- 6*s**2 + 2 + s = 0. Calculate s.
-1, 0
Let f be 12/(-8) + (-88)/(-48). Suppose -4*v + 5*n = -18, 5*n = v - 14 + 2. Solve 4/3*d**3 - f*d**v + 0 - d**4 + 0*d = 0.
0, 1/3, 1
Let t(l) be the second derivative of 9*l**5/20 + 7*l**4/4 + l**3 - 21*l. Let t(i) = 0. Calculate i.
-2, -1/3, 0
Let c be 2/(-7) - 96/(-42). Determine s so that -s**2 + 4*s**c - 2 - 2*s**2 - s = 0.
-1, 2
Let w(r) be the second derivative of r**4 + 3*r**2 + 0 + 3/20*r**5 - r + 5/2*r**3. Factor w(s).
3*(s + 1)**2*(s + 2)
Let j be 5 + (-3 - (-4 - -4)). Let u(g) be the third derivative of -1/45*g**5 + 0 - 1/36*g**4 + 2*g**j + 0*g**3 - 1/180*g**6 + 0*g. Factor u(w).
-2*w*(w + 1)**2/3
Let d(p) = -p**3 - 5*p**2 - 5*p - 2. Let q be d(-4). Let v(b) be the third derivative of 0 - 2/3*b**3 + b**q - 1/6*b**4 - 1/60*b**5 + 0*b. Factor v(i).
-(i + 2)**2
Let c(m) = m**3 + m**2 + 1. Let b(v) = 2*v**3 - v**2 + 1. Let q be b(-1). Let o(j) = -4*j**3 - j**2 + 4*j - 11. Let a(l) = q*o(l) - 6*c(l). Factor a(u).
2*(u - 2)**2*(u + 2)
Let d be (-4)/64 - 840/(-1152). Find s, given that -2/3*s - d*s**3 + 1/6*s**4 + 1/6 + s**2 = 0.
1
Suppose n + n + 204 = 0. Let a be n/(-27) + 2/9. Factor -1/3*s + 2/3*s**a + 1/3*s**5 + 0 - 2/3*s**2 + 0*s**3.
s*(s - 1)*(s + 1)**3/3
Let b(i) be the third derivative of 1/210*i**5 + 0*i**4 + 0*i - 1/280*i**6 + 0 + 0*i**7 + 1/2352*i**8 + i**2 + 0*i**3. Factor b(a).
a**2*(a - 1)**2*(a + 2)/7
Let l(v) = -2*v**4 + 4*v**3 + 2*v**2 + 2. Let z(i) = -i**5 + i**2 + 9*i**3 + 27*i - 3*i**4 + 4*i**2 + 5 - 27*i. Let r(p) = -5*l(p) + 2*z(p). Factor r(f).
-2*f**3*(f - 1)**2
Let j = -76 + 457/6. Let w(p) be the first derivative of 0*p - j*p**4 - 2/9*p**3 - 2 - 1/9*p**2 - 2/45*p**5. Factor w(a).
-2*a*(a + 1)**3/9
Let s = -2 - -2. Suppose -4*h + 13 + 19 = s. Let 2*r**3 - 2 + 8*r + h*r**2 + 2 = 0. Calculate r.
-2, 0
Suppose -15*y + 14*y + 3 = 0. Let x(v) be the second derivative of -1/12*v**4 - 1/30*v**6 + 0*v**y + 1/10*v**5 + 0 + 0*v**2 - 3*v. Factor x(n).
-n**2*(n - 1)**2
Let m(h) be the second derivative of 0 - 6*h - 5/2*h**4 + 3/10*h**6 + 9/10*h**5 - 1/14*h**7 - 21/2*h**3 - 27/2*h**2. Factor m(j).
-3*(j - 3)**2*(j + 1)**3
Let u(t) be the second derivative of -t**7/84 + 7*t**6/30 - 73*t**5/40 + 43*t**4/6 - 44*t**3/3 + 16*t**2 - 17*t. Find g, given that u(g) = 0.
1, 4
Let j(v) be the first derivative of 4*v**3/3 - 5. Factor j(w).
4*w**2
Let u(h) be the first derivative of h**4 + 8*h**3/3 - 2*h**2 - 8*h + 5. Factor u(n).
4*(n - 1)*(n + 1)*(n + 2)
Let d be (-8 - -9)*2*1. Solve -8*t - 4 + 16*t + 9*t - 4*t**d = 0.
1/4, 4
Let o(r) be the second derivative of -5*r**7/42 + r**6/3 - r**5/4 - 23*r. Factor o(k).
-5*k**3*(k - 1)**2
Let o be (-16)/(-18) - ((-25)/(-15) - 1). Factor o*i**4 - 4/9*i**2 + 0*i + 2/9 + 0*i**3.
2*(i - 1)**2*(i + 1)**2/9
Let p(v) = -2*v**3 - 9*v**2 - 2*v. Let g(m) = m**3 + 4*m**2 + m. Let t(u) = -5*g(u) - 2*p(u). Factor t(l).
-l*(l + 1)**2
Let o be (-8)/28 + 60/14. Find j such that 0*j**3 + 0*j**4 + j**o + 3*j + j - 3*j**3 = 0.
-1, 0, 2
Let j = 183 + -181. Suppose 0*o + 0*o**j + 0*o**4 - 1/2*o**5 + 0 + 0*o**3 = 0. Calculate o.
0
Find l, given that 1/7*l**2 + 2/7*l + 1/7 = 0.
-1
Let p(b) = -b**4 - b**3 + b**2 + b + 1. Let u(h) = 6*h**4 + 6*h**3 - 9*h**2 - 9*h - 9. Let a(d) = -9*p(d) - u(d). Factor a(j).
3*j**3*(j + 1)
Let r(j) = -j**2 - j. Let t(s) = 20*s**2 - 54*s + 648. Let w(f) = 36*r(f) + 2*t(f). Factor w(x).
4*(x - 18)**2
Let d(b) = 21*b**3 + 24*b**2 - 15*b + 18. Let x(u) = u**3 + u**2 - u + 1. Let m(c) = -d(c) + 18*x(c). Factor m(s).
-3*s*(s + 1)**2
Let u = 364/295 - 2/59. Suppose -u*w**3 + 0 - 9/5*w**5 + 0*w**2 + 0*w + 3*w**4 = 0. What is w?
0, 2/3, 1
Let m(r) = 3*r - 17. Let a be m(8). Let q = 7 - a. Let -1/4*n**2 + 0 + q*n = 0. What is n?
0
Let d(j) be the first derivative of -j**4/22 + j**2/11 - 5. Factor d(p).
-2*p*(p - 1)*(p + 1)/11
Let t(n) be the first derivative of -n**6/3 - 8*n**5/5 - n**4 + 8*n**3/3 + 3*n**2 - 34. What is z in t(z) = 0?
-3, -1, 0, 1
Factor q**3 + 9*q + 2 - 2 - 10*q.
q*(q - 1)*(q + 1)
Factor -i**4 + 3414 + 5*i**2 - 3414 + 4*i**3.
-i**2*(i - 5)*(i + 1)
Factor -4/17*i + 0 + 8/17*i**3 + 14/17*i**2.
2*i*(i + 2)*(4*i - 1)/17
Let m(j) = -7*j**3 - 5*j**2 + 6. Let p = 21 + -14. Let a(w) = -10*w**2 + 17 - p*w**2 + 3*w**2 - 20*w**3. Let k(q) = -6*a(q) + 17*m(q). Let k(l) = 0. What is l?
0, 1
Let y(t) be the second derivative of -t**6/30 - t**5/5 - 5*t**4/12 - t**3/3 + 12*t - 2. Factor y(l).
-l*(l + 1)**2*(l + 2)
Let p(u) = -695*u**3 - 588*u**2 - 159*u - 25. Let f(y) = -12 - 97*y + 17*y - 225*y**3 + 22*y**3 - 144*y**3 - 294*y**2. Let v(r) = -9*f(r) + 4*p(r). Factor v(i).
(7*i + 2)**3
Suppose 4*q = 4*u, -5*u - 3 = -3*q + 5. Let d = u - -6. Factor -8 + 3*k**d - 3*k + 7 - 6*k**2 + 4 + 3*k**3.
3*(k - 1)**2*(k + 1)
Let b(h) = -2*h - 2. Let y be b(-3). Suppose 2*g + 6*w - 16 = 2*w, -y*g - 4 = -4*w. Determine n so that 4/9*n**g - 2/9*n**3 - 2/9*n + 0 = 0.
0, 1
Let n(w) be the third derivative of -w**5/240 - 7*w**4/96 + 11*w**2 + w. Find i such that n(i) = 0.
-7, 0
Suppose 5*w - 1 = 3*u - 3, 0 = 5*w + 2*u - 18. Suppose l = -w*l. Factor 2*x + 4*x**2 + 0 + l + 4*x + 2.
2*(x + 1)*(2*x + 1)
Let b(g) be the first derivative of 0*g**3 + 0*g**2 - 3/4*g**4 + 0*g + 3 - 12/5*g**5. Factor b(f).
-3*f**3*(4*f + 1)
Let u(d) = -4*d + 152. Let c be u(37). Suppose 1/2*n**3 - 1/3*n - 1/6*n**c - 1/6*n**5 + 0 + 1/6*n**2 = 0. Calculate n.
-2, -1, 0, 1
Let n(a) = -4*a**2 + 12*a + 4. Let t(z) = -3*z**2 + 11*z + 4. Let c(s) = 5*n(s) - 6*t(s). Let c(b) = 0. What is b?
-2, -1
Let q(l) be the second derivative of 0 + l**2 - 1/6*l**4 - 2*l + 0*l**3. Solve q(p) = 0.
-1, 1
Let t(j) be the second derivative of 5*j**4/12 + 5*j**3/2 + 5*j**2 - 6*j. Solve t(h) = 0 for h.
-2, -1
Let x(s) be the third derivative of 0*s - 1/10*s**5 + 1/60*s**6 + 1/3*s**3 - 3*s**2 + 2/105*s**7 + 0 - 1/12*s**4. Solve x(d) = 0 for d.
-1, 1/2, 1
Let g(h) be the second derivative of 0*h**2 - 1/12*h**4 + 1/12*h**3 + 1/40*h**5 + 3*h + 0. Factor g(t).
t*(t - 1)**2/2
Let l(o) be the second derivative of -3*o**5/10 - o**4/4 + 3*o**3 - 11*o. Suppose l(i) = 0. Calculate i.
-2, 0, 3/2
Let x(p) = p**2 - 12*p + 32. Let g be x(8). Let a(t) be the first derivative of -1/6*t**2 + 1/6*t**4 + 0*t**3 - 1/18*t**6 - 2 + g*t**5 + 0*t. Factor a(r).
-r*(r - 1)**2*(r + 1)**2/3
Let r(u) = 6*u**4 + 4*u**2. Let l(g) = 5*g**4 + 3*g**2. Let t(v) = -5*l(v) + 4*r(v). Factor t(o).
-o**2*(o - 1)*(o + 1)
Let s(n) = -n**2 + 2*n + 19. Let f be s(5). Let o = 2/39 + 46/117. Find q such that 2/3*q**3 - 2/9*q**f - o*q**2 + 0 + 0*q = 0.
0, 1, 2
What is v in 0 + 3/2*v**2 + 9/4*v + 1/4*v**3 = 0?
-3, 0
Let p(g) = -g**2 - 2*g + 1. Let u(d) = -2*d**2 - 3*d + 1. Let r(k) = 3*p(k) - 2*u(k). Let z be r(1). Find b, given that -4/5*b + 6/5*b**3 + 0 + 2*b**z = 0.
-2, 0, 1/3
Let t(f) be the second derivative of -f**4/6 - f**3/3 + f. Factor t(k).
-2*k*(k + 1)
Suppose v - 10*v - v + 5*v**2 - 15 = 0. Calculate v.
-1, 3
Let w be 6/8 - (-1842)/8. Let a be 108/w - 4/22. Let 2/7*z**4 + a*z**2 + 0 + 0*z - 4/7*z**3 = 0. What is z?
0, 1
Factor 6*g**4 + 51*g**3 - 12*g**3 + 44*g**2 + 6*g**4 + 6*g - 11*g**2.
3*g*(g + 1)*(g + 2)*(4*g + 1)
Suppose 5 = -a + 6. Let f(y) be the first derivative of 0*y - 1/6*y**3 - 1/2*y**2 - a. Suppose f(n) = 0. What is n?
-2, 0
Suppose -2*g + 6 = g. Let a be (6/(-4) + 1)*(-12)/24. Let 1 + a*m**3 - 3/4*m**g + 0*m = 0. What is m?
-1, 2
Let h(m) = 40*m**3 - 80*m**2 + 50*m - 15. Let o(w) = -w**3 + w + 1. Let c(t) = h(t) + 5*o(t). Factor c(j).
5*(j - 1)**2*(7*j - 2)
Let k(a) be the third derivative of 0*a**6 + 1/210*a**7 + 0*a - 1/30*a**5 + 0 + 1/6*a**3 + 11*a**2 + 0*a**4. Suppose k(d) = 0. Calculate d.
-1, 1
Suppose 46*k = 47*k - 2. Let b(q) be the second derivative of 0*q**6 + 0*q**k + 0*q**4 - 1/10*q**5 + 0 + 1/6*q**3 - 4*q + 1/42*q**7. Find l such that b(l) = 0.
-1, 0, 1
Let v = -11/2232 - -5/72. Let l = 39/124 - v. Factor 1/4*y**5 + 1/4*y**4 - 1/4*y**3 + 0*y - l*y**2 + 0.
y**2*(y - 1)*(y + 1)**2/4
Suppose -3*s = -29 - 22. Let d(f) = -44*f**2 + 7*f**2 + 11*f - f**2. Let h(k) = -13*k**2 + 4*k. Let t(r) = s*h(r) - 6*d(r). Factor t(i).
i*(7*i + 2)
Let b(c) be the third derivative of -1/120*c**5 + 2*c**2 + 0*c + 0 + 1/3*c**3 + 0*c**4 + 1/360*c**6. Let k(r) be the first derivative of b(r). Factor k(z).
z*(z - 1)
Let v(i) = i**2 + i. Suppose -4*y + 3*q + 14