- 4*l**3/3 - 2*l**2 - 1. Let w(s) be the second derivative of x(s). Factor w(h).
4*(h - 2)*(h + 1)**2
Suppose -6*p**2 + 6 - 4*p**2 - 21*p**3 + p**4 + p**2 - 10*p**4 + 9*p = 0. Calculate p.
-1, 2/3
Suppose -1/5*x**2 - 3/5*x + 0 = 0. What is x?
-3, 0
Let w(s) be the third derivative of -s**7/210 + s**6/60 + s**5/60 - s**4/12 + 19*s**2. Find v, given that w(v) = 0.
-1, 0, 1, 2
Solve 0 - 8/13*l**2 + 18/13*l**5 - 14/13*l**4 + 0*l - 40/13*l**3 = 0.
-1, -2/9, 0, 2
Suppose -m = 2*m - 18. Suppose -2*a = -0*a - m. Suppose -3*c**2 - 10*c**3 - 4*c**4 + 2*c + 1 - a*c**2 + 1 = 0. What is c?
-1, 1/2
Let u = 0 + 7. Suppose -8*g = -u*g. Let 0*d + 2/7*d**2 + 2/7*d**3 + g = 0. What is d?
-1, 0
Let n(h) = h**3 - 6*h**2 + h - 5. Let l be n(6). Suppose 5*k + l = -2*p + 34, 5*p = 4*k. Factor 0 - 1/4*r**4 + 0*r + 1/4*r**3 - 1/4*r**k + 1/4*r**2.
-r**2*(r - 1)*(r + 1)**2/4
Let s(r) = 13*r**3 + 10*r**2 + 5*r - 3. Let g(l) = -7*l**3 - 5*l**2 - 2*l + 2. Let y(u) = 11*g(u) + 6*s(u). What is a in y(a) = 0?
-2, -1
Let a(w) be the second derivative of 2*w + 0*w**4 - 1/75*w**6 + 0 - 1/50*w**5 + 0*w**2 + 0*w**3. Suppose a(i) = 0. What is i?
-1, 0
Let y(w) be the third derivative of -w**5/240 - w**4/96 + w**3/12 + 26*w**2. Factor y(g).
-(g - 1)*(g + 2)/4
Let 31*o**3 + 24*o**2 + 9*o**2 + o**4 + 40*o + 16 + 48*o**3 - 69*o**3 = 0. Calculate o.
-4, -1
Factor 24*t - 4*t**2 + 16 - 24*t.
-4*(t - 2)*(t + 2)
Let g(c) be the third derivative of c**7/1680 - c**6/720 + c**3/6 - 4*c**2. Let a(h) be the first derivative of g(h). Factor a(y).
y**2*(y - 1)/2
Let b(i) be the third derivative of 1/150*i**6 - 7/240*i**8 + 0*i - i**2 + 0 + 7/150*i**7 - 1/75*i**5 + 0*i**4 + 0*i**3. Determine x so that b(x) = 0.
-2/7, 0, 2/7, 1
Let v(f) be the first derivative of f**4/10 - 3*f**2/5 - 4*f/5 - 12. Factor v(u).
2*(u - 2)*(u + 1)**2/5
Suppose m - 4*z = -1, -5*z = -1 - 4. Suppose -r + 7 = c, -25 = -0*r - m*r - 5*c. Factor 30*v**3 - 8*v**4 + r*v**2 - 12*v - 16*v**2 + 4 + 33*v**4.
(v + 1)**2*(5*v - 2)**2
Let h(s) be the second derivative of 5*s**4/18 - 8*s**3/9 - 4*s**2/3 - 18*s. Factor h(p).
2*(p - 2)*(5*p + 2)/3
Let r(k) = k**5 - 3*k**4 + 5*k**3 + 5*k**2 + 2*k. Let o(f) = f**5 - f**4 + f**3. Let w(z) = 2*o(z) - r(z). Determine x, given that w(x) = 0.
-1, 0, 2
Suppose 0 = 3*b - 2*f + 6*f - 4, -5*b - f + 18 = 0. Let k be (-2 - -2) + b/10. Suppose -1/5*u**2 - 1/5 - k*u = 0. What is u?
-1
Let a(b) be the third derivative of b**6/180 + b**5/10 + 3*b**4/4 + 3*b**3 - 3*b**2. Let a(m) = 0. Calculate m.
-3
Let v be 90/(-75)*5/(-2). Factor -4*z**v - 2/3 + 22/3*z**2 - 8/3*z.
-2*(z - 1)**2*(6*z + 1)/3
Suppose -q - 3 + 2 = -b, -4*b + 22 = 2*q. Let -h**5 + 3*h**3 - 2*h**3 - 5*h**q + 3*h**5 + 2*h = 0. Calculate h.
-1, 0, 1
Let v(y) be the third derivative of y**6/80 + 3*y**5/20 + 3*y**4/4 + 2*y**3 - 14*y**2. Determine i, given that v(i) = 0.
-2
Let j be ((-6)/(-9))/((-1)/(-3)). Let s be (-3)/(-6)*2 + j. Factor -5*x**s + 2*x**3 + x**3.
-2*x**3
Let -2/5 + 18/5*r**2 + 8/5*r**4 - 2/5*r - 22/5*r**3 = 0. What is r?
-1/4, 1
Let y = 63/10 - 24/5. Factor 4*w**3 - 7/2*w**2 - 9/4*w**4 + y*w + 1/2*w**5 - 1/4.
(w - 1)**4*(2*w - 1)/4
Let o = 143 + -143. Factor -7/3*t**5 - 10*t**4 - 12*t**3 + o*t - 8/3*t**2 + 0.
-t**2*(t + 2)**2*(7*t + 2)/3
Factor -19 + 4*i**2 - 7*i**2 - 29 + 24*i.
-3*(i - 4)**2
Solve -1/3 - t**2 + t + 1/3*t**3 = 0 for t.
1
Let b(o) = -o**3 - o - 1. Let r(q) = 5*q**3 - 15*q**2 + 26*q - 10. Let s(u) = -2*b(u) - r(u). Solve s(t) = 0.
1, 2
Let f(a) be the first derivative of 2*a**5/35 - a**4/7 + 2*a**3/21 + 3. Suppose f(h) = 0. What is h?
0, 1
Factor 0*y**2 - 3*y**2 + y**2 + 5*y**2.
3*y**2
Let y(t) be the second derivative of -t**5/70 + 8*t**4/21 - 64*t**3/21 + 4*t. What is w in y(w) = 0?
0, 8
Let z = 8 - 4. Factor -18*j**z + 2*j**2 + 3*j**5 + 22*j**3 + 27*j + 16*j**3 + 4*j**3 - 6 - 50*j**2.
3*(j - 2)*(j - 1)**4
Let n(v) be the first derivative of -3*v**5/20 + 3*v**3/2 + 3*v**2 - 8*v - 8. Let x(y) be the first derivative of n(y). Factor x(w).
-3*(w - 2)*(w + 1)**2
Find w such that -w**2 - 88 + 2*w + w + 0*w**2 + 86 = 0.
1, 2
Let u(g) be the first derivative of g**3/9 + 5*g**2/2 + 14*g/3 - 37. Factor u(z).
(z + 1)*(z + 14)/3
Let g = 188 - 563/3. Factor v**2 - v + 1/3 - g*v**3.
-(v - 1)**3/3
Let s be (-34)/17*(2 + (-7)/3). Let u = 67/105 - -1/35. Factor a**4 + 1/3 - s*a**3 + u*a - 4/3*a**2.
(a - 1)**2*(a + 1)*(3*a + 1)/3
Let y(n) be the first derivative of -n**7/2940 + n**6/630 - n**5/420 + n**3/3 - 4. Let l(z) be the third derivative of y(z). Let l(p) = 0. What is p?
0, 1
Suppose k + 0 = 1. Let m(s) = 6*s**3 - 9*s**2 + 3. Let x(h) = h**3 - h**2 - h + 1. Let t(f) = k*m(f) - 3*x(f). Factor t(a).
3*a*(a - 1)**2
Let n(g) be the first derivative of 3*g**8/560 + g**7/40 + g**6/40 - 3*g**5/40 - g**4/4 + 2*g**3/3 + 3. Let m(r) be the third derivative of n(r). Factor m(c).
3*(c + 1)**3*(3*c - 2)
Let w(n) = -n**4 - 3*n**3 - 2*n**2 - 2. Suppose 2*l = -l - 15. Let i(u) = -2*u**4 - 7*u**3 - 5*u**2 - 5. Let d(v) = l*w(v) + 2*i(v). Factor d(t).
t**3*(t + 1)
Let u(r) be the second derivative of -1/20*r**4 + 1/10*r**3 - 3/100*r**5 - r + 0 + 3/10*r**2. Find o such that u(o) = 0.
-1, 1
Let v(c) be the third derivative of -c**8/2856 - 2*c**7/357 - 11*c**6/340 - 4*c**5/51 - 4*c**4/51 + 4*c**2. Determine s so that v(s) = 0.
-4, -1, 0
Let h(q) = -110*q**2 - 220*q + 45. Let a(j) = -5*j**2 - 10*j + 2. Let v(f) = -45*a(f) + 2*h(f). What is m in v(m) = 0?
-2, 0
Factor 3 + 9/2*h + 9/2*h**3 - 12*h**2.
3*(h - 2)*(h - 1)*(3*h + 1)/2
Let r(g) be the first derivative of g**2/2 + 4*g + 3. Let u be r(-2). Factor 0 + 2*o**2 - 2/3*o - u*o**3 + 2/3*o**4.
2*o*(o - 1)**3/3
Let n(h) be the first derivative of -h**6/6 - 2*h**5/5 + 2*h**3/3 + h**2/2 + 2. Suppose n(z) = 0. Calculate z.
-1, 0, 1
Let h(z) be the first derivative of -z**5/30 - z**4/6 + z**3 - 3*z**2/2 - 7. Let o(q) be the second derivative of h(q). Factor o(n).
-2*(n - 1)*(n + 3)
Let t(m) be the third derivative of m**7/140 - m**6/80 - m**5/40 + m**4/16 - 4*m**2. Factor t(v).
3*v*(v - 1)**2*(v + 1)/2
Let l = -24 + 193/8. Let h(u) be the first derivative of l*u**4 - 1/20*u**5 - 1 - 1/4*u**2 + 1/4*u + 0*u**3. Suppose h(j) = 0. Calculate j.
-1, 1
Find z such that 4/3*z**2 - 2/3*z - 2/3*z**3 + 0 = 0.
0, 1
Let r(y) be the third derivative of y**5/80 - y**3/8 + 9*y**2. Find f such that r(f) = 0.
-1, 1
Factor 5/6 + 0*l - 5/6*l**2.
-5*(l - 1)*(l + 1)/6
Let h(p) be the first derivative of 5 - 18*p - 2/3*p**3 - 6*p**2. Let h(t) = 0. Calculate t.
-3
Let v(o) be the second derivative of 1/4*o**4 + 3/20*o**5 + 0 - 1/14*o**7 + 0*o**3 + 0*o**2 - 1/10*o**6 + 2*o. Factor v(z).
-3*z**2*(z - 1)*(z + 1)**2
Let d(v) be the second derivative of 7*v**5/4 - 5*v**4/6 - 20*v. Factor d(j).
5*j**2*(7*j - 2)
Let d = -2/439 + 1321/878. Determine k so that -d*k**2 - 6 - 6*k = 0.
-2
Let b(c) be the third derivative of c**5/60 + c**4/18 + c**3/18 + 16*c**2. Factor b(p).
(p + 1)*(3*p + 1)/3
Let b(g) be the second derivative of -g**4/60 - g**3/15 - g**2/10 - 10*g. Let b(x) = 0. Calculate x.
-1
Suppose 7*l = l. Let t(a) be the third derivative of a**2 + 13/120*a**5 - 1/60*a**6 + l*a + 1/6*a**3 + 0 - 11/48*a**4. Factor t(u).
-(u - 2)*(u - 1)*(4*u - 1)/2
Factor -o**2 + 5*o**3 - 2*o**2 - 2*o**2 + 5 - 5*o.
5*(o - 1)**2*(o + 1)
Let o = -10 - -18. Suppose 20*u - 24*u**5 + 6*u**2 - 52*u**3 + 6*u**2 - 68*u**4 + 0*u**2 + o + 8*u = 0. Calculate u.
-1, -1/2, 2/3
Let k = 3 + -1. Find b, given that -27/4*b**k - 3/4 - 9/2*b = 0.
-1/3
Suppose -4*h + 40 = 3*u, 0*u - 3*h + 4 = -u. Suppose 4*c + 3*v - u = v, 3*c = -5*v - 1. What is w in -2/9*w**2 + 0 + 0*w - 2/9*w**c = 0?
-1, 0
Suppose d + 3 = -5*j + j, -5*j - 6 = 2*d. Determine l, given that -2/3*l + 2/9*l**3 + 4/9 + j*l**2 = 0.
-2, 1
Let 34/9*y + 4/3 - 2/9*y**4 + 2/3*y**3 + 10/3*y**2 = 0. Calculate y.
-1, 6
Let c(q) be the third derivative of -1/1344*q**8 + 1/840*q**7 - 1/240*q**5 + 1/480*q**6 - 6*q**2 + 0*q**3 + 0*q + 0*q**4 + 0. Factor c(h).
-h**2*(h - 1)**2*(h + 1)/4
Let w(n) be the first derivative of 0*n**5 - 1 + 1/4*n**2 + 0*n + 1/12*n**6 + 0*n**3 - 1/4*n**4. Factor w(t).
t*(t - 1)**2*(t + 1)**2/2
Suppose 1/2 - 2*v**3 + 1/2*v**4 + 3*v**2 - 2*v = 0. Calculate v.
1
Let f(w) be the second derivative of w**3/2 - 7*w**2 - 2*w. Let d be f(6). Solve 1/4*a - 1/2*a**d + 1/2*a**2 + 0*a**3 - 1/4*a**5 +