ative of 6/5*g**5 - 5/4*g**4 + 3 + 5/2*g**2 + g - 7/3*g**3. Determine p so that f(p) = 0.
-1, -1/6, 1
Let h(w) be the second derivative of 1/15*w**5 + 1/45*w**6 - 2*w - 2/9*w**3 - 1/3*w**2 + 0 + 0*w**4. What is t in h(t) = 0?
-1, 1
Let r(w) be the first derivative of w**3/9 - w/3 + 2. Factor r(l).
(l - 1)*(l + 1)/3
Determine b so that -381*b**4 + 9*b**3 - 60*b**2 - 45*b + b**3 - 5*b**5 + 401*b**4 = 0.
-1, 0, 3
Factor 1/3*p**3 + 1/6*p**2 - 1/3*p + 0 - 1/6*p**4.
-p*(p - 2)*(p - 1)*(p + 1)/6
Let i = -8 - -11. Suppose -2*y**i - y**2 + y**2 + 2*y**2 + 4*y = 0. Calculate y.
-1, 0, 2
Let j = 16 - -71. Let o = -41 + j. Let -29*y - 17*y**3 + 3*y**3 + o*y**2 + 8 - 11*y = 0. Calculate y.
2/7, 1, 2
Let w be 14/(-6)*(-4)/(-14). Let d = w + 13/15. Find i, given that -i - d*i**3 + 2/5 + 4/5*i**2 = 0.
1, 2
Let t(h) be the third derivative of -h**5/20 - 5*h**4/24 - h**3/3 - 2*h**2. Factor t(a).
-(a + 1)*(3*a + 2)
Let x(w) be the second derivative of -w + w**2 - 1/120*w**5 + 0*w**3 + 0 + 1/48*w**4. Let n(q) be the first derivative of x(q). Suppose n(f) = 0. Calculate f.
0, 1
Let p(u) be the second derivative of u**6/15 - 3*u**5/10 + u**4/3 + 2*u. Find i such that p(i) = 0.
0, 1, 2
Let h(o) be the third derivative of -o**6/6 + o**5/5 + o**4/8 - o**3/3 - 10*o**2. Find z such that h(z) = 0.
-2/5, 1/2
Suppose -4*c + 8*c = 8. Determine r so that 6*r**2 + 12*r**c - 20*r**2 = 0.
0
Let x(t) be the first derivative of -t**8/420 - 4*t**7/525 + 2*t**5/75 + t**4/30 + 3*t**2/2 - 1. Let f(w) be the second derivative of x(w). Factor f(h).
-4*h*(h - 1)*(h + 1)**3/5
Let i = -5 - -59. Solve 11*p - 1 - 29*p - 54*p**3 - i*p**2 - 1 = 0.
-1/3
Let h be (-6)/(-180)*6 - (-74)/30. Factor -4/3 - h*v + 5/3*v**2.
(v - 2)*(5*v + 2)/3
Let o be (1/2)/(1/6). Solve -x**5 + 3*x**4 - 2*x**5 + 6*x**5 - 3*x**o - 3*x**2 + 0*x**3 = 0.
-1, 0, 1
Let t(i) = 21*i**2 + 3*i - 5. Let n(q) = -10*q**2 - 2*q + 2. Let l(j) = -13*n(j) - 6*t(j). Factor l(p).
4*(p + 1)**2
Let i be -4 + 8/(120/63). Let l(n) be the first derivative of -1/10*n**2 - 2/5*n + 1 - 1/25*n**5 + i*n**3 + 1/20*n**4. Let l(m) = 0. Calculate m.
-1, 1, 2
Factor 9 + 12*i**3 + 6*i**3 + 23*i + 22*i - 3*i**5 - 12*i - 3*i**4 + 42*i**2.
-3*(i - 3)*(i + 1)**4
Suppose 0 = -0*b - 2*b + i, 4*b = 3*i. Let u(g) be the first derivative of -1/14*g**4 - 2/21*g**3 + 0*g**2 + b*g + 1. Determine h so that u(h) = 0.
-1, 0
Factor l**5 - 358 + 358 - 3*l**3 + 2*l**2.
l**2*(l - 1)**2*(l + 2)
Let z(h) be the first derivative of 1/8*h**2 + 0*h + 1/6*h**3 + 3 + 1/16*h**4. Factor z(i).
i*(i + 1)**2/4
Let m(o) = -o**2 + 12*o - 9. Let n be m(11). Let c = n - 0. Solve 0*u + 2*u**2 - c*u - 4*u**2 = 0.
-1, 0
Let o = 1 - 1. Let b = 3 - o. Suppose 2 - x**3 - 3 + x + 2*x**2 + 0*x**b - 1 = 0. Calculate x.
-1, 1, 2
Let i be (-234)/819 - 13/(-21). Factor 1/3*y**3 - i*y + 2/3*y**2 - 2/3.
(y - 1)*(y + 1)*(y + 2)/3
Let k(q) = q - 3. Let t be k(5). Let x be 4 + (4 + -3 - 0). Let -1/3*w**4 + 1/3*w**t + 1/3*w**x + 0*w - 1/3*w**3 + 0 = 0. What is w?
-1, 0, 1
Let k(j) = -7*j**2 - 7*j + 5. Let h(i) = 18*i**2 + 18*i - 12. Let x(o) = 5*h(o) + 12*k(o). Let a(c) = -c**2. Let f(z) = -3*a(z) - x(z). Factor f(n).
-3*n*(n + 2)
Let r(o) = o**3. Let g(n) = n**2 + 4*n + 1. Let j be g(-4). Let f(a) = 3*a**2 - 4. Let s(x) = j*r(x) - f(x). Let s(y) = 0. What is y?
-1, 2
Let v = -4492986/24445 - 1/4889. Let l = -183 - v. Factor 12/5*c**3 + 0*c - 9/5*c**4 + 0 - l*c**2.
-c**2*(3*c - 2)**2/5
Suppose u - 6 = -0*f - f, u + 3*f = 14. Let -q**3 + 7*q**3 - 7*q**3 + q**2 + u*q = 0. Calculate q.
-1, 0, 2
Factor 1/3*x**3 + 0*x**2 - 1/3*x + 0.
x*(x - 1)*(x + 1)/3
Let a be ((-12)/2)/(3/(-2)). Let x(d) be the second derivative of 0*d**2 - d + 0 - 1/12*d**a - 1/9*d**3. Factor x(p).
-p*(3*p + 2)/3
Let f(b) be the third derivative of b**7/21 + 7*b**6/60 + b**5/15 - 4*b**2. Factor f(t).
2*t**2*(t + 1)*(5*t + 2)
Let f be ((-27)/24)/((-21)/28). What is w in 9/2*w - 9/2*w**2 + f*w**3 - 3/2 = 0?
1
Find k, given that 3/5*k**3 - 3/5*k**5 + 0*k + 0 - 2/5*k**2 + 2/5*k**4 = 0.
-1, 0, 2/3, 1
Find q such that 0*q + 3/2*q**4 + 0*q**2 + 3/2*q**3 + 0 = 0.
-1, 0
Let q = -3/10 - -7/10. Factor 2/5*f**4 + q*f + 6/5*f**3 + 0 + 6/5*f**2.
2*f*(f + 1)**3/5
Let i(d) be the first derivative of 5*d**3/3 - 20*d**2 + 80*d + 21. Solve i(r) = 0.
4
Factor 7*a**4 - 7*a**4 + 3 + 12*a**3 + 14*a**2 + 4*a**2 + 12*a + 3*a**4.
3*(a + 1)**4
Let i(u) be the third derivative of 1/480*u**6 + 0*u**3 + 0*u + 0*u**5 + 0 - 1/840*u**7 + u**2 + 0*u**4. Let i(l) = 0. Calculate l.
0, 1
Let w(o) be the third derivative of o**7/5040 - o**6/720 + o**5/240 - o**4/4 + 3*o**2. Let u(h) be the second derivative of w(h). Factor u(m).
(m - 1)**2/2
Let m(x) be the third derivative of x**6/300 - x**5/75 - 7*x**4/60 - 4*x**3/15 - 3*x**2. Determine l so that m(l) = 0.
-1, 4
Suppose 1/4 - 1/4*j**2 + 0*j = 0. Calculate j.
-1, 1
Let x be ((-13)/(-4) - 3)*1. Factor -x*s**3 - 1 - 5/4*s**2 - 2*s.
-(s + 1)*(s + 2)**2/4
Find p, given that 1/6*p - 1 + p**2 - 1/6*p**3 = 0.
-1, 1, 6
Let r = -1 + 2. Let 3*g + 0 + 2*g**2 + 0*g**2 + 0*g + r = 0. Calculate g.
-1, -1/2
Let w(k) be the second derivative of k**6/300 + k**5/50 + 7*k**2/2 + 5*k. Let f(c) be the first derivative of w(c). Let f(s) = 0. What is s?
-3, 0
Let m(z) be the second derivative of 1/8*z**3 + 0 + 1/48*z**4 + 8*z + 1/4*z**2. Factor m(a).
(a + 1)*(a + 2)/4
Let j be (0 - -1)*435/(-9). Let b = j - -49. Factor 0 + 0*l + b*l**3 + 7/3*l**4 - 1/3*l**2 + 4/3*l**5.
l**2*(l + 1)**2*(4*l - 1)/3
Let y(m) = 18*m**3 - 24*m**2 + 6*m + 9. Let x(b) = 19*b**3 - 24*b**2 + 7*b + 10. Let f(a) = -3*x(a) + 4*y(a). Determine c, given that f(c) = 0.
-2/5, 1
Let r(j) be the second derivative of -j**4/3 - 80*j**3/3 - 800*j**2 - 35*j. Factor r(i).
-4*(i + 20)**2
Let b(n) be the third derivative of n**6/360 - n**5/20 + 5*n**4/24 - 7*n**3/18 - 14*n**2. Let b(j) = 0. What is j?
1, 7
Factor -2*q**2 + 16 - 6*q**2 + 4*q**3 - 4*q**2.
4*(q - 2)**2*(q + 1)
Factor -4*y**2 + 0 + 8/5*y + 4/5*y**4 + 12/5*y**3 - 4/5*y**5.
-4*y*(y - 1)**3*(y + 2)/5
Let a be (-4)/(-10) - 12/30. Suppose -3*b + 5*b = a. Solve b + 0*h + 1/4*h**2 = 0.
0
Let z = 10 - 8. Suppose -t**z - t - t + 0*t = 0. Calculate t.
-2, 0
Factor 3*f**4 - 4*f**2 + f**4 + 4*f + f**3 + 7*f**3 - 12*f.
4*f*(f - 1)*(f + 1)*(f + 2)
Suppose 2*s - 22 = 3*s. Let j(c) = -c**3 + 4*c**2 - 3*c - 2. Let o(l) = -5*l**3 + 21*l**2 - 16*l - 11. Let m(b) = s*j(b) + 4*o(b). Factor m(y).
2*y*(y - 1)**2
Factor 3/2*u - 3/2*u**3 - 3 + 3*u**2.
-3*(u - 2)*(u - 1)*(u + 1)/2
Let j(m) = -3*m**3 - 12*m**2 - 7*m - 2. Let i(y) = 35*y**3 + 145*y**2 + 85*y + 25. Let r(p) = 2*i(p) + 25*j(p). Find u, given that r(u) = 0.
-1, 0
Factor 0 + 2/9*l**2 + 0*l - 8/9*l**4 - 2/3*l**3.
-2*l**2*(l + 1)*(4*l - 1)/9
Let d(o) be the second derivative of -3*o**5/100 - o**4/20 + 13*o. Determine z, given that d(z) = 0.
-1, 0
Let d = 6 + -6. Suppose 2*s + 5*i = 0, 0 = -s + i - d*i. Determine h so that 1/2*h**2 - 1/2 + s*h = 0.
-1, 1
Let r(d) be the third derivative of -d**6/600 + d**2. Factor r(g).
-g**3/5
Let s be ((-4)/2)/2*-5. Suppose 0 = -4*v - 4*l + 4, -3*l - 3 = -s*v - 6*l. Factor -2 - 7*q + v + 2*q**2 + 7*q**2.
(q - 1)*(9*q + 2)
Let -1/3*i**2 + 0*i + 1/3 = 0. Calculate i.
-1, 1
Let a(t) be the first derivative of -t**6/39 + 8*t**5/65 - 3*t**4/13 + 8*t**3/39 - t**2/13 + 7. Factor a(r).
-2*r*(r - 1)**4/13
Let y(d) be the first derivative of 2*d**3/21 - 2*d**2/7 - 5. Determine b, given that y(b) = 0.
0, 2
Let i = -16/11 - -43/22. Let n(x) be the second derivative of -1/10*x**5 - 2/3*x**3 - 3*x + 0 + i*x**4 + 0*x**2. Let n(y) = 0. What is y?
0, 1, 2
Let t = 171361/420 - 408. Let w(a) be the third derivative of 0*a**3 - 1/24*a**4 - t*a**7 + 0*a + 1/120*a**6 - 3*a**2 + 1/120*a**5 + 0. Factor w(f).
-f*(f - 2)*(f - 1)*(f + 1)/2
Let f(k) be the first derivative of -2*k**5/75 + 2*k**3/15 - 2*k**2/15 + 8. Factor f(q).
-2*q*(q - 1)**2*(q + 2)/15
Let f(c) be the second derivative of c**5/4 - 5*c**4/3 + 25*c**3/6 - 5*c**2 + 9*c. Factor f(p).
5*(p - 2)*(p - 1)**2
Let r = 29 - 24. Let s(h) be the third derivative of 1/60*h**r - 1/6*h**4 + 0 + 2/3*h**3 + 4*h**2 + 0*h. Factor s(p).
(p - 2)**2
Factor -2*c + 8/11*c**2 + 12/11 + 2/11*c**3.
2*(c - 1)**2*(c + 6)/11
Let x(a) = 3*a**2 + 4 - 7*a**2 - 4 - 2*a**3. Let i(w) = -3*w**3 - 5*w**2. Let q(t) = 4*i(t) - 5*x(t). Factor q(k).
-2