ne p so that q(p) = 0.
-1, 3
Let g = -18 - -4. Let u be (0 + 0)/(28/g). Factor -1/3*p + u + 1/3*p**2.
p*(p - 1)/3
Suppose 2*k - 14 = 2*t, 0*k - 9 = 3*t + k. Let p be ((-30)/(-80))/((-3)/t). Factor 3/4*u**4 - 1/4 - 1/4*u**5 - p*u**3 - 1/2*u**2 + 3/4*u.
-(u - 1)**4*(u + 1)/4
Let z(i) be the second derivative of i**8/4200 + i**7/1050 + i**6/900 - 5*i**3/6 - 8*i. Let h(g) be the second derivative of z(g). Factor h(b).
2*b**2*(b + 1)**2/5
Let w = 4 + -2. Suppose 0 - 4*a**w + 2*a - 2*a**5 + 4*a**4 + 0 = 0. What is a?
-1, 0, 1
Suppose 2*z + z - 4*i = -4, 3*z + 5*i + 22 = 0. Let k(m) = -m**3 - 4*m. Let o(x) = 2*x**3 + x**2 + 8*x. Let r(n) = z*o(n) - 7*k(n). Suppose r(l) = 0. What is l?
-2, 0
Suppose 4*d = -11 + 35. Let n = d - 1. Factor -p + 2*p**5 + 2*p**3 + 2*p**5 - p**5 - 4*p**n.
-p*(p - 1)**2*(p + 1)**2
Suppose -36 - 12 = -12*o. Let b(f) be the second derivative of 0*f**2 - 1/60*f**6 + 4*f + 0*f**5 + 1/8*f**o - 1/6*f**3 + 0. Suppose b(n) = 0. Calculate n.
-2, 0, 1
Let n(u) be the third derivative of u**8/1680 + 2*u**7/525 + u**6/100 + u**5/75 + u**4/120 - 12*u**2. Factor n(w).
w*(w + 1)**4/5
Let c(i) = i**2 - 3*i + 3. Let x be c(3). Let n(q) = q**3 - 4*q**2 + 4*q. Let s be n(x). What is u in -5*u**4 + 2*u - u**s + u**2 + 4*u**4 - u = 0?
-1, 0, 1
Suppose 2*s + 2*s = 16. Let t(q) be the second derivative of 1/12*q**s + 0*q**2 + 1/20*q**5 + 0 + 2*q - 1/30*q**6 - 1/6*q**3. What is k in t(k) = 0?
-1, 0, 1
Let w(h) be the third derivative of 5*h**8/336 + h**7/42 - h**6/24 - h**5/12 + 45*h**2. Factor w(s).
5*s**2*(s - 1)*(s + 1)**2
Let w = -3 + 4. Let i(k) = k**4 - k**3 + k**2. Let x(d) = 4*d**4 - 10*d**3 + 10*d**2 - 3*d. Let m(u) = w*x(u) - i(u). Factor m(j).
3*j*(j - 1)**3
Let w(b) = -6*b**3 + 3*b. Let c(i) = 11*i**3 - 5*i. Let j(f) = 3*c(f) + 5*w(f). Factor j(y).
3*y**3
Factor -d**2 - 4*d**3 + 5*d**3 - 3*d**2 + 3*d**2.
d**2*(d - 1)
Let p(j) = 4*j - 4. Let w be p(2). Let g(v) be the second derivative of -v + 0 - 5/18*v**3 - 1/60*v**5 + 1/9*v**w + 1/3*v**2. Find m, given that g(m) = 0.
1, 2
Factor -6*z - 6/5*z**2 + 0.
-6*z*(z + 5)/5
Let 39 + 5*a**2 - 14 - 10*a - 21 - 19 = 0. Calculate a.
-1, 3
Let w(d) be the second derivative of -d**6/5 - 2*d**5/5 - d**4/6 - 6*d. Suppose w(i) = 0. Calculate i.
-1, -1/3, 0
Let i(z) = -z**5 - z**4 + z**2 + z - 1. Let r(y) = -3*y**5 - 6*y**4 - 5*y**3 + 2*y - 2. Let l(b) = -2*i(b) + r(b). Factor l(f).
-f**2*(f + 1)**2*(f + 2)
Suppose 0 - 2/3*s**3 + 0*s - 4/9*s**2 = 0. What is s?
-2/3, 0
Let u be 44/(-55)*(-5)/14. Factor 0*s**2 + 0*s + u*s**3 + 0 - 2/7*s**5 + 0*s**4.
-2*s**3*(s - 1)*(s + 1)/7
Let w(v) be the second derivative of 3*v**5/140 + 3*v**4/14 + 5*v**3/14 - 12*v - 2. Solve w(z) = 0 for z.
-5, -1, 0
Find h such that -17*h**4 - 9*h**4 - 18*h**3 - 15*h**4 + 27*h**4 - 4*h**2 = 0.
-1, -2/7, 0
Solve 38*j - 8 - 33*j**3 + 4*j**5 + 89*j**3 + 6*j - 24*j**4 - 64*j**2 - 8*j = 0 for j.
1, 2
Let r = -29 - -89/3. Factor -l**3 - 2/3 + l + r*l**2.
-(l - 1)*(l + 1)*(3*l - 2)/3
Let w(c) be the second derivative of -c**8/9240 + c**7/2310 - c**6/1980 - 11*c**3/6 + 5*c. Let u(j) be the second derivative of w(j). Factor u(y).
-2*y**2*(y - 1)**2/11
Let b(y) be the third derivative of 4*y**2 - 1/600*y**6 + 0*y**4 + 1/300*y**5 + 0*y**3 + 0 + 0*y. Factor b(w).
-w**2*(w - 1)/5
Determine k, given that 4*k**3 - 3*k + k + 2 + 2*k**4 - 2*k**5 - 4*k**2 + 0*k = 0.
-1, 1
Suppose 0 = 2*i - 5 - 1. Suppose 7*z - 5 = 2*q + 2*z, i*q = -5*z + 5. Determine k, given that q + 1/3*k**3 - 1/3*k + 0*k**2 = 0.
-1, 0, 1
Let v(o) be the third derivative of 0*o + 0 + 7*o**2 - 1/60*o**5 + 1/8*o**4 - 1/3*o**3. Determine a, given that v(a) = 0.
1, 2
Let r(c) = 2*c**4 + 10*c**2 + 4*c + 8. Let n(f) = f**3 + f + 1. Let l(v) = 8*n(v) - r(v). Find d, given that l(d) = 0.
0, 1, 2
Let z(h) be the second derivative of 2/5*h**6 + 0 - 1/2*h**4 - 3*h**2 - 1/14*h**7 + 5/2*h**3 - 3/5*h**5 + 2*h. Factor z(w).
-3*(w - 2)*(w - 1)**3*(w + 1)
Let k be -3*(-10 + (-56)/(-6)). Factor 8/3 - 8/3*a + 2/3*a**k.
2*(a - 2)**2/3
Factor 3*z**2 + 4*z**2 + 1 - 8*z**2 + 0.
-(z - 1)*(z + 1)
Let p(m) = -m - 1. Let j be p(0). Let q = j + 3. Factor 2*d + 3*d**q + 6 + 3*d + 4*d.
3*(d + 1)*(d + 2)
Find x such that 8/7*x**3 + 22/7*x - 4/7 - 26/7*x**2 = 0.
1/4, 1, 2
Factor 0*u + 0 + 0*u**2 - 1/3*u**4 - 1/3*u**3.
-u**3*(u + 1)/3
Let k = 1 - 3. Let q = k + 4. Factor -4*y**q + y**3 + 2*y - 2*y + 4*y.
y*(y - 2)**2
Let g(q) = q. Let i(r) = r**2 + 10*r - 9. Let t(m) = -4*g(m) + 2*i(m). Solve t(s) = 0 for s.
-9, 1
Let t(p) be the first derivative of p**6/33 - 6*p**5/55 + 3*p**4/22 - 2*p**3/33 + 3. Factor t(o).
2*o**2*(o - 1)**3/11
Let u be (3/(-27))/((-14)/3). Let g(a) be the second derivative of u*a**7 + 0*a**3 + 0*a**5 - 3*a + 0 + 0*a**4 + 0*a**2 + 0*a**6. Suppose g(p) = 0. What is p?
0
Let p(u) be the second derivative of -1/54*u**4 + 0*u**2 + 0*u**3 + 0 + 3*u. Factor p(v).
-2*v**2/9
Let i(f) be the second derivative of -f**4/28 - f**3/21 + 6*f. Factor i(y).
-y*(3*y + 2)/7
Suppose -2*h = -0*h - 4. Let q(g) be the second derivative of 2*g + 1/4*g**h + 0*g**3 + 0 - 1/24*g**4. Factor q(k).
-(k - 1)*(k + 1)/2
Let c(h) be the third derivative of -1/6*h**4 + 6*h**2 + 0*h - 7/40*h**6 + 7/30*h**7 + 0 + 0*h**3 - 2/5*h**5. Factor c(a).
a*(a - 1)*(7*a + 2)**2
Let k(o) be the third derivative of o**7/420 - o**6/60 + o**5/20 - o**4/12 + o**3/12 + 17*o**2. Factor k(u).
(u - 1)**4/2
Let i(g) be the second derivative of -g**9/11880 - g**8/2310 - g**7/3465 + g**4/4 + 6*g. Let w(y) be the third derivative of i(y). Let w(z) = 0. What is z?
-2, -2/7, 0
Let d(x) = -5*x**3 + 11*x**2 - 8*x - 3. Let m(h) = 44*h**3 - 98*h**2 + 72*h + 26. Let a(n) = -52*d(n) - 6*m(n). Factor a(q).
-4*q*(q - 2)**2
Let p(g) be the second derivative of -g**7/168 + g**6/120 + g**5/80 - g**4/48 + 11*g. Factor p(j).
-j**2*(j - 1)**2*(j + 1)/4
Factor 2/5*f**5 - 4/5*f**3 + 0 + 0*f**2 + 2/5*f**4 + 0*f.
2*f**3*(f - 1)*(f + 2)/5
Let s be (-9)/15 - 2247/(-45). Let h = 50 - s. Factor -2/3 + 4/3*y - h*y**2.
-2*(y - 1)**2/3
Suppose 0*d = 4*g - 2*d - 8, 5*g - 23 = -4*d. Suppose -c**g - 2*c + 2*c - 2*c**2 + 3*c - 4*c = 0. What is c?
-1, 0
Let b = 2 + -2. Suppose b = -d - 3*d + 8. Factor -2*t**3 + 0*t**2 - 4*t**2 + d*t**2.
-2*t**2*(t + 1)
Let m(x) be the first derivative of 0*x**3 + 0*x + 0*x**4 - 1/10*x**5 - 2 + 0*x**2. Find s, given that m(s) = 0.
0
Let b(g) be the second derivative of -g**5/12 + g**4/12 + g**3/9 + g. Factor b(x).
-x*(x - 1)*(5*x + 2)/3
Let a(s) = s**3 + 3*s**2 - s + 1. Let i(k) = 4*k**3 + 13*k**2 - 4*k + 5. Let x(o) = 18*a(o) - 4*i(o). Factor x(c).
2*(c - 1)*(c + 1)**2
Let k(o) = 6*o**2 + 33*o + 102. Let m(n) = 17*n**2 + 100*n + 308. Let t(b) = 8*k(b) - 3*m(b). Solve t(s) = 0.
-6
Let y(h) = -5*h**4 + 3*h**3 + 25*h**2 + 13*h - 2. Let d(t) = 10*t**4 - 5*t**3 - 50*t**2 - 25*t + 5. Let p(c) = 2*d(c) + 5*y(c). Determine m so that p(m) = 0.
-1, 0, 3
Suppose 4*l = 3*l - 3*l. Solve 0*t - 2/3*t**4 + l*t**2 + 0 - 2/3*t**3 = 0.
-1, 0
Let z(x) be the second derivative of -x**5/120 - x**4/12 - x**3/3 + x**2/2 + 2*x. Let b(n) be the first derivative of z(n). Factor b(l).
-(l + 2)**2/2
Suppose 4*s - 35 = -5*i, -3*i - 1 + 10 = 0. Factor -2*m**s + m**3 + 5*m**5 - 4*m**3 + 6*m**3 - 6*m**4.
3*m**3*(m - 1)**2
Let c**2 - 7*c + 3*c - 46 + c**3 + 42 = 0. What is c?
-2, -1, 2
Let v be (-104)/(-306) - (-10)/(-1700)*20. Factor 2/9*c**3 + v*c**2 - 4/9*c + 0.
2*c*(c - 1)*(c + 2)/9
Let w(r) be the second derivative of -r**7/588 - r**6/180 - r**5/210 + r**3/3 - 2*r. Let u(y) be the second derivative of w(y). Find a such that u(a) = 0.
-1, -2/5, 0
Let k be (-4)/16 + (-6)/8 + 1. Let i(l) be the third derivative of 0*l + 4/15*l**3 + k + 1/150*l**5 + 4*l**2 - 1/15*l**4. Suppose i(h) = 0. What is h?
2
Let p be ((-1)/(-30))/(-2*3/(-3)). Let g(f) be the second derivative of 1/6*f**3 + p*f**5 + 1/6*f**2 + 1/12*f**4 + f + 0. Factor g(t).
(t + 1)**3/3
Factor -12 + 46*i**2 - 18*i**3 - 36*i - 3*i**4 - 112*i**2 + 27*i**2.
-3*(i + 1)**2*(i + 2)**2
Let o = -6 + 8. Let -5*v - 2*v + 5*v - 2*v**o = 0. What is v?
-1, 0
Let c(j) = j**2 - j. Let w(p) = -4*p**2 - p + 9. Let d(u) = -5*c(u) - w(u). Factor d(q).
-(q - 3)**2
Factor 0*c - 3/4*c**2 + 0 + 3/4*c**3.
3*c**2*(c - 1)/4
Let d(r) = 9*r**2 + 3*r - 7. Let i(u) be the second derivative of 5*u**4/12 + u**3/6 - 3*u**2/2 - 2*u. Let g(h) = 3*d(h) - 5*