 + z**2 - v*z = 0. Calculate z.
0, 1, 2
Let f(m) = m**3 - 7*m**2 + m - 5. Let l be f(7). Suppose -3*j + j = 0. Factor j - 2*y**l - 4/3*y.
-2*y*(3*y + 2)/3
Suppose 26*g - 23*g - 14 = -5*w, -4*w = -5*g + 11. Factor -4/5*i + 4/5*i**g + 2/5 - 2/5*i**2.
2*(i - 1)*(i + 1)*(2*i - 1)/5
Solve 8/9 - 8/9*l - 2/3*l**2 = 0 for l.
-2, 2/3
Let i(t) be the second derivative of t**4/60 - t**3/10 - t**2 + 6*t. Let i(a) = 0. Calculate a.
-2, 5
Let j(a) = -a**5 + a**3 - a**2 - a + 1. Let g(v) = 2*v**5 - 10*v**4 - 24*v**3 - 16*v**2 - 6*v - 6. Let l(x) = -g(x) - 4*j(x). Solve l(z) = 0 for z.
-1
Suppose 0 = 2*o - 1 - 1. Let v be ((-2)/(-2))/(o/4). Find a, given that -4*a**2 - a**3 + 3*a**2 + 2*a**4 + a**5 - a**v = 0.
-1, 0, 1
Let o be (-72)/(-48) - 3/2. Factor 8/5*k**3 - 14/5*k**2 + o - 4/5*k.
2*k*(k - 2)*(4*k + 1)/5
Factor 1/2*g + 3/4 - 1/4*g**2.
-(g - 3)*(g + 1)/4
Let p be (-4)/(-3)*1/6. Let j(q) = q**3 - 8*q**2 + 8*q - 7. Let f be j(7). Factor p*n**3 + 0 + f*n**2 + 0*n - 2/9*n**4.
-2*n**3*(n - 1)/9
Suppose -4*f + f = l - 11, -4*l = -20. Suppose 4*y = 3*h + 2, -2*h + 16 = 4*y + f*h. Solve 1/4 + 0*z - 1/4*z**y = 0 for z.
-1, 1
Let d = 9 + -4. Let s(u) be the third derivative of 1/60*u**6 + 0 - 1/20*u**d + 1/24*u**4 - u**2 + 0*u + 0*u**3. Solve s(v) = 0.
0, 1/2, 1
Let w(b) be the second derivative of 0 + 0*b**2 - 3*b + 1/12*b**4 + 0*b**3. Solve w(c) = 0.
0
Suppose 2*j - 1 - 3 = 0. Let f be (-3)/(-6)*j - 1. Solve r - 7*r**4 - 15*r**2 + f - 2*r + 2 - 19*r**3 = 0 for r.
-1, 2/7
Let s be 2/6*(-42)/7. Let y be 8/6 - s/(-2). Factor 1/3*a**2 + 0*a - y.
(a - 1)*(a + 1)/3
Let q(j) = -j**3 - 3*j**2 + 2. Let b(a) = a**3 - 6*a**2 - 4*a + 6. Let c(s) = -s**3 + s - 1. Let g(z) = b(z) + 3*c(z). Let f(l) = 3*g(l) - 5*q(l). Factor f(h).
-(h + 1)**3
Let g(t) be the second derivative of 3*t + 0*t**2 + 0*t**3 - 1/36*t**4 + 0. Factor g(o).
-o**2/3
Let w(g) be the third derivative of g**8/224 - 11*g**7/140 + 21*g**6/40 - 17*g**5/10 + 5*g**4/2 - 10*g**2. Determine p so that w(p) = 0.
0, 2, 5
Let i(x) be the second derivative of x**5/20 - x**4/6 - x**3 - 3*x**2/2 + x. Let u(a) = a + 1. Let w(d) = i(d) + 5*u(d). Determine p so that w(p) = 0.
-1, 1, 2
Let r(q) be the third derivative of q**7/140 - q**6/80 - q**5/20 - 7*q**2. Factor r(k).
3*k**2*(k - 2)*(k + 1)/2
Suppose 4*t + 3*v = 17 + 17, -5*v + 10 = 0. Let o = t + -7. Solve -3*p**2 + 0*p**4 + o*p + 3*p**3 - p**4 + p + 0*p**4 = 0.
0, 1
Let p(u) be the second derivative of u**6/150 + u**5/100 - 11*u. Factor p(w).
w**3*(w + 1)/5
Let m(g) be the second derivative of g**7/105 - g**6/25 + 3*g**5/50 - g**4/30 + 2*g. Factor m(q).
2*q**2*(q - 1)**3/5
Solve -3*c**3 - 1/3*c + 4/3*c**4 + 2*c**2 + 0 = 0 for c.
0, 1/4, 1
Let m be (9/60*1/(-9))/(-1). Let i(k) be the third derivative of -1/8*k**4 + 0 + 0*k - 1/3*k**3 + 3*k**2 - m*k**5. Factor i(y).
-(y + 1)*(y + 2)
Factor -1 + 16*p + 9*p**2 + 28*p**4 - 57*p**2 - 36*p**3 + 1.
4*p*(p - 2)*(p + 1)*(7*p - 2)
Let d(k) = 0*k**2 + 7 + k**2 + 1. Let b be d(0). What is f in -b - f**2 + 8 = 0?
0
Let x(w) be the first derivative of 0*w**3 - 3 + 1/6*w**2 + 0*w - 1/12*w**4. Factor x(c).
-c*(c - 1)*(c + 1)/3
Let w(y) be the first derivative of 4*y**5/5 + y**4 - 20*y**3/3 + 6*y**2 + 8. Solve w(t) = 0 for t.
-3, 0, 1
Let g(y) = 2*y - 36. Let b be g(19). Factor 0*r + 0 - 2/5*r**b + 2/5*r**4 + 0*r**3.
2*r**2*(r - 1)*(r + 1)/5
Let u be 48/(-21) - -2 - 23/(-7). Let v(l) be the first derivative of -4*l - 1/2*l**4 + l**2 + 4/3*l**u + 4. Factor v(q).
-2*(q - 2)*(q - 1)*(q + 1)
Factor 6*n**3 + 3*n**4 + 2*n**4 - 2*n**4 - 2*n**2 + 5*n**2.
3*n**2*(n + 1)**2
Let o(u) be the third derivative of -u**8/2940 + u**7/735 + u**6/630 - u**5/105 + u**3/6 + 6*u**2. Let t(z) be the first derivative of o(z). Factor t(r).
-4*r*(r - 2)*(r - 1)*(r + 1)/7
Factor -12*b**2 - 28*b**2 + 13*b - 25*b**3 + 0*b + 7*b.
-5*b*(b + 2)*(5*b - 2)
Let n(y) be the third derivative of -y**5/60 - 5*y**4/24 - 12*y**2. Determine x, given that n(x) = 0.
-5, 0
Let g(z) be the first derivative of z**5/5 + z**4/4 - z**3 - z**2/2 + 2*z + 30. Solve g(d) = 0 for d.
-2, -1, 1
Let s(p) be the first derivative of p**5/5 - 3*p**4/4 + 2*p**2 + 15. Factor s(b).
b*(b - 2)**2*(b + 1)
Let z(p) be the first derivative of 4*p**6 + 14*p**5/5 - 11*p**4/2 - 14*p**3/3 - p**2 - 3. Suppose z(n) = 0. What is n?
-1, -1/3, -1/4, 0, 1
Let x be 4/(18/10 - 2). Let v = -18 - x. Find p such that -4/5*p**v + 2/5*p**3 + 2/5*p + 0 = 0.
0, 1
Determine n, given that 29*n**2 + 33*n**2 - 58*n**2 + 4*n = 0.
-1, 0
Find x such that -2/7 + 2/7*x - 2/7*x**3 + 2/7*x**2 = 0.
-1, 1
Let d = 17/60 + -1/30. Factor t + d*t**2 + 1.
(t + 2)**2/4
Suppose -3*i + 30 = 5*u, 2*u - 3*i = -2*i + 12. Factor 12*w - 3*w**2 + 3 - 9 - u.
-3*(w - 2)**2
Let h(f) be the second derivative of -4*f**5/15 - f**4/3 + 2*f**3/9 - 17*f. Factor h(k).
-4*k*(k + 1)*(4*k - 1)/3
Let d(p) = p**2 - 10*p + 13. Suppose 0 = -5*r - 7 - 13. Let i(c) = c**2 - 11*c + 14. Let g(a) = r*i(a) + 5*d(a). Suppose g(j) = 0. Calculate j.
3
Let h(x) be the first derivative of x**3 - 6*x**2 - 21. Factor h(n).
3*n*(n - 4)
Factor -3/2*r - 6 - 3/4*r**3 + 15/4*r**2.
-3*(r - 4)*(r - 2)*(r + 1)/4
Let h(z) = -6*z**4 - 5*z**2 + 11*z - 11. Let s(k) = 6*k - 4*k - 3 + 5 - k**4 - 4 - k**2. Let r(w) = -4*h(w) + 22*s(w). Factor r(f).
2*f**2*(f - 1)*(f + 1)
Let p(y) be the third derivative of 5*y**8/1344 + y**7/168 - y**6/96 - y**5/48 + 7*y**2. Suppose p(i) = 0. What is i?
-1, 0, 1
Let o(l) be the third derivative of -l**5/570 - l**4/76 - 2*l**3/57 - 18*l**2. Factor o(k).
-2*(k + 1)*(k + 2)/19
Let n(j) = j**3 + 4*j**2 + 4*j + 1. Let x(d) = -2*d**2 + 10*d - 8*d + 0*d**2 - 4*d. Let a(y) = 2*n(y) + 5*x(y). Factor a(p).
2*(p - 1)**2*(p + 1)
Determine c so that 42*c + 5 - 12*c + 41*c**2 + 4*c**2 = 0.
-1/3
Let d(s) = 5*s - 5*s + 4 + 5 + s. Let i be d(-7). Suppose 0 + 1/2*z**3 + 1/2*z**i + 0*z = 0. What is z?
-1, 0
Let n(j) be the third derivative of j**6/360 - j**5/90 - j**4/9 - 2*j**2 - 6. Factor n(a).
a*(a - 4)*(a + 2)/3
Let f(z) be the second derivative of -z**4/4 + 3*z**3/2 - 3*z**2 + 3*z. Factor f(v).
-3*(v - 2)*(v - 1)
Let y(g) be the third derivative of g**5/15 + g**4/2 + 4*g**3/3 + 13*g**2. Factor y(t).
4*(t + 1)*(t + 2)
Let t(p) be the first derivative of 4*p**6/75 - 3*p**5/50 - p**4/30 + p + 3. Let l(j) be the first derivative of t(j). Solve l(i) = 0 for i.
-1/4, 0, 1
Let n be (-541)/321 - 2/(-6). Let t = -2/107 - n. Suppose 2/3 - t*z + 2/3*z**2 = 0. Calculate z.
1
Let v(u) = -u**4 - u**3 - 9*u**2 - 4*u - 4. Let c(o) = -2*o**2 - o. Let s be c(1). Let p(w) = w**4 + 10*w**2 + 4*w + 5. Let z(y) = s*p(y) - 4*v(y). Factor z(i).
(i + 1)**4
Let z(i) be the third derivative of -i**7/840 - i**6/240 - i**4/6 - 5*i**2. Let g(x) be the second derivative of z(x). Solve g(j) = 0 for j.
-1, 0
Factor 2/7*l**3 + 4/7*l**2 - 16/7 - 8/7*l.
2*(l - 2)*(l + 2)**2/7
Let k(h) = -h**3 + h**2 + h + 1. Let s(y) = 4*y + 2*y**2 - 2*y**2 + 3*y**2 + 4 - 5*y**3. Let f(v) = 4*k(v) - s(v). Let f(d) = 0. Calculate d.
-1, 0
Find a, given that -2/9*a**2 + 2/3 - 4/9*a = 0.
-3, 1
Let a(x) = x**2 + x + 1. Let b(t) = -4*t**2 - 8*t - 9. Let o(g) = -10*a(g) - 2*b(g). Suppose o(f) = 0. What is f?
-1, 4
Suppose -5*o + 2*o = p + 10, 2*o + p + 6 = 0. Let t be (-6)/(-4) + (-2)/o. Factor -4*k**3 + k - 2*k**2 - 3*k**2 - t*k.
-k*(k + 1)*(4*k + 1)
Let v(y) = y**3 - 6*y**2 + 2*y. Let d be v(6). Solve 2*t + d - 4*t**2 + 2*t**3 - 12 = 0 for t.
0, 1
Let v(s) be the second derivative of -s**5/210 + s**3/21 - 3*s**2/2 + s. Let j(m) be the first derivative of v(m). Factor j(c).
-2*(c - 1)*(c + 1)/7
Let x(v) be the first derivative of -8*v**5/25 - 17*v**4/10 - 8*v**3/3 - 4*v**2/5 - 6. Factor x(j).
-2*j*(j + 2)**2*(4*j + 1)/5
Factor -1/4 + 1/4*w**2 - 1/4*w + 1/4*w**3.
(w - 1)*(w + 1)**2/4
Suppose -4*p + 14 = 3*x - 2*x, -2*x - 3*p = -18. Suppose -2*o = 4, 3*g + x*o + 4 = o. Factor 0*h + 8/3*h**5 + 2/3*h**3 + 0 + 0*h**g - 10/3*h**4.
2*h**3*(h - 1)*(4*h - 1)/3
Suppose -53*c + 180 = -8*c. Factor 0*j - 3/4*j**2 + 1/4*j**c + 0 - 1/2*j**3.
j**2*(j - 3)*(j + 1)/4
Let t(o) be the second derivative of -o**4/66 + o**2/11 + 7*o. Factor t(r).
-2*(r - 1)*(r + 1)/11
Let n(t) be the first derivative of 2/9*t**2 + 1/54*t**4 + 1/9*t**3 + 1 - 3*t. Let a(v) be the first derivative of n(v). Factor a(i).
2*(i + 1)*(i + 2)/9
Let l(h) be the third derivati