*p(t). Solve r(l) = 0 for l.
-1, 0
Let p(a) be the first derivative of a**6/105 - 3*a**5/70 + a**4/14 - a**3/21 + 2*a - 4. Let r(x) be the first derivative of p(x). Let r(j) = 0. Calculate j.
0, 1
Suppose -53*u + 56*u = 6. Let p(s) be the first derivative of 0*s + 0*s**u + 1/18*s**4 - 2 + 2/27*s**3. What is y in p(y) = 0?
-1, 0
Let c be (-21)/(-9) + -5 - -3. Determine k so that -5/3*k**3 - c*k**2 + 0*k + 0 - 4/3*k**4 = 0.
-1, -1/4, 0
Suppose 0 = 8*f - 6*f - 28. Let j = f + -11. Determine d so that -1/4*d**4 - 5/4*d**j - 1/2 - 7/4*d - 9/4*d**2 = 0.
-2, -1
Determine x so that x**5 + 12*x**4 + 6*x**5 + 4*x**2 + 12*x**3 - 3*x**5 = 0.
-1, 0
Let d(j) be the first derivative of -5/8*j**2 + 1/2*j + 4 - j**3. Find w, given that d(w) = 0.
-2/3, 1/4
Factor 6 + 20*x + 4*x**2 + 2 + 8.
4*(x + 1)*(x + 4)
Let z = -4 + 0. Let b be (-8)/(-3) - z/(-6). Factor -o - 3*o**2 + 4*o**b - 2*o**2.
-o*(o + 1)
Suppose 4*f - 5 = 3. Let r(b) = b**2 + 8*b + 9. Let s be r(-7). What is w in -w - w**s - w + w + f = 0?
-2, 1
Let c(v) be the second derivative of v**5/20 - v**4/6 + v**2/2 - 2*v. Let f be c(2). What is k in 3 + 0 + 4*k**3 - 4*k - f - 2*k**4 = 0?
-1, 1
Suppose g = -a + 3, 2*g + 0*a = -5*a + 12. Suppose 2*k - 2*u = 4, 2*k - 3*u - 4 = -5*u. Solve -5/2*l**5 - 5*l**k + 1/2*l + 4*l**4 + g + 2*l**3 = 0.
-1, -2/5, 1
Let i(h) be the first derivative of 4*h**3/3 - 4*h**2 + 4*h - 20. Factor i(y).
4*(y - 1)**2
Suppose 5*z + 5 = 15. Let g be (-1)/z - (-78)/108. What is i in g*i**2 + 0 + 2/9*i = 0?
-1, 0
Let z(r) be the second derivative of r**7/1960 - r**6/840 + r**5/840 - r**4/3 + r. Let i(o) be the third derivative of z(o). Factor i(w).
(3*w - 1)**2/7
Let j(t) be the first derivative of -27*t**3 - 2*t + 0 - 2*t - 3 - 18*t**2. Factor j(u).
-(9*u + 2)**2
Let y = 207 + -207. Solve 2/7*m + 2/7*m**3 + 4/7*m**2 + y = 0.
-1, 0
Let n(w) be the first derivative of 2*w**3/3 + 10*w**2 + 50*w + 8. Factor n(k).
2*(k + 5)**2
Let b(k) be the third derivative of 1/15*k**5 + 8*k**2 + 0*k + 0*k**4 + 0*k**3 + 0. Factor b(n).
4*n**2
Let k(t) be the second derivative of t**7/840 + t**6/90 + t**5/24 + t**4/12 + 2*t**3/3 - 9*t. Let u(f) be the second derivative of k(f). Factor u(z).
(z + 1)**2*(z + 2)
Suppose -2*b = 5*a - 23 + 3, 3*a + 4 = 2*b. Suppose 0 = b*j + 3*l - 21, j = 3*l + 2*l - 7. Let -2/9*o**j - 4/9*o**2 - 2/9*o + 0 = 0. What is o?
-1, 0
Let n(k) = 2*k**2 - 3*k + 7. Let o(m) = -m**2 + m - 3. Let y(c) = 3*n(c) + 7*o(c). Factor y(d).
-d*(d + 2)
Let r be (15/(-4))/((-15)/20). Let q(c) be the second derivative of 0*c**2 + 1/70*c**r + 0*c**3 + 0 + 3*c + 1/21*c**4. Find l such that q(l) = 0.
-2, 0
Let x(i) be the second derivative of 0 + 8*i - 1/15*i**4 + 0*i**2 - 9/50*i**5 + 2/75*i**6 + 0*i**3 + 3/35*i**7. Solve x(h) = 0.
-1, -2/9, 0, 1
Let d(l) = -l - 2. Let c be d(-3). Let v = 1 - c. Factor 5*n + v*n - 4*n + n**2.
n*(n + 1)
Let q(j) be the third derivative of j**9/1008 + j**8/1120 + j**4/12 + 4*j**2. Let y(t) be the second derivative of q(t). Factor y(k).
3*k**3*(5*k + 2)
Let z be 12/(-20) + (-24)/(-15). Let m be 7*(-2)/(-10) - z. Factor 0 + 0*t**2 + 2/5*t - m*t**3.
-2*t*(t - 1)*(t + 1)/5
Let i(b) be the first derivative of -8 - 3/2*b**2 + 6*b - b**3. Factor i(d).
-3*(d - 1)*(d + 2)
Let q(a) be the first derivative of 3*a**8/112 + 2*a**7/35 - a**6/40 - a**5/10 + a**2 - 1. Let c(x) be the second derivative of q(x). Factor c(u).
3*u**2*(u + 1)**2*(3*u - 2)
Let i be 0*((-1)/(-4) - (-1)/(-2)). Solve -1/3*o**4 + 0*o + 0*o**3 + i + 1/3*o**2 = 0.
-1, 0, 1
Let b(g) = -6*g - 27. Let n be b(-5). Let l(u) be the second derivative of 1/20*u**5 - 1/24*u**4 + 0*u**3 + 0*u**2 - n*u + 0 - 1/60*u**6. Factor l(f).
-f**2*(f - 1)**2/2
Let o(m) be the first derivative of m**6/360 - m**5/120 - m**3 + 4. Let l(a) be the third derivative of o(a). Solve l(p) = 0 for p.
0, 1
Let k = -9 - -11. Let d(p) be the first derivative of 0*p - 16/35*p**5 + 3 + 1/14*p**4 + 0*p**k + 4/21*p**3 + 5/21*p**6. What is o in d(o) = 0?
-2/5, 0, 1
Let o(j) = 9*j - 193. Let i be o(22). Suppose 0*a - 1/2*a**4 + 1/2*a**3 + 1/2*a**2 - 1/2*a**i + 0 = 0. Calculate a.
-1, 0, 1
Let h(r) be the first derivative of -r**3/4 + 3*r/4 + 12. Determine d so that h(d) = 0.
-1, 1
Let x(n) be the first derivative of 5*n**4/3 + 35*n**3/9 - 5*n**2/3 + 22. Factor x(u).
5*u*(u + 2)*(4*u - 1)/3
Let k = -86 - -776/9. Let j be (-2)/(-5) - 16/90. Factor 0 - 4/9*d**2 + 0*d**3 + j*d + 4/9*d**4 - k*d**5.
-2*d*(d - 1)**3*(d + 1)/9
Let v(p) be the second derivative of p**4/24 - p**2/4 + 12*p. Find t such that v(t) = 0.
-1, 1
Let k = -3 - -7. Factor -5*n - n**4 - n**3 + 5*n + 2*n**k.
n**3*(n - 1)
Suppose 0 = 4*q - 0*q. Let p(l) be the first derivative of -1 - 1/9*l**3 + 0*l + q*l**2. Let p(f) = 0. What is f?
0
Let h(p) be the first derivative of -2*p**3/15 + 4*p**2/5 - 6*p/5 + 15. Factor h(j).
-2*(j - 3)*(j - 1)/5
Let f(z) be the first derivative of z**6/42 - z**5/35 - z**4/28 + z**3/21 - 2. Suppose f(v) = 0. What is v?
-1, 0, 1
Determine h so that 0 + 1/4*h - 1/4*h**2 = 0.
0, 1
Suppose 0*t - 2*m + 3 = -t, -7 = 4*t - 3*m. Let a be (3 + -3)/(t + 2). Factor -r**2 + 1/2*r**5 + a*r**3 + r**4 + 0 - 1/2*r.
r*(r - 1)*(r + 1)**3/2
Let d be (-2)/(-5) + (-148)/(-2). Let y = d - 74. Factor 4*a**2 + 2/5*a**5 + 4*a**3 + y + 2*a**4 + 2*a.
2*(a + 1)**5/5
Let a(d) = -37*d**2 - 21*d - 2. Let s(l) be the first derivative of -11*l**2 - 2*l - 38/3*l**3 + 2. Let g(z) = 6*a(z) - 5*s(z). What is w in g(w) = 0?
-1/4
Let o(a) be the third derivative of -1/14*a**4 - 1/210*a**5 - 3/7*a**3 + 0*a + 0 - 4*a**2. Determine n so that o(n) = 0.
-3
Let z(y) be the first derivative of 5*y**3/3 - 55*y**2 + 605*y + 8. Factor z(l).
5*(l - 11)**2
What is d in -d - 128*d**2 - d + 127*d**2 = 0?
-2, 0
Let p be -3 - 111/12*8/(-14). Factor p*r**2 + 10/7*r**3 + 2/7*r - 4/7.
2*(r + 1)**2*(5*r - 2)/7
Factor 2/13*b**4 - 8/13*b + 0 - 4/13*b**3 - 14/13*b**2.
2*b*(b - 4)*(b + 1)**2/13
Let v(d) = -2*d**2 + 2*d - 1. Let p be v(1). Let u = p - -31. Factor u*k**3 - 16*k**2 - 50/3*k**4 + 0 + 8/3*k.
-2*k*(k - 1)*(5*k - 2)**2/3
Let m(z) be the second derivative of 0 - z**2 + 1/6*z**3 - 8*z + 1/12*z**4. Factor m(t).
(t - 1)*(t + 2)
Suppose 0 = 4*l + 7 + 1. Let s be l/(-8) - (-28)/16. Factor 2*x**2 + 2 + x**2 - 4*x**2 - s*x**3 + 7*x**2 - 6*x.
-2*(x - 1)**3
Let h(d) be the first derivative of -d**4/14 + 6*d**3/7 - 24*d**2/7 + 32*d/7 + 14. Factor h(m).
-2*(m - 4)**2*(m - 1)/7
Let u be -2 + (-5 - 0)*(-13)/26. Suppose 0*t - 1/2*t**3 + 0 + 0*t**2 + 0*t**4 + u*t**5 = 0. What is t?
-1, 0, 1
Let y(v) be the third derivative of 1/90*v**5 + 3*v**2 + 0*v - 1/9*v**3 + 0*v**4 + 0. Factor y(a).
2*(a - 1)*(a + 1)/3
Let c(h) = -h**5 - 7*h**4 + 37*h**3 - 19*h**2 + 5*h + 5. Let w(n) = 3*n**4 - 18*n**3 + 9*n**2 - 3*n - 3. Let f(m) = -3*c(m) - 5*w(m). Factor f(i).
3*i**2*(i - 1)**2*(i + 4)
Factor -4/5 - 2*w + 36/5*w**2.
2*(2*w - 1)*(9*w + 2)/5
Let z = -3032/5 + 607. Solve z*s**5 + 0*s**4 + 0*s**3 + 0*s + 0 + 0*s**2 = 0 for s.
0
Find y such that 1/2*y**2 + 0 - 1/2*y = 0.
0, 1
Let f(k) be the third derivative of 0*k**3 + 0 + 0*k - 1/12*k**5 + 1/12*k**4 + k**2. Factor f(m).
-m*(5*m - 2)
Suppose -26 = -3*z + 5*l, z - 2*l = 11 - 1. Let d(h) be the second derivative of 0 + 1/40*h**6 + 1/12*h**4 + 0*h**z + 3*h - 1/3*h**3 + 1/8*h**5. Factor d(a).
a*(a + 2)**2*(3*a - 2)/4
Factor -1 + 17*x + 6*x**3 + x**4 + 5 - 2*x - 3*x + 13*x**2.
(x + 1)**2*(x + 2)**2
Let a(r) be the third derivative of -r**6/120 + r**5/30 - r**4/24 + 5*r**2. Determine g so that a(g) = 0.
0, 1
Suppose 3*s - 11 = c, -12*s = -9*s + 4*c + 14. Suppose 16/9*y**s - 8/9*y - 2/3*y**3 + 0 = 0. What is y?
0, 2/3, 2
Factor 3/4*g - 1/4*g**4 + 1/2 - 1/4*g**2 - 3/4*g**3.
-(g - 1)*(g + 1)**2*(g + 2)/4
Suppose l = -3*l + 4. Suppose 2*g = 3*j - 1, j + 4 = 2*g - l. Factor -x**j + x**3 - x**3 + x.
-x*(x - 1)*(x + 1)
Let g