 Factor b(x).
-3*(x + 1)*(x + 3)/2
Let m be 3/(-3) + (3 - 0). Factor -10*t - 1 - 75*t**m - 5*t - 71*t**3 - 54*t**3.
-(5*t + 1)**3
Let v be (-23)/2 - (-1)/(-2). Let z be (-1 - v/9)*9. Let -5*b**2 + 2*b + b**z - 3*b + 6*b**2 - 1 = 0. What is b?
-1, 1
Factor 3*y**4 - 12*y**2 + 16 + 16*y - 8*y**3 - 2*y**4 + 3*y**4.
4*(y - 2)**2*(y + 1)**2
Let u(a) be the second derivative of a**4/90 + 2*a**3/45 - 6*a. Determine q so that u(q) = 0.
-2, 0
Let p = -662/21 - -92/3. Let g = p + 32/21. Factor 2/3 + 0*m - g*m**2.
-2*(m - 1)*(m + 1)/3
Let w(d) be the third derivative of -d**5/80 - 3*d**4/16 - 5*d**3/8 + 24*d**2. Factor w(j).
-3*(j + 1)*(j + 5)/4
Let j(m) be the second derivative of m**7/14 + 3*m**6/5 + 27*m**5/20 - 2*m - 2. Suppose j(t) = 0. Calculate t.
-3, 0
Suppose 0*g = g. Let u = 124/9 + -832/63. What is s in -u*s**2 + 0*s + 2/7*s**3 + g = 0?
0, 2
Let k be (0/8 + 6)/3. Find x such that -1/4*x**k + 0*x + 1/4 = 0.
-1, 1
Suppose 105*g**4 - 8*g - 8*g**2 + 44*g**3 - 149*g**4 + 4*g**2 + 12*g**5 = 0. What is g?
-1/3, 0, 1, 2
Let x = 54 + -51. Suppose t**x - 1/2 + 1/2*t**4 + 0*t**2 - t = 0. What is t?
-1, 1
Let c(r) be the third derivative of r**7/420 + r**6/48 + r**5/15 + r**4/12 + 24*r**2. Factor c(x).
x*(x + 1)*(x + 2)**2/2
Let q be 17/5 + (-6)/15. Determine p, given that -9*p + 6*p**4 - 3 + 0*p**5 - 6*p**2 + q*p**5 + 6*p**3 + 3*p**4 = 0.
-1, 1
Let c(q) = -9*q**3 - 57*q**2 - 42*q - 6. Let w(f) = f**3 - f**2 + f + 1. Suppose 0 = -0*b + 2*b + 12. Let n(j) = b*w(j) + c(j). Find x, given that n(x) = 0.
-2, -1, -2/5
Let v(s) be the second derivative of 1/20*s**6 - 1/42*s**7 - 1/40*s**5 + 6*s + 0 + 0*s**4 + 0*s**2 + 0*s**3. Suppose v(g) = 0. What is g?
0, 1/2, 1
Let t(c) = -29*c**3 - c**2 + 1. Let j be t(-1). Let o = -27 + j. Factor 0 - 1/3*p - 1/3*p**o.
-p*(p + 1)/3
Suppose 3*h - 9 + 0 = 0. Let a(w) = 6*w - 2. Let p be a(1). Factor -4*z**3 - 15*z**p + 4*z**3 - 9*z**5 - 4 + 5*z**h + 15*z**2.
-(z + 1)**3*(3*z - 2)**2
Let s(b) be the second derivative of b**6/105 - b**5/70 - b**4/14 + 5*b**3/21 - 2*b**2/7 + 7*b. Factor s(i).
2*(i - 1)**3*(i + 2)/7
Let 18/5*x + 0 + 6*x**2 + 14/5*x**3 + 2/5*x**4 = 0. What is x?
-3, -1, 0
Suppose 0*m = -0*m - 2*m. Factor m*u + 2*u**3 - u**2 + 21/4*u**4 + 0.
u**2*(3*u + 2)*(7*u - 2)/4
Suppose 96/7*q - 12/7 + 75/7*q**5 - 291/7*q**2 + 417/7*q**3 - 285/7*q**4 = 0. Calculate q.
2/5, 1
Let j = -8 + 10. Suppose -2*i = 5*g + 3 - 17, 0 = 5*i + 5*g - 20. Factor -1 + 5 - 8*s - j*s + 6*s**i.
2*(s - 1)*(3*s - 2)
Let u(k) = k + 3. Let g be u(6). Let d be (6/(-4))/(g/(-12)). Factor 2*i**2 + i**2 + 1 - 2*i - 2*i**d.
(i - 1)**2
Let h(d) be the first derivative of d + 1 - 2/5*d**3 - 3/100*d**5 + 0*d**2 - 1/5*d**4. Let q(w) be the first derivative of h(w). Factor q(o).
-3*o*(o + 2)**2/5
Let d be 196/110 - 36/198. Let i be 2/6 - 16/(-6). Find q, given that 8/5*q**i + 2/5*q**4 + 12/5*q**2 + d*q + 2/5 = 0.
-1
Factor 1/3*k**3 + 2/3*k**2 - 8/3 - 4/3*k.
(k - 2)*(k + 2)**2/3
Factor -7/6*o**2 + 2/3*o**3 + 0 - 1/3*o.
o*(o - 2)*(4*o + 1)/6
Let y(a) = a - 1. Let z(q) = -14*q + 4. Let o(x) = 5*y(x) + z(x). Let k be o(-1). Suppose k*s**2 - 2*s**2 + s + 3*s**3 + 6*s**3 = 0. Calculate s.
-1/3, 0
Determine g so that -2/9*g**3 + 2/3*g**2 - 2/3 + 2/9*g = 0.
-1, 1, 3
Factor 1/7*l**3 + 0 + 2/7*l**2 + 1/7*l.
l*(l + 1)**2/7
Let o(k) be the second derivative of -k**5/110 + 3*k**4/22 - 9*k**3/11 + 27*k**2/11 + 2*k + 13. Factor o(r).
-2*(r - 3)**3/11
What is w in 3*w - 3 + 3/4*w**4 + 9/4*w**2 - 3*w**3 = 0?
-1, 1, 2
Let x(q) be the second derivative of -2*q**2 + 1/10*q**5 + 0 - 2/3*q**3 - 1/30*q**6 - 5*q + 1/4*q**4. Let x(g) = 0. What is g?
-1, 2
Let z(i) be the second derivative of i**5/200 + i**4/30 + i**3/15 + 9*i. Factor z(k).
k*(k + 2)**2/10
Let r(c) be the third derivative of -4*c**2 + 1/1344*c**8 + 1/96*c**4 + 0*c**7 + 0*c**5 - 1/240*c**6 + 0*c**3 + 0 + 0*c. Factor r(q).
q*(q - 1)**2*(q + 1)**2/4
Let b(r) = 3*r**2 - 3*r - 4. Let j be b(-2). Let y = 14 - j. Let 2/7*l**4 - 2/7*l**2 - 2/7*l**3 + 2/7*l + y = 0. What is l?
-1, 0, 1
Let y(z) be the third derivative of -z**6/480 - z**5/30 - z**4/6 + 20*z**2. Determine u so that y(u) = 0.
-4, 0
Let r(x) be the third derivative of -5*x**8/1008 - x**7/63 + x**6/24 + x**5/9 - 5*x**4/18 - 19*x**2. Determine n so that r(n) = 0.
-2, 0, 1
Factor 6/5*m + 4/5 - 2/5*m**3 + 0*m**2.
-2*(m - 2)*(m + 1)**2/5
Let o(s) be the first derivative of 54*s**3/5 - 36*s**2/5 + 8*s/5 - 3. Factor o(h).
2*(9*h - 2)**2/5
Factor j**4 + 0*j**5 + 5*j**4 + 14*j**4 - 4*j**5 - 24*j**3.
-4*j**3*(j - 3)*(j - 2)
Suppose -5*x = -13 - 22. Suppose x*l - 2*l = 115. What is r in -r**2 - 23*r + l*r = 0?
0
Find h, given that 8*h**3 - 8*h - 12*h**4 + 2*h**2 + 4*h**2 + 3*h**2 + 3*h**2 = 0.
-1, 0, 2/3, 1
Suppose -3*g + 20 = g, 3*o = 2*g - 4. Let b(u) be the second derivative of -3*u + 5/24*u**3 + 1/4*u**o + 1/12*u**4 + 0 + 1/80*u**5. Factor b(c).
(c + 1)**2*(c + 2)/4
Let z = 19 + -19. Let g(l) be the second derivative of 1/18*l**4 - 3*l + 0*l**2 + 2/9*l**3 + z. Factor g(i).
2*i*(i + 2)/3
Let q(m) = -4*m**3 - 1. Let h(a) = -1 - 11*a**3 - 2 + 0*a + a. Let l(i) = 3*h(i) - 8*q(i). Let f(w) be the first derivative of l(w). Find v such that f(v) = 0.
-1, 1
Suppose o - 3*o = 4*j - 12, o + 5*j - 12 = 0. Let p(q) be the second derivative of -2/15*q**4 + 2*q + 0*q**o + 0 + 3/50*q**5 + 1/15*q**3. Factor p(z).
2*z*(z - 1)*(3*z - 1)/5
Let f(w) = -w + 5. Let u be f(3). Suppose -u = -m - 0. Factor 2 - 4 - m*c**2 + 4*c + 0*c**2.
-2*(c - 1)**2
Let n(r) be the second derivative of 1/195*r**6 - 2*r + 0*r**2 + 0*r**3 + 1/130*r**5 + 0 + 0*r**4. Factor n(q).
2*q**3*(q + 1)/13
Let x(z) be the first derivative of -2*z**3/27 - 2*z**2/9 + 3. Factor x(s).
-2*s*(s + 2)/9
Let d be 8*((-9)/44)/(-9). Find t, given that d*t**4 + 0*t**2 + 0*t**3 + 0 + 0*t = 0.
0
Factor 0 - 1/5*y**3 + 0*y + 1/5*y**2.
-y**2*(y - 1)/5
Suppose 2 + 4*u**5 + 1 - 3 + 40*u**3 + 4 + 20*u + 40*u**2 + 20*u**4 = 0. What is u?
-1
Factor 2/13*z - 18/13*z**2 + 0 + 16/13*z**3.
2*z*(z - 1)*(8*z - 1)/13
Suppose 11*f + 32 = 19*f. What is d in d**f - d**2 + 1/3*d**3 + 0 - 1/3*d = 0?
-1, -1/3, 0, 1
Let u = -84/5 + 6903/410. Let b = 137/738 + u. Factor 2/9*s - 2/9*s**4 - b*s**3 + 0 + 2/9*s**2.
-2*s*(s - 1)*(s + 1)**2/9
Factor -4*m - 4*m**2 + 3 + 3 + 2*m**3 - 2 + 2*m.
2*(m - 2)*(m - 1)*(m + 1)
Let f = 63 + -4. Let n = -235/4 + f. Let 0*p + 1/4*p**3 - n*p**5 + 0*p**4 + 0*p**2 + 0 = 0. Calculate p.
-1, 0, 1
Let p(m) be the first derivative of -m**6/27 + 4*m**5/15 - 7*m**4/9 + 32*m**3/27 - m**2 + 4*m/9 + 1. Suppose p(c) = 0. Calculate c.
1, 2
Suppose -4*x + 9 = 1. Let u be (-2 + 1)*1*-2. Find y, given that 4*y**u - x*y**2 + 0*y**2 - 8*y + 10*y = 0.
-1, 0
Let g(l) = l**4 - 1. Let k(o) = -7*o**4 - 2*o**3 + 2*o + 7. Let h(v) = -6*g(v) - k(v). Determine j so that h(j) = 0.
-1, 1
Let z(u) = -u - 23. Let d be z(-28). Factor 1/2*s**3 - 3/2*s**d + 0 + s**2 + 0*s - 2*s**4.
-s**2*(s + 1)**2*(3*s - 2)/2
Let f be (20/(-8))/(2/4). Let t be ((-10)/25)/(1/f). Find a, given that a**2 - 5*a**2 + 4 + t*a + 2*a**2 = 0.
-1, 2
Let d be (889/189 + -5)*-12. Determine c, given that -4/9*c**2 + 0*c - d*c**4 - 14/9*c**5 - 22/9*c**3 + 0 = 0.
-1, -2/7, 0
Let q = 2/275 + 257/2475. Let w(u) be the second derivative of -1/45*u**5 + 3*u + 0 + q*u**3 - 2/9*u**2 + 1/18*u**4. Factor w(c).
-2*(c - 2)*(c + 1)*(2*c - 1)/9
Let a(x) be the second derivative of x**7/14 + x**6/10 - 3*x**5/4 + 3*x**4/4 - 22*x. Factor a(j).
3*j**2*(j - 1)**2*(j + 3)
Let y be 4/(-6)*3 - -4. Let w be 5/40*18*(-2)/(-9). Solve -w*i**y - 1 + 3/2*i = 0 for i.
1, 2
Suppose -k = -0 - 4. Suppose -w + k*w = 21. Find j, given that w + j**4 + 2*j + 5*j**3 + 8*j**2 + 2*j - 7 = 0.
-2, -1, 0
Let y(u) be the third derivative of u**10/226800 - u**9/90720 - 2*u**5/15 - 6*u**2. Let o(h) be the third derivative of y(h). Solve o(a) = 0 for a.
0, 1
Determine y so that -3/4*y**3 + 0*y + 0 - 1/2*y**2 - 1/4*y**4 = 0.
-2, -1, 0
What is j in -1/4*j**2 - 1/2 - 3/4*j = 0?
-2, -1
Factor 4/7*f**2 + 4/7*f + 0.
4*f*(f + 1)/7
Factor -1/5*k**2 + 0 - 4/5*k.
-k*(k + 4)/5
Factor 10571 - 10571 - 8*v - 12*v**2 + 4*v**4.
4*v*(v - 2)*(v + 1)**2
Suppose -5*f - 110 = -0*f. Let p be 62/22 + (-4)/f. Find j, given that -j**p - j**2 + j**2 + j = 0.
-1, 0, 1
Let s(j) be the third derivative of j**6/240 + j**5/40 - j**3/3 + 9*j**2. Solve s(u) = 0 for u