a(z) + 14*p(z). Determine c, given that i(c) = 0.
-1, 1
Let r be (-38)/(-14) + 6/21. Let l(q) = q - 6. Let v be l(10). Find w, given that 8 - v*w**2 - 14*w**r - 8 = 0.
-2/7, 0
Suppose 4*p = 0, 0 = 5*h - 2*h + 3*p + 9. Let x be (0 - h) + 68/(-28). Find b, given that -x + 10/7*b - 6/7*b**2 = 0.
2/3, 1
Let y(b) be the first derivative of b**3 - 9*b**2 - 21*b - 14. What is c in y(c) = 0?
-1, 7
Let c(z) = z**3 + 10*z**2 + 10*z + 12. Let q be c(-9). Factor s**2 + 2*s**3 + q*s**2 - 3*s**2 - s.
s*(s + 1)*(2*s - 1)
Let c be (1/(-30))/(40/(-540)). Let x = 5/4 - c. Factor -x + 2/5*i**2 - 2/5*i.
2*(i - 2)*(i + 1)/5
Let t(z) be the third derivative of -3*z**6/160 + z**5/15 - 5*z**4/96 - z**3/12 - z**2. Factor t(d).
-(d - 1)**2*(9*d + 2)/4
Let m(q) be the second derivative of -q**7/147 - q**6/105 + q**5/35 - 3*q. Factor m(o).
-2*o**3*(o - 1)*(o + 2)/7
Let b = 13 + -15. Let w be -2*(b - (-14)/8). Determine o, given that 1/2*o**3 - 1/2*o + w*o**4 + 0 - 1/2*o**2 = 0.
-1, 0, 1
Solve -5/3*d**2 - 4/3 - 2/3*d**3 + 11/3*d = 0.
-4, 1/2, 1
Let c(q) = q**3 - 6*q**2 + 3*q - 14. Let s be c(6). Let a = s - 2. Find g, given that -2/3*g**a - 4/3 - 2*g = 0.
-2, -1
Let p(u) be the first derivative of 1/4*u**4 - 1/3*u**3 + 0*u + 0*u**2 - 2. Factor p(x).
x**2*(x - 1)
Let b(k) be the first derivative of k**5/240 + k**4/32 + k**3/12 + 4*k**2 + 6. Let r(m) be the second derivative of b(m). What is l in r(l) = 0?
-2, -1
Let x(i) be the second derivative of -i**6/600 - i**5/100 - i**4/60 + 5*i**2/2 - 2*i. Let m(q) be the first derivative of x(q). Determine p so that m(p) = 0.
-2, -1, 0
Let p be 3/(-2) + (-25)/(-15). Let k = p - -5/42. Solve -120/7*j**3 - 20/7*j + 74/7*j**2 + 72/7*j**4 + k = 0 for j.
1/3, 1/2
Let b(y) be the second derivative of y**4/24 - y**3/4 - y**2 + 28*y. Factor b(g).
(g - 4)*(g + 1)/2
Let t = 321 + -2241/7. Suppose -t*n - 4/7 - 2/7*n**2 = 0. What is n?
-2, -1
Let h(k) = -4*k**3 + 8*k**2 + 6*k + 8. Let m(v) = -v + 1. Let g(q) = 4*h(q) - 20*m(q). Factor g(a).
-4*(a - 3)*(2*a + 1)**2
What is v in 9/5*v**2 + 3/5*v - 2/5 - 2*v**3 = 0?
-1/2, 2/5, 1
Let b(y) be the third derivative of -y**8/224 + y**7/70 - y**5/20 + y**4/16 + 6*y**2. Factor b(n).
-3*n*(n - 1)**3*(n + 1)/2
Let z = -5 - -9. Factor -6*m**2 + 5*m**z - 3 + 7*m**3 - 9*m - m**3 + 3*m**5 + 4*m**4.
3*(m - 1)*(m + 1)**4
Let t(i) be the second derivative of -i**8/13440 + i**7/5040 - i**4/3 + 2*i. Let s(f) be the third derivative of t(f). Find v such that s(v) = 0.
0, 1
Find g such that 1/2*g**4 - 1/2*g**2 + 0 + 1/2*g**3 - 1/2*g = 0.
-1, 0, 1
Let q(b) = -13*b**5 + 37*b**3 + 11*b**2 - 24*b - 16. Let v(z) = 20*z**5 - 56*z**3 - 16*z**2 + 36*z + 24. Let y(f) = 8*q(f) + 5*v(f). Factor y(w).
-4*(w - 2)*(w - 1)*(w + 1)**3
Let v(c) = 3*c**3 + 9*c**2 - 3*c - 3. Let q(h) = -6*h**3 - 17*h**2 + 6*h + 6. Let l(u) = 6*q(u) + 11*v(u). Let l(o) = 0. What is o?
-1, 1
Let v be -3 + 10 + -4 + 3. Suppose -7 = v*p - 31. Factor 1/3*h**p - 2/3*h + 0*h**2 + 2/3*h**3 - 1/3.
(h - 1)*(h + 1)**3/3
Let k(h) be the third derivative of h**8/6720 + h**7/840 + h**6/240 - h**5/15 - 3*h**2. Let v(b) be the third derivative of k(b). Factor v(i).
3*(i + 1)**2
Let j(s) be the first derivative of 3*s**5/20 + 3*s**4/16 - s**3/2 + 10. Factor j(d).
3*d**2*(d - 1)*(d + 2)/4
Let o(j) be the first derivative of j**7/630 - j**6/120 + j**5/90 + 5*j**2/2 + 4. Let l(t) be the second derivative of o(t). Let l(p) = 0. Calculate p.
0, 1, 2
Factor -24*h**2 - 3 - 27/2*h - 3/2*h**5 - 21*h**3 - 9*h**4.
-3*(h + 1)**4*(h + 2)/2
Let b(g) be the second derivative of -g**7/14 - 7*g**6/10 - 27*g**5/10 - 5*g**4 - 4*g**3 - 3*g. Solve b(j) = 0 for j.
-2, -1, 0
Let u(b) = -b**2 - 4*b + 5. Let w(x) = -x**2 - 5*x + 6. Let f(k) = -6*u(k) + 5*w(k). Find r such that f(r) = 0.
0, 1
Let d(i) be the first derivative of -5 + 3/8*i**2 - 1/2*i + 0*i**3 - 1/16*i**4. What is s in d(s) = 0?
-2, 1
Let c(s) be the third derivative of -s**6/840 + s**5/420 - s**2. Solve c(w) = 0 for w.
0, 1
Factor 8*o + 2/7*o**2 + 56.
2*(o + 14)**2/7
Let t(q) be the second derivative of -q**6/180 - q**5/60 + q**3/18 + q**2/12 + q. Factor t(j).
-(j - 1)*(j + 1)**3/6
Let c(n) be the third derivative of 0*n**4 + 0*n + 1/6*n**3 - n**2 + 0 - 1/60*n**5. Determine w, given that c(w) = 0.
-1, 1
Factor -5*y**2 - 10*y**3 - 5*y**3 + 10*y**4 + 10 - 15*y**4 + 15*y.
-5*(y - 1)*(y + 1)**2*(y + 2)
Let c(a) be the third derivative of a**6/420 - a**5/210 + 30*a**2. What is l in c(l) = 0?
0, 1
Let n(c) be the first derivative of c**7/105 + c**6/10 + 13*c**5/30 + c**4 + 4*c**3/3 - 3*c**2/2 - 3. Let g(w) be the second derivative of n(w). Factor g(y).
2*(y + 1)**2*(y + 2)**2
Let y = 4 - 2. Suppose 3*h**2 - h**y + 33*h - 27*h + 4 = 0. What is h?
-2, -1
Let z = -134/11 - -424/33. Factor -1/3 + o**4 + z*o**3 - 2/3*o**2 + 1/3*o**5 - o.
(o - 1)*(o + 1)**4/3
Let n be 4 - (-3 - (-9 - -2)). What is f in -1/2*f**3 + n - 1/6*f - 2/3*f**2 = 0?
-1, -1/3, 0
Let f(z) = 12*z**3 + 16*z**2 - 12*z - 8. Let h(w) = -w**3 - w**2 + w. Let m(d) = -f(d) - 8*h(d). Factor m(c).
-4*(c - 1)*(c + 1)*(c + 2)
Let u(v) be the third derivative of -v**6/72 - v**5/36 - 11*v**2. Factor u(g).
-5*g**2*(g + 1)/3
Suppose -r + 4 = -0. Let -4*v**r + 2*v**4 + 2*v**2 + v**3 + 0*v**2 - 2*v + v**3 = 0. What is v?
-1, 0, 1
Let f be (12/396)/(1/6). Factor 0*h**3 + 0*h**2 + 0 + f*h**5 - 2/11*h**4 + 0*h.
2*h**4*(h - 1)/11
Let p(u) be the first derivative of u**5/40 - u**4/16 - u**3/24 + u**2/8 - 11. Factor p(f).
f*(f - 2)*(f - 1)*(f + 1)/8
Let v(m) be the third derivative of m**7/70 + 3*m**6/20 + 13*m**5/20 + 3*m**4/2 + 2*m**3 - 45*m**2. Factor v(y).
3*(y + 1)**2*(y + 2)**2
Factor a + a**2 + 2*a**3 + 25*a**3 - 28*a**3 - a**4.
-a*(a - 1)*(a + 1)**2
Let g(n) = 3*n**3 - 4*n**2 + 3*n - 5. Let i(s) = -s**2 + s - 1. Let d(c) = -g(c) + 5*i(c). Factor d(y).
-y*(y + 1)*(3*y - 2)
Suppose 5*h - 4*s - 8 = 3*h, 0 = 4*h + 4*s - 4. Let w = -7/6 - -59/30. Find p, given that w + 6/5*p**2 - h*p = 0.
2/3, 1
Suppose -19*u = -18*u - 2. What is y in 0 - 6/5*y**4 - 4/5*y - u*y**5 + 6/5*y**2 + 14/5*y**3 = 0?
-1, 0, 2/5, 1
Let l(y) be the first derivative of -5*y**3/9 - 5*y**2/6 + 10*y/3 + 10. Factor l(h).
-5*(h - 1)*(h + 2)/3
Determine y so that 133*y - 133*y + 4*y**4 = 0.
0
Let i(p) be the second derivative of p**5/30 + p**4/9 - p**3/9 - 2*p**2/3 - 8*p. Determine y, given that i(y) = 0.
-2, -1, 1
Let x(s) be the third derivative of 0 + 1/300*s**5 - 3*s**2 + 0*s**3 - 1/1050*s**7 + 0*s + 0*s**4 + 0*s**6. Let x(f) = 0. What is f?
-1, 0, 1
Suppose -2*j - 62 = -3*y - 6*j, 0 = -5*y - j + 92. Let p be (-24)/y - (-20)/6. Let -7/2*s - 7/2*s**p - 1 - s**3 = 0. What is s?
-2, -1, -1/2
Let r(h) be the second derivative of -7*h**5/90 + 13*h**4/27 - 13*h**3/27 - 2*h**2/3 + 19*h. Factor r(f).
-2*(f - 3)*(f - 1)*(7*f + 2)/9
Let m = -2 - -4. Let x**5 - 13*x**3 + 4*x**3 + 2*x**5 + 6*x**m = 0. What is x?
-2, 0, 1
Let v = -1 - -4. Factor -l + 4*l**3 - 8*l**3 + l**2 + 5*l**v - l**4.
-l*(l - 1)**2*(l + 1)
Let n(j) = -26*j**2 + 18*j - 9. Let r(w) = 5*w**2 - 7*w + 4*w**2 + 4 + w - 1. Let k(h) = 6*n(h) + 17*r(h). Suppose k(p) = 0. Calculate p.
1
Factor 28*z**2 + 1/4*z**5 + 0 + 39/2*z**3 + 4*z**4 + 49/4*z.
z*(z + 1)**2*(z + 7)**2/4
Factor -13*z + z**5 + 6*z - 10*z**3 - 8*z - 20*z**2 + 1 - 5.
(z - 4)*(z + 1)**4
Let r be (75 - 65) + (-67)/7. Factor 6/7*z + r*z**4 - 6/7*z**3 + 0*z**2 - 3/7.
3*(z - 1)**3*(z + 1)/7
Let m be -3*1 + 24/4. What is o in -4*o**m - 4*o**2 - 16*o**4 + 5*o**3 - 21*o**3 = 0?
-1, -1/4, 0
Let h(r) = -4*r**3 + r**2 + r - 1. Let u be h(-1). Factor 3/2*t**4 + 0 - 3/2*t**2 - 3/2*t**u + 3/2*t.
3*t*(t - 1)**2*(t + 1)/2
Let h(g) be the first derivative of -g**6/8 - 3*g**5/10 + g**3/2 + 3*g**2/8 - 2. Solve h(k) = 0.
-1, 0, 1
Determine h, given that 0 - 4/7*h**2 + 4/7*h = 0.
0, 1
Solve 8/9*m + 0 - 4/9*m**4 + 2/3*m**3 + 16/9*m**2 - 2/9*m**5 = 0.
-2, -1, 0, 2
Let y(k) = 3*k**4 - k**3 + 8*k**2 + 4*k + 8. Let t(m) = 2*m**4 - m**3 + 5*m**2 + 3*m + 5. Let w(u) = -8*t(u) + 5*y(u). Factor w(d).
-d*(d - 2)**2*(d + 1)
Let a be (-4 - -2)/(5/(-10)). Let -a*j**2 + 4 + 0 + 2*j**2 - 2*j = 0. What is j?
-2, 1
Let b(u) = u. Let i(a) = -10 + 6 - 3*a**3 - 5*a + 16*a**2 - 7*a**3. Let j(f) = -3*b(f) - i(f). What is z in j(z) = 0?
-2/5, 1
Let a(b) be the first derivative of 1 + 0*b - 1/8*b**4 + 0*b**3 + 1/4*b**2. Let a(v) = 0. Calculate 