k such that h(k) = 0.
-2, -1, 0
Let c(y) = -y**2 + 10*y - 9. Let x be c(9). Factor 1/3*g**2 - 1/3*g**4 + 0 + 0*g**3 + x*g.
-g**2*(g - 1)*(g + 1)/3
Suppose 5*h + 20 = 0, h = 4*f + 2*h - 140. Let r be f/(-21) - 6/(-3). Factor 2/7*t**4 + 0*t + 0 + 0*t**2 + r*t**3.
2*t**3*(t + 1)/7
Let v(r) be the second derivative of -r**7/14 + r**6/5 - r**4/2 + r**3/2 - 15*r. Suppose v(y) = 0. What is y?
-1, 0, 1
Let p(r) be the third derivative of 49*r**5/90 + 7*r**4/9 + 4*r**3/9 - 2*r**2. Determine b so that p(b) = 0.
-2/7
Let -147/4 - 21/2*v - 3/4*v**2 = 0. Calculate v.
-7
Let j(b) be the second derivative of b**6/150 - b**5/100 - b**4/30 + 9*b. Solve j(m) = 0 for m.
-1, 0, 2
Suppose m - 12 = -3*m. Factor -g**3 + m + g**2 - 3.
-g**2*(g - 1)
Factor 3*f**2 - 3/2*f**4 - 3/2 + 0*f + 0*f**3.
-3*(f - 1)**2*(f + 1)**2/2
Let o(f) be the second derivative of 2/15*f**3 - 11/30*f**4 + f + 11/75*f**6 + 1/5*f**5 + 0*f**2 + 0 - 4/35*f**7. Determine n so that o(n) = 0.
-1, 0, 1/4, 2/3, 1
Let r = 2/477 + 634/477. Factor -4/3*b - 8/3*b**2 + r.
-4*(b + 1)*(2*b - 1)/3
Let h(y) = -y**3 + 9*y**2 - 6*y - 10. Let p be h(8). Let 2*k + 0*k + 20*k**3 + p*k**4 - 6*k**3 + 3*k**2 + 7*k**2 = 0. What is k?
-1, -1/3, 0
Let q = -302/3 - -102. Factor q*z - 2/3*z**2 + 0.
-2*z*(z - 2)/3
Suppose -l + 5 = 2*j, 6*l + 5 = 3*j + 5*l. Suppose 4*u = -j*v - 2, -4*u = 3*v + 13 - 6. Factor 3*g + 7*g + 0*g**u - 4 - 6*g**2.
-2*(g - 1)*(3*g - 2)
Let l(c) be the second derivative of -c**6/3 - 29*c**5/30 + 7*c**4/9 + 20*c**3/9 - 8*c**2/3 - 31*c. What is o in l(o) = 0?
-2, -1, 2/5, 2/3
Let z = 27/2 - 13. Factor -z - 3/2*u - u**2.
-(u + 1)*(2*u + 1)/2
Let g = -139 - -975/7. Suppose -g*d**5 - 50/7*d**2 - 8/7 - 38/7*d**3 - 32/7*d - 2*d**4 = 0. Calculate d.
-2, -1
Let o(n) be the third derivative of -n**7/70 - 3*n**6/40 - 3*n**5/20 - n**4/8 - 2*n**2. Factor o(a).
-3*a*(a + 1)**3
Suppose 27*z**4 + 166*z**3 - z**2 - 5*z**2 - 145*z**3 = 0. Calculate z.
-1, 0, 2/9
Let g(n) be the first derivative of -n**2/2 - 3*n + 1. Let h be g(-6). Factor 4*p**4 + 4*p**2 - p**5 - p + h*p**2 - 3*p**2 - 6*p**3.
-p*(p - 1)**4
Let h(f) = 2*f**3 + f**2 - 1. Let q be h(1). Factor -2*l**2 + l**q + 0*l**2.
-l**2
Factor 6/5*d - 18/5*d**4 - 6*d**2 + 0 + 42/5*d**3.
-6*d*(d - 1)**2*(3*d - 1)/5
Let x(q) = q**2 + 6*q - 12. Let l be x(-8). Let w(c) be the first derivative of 0*c**2 + 0*c**3 + 0*c + 1/4*c**l - 1/5*c**5 + 3. Let w(y) = 0. What is y?
0, 1
Let p be 2/10 - 32/10. Let v = -1 - p. Determine h so that 1/4*h**4 + 1/4*h + 0 - 1/4*h**3 - 1/4*h**v = 0.
-1, 0, 1
Let j(h) be the second derivative of -h**6/15 - 3*h**5/10 - 3*h - 11. Solve j(b) = 0 for b.
-3, 0
Let 3/5*u**3 + 0 - 3/5*u**4 - 3/5*u + 3/5*u**2 = 0. What is u?
-1, 0, 1
Suppose 5 = 4*f - 3. Factor -14 - 2*m**f + 14 + 4*m + 0*m**2.
-2*m*(m - 2)
Let w(g) = 5*g**5 - g**4 + g**3 - 5*g**2 - 6*g + 6. Let m(c) = c**4 - c**3 + c - 1. Let n(r) = -6*m(r) - w(r). Determine x so that n(x) = 0.
-1, 0, 1
Let d(v) be the second derivative of 1/48*v**4 + 0 - 1/6*v**3 + 1/2*v**2 + 3*v. Determine n, given that d(n) = 0.
2
Let s(y) be the third derivative of y**7/5040 - y**4/6 + 4*y**2. Let z(k) be the second derivative of s(k). Factor z(x).
x**2/2
Factor -10/7 - 2/7*z + 8/7*z**2.
2*(z + 1)*(4*z - 5)/7
Determine w, given that -4*w**2 - 4*w**3 + 31*w**4 - 2*w**5 - 39*w**4 - 6*w**3 = 0.
-2, -1, 0
Let u(c) be the second derivative of c**2 + 0*c**5 + 0 + 0*c**3 + 2*c - 1/360*c**6 + 0*c**4. Let y(w) be the first derivative of u(w). Factor y(b).
-b**3/3
Let b(y) be the third derivative of y**8/5040 + y**7/840 + y**6/360 + y**5/360 - 2*y**3/3 + 6*y**2. Let j(g) be the first derivative of b(g). Factor j(w).
w*(w + 1)**3/3
Let g(i) be the third derivative of -i**7/735 + i**6/60 - 3*i**5/70 - 9*i**4/28 + 18*i**3/7 + 15*i**2. What is q in g(q) = 0?
-2, 3
Let m(f) be the first derivative of f**4/2 - f**3/3 - 7*f**2/16 - f/8 + 22. Let m(t) = 0. Calculate t.
-1/4, 1
Let h(r) be the first derivative of 1/45*r**6 + 1/30*r**5 + 2 - 1/18*r**4 - 1/9*r**3 + r + 0*r**2. Let o(p) be the first derivative of h(p). Factor o(b).
2*b*(b - 1)*(b + 1)**2/3
Let n = 15 + -22. Let a be ((-2)/n)/((-8)/(-14)). Solve -3/2*w**2 + 0 - 1/2*w - a*w**4 - 3/2*w**3 = 0.
-1, 0
Let q be (8/(-12))/((-2)/18). Suppose -m - 2*m = -q. What is y in 0*y - 3/4*y**3 + 0*y**4 + 1/4*y**5 + 1/2*y**m + 0 = 0?
-2, 0, 1
Let f(x) be the third derivative of x**8/2184 - x**7/455 + 2*x**5/195 - 8*x**2. Factor f(u).
2*u**2*(u - 2)**2*(u + 1)/13
Let s(j) be the second derivative of 3*j**5/140 - 3*j**4/28 + 6*j**2/7 - 5*j. Factor s(d).
3*(d - 2)**2*(d + 1)/7
Find z, given that -118/5*z**2 - 24/5 - 9/5*z**4 - 92/5*z - 57/5*z**3 = 0.
-3, -2, -2/3
Find t such that -5/3*t + 0*t**3 - 10/3*t**2 + 0 + 10/3*t**4 + 5/3*t**5 = 0.
-1, 0, 1
Let w(a) be the third derivative of -3*a**6/200 + a**5/25 - a**4/30 + 26*a**2. Determine q so that w(q) = 0.
0, 2/3
Factor -2/5*d**2 + 2/5*d + 0.
-2*d*(d - 1)/5
Let o be 4/(-7) + (-486)/(-42) + -11. What is r in o*r - 3/4*r**3 - 1/4*r**5 + 0 + 3/4*r**4 + 1/4*r**2 = 0?
0, 1
Let b be (2 + -3 + 2)/(-1). Let d be 2 + 0 + b + 1. Let -2 + d*k**2 + 2*k + 2 = 0. Calculate k.
-1, 0
Let s(b) = b**2 - b - 1. Let w(d) = -3*d**2 + 3*d + 2. Let p(o) = -4*s(o) - w(o). Factor p(u).
-(u - 2)*(u + 1)
Let r be (-20)/15*(-3 - 0). Let p(q) be the second derivative of -1/35*q**6 - 2/21*q**3 + 0*q**2 - 1/6*q**r + 0 - 4/35*q**5 + 2*q. Find u, given that p(u) = 0.
-1, -2/3, 0
Let r = 3/2 - 1. Let i(j) be the first derivative of -r*j - 1/8*j**4 + 3 + 1/6*j**3 + 1/4*j**2. Factor i(k).
-(k - 1)**2*(k + 1)/2
Factor -7*h**2 - 7 + 3*h**2 + 23.
-4*(h - 2)*(h + 2)
Let o = 0 - -4. Let h(y) be the third derivative of y**2 + 1/180*y**5 + 0 + 1/630*y**7 + 0*y**3 + 1/180*y**6 + 0*y**o + 0*y. Factor h(f).
f**2*(f + 1)**2/3
Let r be (-1*33)/(9/(-6)). Let f = -64/3 + r. Determine j, given that f*j + 1/3 - 2/3*j**3 + j**4 - 4/3*j**2 = 0.
-1, -1/3, 1
Let u = -9 - -11. Let q(x) = x**3 + 2*x**2 - 3*x. Let c(j) = -j**2 + j. Let l(p) = u*c(p) + q(p). Suppose l(z) = 0. What is z?
-1, 0, 1
Let f = -1/81 - -55/81. Factor 0 - 2/3*b**3 + 0*b**2 - f*b**4 + 0*b.
-2*b**3*(b + 1)/3
Let j(s) be the third derivative of 1/12*s**4 + 0*s + 1/180*s**6 + 0 - 4*s**2 - 1/9*s**3 - 1/30*s**5. Factor j(a).
2*(a - 1)**3/3
Let i(c) be the third derivative of -c**5/300 + c**4/24 - 27*c**2. Suppose i(n) = 0. What is n?
0, 5
Let b = 10/241 - 31139/1205. Let i = 132/5 + b. What is c in i*c + 0*c**2 - 1/5*c**3 + 2/5 = 0?
-1, 2
Let w(b) be the second derivative of b**7/14 + 2*b**6/5 + 9*b**5/20 - b**4 - 2*b**3 - 5*b. Solve w(t) = 0 for t.
-2, -1, 0, 1
Let a(g) be the first derivative of -g**4/30 + 4*g**3/45 - g**2/15 + 2. Factor a(z).
-2*z*(z - 1)**2/15
Let a be 175/(-60) - (2 - 5). Let j(p) be the third derivative of 0*p + 0*p**5 + 2*p**2 + 0 + 0*p**3 - 1/60*p**6 + a*p**4. Find c, given that j(c) = 0.
-1, 0, 1
Let w(z) be the first derivative of 57/2*z**2 + 45/2*z**4 + 9 + 9*z + 15/4*z**5 + 159/4*z**3. What is i in w(i) = 0?
-3, -1, -2/5
Let d(w) be the second derivative of w**4/6 - 5*w**3/3 + 17*w. Determine x so that d(x) = 0.
0, 5
Let h = -16 - -16. What is i in h + 1/2*i - 1/4*i**2 = 0?
0, 2
Let a = -180 - -1262/7. Solve -a*x - 2/7*x**2 + 0 = 0 for x.
-1, 0
Let -2/5*n**2 + 0 - 4/5*n = 0. Calculate n.
-2, 0
Let c(z) be the first derivative of -2*z**5/15 - z**4/6 + 2*z**3/3 + z**2/3 - 4*z/3 + 46. Suppose c(b) = 0. Calculate b.
-2, -1, 1
Let j(k) = -k + 4. Let d be j(2). Factor -8*l**3 + 11*l + 0*l - 3*l + 2*l**d - 2.
-2*(l - 1)*(l + 1)*(4*l - 1)
Let g(o) be the first derivative of 1/3*o**3 - 1/5*o**5 + 0*o + 0*o**2 + 0*o**4 - 3. Factor g(b).
-b**2*(b - 1)*(b + 1)
Let v be 12/(-30)*5/(-6). Factor -1/3*a + 0 - v*a**2.
-a*(a + 1)/3
Let c(f) be the first derivative of 3 - 1/5*f**5 + 0*f**2 - 2/3*f**3 + 0*f + 3/4*f**4. Suppose c(a) = 0. What is a?
0, 1, 2
Let o(x) be the first derivative of 8*x**3/3 + 18*x**2 + 28*x - 14. Factor o(n).
4*(n + 1)*(2*n + 7)
Suppose -19*v + 14*v = -15. Suppose -4*x = 3*n - 18, -2*n + v*x = x + 2. Find i, given that 3*i**n - 4/3*i**3 + 0 - 2/3*i = 0.
0, 1/4, 2
Let q(f) be the third derivative of -f**7/1260 + f**6/60 - 3*f**5/20 - f**4/8 + 4*f**2. Let a(p) be the second derivative of q(p). What is m in a(m) = 0?
3
Let i(v) be the first derivative of -2/5*v**4 + 72/25*v**5 + 0*v**2 + 0*v 