2. Factor l(x).
-5*(x - 2)*(x + 1)/6
Suppose -8 = -m - 0*n + n, -4*n - 17 = -m. Find a, given that -a**2 + 4*a**5 + 3*a**3 + 0*a**m - 7*a**3 + a**4 = 0.
-1, -1/4, 0, 1
Let s(x) be the first derivative of -x**3/15 - 2*x**2/5 - 3*x/5 + 44. Suppose s(u) = 0. What is u?
-3, -1
Let k be (0 - 0 - 0)*(-28)/56. Let i(c) be the third derivative of -1/9*c**4 - 1/180*c**6 + 2*c**2 + 0*c**3 + k*c + 2/45*c**5 + 0. Factor i(p).
-2*p*(p - 2)**2/3
Let v(l) = 4*l**2 - 12*l. Let p(y) = -3*y**2 + 8*y. Let m(c) = 8*p(c) + 5*v(c). Find o such that m(o) = 0.
0, 1
Let w be (5 - 1) + 0 + 1. Suppose 2*v + 2*v**2 - 3 - 2*v + 4*v + w = 0. What is v?
-1
Let n be (4/5)/(3/15). Suppose -4*m = 4*c + 4, -4*c = 4*m - 2*c - 2. Solve -1/2*o**3 - o**n + 1/4*o**m + 0 + 2*o**5 + 0*o = 0.
-1/2, 0, 1/2
Let l(w) be the second derivative of 2*w**6/15 - w**4 - 4*w**3/3 + 8*w. Determine n so that l(n) = 0.
-1, 0, 2
Determine k, given that 12/7 + 10/7*k + 2/7*k**2 = 0.
-3, -2
Let s(a) = 3*a - 4. Let n be s(2). Let j(q) be the third derivative of q**n + 0*q**3 + 0*q + 0 - 1/120*q**6 + 1/60*q**5 + 0*q**4. Factor j(y).
-y**2*(y - 1)
Factor -3/5 + 6/5*c - 3/5*c**2.
-3*(c - 1)**2/5
Let g be (-2*(-3 - -5))/(-2). Factor -q**2 + 2*q**3 + 7*q**g - 4*q**2.
2*q**2*(q + 1)
Let b be (-1 - (-1 - 1))*-1. Let s(o) = -o**3 - 1. Let a be s(b). Solve a + 1/5*j + 1/5*j**2 = 0.
-1, 0
Let r(m) be the third derivative of -1/18*m**3 - 1/180*m**5 + 4*m**2 + 0 + 1/36*m**4 + 0*m. Factor r(p).
-(p - 1)**2/3
Let h(a) be the first derivative of 3*a**4/16 + a**3/2 + 2. Factor h(b).
3*b**2*(b + 2)/4
Let s = -247/48 - -16/3. Let r = 53/112 - s. Factor 10/7*f + 6/7*f**2 + r - 18/7*f**3.
-2*(f - 1)*(3*f + 1)**2/7
Let w(d) = d + 1. Let s(z) = -z**2 - 5*z - 4. Let n(h) = h**2 - 4*h + 2. Let a be n(3). Let q(x) = a*s(x) - 5*w(x). Suppose q(t) = 0. Calculate t.
-1, 1
Let v(x) be the first derivative of 5*x**7/252 + x**6/90 - x**5/24 - x**4/36 + 6*x + 2. Let c(a) be the first derivative of v(a). Determine n so that c(n) = 0.
-1, -2/5, 0, 1
Let p(u) be the first derivative of u**4/30 - 2*u**3/15 + u**2/5 + u + 3. Let h(j) be the first derivative of p(j). Factor h(l).
2*(l - 1)**2/5
Factor 2*w**5 + 8*w**4 - 6*w - 8*w**2 + 4*w**3 + 7 - 8 + 1.
2*w*(w - 1)*(w + 1)**2*(w + 3)
Suppose 0 - 4/5*f + 2/5*f**2 + 2/5*f**3 = 0. What is f?
-2, 0, 1
Let c = 0 + 2. Determine o, given that -17*o**3 + 3*o**2 + 20*o - 2*o**2 + 8 + 15*o**c + 21*o**3 = 0.
-2, -1
Suppose -2*h = -t + 7, t - 3*h = -0*t + 9. Let -4/9*i**4 + 0*i + 0*i**2 + 0 + 2/9*i**t + 2/9*i**5 = 0. Calculate i.
0, 1
Let v(f) be the first derivative of -f**6/45 + 4*f**5/75 - 4*f**3/45 + f**2/15 + 1. Solve v(y) = 0.
-1, 0, 1
Let m(o) be the first derivative of 4/5*o**2 - 4/5*o**3 + 3*o + 7/50*o**5 - 3/10*o**4 + 3. Let j(c) be the first derivative of m(c). Find f such that j(f) = 0.
-1, 2/7, 2
Let x(m) = 2*m + 13. Let v be x(-6). Let k(w) = 3*w**3 - w**2 + w - 1. Let h be k(v). Factor 2*g + 2 + 1/2*g**h.
(g + 2)**2/2
Let n(s) be the second derivative of -s**4/20 + 2*s**3/5 - 9*s**2/10 - 6*s. Factor n(r).
-3*(r - 3)*(r - 1)/5
Let u be 33/6 + (-7)/(-2) + -6. Factor -1/4*b + 0 - b**4 - b**2 - 3/2*b**u - 1/4*b**5.
-b*(b + 1)**4/4
Let i(g) be the first derivative of -2/21*g**6 - 2/35*g**5 + 1/7*g**4 + 0*g**2 + 0*g + 2/21*g**3 + 1. Suppose i(q) = 0. Calculate q.
-1, -1/2, 0, 1
Let m = 22 + -22. Let d(x) be the first derivative of 4 + 0*x - 1/2*x**4 + m*x**3 - 2/5*x**5 + 0*x**2. Factor d(i).
-2*i**3*(i + 1)
Factor 5*c + 4*c**2 + 5*c**2 - 3 - 2*c - 6*c**2 - 3*c**3.
-3*(c - 1)**2*(c + 1)
Let a(y) be the third derivative of 0*y**6 + 0*y**5 + 0*y**4 + 0*y**3 + 2*y**2 + 0*y**7 + 0 + 0*y - 1/1344*y**8. Factor a(o).
-o**5/4
Let p(c) = -13*c**4 + 42*c**3 - 17*c**2 - 10*c - 2. Let r(u) = 51*u**4 - 169*u**3 + 69*u**2 + 40*u + 9. Let f(o) = 9*p(o) + 2*r(o). Find q, given that f(q) = 0.
-1/3, 0, 1, 2
Let m = 11 + -8. Determine s, given that -m*s**3 + 7 - 7 + 3*s = 0.
-1, 0, 1
Determine p, given that -2/5*p - 2*p**2 + 16/5*p**4 + 2/5 + 8/5*p**5 + 2/5*p**3 = 0.
-1, 1/2
Suppose 3/2*d**4 + 0*d + 0 + 2*d**3 + 1/2*d**2 = 0. What is d?
-1, -1/3, 0
Let x be (-1)/(-1*3/12). Let v(n) be the first derivative of -1 + 1/12*n**3 + 0*n + 0*n**2 + 1/16*n**x. Factor v(s).
s**2*(s + 1)/4
Let z be (-10)/(-3) + (-12)/(-18). Suppose -z = -k - 1. Factor 2*s + 0 - 2 + 4*s + 2*s**4 - 2*s - 4*s**k.
2*(s - 1)**3*(s + 1)
Let l(m) = -m**3 + 5*m**2 - 5*m + 6. Let d be l(4). Let v(q) = q**2 + 2*q + 1. Let z be v(-1). Find r such that 0*r + 2/9*r**d + z = 0.
0
Let l(s) be the third derivative of s**7/1260 - s**6/144 + s**5/45 - s**4/36 - s**2. Factor l(v).
v*(v - 2)**2*(v - 1)/6
Suppose 0 = 552*u - 551*u - 4. Let d = -1 - -1. Determine o, given that -2/11*o**2 + 0 + 2/11*o**u + 0*o + d*o**3 = 0.
-1, 0, 1
Suppose -2*n = -5*h + 1, -h + 6 = n + 3. Let v(d) be the first derivative of -1/10*d**4 - 2/15*d**3 + 0*d**2 + h + 0*d. Find r, given that v(r) = 0.
-1, 0
Factor -4*p**3 - 367*p - 23328 - 3192*p**2 - 3521*p + 2976*p**2.
-4*(p + 18)**3
Suppose -8 = o - 5*o. Solve 5*c**o + 2*c - 2*c**2 - 3*c**3 + 0*c - 2*c**3 = 0.
-2/5, 0, 1
Let q(b) = -b**2 - 4*b. Let s be q(-4). Let h be 672/147 - 8/14. Factor 1/4*i**3 + 0*i**2 + 0 + s*i + 1/4*i**h.
i**3*(i + 1)/4
Suppose 4/3*z + 2/3 + 2/3*z**2 = 0. What is z?
-1
Let c = 22 - 15. Suppose 0 = -2*m + c*m. Factor -2*v - 2*v**4 + 0*v**3 + 2*v**2 + m*v + 2*v**3.
-2*v*(v - 1)**2*(v + 1)
Let n = 395/4 + -98. Factor 0 - n*b**2 - 3/2*b.
-3*b*(b + 2)/4
Let o(c) be the first derivative of -c**7/147 + c**6/105 + c**5/70 - c**4/42 + 3*c - 1. Let t(r) be the first derivative of o(r). Factor t(j).
-2*j**2*(j - 1)**2*(j + 1)/7
Factor 18*p**2 + 12*p - 20*p**2 + 11*p**3 + 38*p**2 + 4*p**3.
3*p*(p + 2)*(5*p + 2)
Let n be (4*1)/((-3)/(-6)). Let g = n - 6. Factor g*p**2 + 3*p**5 + p**4 - 2*p**2 - 2*p**5.
p**4*(p + 1)
Let n(g) be the second derivative of 2*g + 1/8*g**4 + 3/2*g**3 + 0 + 27/4*g**2. Factor n(y).
3*(y + 3)**2/2
Factor -3*h - 5*h**2 - 3*h**3 + h**4 + 4*h**4 + 6*h**3.
h*(h - 1)*(h + 1)*(5*h + 3)
Let i(m) = -m**2 + 7*m + 10. Let v be i(8). Suppose 0*x = -v*x. Determine q so that -2*q + 3*q**4 + 2*q + x*q**4 = 0.
0
Let g = -2 - -4. Let m(o) be the second derivative of 1/3*o**3 + 1/120*o**6 + 0*o**g + 1/4*o**4 + 2*o + 3/40*o**5 + 0. Determine k so that m(k) = 0.
-2, 0
Let a(u) be the first derivative of -3*u**4/16 - 5*u**3/4 - 21*u**2/8 - 9*u/4 - 8. Determine q, given that a(q) = 0.
-3, -1
Let p = 41 + -29. Suppose -2*a - 2*a = -p. Factor -32/7*l**4 + 48/7*l**a - 2/7*l**2 - 2/7 - 12/7*l.
-2*(l - 1)**2*(4*l + 1)**2/7
Let a be 4*2/16 + (-1 - -2). Factor -3/2 + a*d**2 + 0*d.
3*(d - 1)*(d + 1)/2
Factor -4/5*w**3 - 308/5*w + 64/5*w**2 + 392/5.
-4*(w - 7)**2*(w - 2)/5
Let o be 6/15*(7 - 2). Let a(d) be the second derivative of 0*d**5 - o*d - 1/48*d**4 + 0*d**3 + 1/120*d**6 + 0 + 0*d**2. Factor a(n).
n**2*(n - 1)*(n + 1)/4
Factor 2*s**3 + 0*s**4 - 3*s**4 + s**4.
-2*s**3*(s - 1)
Suppose 5*v - 3 = 2. Let b(x) be the first derivative of 0*x + 1/6*x**3 + 0*x**2 - 1/8*x**4 - v. Factor b(s).
-s**2*(s - 1)/2
Let r(i) be the second derivative of 0 + 0*i**2 + 2*i**3 + 1/5*i**5 - 4/3*i**4 + 6*i. Factor r(w).
4*w*(w - 3)*(w - 1)
Suppose n = y - 0*n - 2, -y + 3*n + 2 = 0. Let m be y/9 + 8/18. Solve 0*c + 0 - 2/3*c**4 - 8/3*c**3 + m*c**2 + 8/3*c**5 = 0.
-1, 0, 1/4, 1
Let j be -2*5/2*-5. Factor -1 - 8*s**3 - 2 + j*s**2 - s**3 - 3*s - 10*s**2.
-3*(s - 1)**2*(3*s + 1)
Suppose 16*a**3 - 5*a**2 + a**2 - 18*a**3 = 0. What is a?
-2, 0
Factor -2*z + 4*z - 4*z**2 + 3*z**2 + z**4 - 3*z**3 + z**5.
z*(z - 1)**2*(z + 1)*(z + 2)
Let j(l) = 10*l**2 + 14*l + 10. Let g(d) = 9*d**2 + 15*d + 11. Let c(n) = 6*g(n) - 5*j(n). Factor c(q).
4*(q + 1)*(q + 4)
Let b(z) = z**4 - z**3 + z**2 - z + 1. Let w(k) = -k**2 + 6*k - 1 - 7*k**2 - 5*k**4 - 4 + 6*k**3. Let n(v) = 6*b(v) + w(v). Factor n(s).
(s - 1)**2*(s + 1)**2
Let c(v) = 0 + 20*v - 16*v - 4. Let x(a) = a**2 - 17*a + 16. Let f = 7 - 5. Let i(n) = f*x(n) + 9*c(n). Suppose i(p) = 0. What is p?
-2, 1
Let p = 21 - 14. Factor 6*s**3 + 6*s**5 - 21*s**4 + 0*s**2 + p*s**4 + 6*s**2 - 4*s.
2*s*(s - 1)**3*(3*s + 2)
Factor 0*z + 0 + 1/3*z**4 + 0*z**2 - 2/3*z**3.
z**3*(z - 2)/3
Suppose -x = -5*x + 20. Suppose 6 = -3*r + x*r. Factor -6/5*h + 2/5 + 6/5*h**2 - 2/5*h**r.
-2*(h - 1)**3/5
Let x(h) be the first derivativ