b**2 + b - 1. Let v(q) = i*p(q) - j(q). Factor v(z).
3*z**2*(z - 2)
Let a be (-3 + -1 + 5)*1. Let l be -2 - 1 - (-2 - a). Factor l - 1/3*z**4 + 0*z**2 - 1/3*z**3 + 0*z.
-z**3*(z + 1)/3
Let s(x) be the first derivative of 2*x**5/5 - 3*x**4 + 16*x**3/3 + 6*x**2 - 18*x + 22. Factor s(r).
2*(r - 3)**2*(r - 1)*(r + 1)
Let w(l) = l**2 + 3*l + 3. Let y be w(-3). Determine x, given that -21*x + 0 + 24*x**4 - 51*x**y + 0 - 3 + 120*x**3 - 21*x**2 - 48*x**5 = 0.
-1, -1/4, 1
Suppose 5*s = 3*h + 16, 6 = 2*h - 3*s + 15. Find t, given that 0*t**3 + 0*t**3 + t**h - 2*t**3 + t = 0.
-1, 0, 1
Let d be (-13)/5 + 30/10. Let b be (6 + 2)*-1*(-2)/20. Suppose 2/5*k**4 - b*k**2 + d + 0*k + 0*k**3 = 0. Calculate k.
-1, 1
Let p be (-1)/6*-3*1. Let a be (-14)/(-14)*1/(-4)*-2. Factor 0*z + 1/2*z**5 + 0 + 1/2*z**4 - a*z**3 - p*z**2.
z**2*(z - 1)*(z + 1)**2/2
Let j(r) = r**4 - 9*r**3 + 3*r**2 + r - 4. Let c(a) = a**4 - 17*a**3 + 5*a**2 + 2*a - 7. Let f = 16 + -9. Let h(b) = f*j(b) - 4*c(b). Factor h(m).
m*(m + 1)**2*(3*m - 1)
Factor -3*s**2 - 10*s**2 + 8*s**2 + 10*s**3.
5*s**2*(2*s - 1)
Let j = 9 + -5. Solve 0*y**j + y**5 - 2*y**4 - 2*y**4 + 3*y**4 = 0.
0, 1
Let u(k) be the third derivative of -k**5/210 + k**4/28 - 2*k**3/21 - 5*k**2. Solve u(j) = 0.
1, 2
Find z, given that -2/7 + 6/7*z - 6/7*z**2 + 2/7*z**3 = 0.
1
Let x = -29/2 + 16. Let t(z) be the first derivative of -4/9*z**6 + 2/9*z**3 + 0*z - 1 + 1/3*z**2 + 22/15*z**5 - x*z**4. Suppose t(l) = 0. Calculate l.
-1/4, 0, 1
Suppose -2*z = -2*t + 6 - 14, 0 = 4*z - 5*t - 18. Find j, given that -j**3 + 0 + 3/4*j**z + 1/4*j = 0.
-1/4, 0, 1
Suppose 2 + 6 = 5*q - 4*j, 0 = -5*q - 4*j - 8. Let m(g) be the second derivative of 0*g**2 - 1/12*g**3 - 3*g + q - 1/48*g**4. Solve m(u) = 0.
-2, 0
Let w(r) = -r. Let b be w(-5). Let g(t) be the first derivative of 3/2*t**3 + 3 + t - 7/4*t**2 - 5/8*t**4 + 1/10*t**b. Factor g(h).
(h - 2)*(h - 1)**3/2
Let k(x) = -10*x**2 + 2*x**4 + 17 - 6*x**2 + 1 - 2*x**2. Let c(s) = s**2 - 1. Let j(m) = 36*c(m) + 2*k(m). Let j(z) = 0. Calculate z.
0
Let f(x) be the second derivative of -x**7/3780 + x**6/1620 + x**3/3 + 2*x. Let p(o) be the second derivative of f(o). Factor p(u).
-2*u**2*(u - 1)/9
Let z be 1 - (-4)/(264/(-54)). Factor -z*x**3 - 2/11*x**2 + 0 + 0*x.
-2*x**2*(x + 1)/11
Let s = -8 - -14. Find r such that -3*r**2 - 2*r**4 + s*r**3 + r**2 + 0*r**2 + 4 - 6*r = 0.
-1, 1, 2
Suppose -7*p = -2*p. Suppose p = -4*y + 5 + 3. What is t in -y*t**2 + t + 0*t**2 - 18 + 11*t = 0?
3
Let -13/4*r + 5/4*r**2 - 3/2 = 0. Calculate r.
-2/5, 3
Let r(m) be the first derivative of -m**3/18 + m/6 - 34. Factor r(o).
-(o - 1)*(o + 1)/6
Let v(f) be the first derivative of 2*f**3/3 - f**2 - 7. Factor v(j).
2*j*(j - 1)
Let t be (55/10)/(2/4). Let a(u) = u**2. Let c(x) = -2*x**2. Let v(j) = t*a(j) + 6*c(j). Factor v(p).
-p**2
Let w(i) be the first derivative of 2*i**3/15 - 2*i**2/5 - 20. Solve w(d) = 0.
0, 2
Let q = -13 + 16. Factor -3*h**2 + 3*h**2 - 11*h + q*h**3 + 8*h.
3*h*(h - 1)*(h + 1)
Let h(u) = -2*u + 1. Suppose 2 + 0 = -2*j. Let o be h(j). Factor -2 + o*d + 2*d - d**2 - 2*d.
-(d - 2)*(d - 1)
Suppose 4*a + 5 - 31 = -5*f, f = a - 2. Let n be 6*f*(-1)/(-3). Find k, given that 2*k**2 + n*k - 2*k**2 - 2*k**2 - 2 = 0.
1
Let z be (-1)/(2/12*-3). Suppose -y = -b + 5, -5*y - z*b - 2 = -12. Determine f, given that -1/2*f**4 + 1/2*f**5 + 1/2*f**2 - 1/2*f**3 + 0 + y*f = 0.
-1, 0, 1
Let d(h) be the third derivative of -h**6/1080 - h**5/360 + h**4/36 + h**3/2 - 2*h**2. Let b(q) be the first derivative of d(q). Find x such that b(x) = 0.
-2, 1
Solve -2*q**2 - 2*q**2 + 12*q**2 - 5*q**2 + 3*q**3 = 0 for q.
-1, 0
Suppose -2*j = 1 - 7. Factor 12*u**j + u**4 - 2*u**4 - 13*u**3.
-u**3*(u + 1)
Let w(r) be the second derivative of -r**5/35 - 16*r**4/21 - 128*r**3/21 - 14*r - 2. Let w(p) = 0. What is p?
-8, 0
Let g(d) = d**3 + d + 1. Let m(a) = 2*a**3 - a**2 + 12*a - 2. Let r(s) = 2*s**3 + 11*s - 1. Let l(o) = 3*m(o) - 4*r(o). Let t(p) = -5*g(p) - l(p). Factor t(j).
-3*(j - 1)**2*(j + 1)
Determine o, given that 2*o**2 + o**2 + 8*o - 8*o = 0.
0
Let u be (4/3)/(4/12). Factor 4*r - u*r**2 - 6 - 5*r + 10*r + r**2.
-3*(r - 2)*(r - 1)
Suppose 0 = 12*f - 50 + 2. Let d be (4/50)/(1/10). Let 2/5*m**f + 0*m**3 + 0*m + 2/5 - d*m**2 = 0. What is m?
-1, 1
Let g(m) be the third derivative of 15*m**8/112 - 8*m**7/35 - 13*m**6/120 + m**5/3 - m**4/6 + 13*m**2. Let g(i) = 0. Calculate i.
-2/3, 0, 1/3, 2/5, 1
Determine w, given that -12/5*w**4 - 12/5*w**2 + 0 - 18/5*w**3 - 3/5*w - 3/5*w**5 = 0.
-1, 0
Let o(v) = -4*v**2 - 14*v. Let n(k) = -4*k**2 - 15*k + 1. Let q(s) = -5*n(s) + 4*o(s). Find m, given that q(m) = 0.
-5, 1/4
Let t(s) be the second derivative of -2/7*s**2 + 0 + s + 1/42*s**4 + 1/21*s**3. Factor t(w).
2*(w - 1)*(w + 2)/7
Let n(l) = l**2 - 35*l + 37. Let y be n(34). Find a such that -1/2*a**y + 0 - a**2 - 1/2*a = 0.
-1, 0
Suppose 0*w**3 + 3/7*w**5 + 0 - 6/7*w**4 - 3/7*w + 6/7*w**2 = 0. What is w?
-1, 0, 1
Factor 6/5*i**2 + 2/5*i**3 - 2/5*i - 6/5.
2*(i - 1)*(i + 1)*(i + 3)/5
Let t(r) = r**3 + r**2 + r - 1. Let m(n) = 9*n**3 + 12*n**2 + 3*n - 12. Let u(v) = -m(v) + 6*t(v). Determine j so that u(j) = 0.
-2, -1, 1
Solve 0 - 64/3*v**4 - 12*v**5 - 20/3*v**3 + 0*v + 8/3*v**2 = 0.
-1, 0, 2/9
Let w(q) = 5*q - 5. Let a be w(2). Let r(v) be the second derivative of 2/3*v**3 + 1/15*v**6 + 0*v**4 - v - 1/5*v**a + 0 - v**2. Let r(f) = 0. What is f?
-1, 1
Let k(l) be the third derivative of -l**6/39 - 47*l**5/390 + 37*l**4/156 - 2*l**3/13 - 15*l**2. Let k(w) = 0. Calculate w.
-3, 1/4, 2/5
Suppose -3*p - 12 = -3*a, -4*a - 4*p + 3 = 19. Factor 4/7*n + a - 6/7*n**2 - 2*n**4 - 24/7*n**3.
-2*n*(n + 1)**2*(7*n - 2)/7
What is f in 0*f**3 + 0*f**3 - 5*f**4 + 11*f + 5*f**2 - 10*f**3 - f = 0?
-2, -1, 0, 1
Let q be (-16)/(-40) + 18/5. Suppose -j - q = -2*j. Let -1/3*z**2 + 0 + 1/6*z**3 + 0*z + 1/6*z**j = 0. What is z?
-2, 0, 1
Let u(t) be the third derivative of 3*t**7/40 + 9*t**6/40 + 4*t**5/15 + t**4/6 - t**3/3 + 3*t**2. Let b(x) be the first derivative of u(x). Factor b(n).
(3*n + 1)*(3*n + 2)*(7*n + 2)
Factor 2/5*p**4 + 2/5*p**3 - 4/5*p**2 + 0*p + 0.
2*p**2*(p - 1)*(p + 2)/5
Let f = -24 + 32. Let g(l) be the third derivative of 0 - l**2 + 0*l**3 + 0*l**5 + 0*l - 1/168*l**f + 1/105*l**7 + 0*l**6 + 0*l**4. Factor g(s).
-2*s**4*(s - 1)
Let m(y) be the second derivative of -y**6/70 - 3*y**5/35 - y**4/7 + y. Factor m(z).
-3*z**2*(z + 2)**2/7
Let x(t) be the first derivative of -2*t**3/9 - t**2/3 + 4*t - 16. Let x(s) = 0. Calculate s.
-3, 2
Let a(w) be the first derivative of -2*w**5/15 + 7*w**4/18 + 4*w**3/9 + 7. Find x such that a(x) = 0.
-2/3, 0, 3
Factor -2/5*t**3 - 14/5*t + 2*t**2 + 6/5.
-2*(t - 3)*(t - 1)**2/5
Suppose -10*x + 35*x = 0. Factor x*t**2 - 2/9*t**3 + 0*t**4 + 0 + 0*t + 2/9*t**5.
2*t**3*(t - 1)*(t + 1)/9
Let j(c) be the third derivative of -c**8/6720 + c**6/240 - 2*c**5/15 - 3*c**2. Let v(t) be the third derivative of j(t). Let v(f) = 0. Calculate f.
-1, 1
Let u(m) = -m**2 - m. Suppose 3 + 1 = -4*y. Let s be u(y). Factor 1/4*b**2 - 1/4*b + s.
b*(b - 1)/4
Let d = -20 + 20. Let s(w) be the third derivative of 1/21*w**3 - 1/210*w**5 - 1/105*w**6 + 1/21*w**4 + d - 2*w**2 + 0*w. Solve s(m) = 0 for m.
-1, -1/4, 1
Let b(z) be the third derivative of -1/945*z**7 + 0*z**4 - z**2 + 1/135*z**6 - 2/135*z**5 + 0*z**3 + 0 + 0*z. Suppose b(v) = 0. Calculate v.
0, 2
Let z(s) = 6*s**2 - 6*s - 1. Let h(b) = b**3 - b - 1. Let g(x) = -h(x) - z(x). Let v be g(-7). Factor 2/7*o**v + 8/7*o + 8/7.
2*(o + 2)**2/7
Let s(k) be the first derivative of 78/5*k**5 + 4*k**3 - 6*k**2 + 7/2*k**6 - 5 + 0*k + 81/4*k**4. Suppose s(o) = 0. What is o?
-2, -1, 0, 2/7
Let u be (-11)/((-110)/(-48))*8/(-6). Factor -u - 16/5*b - 2/5*b**2.
-2*(b + 4)**2/5
Suppose -5*h - 15 + 15 = 0. Factor 0*r**2 - 2/9*r**3 - 2/9*r**4 + h*r + 0.
-2*r**3*(r + 1)/9
Let s be -6 + (-1 - 3/(-1)). Let u(w) = -w**3 - 4*w**2 + w + 6. Let h be u(s). Let 10/3*b**2 - 4/3 - h*b = 0. Calculate b.
-2/5, 1
Suppose 3/2*x**4 - 5/2*x**3 - 5/2*x**2 + 1 + 5/2*x = 0. What is x?
-1, -1/3, 1, 2
Factor -v**3 + 5*v**4 - 12*v + 12 - 9*v**2 - 8*v**4 + 13*v**3.
-3*(v - 2)**2*(v - 1)*(v + 1)
Let c(o) be the third derivative of -o**6/1020 - o**5/102 + o**4/204 + 5*o**3/51 - 7*o**2. Factor c(z).
-2*(z - 1)*(z + 1)*(z + 5)/17
Let m(s) be the first