0.
3
Factor 0*n**2 - 3*n**2 + 4*n**2.
n**2
Let p = 1/4 - -1/12. Determine a, given that p*a**2 - 2/3*a + 1/3 = 0.
1
Let n(s) be the first derivative of 5*s**3/9 + 5*s**2/3 - 5*s - 14. Factor n(o).
5*(o - 1)*(o + 3)/3
Let n(c) be the first derivative of 9/5*c**5 + 0*c**2 + 3/2*c**4 + 2 + 0*c + 0*c**3 + 1/2*c**6. Solve n(s) = 0 for s.
-2, -1, 0
Let d(j) = -4*j**4 - 3*j**2 - 2*j - 3. Let p(s) = 7*s**4 - s**3 + 6*s**2 + 3*s + 5. Let k(a) = -5*d(a) - 3*p(a). Factor k(u).
-u*(u - 1)**3
Suppose 99*l - 3 = 98*l. Factor -2*p**l + 1/2*p**2 + p - 3/2*p**4 + 0.
-p*(p + 1)**2*(3*p - 2)/2
Let n(u) = 2*u**3 + 13*u**2 + 15*u. Let i(f) = -2*f**3 - 12*f**2 - 14*f. Let x(t) = -3*i(t) - 2*n(t). Factor x(v).
2*v*(v + 2)*(v + 3)
Let f(q) be the first derivative of 2*q**3/51 + q**2/17 - 4*q/17 + 11. Suppose f(s) = 0. Calculate s.
-2, 1
Suppose -q + 6 = -y, -65 = 5*y + 2*q - 0*q. Let w = -8 - y. Let z**w + 1 + 9*z - 4*z - z**2 - 6*z = 0. Calculate z.
-1, 1
Let a(u) be the second derivative of 0 + 2/3*u**6 + 0*u**3 + 0*u**2 - 4*u - 4/3*u**4 - 1/7*u**7 - 2/5*u**5. Factor a(z).
-2*z**2*(z - 2)**2*(3*z + 2)
Let h(n) = 8*n**2 - 20*n + 8. Let s(r) = -9*r**2 + 21*r - 7. Let y(i) = -5*h(i) - 4*s(i). Factor y(p).
-4*(p - 3)*(p - 1)
Let i(k) = -12*k**2 - 2*k. Let v(t) = -11*t**2 - 2*t. Let z(h) = -6*i(h) + 7*v(h). Factor z(b).
-b*(5*b + 2)
Factor 0 + 0*h + 0*h**3 - 2/15*h**5 - 2/5*h**4 + 0*h**2.
-2*h**4*(h + 3)/15
Let c(z) be the first derivative of z**4/2 - 3*z**2 - 4*z + 9. Factor c(r).
2*(r - 2)*(r + 1)**2
Let p(q) = q**2 - 9*q + 10. Let l be p(8). Let j be 2*(6/(-3))/(-2). Factor -9*v**3 + 9*v**4 - 3*v**5 - j*v**l + 7*v**2 - 2*v**2.
-3*v**2*(v - 1)**3
Let w(b) be the second derivative of b**4/54 - 2*b**3/27 + b**2/9 + 6*b. Factor w(c).
2*(c - 1)**2/9
Let v be (-40)/(-8) - 28/6. Factor 2/3 + 1/3*u - v*u**2.
-(u - 2)*(u + 1)/3
Let u(b) be the second derivative of -3*b**2 + 1/6*b**4 - 2/3*b**3 + 6*b + 0. Factor u(z).
2*(z - 3)*(z + 1)
Let d(v) be the second derivative of -v**9/52920 - v**8/23520 - v**4/3 + 4*v. Let i(k) be the third derivative of d(k). Factor i(f).
-2*f**3*(f + 1)/7
Let t = 131 + -261/2. Factor -2*j**2 - t*j**3 - 5/2*j - 1.
-(j + 1)**2*(j + 2)/2
Factor 17*i**5 - 10*i**5 - 8*i - 7*i**5 + 4*i**4 + 6*i**3 - 2*i**5 - 8*i**2.
-2*i*(i - 2)**2*(i + 1)**2
Suppose 4 = -2*o + 2*a, -3*o - 3*a = o - 6. Let t(r) be the second derivative of 3/50*r**5 - 3/25*r**6 + o*r**2 + 2*r - 4/15*r**3 + 0 + 4/15*r**4. Factor t(x).
-2*x*(x + 1)*(3*x - 2)**2/5
Let l(k) be the first derivative of k**8/1680 - 2*k**3/3 + 1. Let r(x) be the third derivative of l(x). Factor r(q).
q**4
Factor -17*l - 4 - 4*l**2 + 8*l**2 + 8.
(l - 4)*(4*l - 1)
Let c(w) be the second derivative of -w**5/30 + w**3/3 + 2*w**2/3 - 8*w. Find d such that c(d) = 0.
-1, 2
Let a(i) = -i**3 - 5*i**2 + 13*i + 12. Let c(w) = -3*w**2 + 6*w + 6. Let x(k) = 3*a(k) - 5*c(k). Find h, given that x(h) = 0.
-1, 2
Let z(a) be the third derivative of -a**5/12 - 35*a**4/12 + 16*a**2 + 1. Find x, given that z(x) = 0.
-14, 0
Let z = -2 - 0. Let j(k) be the second derivative of k**4/12 - k**3/2 + k**2/2 + 2*k. Let y(a) = -a. Let i(x) = z*j(x) + 10*y(x). Let i(c) = 0. Calculate c.
-1
Suppose 102 = 3*r + 39. Suppose 0 = -2*n - 2*t + 6, n - 3*t = -2*n + r. Solve -4*h**4 + 2*h**n + 2*h**4 + 0*h**5 + 4*h**4 = 0 for h.
-1, 0
Let n(u) be the first derivative of -u**7/14 + 2*u**6/5 - 9*u**5/20 - u**4 + 2*u**3 + u + 2. Let d(j) be the first derivative of n(j). Let d(t) = 0. What is t?
-1, 0, 1, 2
Let l(g) be the second derivative of -1/12*g**4 + 0 + 0*g**3 + g**2 - 2*g + 1/12*g**5. Let x(r) be the first derivative of l(r). Factor x(n).
n*(5*n - 2)
Let r be ((-11)/308)/(-3 + (-44)/(-16)). Determine h so that -r*h**2 - 2/7*h + 0 = 0.
-2, 0
Factor -1/2*s**3 + 0*s + 0*s**2 + 0 - 3/4*s**4.
-s**3*(3*s + 2)/4
Let l = 23 - 20. Factor -3*q**l + 2*q**3 - q**5 + 2*q**3.
-q**3*(q - 1)*(q + 1)
Factor -5*i**2 + 5*i**2 - i + i**2.
i*(i - 1)
Let y be (-10)/(-45) - (-4)/(-18). Let r(h) be the second derivative of 1/2*h**2 + h - 1/6*h**3 + y + 1/48*h**4. Factor r(a).
(a - 2)**2/4
Suppose 0 = 4*w - 5 - 3. Factor w*r**2 + 2/3*r**3 + 0 + 4/3*r.
2*r*(r + 1)*(r + 2)/3
Let o(d) be the second derivative of 1/15*d**6 + 7/8*d**4 + 2/5*d**5 + 11/12*d**3 + 1/2*d**2 + 0 - 2*d. Factor o(t).
(t + 1)*(t + 2)*(2*t + 1)**2/2
Let h(o) be the third derivative of -o**8/1176 - o**7/245 - o**6/210 - o**2 - 2. Factor h(i).
-2*i**3*(i + 1)*(i + 2)/7
Let b(t) be the first derivative of 0*t**2 - 6/25*t**5 + 0*t - 4/15*t**6 + 5 + 1/10*t**4 + 0*t**3. Factor b(x).
-2*x**3*(x + 1)*(4*x - 1)/5
Let x = 6 + -3. Suppose 0*p = x*p - 6. Find s, given that 2 - 1 - 4*s**2 - 2*s**3 + p*s + 3 = 0.
-2, -1, 1
What is w in 8*w**2 + 6 - 4*w + 2*w**2 - 12*w**2 = 0?
-3, 1
Let q(m) = -m**3 - 4*m**2 - 6*m - 6. Let x be q(-4). Suppose b + 26 - 20 - 14 - x*b**3 + 7*b + 18*b**2 = 0. What is b?
-2/3, 2/3, 1
Let k = 1326/7 + -189. Factor k*z**3 - 3/7*z**2 + 3/7 - 3/7*z.
3*(z - 1)**2*(z + 1)/7
Suppose 3*p = z - 20 - 15, 2*z - 37 = -5*p. Suppose -z = -5*v - 11. Factor -3*m**3 + 3*m**3 + 2*m**v.
2*m**3
Factor 0 + 5/2*x**3 - 25/3*x**2 + 5/2*x.
5*x*(x - 3)*(3*x - 1)/6
Let i(u) be the second derivative of 0*u**2 + 1/6*u**4 - 3/35*u**5 - 3*u - 2/21*u**3 + 0. Factor i(v).
-2*v*(2*v - 1)*(3*v - 2)/7
Let d(s) = 4*s**2 - 3*s - 5. Let h(n) = 4*n**2 - 4*n - 4. Let y(r) = -4*d(r) + 5*h(r). Find c such that y(c) = 0.
0, 2
Let a(l) be the second derivative of l**4/4 + l**3 + 3*l**2/2 + 3*l. Factor a(n).
3*(n + 1)**2
Let w = -65/3 - -275/12. Let x be ((-6)/(-8))/((-3)/(-2)). Factor -w*p**2 - x + 7/4*p.
-(p - 1)*(5*p - 2)/4
Solve -8/3 + 4/3*t**2 + 4/3*t**4 + 4*t**3 - 4*t = 0 for t.
-2, -1, 1
Suppose 3/2*h + 1/3 + 8/3*h**2 + h**4 + 7/3*h**3 + 1/6*h**5 = 0. What is h?
-2, -1
Let u(x) be the third derivative of -x**4/8 - 5*x**3/2 + 7*x**2. Let g be u(-5). Solve 0 + 1/2*l**4 + 0*l + g*l**2 + 1/2*l**3 = 0 for l.
-1, 0
Let s = -3 - -5. Suppose 4*r**3 - 4*r - 2*r**4 + r**s - 7 - r**2 + 9 = 0. What is r?
-1, 1
Let 3/5*h**4 - 3/5*h**2 + 0 - 3/5*h**3 + 3/5*h = 0. Calculate h.
-1, 0, 1
Let w(a) be the third derivative of -2*a**7/35 + 7*a**6/30 - a**5/3 + a**4/6 + 30*a**2. Factor w(d).
-4*d*(d - 1)**2*(3*d - 1)
Suppose -36*l = 7*l + 21*l. Factor 0*v - 2/3*v**2 + l.
-2*v**2/3
Let m = -131 + 211. Let c be (1/14)/(5/m). Determine w so that -8/7*w - c*w**2 - 2/7*w**3 + 0 = 0.
-2, 0
Find q, given that -2*q**2 - q**4 - 1/6*q**5 - 13/6*q**3 - 2/3*q + 0 = 0.
-2, -1, 0
Let g(r) = -7*r**5 + 10*r**4 - 11*r**3 + 2*r**2 + 3. Let k(h) = 8*h**5 - 9*h**4 + 11*h**3 - 2*h**2 - 4. Let z(v) = 4*g(v) + 3*k(v). Let z(p) = 0. What is p?
0, 1/4, 1, 2
Factor 2/11*g + 0*g**2 + 2/11*g**5 + 0 + 0*g**4 - 4/11*g**3.
2*g*(g - 1)**2*(g + 1)**2/11
Let i(j) be the first derivative of 4*j**3/3 + 4*j**2 + 7. Factor i(f).
4*f*(f + 2)
Let h(y) be the third derivative of -y**5/60 - 7*y**4/96 + y**3/12 + 17*y**2. Factor h(z).
-(z + 2)*(4*z - 1)/4
Let r(t) = t**3 - 2*t**2 - 9*t + 6. Let x be r(4). Let 0*d + 6/5*d**x - 2/5*d**3 + 0 = 0. What is d?
0, 3
Suppose 4*f - 3*k = -12, -k = -0*k. Let i be f - (-1 - 5/2). Factor -i*y**2 + y - 1/2.
-(y - 1)**2/2
Let b(u) = -13*u**5 + 3*u**4 + 29*u**3 - 23*u**2 - 8*u + 12. Let c(m) = -m**5 - m**3 + m**2 + m. Let k(t) = -b(t) + 4*c(t). What is g in k(g) = 0?
-2, -2/3, 1
Suppose l - 7 = -0*l. Let x = l - 2. Factor -3*u**2 - 8*u**2 - 2*u - 5*u**2 + x - 1 - 10*u**3.
-2*(u + 1)**2*(5*u - 2)
Let u(q) be the first derivative of -20/3*q**3 - 1 + 2*q**2 + 8*q**4 + 0*q - 16/5*q**5. Factor u(h).
-4*h*(h - 1)*(2*h - 1)**2
Let p(h) = -h**3 - 8*h**2 - 8*h - 1. Let l be p(-7). Let 4*u - 22*u - l - 3*u**2 - 21 = 0. Calculate u.
-3
Let u be (-6)/1*(-1)/3. Let h(d) be the first derivative of -2/3*d**3 + 0*d - u - d**2. Factor h(k).
-2*k*(k + 1)
Factor -2/19*r**3 + 0 + 4/19*r + 2/19*r**2.
-2*r*(r - 2)*(r + 1)/19
Let w(s) be the first derivative of -3 - 3*s**2 + 2/3*s**3 + 2/5*s**5 - 4*s + 3/2*s**4. Factor w(k).
2*(k - 1)*(k + 1)**2*(k + 2)
Let o be ((-2)/4)/(1/6). Let n(x) = x**2. Let h(l) = 7*l**2 + l + 2. Let d(w) = o*h(w) + 24*n(w). Solve d(g) = 0.
-1, 2
Let g = 165 - 55. Let o be 12/70*g/33. Determine x so that 10/7*x**2 + 0 + 4/7*x - 10/7*x**4 - o*x**3 = 0.
-1, -2/5, 0, 1
Factor 3/5*d**2 - 1/5 - 1/5*d + 2/5*d**4 + d**3.
(d + 1)**3*(2*d - 1)/5
Let h(k) = 6*