. Factor p(z).
-2*z*(z - 1)/7
Suppose -2*x = 7 + 5. Let f be -1 - x - (4 - 1). Let s(t) = -t**2 - 5*t. Let d(r) = r**2 + 4*r. Let c(a) = f*s(a) + 3*d(a). Factor c(y).
y*(y + 2)
Let t = -1 - -11. Let i = t - 8. Factor 16/3*b + 8/3 + 2*b**i.
2*(b + 2)*(3*b + 2)/3
Suppose 13*l = -x + 15*l, 3*l = 0. Factor x - 3/2*w**2 - 1/2*w.
-w*(3*w + 1)/2
Suppose -7 = -l + 3. Suppose 14*w = l*w. Determine v, given that 1/3*v - 1/3*v**3 + w + 0*v**2 = 0.
-1, 0, 1
Let z(f) be the second derivative of f**6/225 - f**5/50 + f**4/30 - f**3/45 + f. Factor z(h).
2*h*(h - 1)**3/15
Let h(r) be the first derivative of -2*r**2 - r**3 + 2*r**3 + 3*r - 7*r + 5*r - 3. Find s, given that h(s) = 0.
1/3, 1
Let i = 118 + -1179/10. Let s(z) be the second derivative of 0*z**2 + 1/60*z**6 + 1/6*z**4 + 0*z**3 - i*z**5 + 0 + 2*z. Factor s(f).
f**2*(f - 2)**2/2
Let j = -5 + 17. Determine q so that -12 + j + 3*q**2 = 0.
0
Let a(v) be the second derivative of v**6/40 + 3*v**5/40 - 3*v**4/16 - v**3/2 + 3*v**2/2 + 9*v. Suppose a(x) = 0. Calculate x.
-2, 1
Factor -9*u + 4 + 2*u**2 - 2*u**2 + 3*u**2 + 2.
3*(u - 2)*(u - 1)
Let c(u) be the first derivative of -u**3/3 - 5*u**2/2 - 6*u + 30. Suppose c(t) = 0. What is t?
-3, -2
Let v = 0 - -1. Let d be 0 - (v/(-1) + 1). Suppose 2/5*f**3 + 2/5*f**2 + d - 4/5*f = 0. Calculate f.
-2, 0, 1
Let h be 24/27*(2 - 1/2). Factor 0 + h*g**4 - 2*g**3 + 4/3*g**2 - 1/3*g**5 - 1/3*g.
-g*(g - 1)**4/3
Factor -64*c + 17 - 27 + 90 - 11*c - 5*c**2.
-5*(c - 1)*(c + 16)
Find j such that 0 - 1/7*j**5 + 1/7*j**3 + 1/7*j**4 + 0*j - 1/7*j**2 = 0.
-1, 0, 1
Let m(q) = -2*q**2 - q**2 - 4*q + 3*q - q**3. Let r be m(-3). Factor -2*o**r + o**3 - 2*o**4 + o - o**2 + 3*o**2.
-o*(o - 1)*(o + 1)*(2*o + 1)
Let m(y) = -y**3 - 2*y**2 + 5*y + 4. Let g be m(-3). Let s be 0*(-2)/4 - g. Factor -d**2 + d + 0 + 1 - 3*d**3 + s*d**3.
-(d - 1)*(d + 1)**2
Let x(w) = 15*w**2 - w. Let q be x(1). Let s be 6/q - (-5)/(-28). Factor 1/4*g**2 + s*g + 0.
g*(g + 1)/4
Let r(u) = -u**2 + 2*u. Let a(l) = -3*l**2 + 7*l. Let t(w) = -2*a(w) + 7*r(w). Let y(n) = n**3 - 4*n**2. Let k(m) = -4*t(m) + y(m). Factor k(j).
j**3
Let n(q) be the first derivative of -q**4/5 + 2*q**3/15 + 2*q**2/5 - 2*q/5 - 5. Factor n(a).
-2*(a - 1)*(a + 1)*(2*a - 1)/5
Let x = 243/46 - 18/23. Let g(f) = -f + 9. Let s be g(7). Suppose -1 - x*k**s - 11/2*k = 0. Calculate k.
-1, -2/9
Let r be 3 - 1/((-2)/(-3))*1. Determine h, given that 3/2*h**2 - r*h + 0 = 0.
0, 1
Factor 0 + 16/3*w - 112/3*w**2 - 280/3*w**4 + 100/3*w**5 + 92*w**3.
4*w*(w - 1)**2*(5*w - 2)**2/3
Let s be (-18)/(-4) + (-6)/4. Determine q, given that -5*q**2 - 8*q**2 + s*q + 14*q**2 = 0.
-3, 0
Let i(u) be the first derivative of u**7/105 + u**6/20 - u**4/3 - u**2/2 - 2. Let s(h) be the second derivative of i(h). Factor s(l).
2*l*(l - 1)*(l + 2)**2
Let f(a) be the first derivative of a**4/6 + 14*a**3/45 + 2*a**2/15 - 6. Let f(b) = 0. Calculate b.
-1, -2/5, 0
Factor -9/4*q**3 + 3/2 + 3/8*q**4 + 39/8*q**2 - 9/2*q.
3*(q - 2)**2*(q - 1)**2/8
Let w be -5*(2 + -2 - -1). Let a be 35/w - 0/2. Let d(y) = 15*y**3 - 13*y**2 - 2*y. Let g(o) = -7*o**3 + 6*o**2 + o. Let h(u) = a*g(u) - 3*d(u). Factor h(z).
z*(z - 1)*(4*z + 1)
Let v(r) = -3*r**2 + r**2 + 1 + 3*r**2. Let l(o) be the first derivative of o**3/3 + o**2 + 3*o - 1. Let p(d) = -l(d) + 3*v(d). Let p(b) = 0. What is b?
0, 1
Let j(m) = -5*m**4 - 8*m**3 - 2*m**2 + 4*m + 3. Let a(s) = -11*s**4 - 17*s**3 - 5*s**2 + 7*s + 6. Let r(c) = -2*a(c) + 5*j(c). Factor r(g).
-3*(g - 1)*(g + 1)**3
Let k(n) = n + 1. Let s be k(5). Let w(q) be the first derivative of -1/8*q**2 - 2/5*q**5 + 1/8*q**s - 1 + 3/8*q**4 + 0*q + 0*q**3. Factor w(c).
c*(c - 1)**3*(3*c + 1)/4
Let k(u) be the second derivative of 0 + 2/5*u**2 - 3*u - 1/30*u**4 - 1/15*u**3. What is y in k(y) = 0?
-2, 1
Suppose 2*f + 7 = -3. Let n = f + 13. Factor -4*c**2 - 2*c**2 - n*c - 4 - 2*c.
-2*(c + 1)*(3*c + 2)
Factor -2 - 12*b - 26*b**2 - 6 + 22*b**2.
-4*(b + 1)*(b + 2)
Let g(c) be the first derivative of -c**6/15 + c**5/5 - c**4/6 + 2*c - 6. Let p(v) be the first derivative of g(v). Suppose p(i) = 0. What is i?
0, 1
Let y be (0 + 1)/(2/26). Let m = y - 10. Factor 1/2*x**4 + 0 - 1/2*x**2 - 1/4*x**m + 0*x + 1/4*x**5.
x**2*(x - 1)*(x + 1)*(x + 2)/4
Let k(m) = m + 25. Let o be k(0). Let a be 10/o - (-4)/(-10). Suppose a + 1/3*i**2 + 2/3*i = 0. Calculate i.
-2, 0
Let f(q) be the first derivative of 2*q**3/9 - 8*q**2/3 + 32*q/3 + 4. Solve f(k) = 0.
4
Let n = -2 + -3. Let f be (-12)/n + 6/(-15). Suppose 0*j**f + 0 + 0*j - 2/7*j**3 = 0. Calculate j.
0
Factor -28/9 - 4/9*h**2 - 32/9*h.
-4*(h + 1)*(h + 7)/9
Factor 6 + 6*p**4 + 20*p**3 + 92/3*p**2 + 2/3*p**5 + 22*p.
2*(p + 1)**3*(p + 3)**2/3
Let q be (2/3*3)/4. Let m(z) = -z - 1. Let o be m(-5). Factor 0*v + 0 + 0*v**2 + 0*v**3 + q*v**o.
v**4/2
Let o(l) be the first derivative of 2*l**3/9 - 5*l**2/3 + 4*l + 33. Find d such that o(d) = 0.
2, 3
Let v(o) be the first derivative of -o**4/60 - o**3/5 - 9*o**2/10 - 4*o + 4. Let a(y) be the first derivative of v(y). Find w, given that a(w) = 0.
-3
Find a, given that -2*a**3 - 14*a - 4 + 14*a + 3*a**2 + 3*a**3 = 0.
-2, 1
Let -5*o**2 - 16 - 5*o + 16 + 5*o**3 + 5*o**4 = 0. Calculate o.
-1, 0, 1
Factor -2/3 + 1/6*q**2 - 1/2*q.
(q - 4)*(q + 1)/6
Let b be (-18)/(-15)*(-15)/(-6). Factor 1/4*f**b + 3/4*f + 1/4 + 3/4*f**2.
(f + 1)**3/4
Let r = -2/1787 - -10744/19657. Factor -8/11*a - 2/11*a**2 - r.
-2*(a + 1)*(a + 3)/11
Let c(f) = f**3 - 3*f**2 + 4*f - 2. Let t(j) = -j**3 + j**2 - j + 1. Let k(u) = -2*u - 14. Let q be k(-6). Let p(h) = q*t(h) - c(h). Factor p(n).
n*(n - 1)*(n + 2)
Let t(d) be the second derivative of -1/60*d**4 + 6*d + 0*d**2 + 0 - 1/30*d**3. Factor t(o).
-o*(o + 1)/5
Let z(o) = -2*o**2 + 29 - 44 - o**2 + 18*o. Let s(h) = -h + 1. Let k(v) = 6*s(v) + z(v). Factor k(a).
-3*(a - 3)*(a - 1)
Let j = -2/691 - -4849/4146. Factor j*h**3 + 0 + 2/3*h + 8/3*h**2.
h*(h + 2)*(7*h + 2)/6
Let k(h) be the first derivative of 2*h**3/21 - h**2/7 - 4. Factor k(c).
2*c*(c - 1)/7
Let u(a) = 2*a**3 + 8*a**2 + 8*a + 4. Let t(s) = -s**2 - s - 1. Let i = -27 + 26. Let f(p) = i*u(p) - 2*t(p). Factor f(d).
-2*(d + 1)**3
Suppose -5*r - 3*h - 15 = 0, 6*r - 5*h - 25 = r. Let v be (-84)/(-20) - (4 - r). What is m in v*m**2 + 1/5*m + 0 = 0?
-1, 0
Let r(x) = x**2 + x + 3. Suppose 0*c + 2*c + 5*o = -25, -2*c + 5 = -o. Let n be r(c). What is w in -w**4 + 1/4*w**2 + 0 - 3/4*w**n + 0*w = 0?
-1, 0, 1/4
Let s(g) be the first derivative of g**7/2100 - g**6/300 + g**5/150 + 4*g**3/3 - 4. Let r(j) be the third derivative of s(j). Factor r(b).
2*b*(b - 2)*(b - 1)/5
Let d(o) be the first derivative of -4*o**6/15 - 62*o**5/25 - 28*o**4/5 + 32*o**3/15 - 51. Factor d(f).
-2*f**2*(f + 4)**2*(4*f - 1)/5
Let i = 4 - 2. Let r(l) = l - 2. Let n be r(5). Suppose -5 + 5 - p**n - p**i = 0. Calculate p.
-1, 0
Let y = -26 + 28. Factor 1/4*z - 1/4*z**y + 0.
-z*(z - 1)/4
Let o(r) be the third derivative of -r**5/210 - r**4/84 - 3*r**2. Solve o(k) = 0.
-1, 0
Solve 41*o**3 + 1 - 4*o**5 - 16*o - 5 - o**2 + 5*o**4 - 11*o**5 - 10*o**5 = 0.
-1, -2/5, 1
Let y(j) be the second derivative of j**5/30 - j**3/3 + 5*j**2/2 - 5*j. Let h(q) be the first derivative of y(q). Factor h(a).
2*(a - 1)*(a + 1)
Let r(x) = 3*x**3 + 10*x**2 - 15*x + 16. Let g(l) = 3*l**3 + 9*l**2 - 15*l + 15. Let k(u) = 7*g(u) - 6*r(u). Factor k(v).
3*(v - 1)**2*(v + 3)
Let l(u) = u**2 - 4*u - 8. Let i be l(6). Suppose -3*d - 2*g = -2*d - 4, 4 = i*g. Factor -d*p**2 - 2*p**5 + 2*p**4 + p**5 + 2*p**3 - p**5 + 0*p**4.
-2*p**2*(p - 1)**2*(p + 1)
Find o such that -35/2*o**4 - 40*o**3 + 0*o - 10*o**2 + 0 = 0.
-2, -2/7, 0
Let d(u) = 3*u**3 + 7*u**2 - 6*u + 4. Let o(g) = 6*g**3 + 15*g**2 - 12*g + 9. Let c(r) = 9*d(r) - 4*o(r). Suppose c(t) = 0. Calculate t.
-2, 0, 1
Let o(a) be the third derivative of 5*a**8/336 - a**7/21 - a**6/24 + a**5/6 - 18*a**2. Solve o(b) = 0 for b.
-1, 0, 1, 2
Let m = 16 - 13. Suppose 0 = m*a + 3*f - 24, 3*a - 4*f = -2*f - 1. Factor -2/9*x**a + 2/9*x**5 + 0*x**2 + 0*x + 0*x**4 + 0.
2*x**3*(x - 1)*(x + 1)/9
Let i = 161/55 + -30/11. Factor -2/5*t**2 + 1/5 - 2/5*t**3 + 1/5*t + i*t**4 + 1/5*t**5.
(t - 1)**2*(t + 1)**3/5
Let i = 880/3 - 297. Let a = 4 + i. Factor -2/3*g**2 + 0 + 0*g + a*g**3.
g**2*(g - 2)/3
Suppose -9 = -2*b + x, b = 5*x + 5 + 4. Find c such that 8*c - 8 + 7*c**3