). Find s, given that h(s) = 0.
-1, 2
Suppose 0 = -k + 6*k + 10. Let b = 6 - k. Factor -2*s**2 + 0 + 7*s + s - b.
-2*(s - 2)**2
Let d(h) = -6*h**2 + 40*h + 24. Let w(t) = t**2 + 7*t + t + 5 - 2*t**2. Let q(z) = -3*d(z) + 16*w(z). Suppose q(i) = 0. What is i?
-2
Let q = 3 - -7. Let k be (-2)/q + 27/35. Factor -2/7 - 2/7*p**2 + k*p.
-2*(p - 1)**2/7
Factor 0 + 1/2*k + 1/4*k**2 - 1/2*k**3 - 1/4*k**4.
-k*(k - 1)*(k + 1)*(k + 2)/4
Let p(c) = -3*c**2 + 7 - 3*c**2 - 6*c + 6*c + 4*c. Let s(g) = -7*g**2 + 5*g + 8. Let q(f) = -6*p(f) + 5*s(f). Factor q(l).
(l - 1)*(l + 2)
Let w(v) = v**2 - 4*v - 3. Let q be w(5). Determine c, given that -c**2 - 8*c**2 - 3*c + 12*c**q = 0.
0, 1
Let s(u) = 6*u**2. Let v(r) = 2*r**2. Let b(k) = -3*s(k) + 8*v(k). Let b(j) = 0. Calculate j.
0
Let x(a) be the third derivative of -a**6/360 - a**5/30 - a**4/6 + a**3/6 + a**2. Let t(m) be the first derivative of x(m). Determine r so that t(r) = 0.
-2
Suppose -3*o = -g - 4*g + 4, -o - g + 4 = 0. Let w(y) be the first derivative of o - 2/3*y**3 + 0*y - 1/2*y**2 - 1/4*y**4. Factor w(n).
-n*(n + 1)**2
Suppose 4*m - 45 = m. Factor m*o**3 - 175 - 12*o**4 - 6*o**2 + 175 + 3*o**5.
3*o**2*(o - 2)*(o - 1)**2
Find i, given that -2 - 1/3*i**2 + 7/3*i = 0.
1, 6
Let t(y) = -3*y**2 - 1. Let j be t(3). Let f = -28 - j. Factor f*x - 1/3 - 1/3*x**4 + 2/3*x**2 + 0*x**3.
-(x - 1)**2*(x + 1)**2/3
Let s(m) be the second derivative of -m**6/75 - m**5/100 - 31*m. Find o such that s(o) = 0.
-1/2, 0
Let f(x) be the third derivative of x**5/20 + x**4/8 - 7*x**2. Find i such that f(i) = 0.
-1, 0
Factor 0*i - 4/3 + 4/3*i**2.
4*(i - 1)*(i + 1)/3
Let c(p) be the first derivative of -p**7/735 - 3*p**2/2 + 2. Let q(g) be the second derivative of c(g). Suppose q(z) = 0. Calculate z.
0
Let a(q) be the second derivative of -q**4/48 - q**3/3 - 2*q**2 + 23*q. Factor a(l).
-(l + 4)**2/4
Solve d - 1/4*d**2 - 3/4 = 0.
1, 3
Let s(j) be the first derivative of 2/3*j**2 + 11/12*j**4 - 3 + 11/30*j**5 + 1/18*j**6 + 10/9*j**3 + j. Let k(t) be the first derivative of s(t). Factor k(g).
(g + 1)**2*(g + 2)*(5*g + 2)/3
Suppose 0 = 9*t - 55 + 1. Let r(n) be the third derivative of 0*n**4 - 1/15*n**5 - 1/60*n**t + 3*n**2 + 0*n + 0 + 0*n**3. What is m in r(m) = 0?
-2, 0
Factor 1/4*z**2 + 0 + 0*z + 1/4*z**3.
z**2*(z + 1)/4
Let r(q) be the second derivative of 0 + 0*q**2 - 2*q + 1/3*q**4 + 1/20*q**5 + 2/3*q**3. Find t such that r(t) = 0.
-2, 0
Let b = -56 + 56. Find w such that 0 - 2/7*w - 2/7*w**5 + b*w**4 + 0*w**2 + 4/7*w**3 = 0.
-1, 0, 1
Solve 290*p**3 + 108*p**4 + 12*p**4 + 3*p**5 + 16 + 300*p**2 + 120*p + 15*p**5 = 0.
-2, -1/3
Factor -4/19*d + 2/19 + 2/19*d**2.
2*(d - 1)**2/19
Let u(i) be the second derivative of -i**6/195 - 2*i**5/65 - 5*i**4/78 - 2*i**3/39 + 16*i. Let u(w) = 0. Calculate w.
-2, -1, 0
Let s(d) be the third derivative of 0*d - 2/55*d**5 + 0 + 4*d**2 + 1/33*d**4 + 1/1848*d**8 - 2/385*d**7 + 13/660*d**6 + 0*d**3. Suppose s(t) = 0. Calculate t.
0, 1, 2
Let u(q) be the second derivative of q**6/45 - q**4/9 + q**2/3 - 14*q. Factor u(b).
2*(b - 1)**2*(b + 1)**2/3
Let l(p) = -6*p**2 + 23*p. Let x(a) = -5*a**2 + 8*a + 4. Let r(t) = -9*t**2 + 15*t + 7. Let j(n) = 4*r(n) - 7*x(n). Let g(i) = 34*j(i) - 6*l(i). Factor g(m).
2*m*(m - 1)
Let h = -382/3 + 135. Solve h*k**3 - 4*k + 4/3 + k**2 - 9*k**4 + 3*k**5 = 0 for k.
-2/3, 2/3, 1
Let z = -20 + 21. Let a be 12/36*1/z. Find p, given that -1/3*p**2 + 0 + 0*p + a*p**3 = 0.
0, 1
Let i be (-2)/(1/(-1)) - 24/15. Factor 6/5*x**3 + 6/5*x**2 + 2/5*x**4 + i*x + 0.
2*x*(x + 1)**3/5
Factor 8*v**5 - 17*v**5 + 10*v**5.
v**5
Let w = 0 + 9. Find z, given that 5*z**2 - 12 + 0 - w*z**2 + 16*z = 0.
1, 3
Factor 12*d**3 + 14*d**3 + 12*d - 29*d**3.
-3*d*(d - 2)*(d + 2)
Let t(h) be the first derivative of 1/2*h**6 + 0*h - 12/5*h**5 + 3/2*h**2 - 1 - 4*h**3 + 9/2*h**4. Solve t(b) = 0.
0, 1
Let o(h) be the first derivative of 3*h**4/4 - 4*h**3 + 6*h**2 - 24. Factor o(f).
3*f*(f - 2)**2
Let w(q) be the first derivative of 0*q - 1/40*q**5 + 1/2*q**2 + 2 + 1/3*q**3 - 1/12*q**4. Let u(i) be the second derivative of w(i). What is v in u(v) = 0?
-2, 2/3
Let u be (-44)/(-12) - (-2)/(-3). Let 2*p**5 - 4*p + u*p + 3*p - 4*p**3 = 0. What is p?
-1, 0, 1
Let o be ((1 - -1) + -2)/2. Let d(l) = -l**2 - 12*l. Let z be d(-12). Solve h**2 + z*h**2 - h + o*h**2 = 0 for h.
0, 1
Let n(m) be the second derivative of -m**8/168 - m**7/105 + 3*m**2/2 + 3*m. Let i(t) be the first derivative of n(t). Factor i(a).
-2*a**4*(a + 1)
Let d = 189 + -187. Let q(j) be the second derivative of -1/60*j**5 + d*j + 0*j**3 + 0 + 0*j**2 - 1/36*j**4. Suppose q(h) = 0. Calculate h.
-1, 0
Let h = 234/271 + 48449/9485. Let t = h + -39/7. Factor 4/5*u**2 - 2/5*u**4 + 2/5*u**5 + t*u - 4/5*u**3 - 2/5.
2*(u - 1)**3*(u + 1)**2/5
Suppose w = 3*c - 13, 5 = -c - 4*w - 8. Let -c*f**2 + 3 + 3*f**4 - 3*f**2 - 3 + 3 = 0. Calculate f.
-1, 1
Let i(y) be the first derivative of 4*y**6/15 + y**5/2 - y**4/2 - 5*y**3/3 - y**2 - 4*y + 3. Let j(u) be the first derivative of i(u). Factor j(o).
2*(o - 1)*(o + 1)**2*(4*o + 1)
Let k(q) be the first derivative of 3*q**6/40 + q**5/5 - 5*q**4/8 - q**3 + q**2/2 - 4. Let c(p) be the second derivative of k(p). Let c(x) = 0. Calculate x.
-2, -1/3, 1
Suppose -4*f + 5 + 0 = 3*k, 2*k + 5*f - 1 = 0. What is d in 4/5 + 2/5*d**k + 8/5*d**2 + 2*d = 0?
-2, -1
Let q(m) be the second derivative of 5*m + 0*m**2 + 0*m**3 - 1/54*m**4 + 0. Find t, given that q(t) = 0.
0
Let g(f) = 2*f**2 - f - 1. Let i be g(2). Suppose i*w = 6 + 4. Solve -s + 1 + 2*s**w + 3 - 5*s = 0.
1, 2
Let g(b) be the second derivative of 0 + 1/6*b**3 + 0*b**2 - 3*b + 1/12*b**4. Factor g(y).
y*(y + 1)
Let w be -1 - ((-667)/276 + (-6)/(-8)). Let -2/3*y**3 + 0 - 4/3*y**2 - w*y = 0. Calculate y.
-1, 0
Suppose w + 7*w - 32 = 0. Let m(a) be the third derivative of 1/60*a**6 + 0 - 1/12*a**w + 2/3*a**3 + 0*a - 4*a**2 - 1/15*a**5. Suppose m(k) = 0. Calculate k.
-1, 1, 2
Let y be (-4)/18 - (-50)/(-18). Let m(x) = -2*x**2 - 8*x - 5. Let j(p) = -6*p**2 - 24*p - 16. Let v(s) = y*j(s) + 8*m(s). Factor v(z).
2*(z + 2)**2
Let z = -8 - -8. Suppose -2*r = -z*r. Factor r + 1/2*a - 1/2*a**2.
-a*(a - 1)/2
Let q(i) = 4*i**3 - 13*i**2 + 10*i + 13. Let x(o) = -o**3 + 5*o - 9*o**2 + 9 + 4*o**3 + 2*o. Let y(z) = -5*q(z) + 7*x(z). Determine k so that y(k) = 0.
-2, -1, 1
Suppose -v + 3*t = 7, 2*v - 3*v - 2*t = -8. Factor 18 + 2/3*x**3 + 6*x**v + 18*x.
2*(x + 3)**3/3
Let o(h) = -12*h**4 - 16*h**3 - 4*h**2 + 10*h - 10. Let d(r) = -r**3 + r + r**4 - 1 + 0*r - 2*r**4. Let q(n) = 10*d(n) - o(n). Factor q(b).
2*b**2*(b + 1)*(b + 2)
Let p(f) be the first derivative of 3*f**4/16 + 7*f**3/6 + 5*f**2/2 + 2*f + 2. Factor p(u).
(u + 2)**2*(3*u + 2)/4
Suppose -6/5*u**5 - 3*u**3 + 21/5*u - 18/5 - 27/5*u**4 + 9*u**2 = 0. What is u?
-3, -2, -1, 1/2, 1
Factor 22*k**3 + 0*k**2 + 8*k**4 + 2*k**2 - 12*k**3.
2*k**2*(k + 1)*(4*k + 1)
Let s(g) be the first derivative of 3 - 2*g**3 + 3*g**2 + 1/2*g**4 - 2*g. Factor s(q).
2*(q - 1)**3
Suppose -3*s = 4*s. Let l(w) be the second derivative of -3*w - 1/63*w**7 + 0*w**5 + s + 0*w**2 - 1/9*w**4 + 2/45*w**6 + 1/9*w**3. Factor l(y).
-2*y*(y - 1)**3*(y + 1)/3
Let u(m) be the third derivative of -1/315*m**7 - 1/9*m**3 + 0*m**6 + 0 + 0*m + 1/45*m**5 + m**2 + 0*m**4. Find h such that u(h) = 0.
-1, 1
Let l be (-3)/7 - (-16)/21. Factor l*z**2 - z + 2/3.
(z - 2)*(z - 1)/3
Suppose 2*v = 4*v - 14. Factor 25*r + 8 - 81*r**2 + v*r + 4 + 4*r.
-3*(3*r - 2)*(9*r + 2)
Let f(h) be the first derivative of 3 + h**2 - 4/3*h**3 - 1/2*h**4 + 4*h. Find s such that f(s) = 0.
-2, -1, 1
Suppose -4*u + 3*t - 6 + 0 = 0, -3*t = -2*u - 6. Let i(p) be the third derivative of 2/105*p**5 - 1/21*p**3 + u - p**2 + 0*p - 1/28*p**4. Factor i(m).
2*(m - 1)*(4*m + 1)/7
Factor -2/5*i**5 - 4/5*i + 2*i**4 - 18/5*i**3 + 14/5*i**2 + 0.
-2*i*(i - 2)*(i - 1)**3/5
Let r(o) be the third derivative of o**5/690 + o**4/92 + 9*o**2. Factor r(n).
2*n*(n + 3)/23
Let w(b) be the first derivative of 6*b**5/25 + b**4/5 - 2*b**3/15 + 4. Determine h, given that w(h) = 0.
-1, 0, 1/3
Let q be 4 - 0 - (5 + -1). Let n(v) be the third derivative of q*v**4 + 0*v + 0 - 3*v**2 + 1/6*v**3 - 1/60*v**5. Determine m so that n(m) = 0.
-1, 1
Suppose 3/8*z**4 + 0 + 3/8*z**5 - 3/8*z**2 + 3/4*z - 9/8*z**3 = 0. What is z?
-2, -1, 0, 1
Let o be (