the third derivative of y(x). Factor b(f).
3*(f - 1)**2*(f + 2)
Let x(t) be the second derivative of -2*t**7/105 - 2*t**6/25 + 2*t**5/25 + 2*t**4/5 - 2*t**3/15 - 6*t**2/5 - 22*t. Find g, given that x(g) = 0.
-3, -1, 1
Let n = 19/8 + -79/40. Factor 0 - 6/5*q**4 + n*q**5 + 0*q + 0*q**2 + 4/5*q**3.
2*q**3*(q - 2)*(q - 1)/5
Let p(k) = -k**2 - 3*k - 2. Let j be p(-1). Suppose -2*x - 3*b = j, -5*x - 3*b = -x. Solve x + 3/2*d**5 - 4*d**4 + 7/2*d**3 + 0*d - d**2 = 0 for d.
0, 2/3, 1
Let y(f) be the first derivative of f**6/180 - f**5/90 - f**4/36 + f**3/9 + 2*f**2 + 4. Let a(x) be the second derivative of y(x). Find s, given that a(s) = 0.
-1, 1
Factor -8/11 - 2/11*z**3 + 0*z + 6/11*z**2.
-2*(z - 2)**2*(z + 1)/11
Let t(q) = -8*q**4 - 16*q**3 + 8*q**2 - q - 17. Let i(c) = -c**4 - 2*c**3 + c**2 - 2. Let p(d) = -51*i(d) + 6*t(d). Determine g so that p(g) = 0.
-2, -1, 0, 1
Let m(j) be the second derivative of j**8/43680 - j**7/16380 - j**6/4680 + j**5/780 + j**4/12 + j. Let a(b) be the third derivative of m(b). Factor a(h).
2*(h - 1)**2*(h + 1)/13
Let v = 81/70 + -5/14. Determine j so that -2/5*j - 2/5*j**5 + 4/5*j**3 + v*j**2 - 2/5*j**4 - 2/5 = 0.
-1, 1
Let x(f) be the second derivative of -f**4/12 - 5*f**3/6 - 2*f**2 - 12*f. Factor x(o).
-(o + 1)*(o + 4)
Let z(p) = 26*p**2 + 15*p - 6. Let q(j) = -j**2. Suppose -13 = -5*b - 4*x, -2*b + x = -5*b + 5. Let f(y) = b*z(y) + 5*q(y). Factor f(k).
3*(k + 1)*(7*k - 2)
Let -69*d**2 + 6*d**2 - 2*d**3 + 90*d**3 + 4*d + 336*d**4 + 196*d**5 + 15*d**2 = 0. Calculate d.
-1, 0, 1/7
Let v be (12/55)/(3/5). Let 2/11*i**3 + 10/11*i**5 - v*i**2 + 16/11*i**4 + 0 + 0*i = 0. What is i?
-1, 0, 2/5
Let x be (-4)/22 - (-248)/396. Factor -2/9*j**2 - x + 2/3*j.
-2*(j - 2)*(j - 1)/9
What is l in -53*l**4 + 3*l**3 - 4*l**5 - 12*l + l**5 + 6*l**3 + 47*l**4 + 12*l**2 = 0?
-2, 0, 1
Let d = -7/181 + 557/362. Factor -d*x**2 + 0*x + 0 + 3/2*x**3.
3*x**2*(x - 1)/2
Let a = -1088/9 + 121. Let k(d) be the second derivative of a*d**3 + 1/18*d**4 - 2/3*d**2 + 2*d + 0. Determine h, given that k(h) = 0.
-2, 1
Let x(d) be the third derivative of -d**7/1995 - d**6/570 + d**5/570 + d**4/114 + 2*d**2. Determine w so that x(w) = 0.
-2, -1, 0, 1
Suppose -17*c + 22 + 12 = 0. Factor z**c + 3/2*z - 1/2*z**5 - 3/2*z**4 - z**3 + 1/2.
-(z - 1)*(z + 1)**4/2
Let j = 77 + -49. Suppose 0 = -2*g - b, 5*g - 5*b - j = g. Factor 2*x - x**2 - 2*x**2 - g*x.
-3*x**2
Let n(i) be the first derivative of -i**3 - 9*i**2/2 - 6*i - 29. Factor n(w).
-3*(w + 1)*(w + 2)
Suppose 0*x + 0 + 3/2*x**5 + 3/2*x**4 + 0*x**2 - 3*x**3 = 0. Calculate x.
-2, 0, 1
Let s be (-5)/(-1) + (2 - 5). What is i in -10*i**5 - 4*i**s + 4*i**2 + 4*i**4 - 4*i**2 + 10*i**3 = 0?
-1, 0, 2/5, 1
Let s(c) be the first derivative of c**3/6 + c**2 - 5*c/2 + 29. Factor s(u).
(u - 1)*(u + 5)/2
Let f(h) be the third derivative of 1/12*h**4 + 0*h + 1/6*h**3 + 0 + 2*h**2 + 1/60*h**5. Factor f(y).
(y + 1)**2
Let x be (-6)/(-4)*(-16)/21. Let c = x + 10/7. Factor 0 + 2/7*f**3 - 2/7*f - c*f**2 + 2/7*f**4.
2*f*(f - 1)*(f + 1)**2/7
Suppose c + 4*l - 4 = 0, -c - c + l = -8. Factor 0 + 3*j**2 - j**2 + 3*j**4 - 1 - c*j**4.
-(j - 1)**2*(j + 1)**2
Factor 1/9*h**3 + 0 + 2/3*h - 5/9*h**2.
h*(h - 3)*(h - 2)/9
What is q in 2/11*q**4 - 6/11*q**3 + 0 + 6/11*q**2 - 2/11*q = 0?
0, 1
Suppose -c = -g + 6, g - 2*c - 11 = -6*c. Let s = g - 13/2. Determine o, given that -s - 1/2*o**2 - o = 0.
-1
Let v(p) be the second derivative of 3*p**5/40 - p**4/4 + p**3/4 - p. Factor v(g).
3*g*(g - 1)**2/2
Let s(a) be the third derivative of -a**6/60 - a**5/15 - a**4/12 - 17*a**2. Determine r, given that s(r) = 0.
-1, 0
Let y be ((-1)/(-7))/(168/49). Let d(t) be the third derivative of 0*t**3 + 0*t - 1/30*t**7 + 1/30*t**5 + t**2 - y*t**6 + 0*t**4 + 0. Factor d(q).
-q**2*(q + 1)*(7*q - 2)
Let i(l) be the first derivative of l**7/540 - l**6/135 + l**5/180 + l**4/54 + l**3/3 - 6. Let m(h) be the third derivative of i(h). What is a in m(a) = 0?
-2/7, 1
Factor -6*q**4 - 2/3*q**5 - 22*q - 20*q**3 - 6 - 92/3*q**2.
-2*(q + 1)**3*(q + 3)**2/3
Let r be 0/22*(9/6 - 1). Let p = 2 - 0. Factor 2*f**3 + 1/2*f + r + 7/4*f**p + 3/4*f**4.
f*(f + 1)**2*(3*f + 2)/4
Let s(r) = r. Let b(i) = 12*i**2 - 3*i**2 + 3*i - 8*i**2. Let f(k) = 2*b(k) - 4*s(k). Determine j so that f(j) = 0.
-1, 0
Let w(n) = n - 8. Let m be w(6). Let a(o) = o**2 + 2*o. Let v be a(m). Suppose 2/9*i + 0 + v*i**2 - 2/9*i**3 = 0. Calculate i.
-1, 0, 1
Let m = -5 - -9. Let b(x) be the third derivative of 0*x**m + 0*x + 1/120*x**6 - 3*x**2 - 1/210*x**7 + 0 + 1/30*x**5 + 0*x**3. Factor b(s).
-s**2*(s - 2)*(s + 1)
Suppose 0 = -3*m + m - 3*g + 8, -2*m - 5*g = -4. Let c(j) = -j**3 + 7*j**2 + 2*j - 10. Let r be c(m). Factor x**r - x**4 + 2*x**4 - 2*x**5.
-2*x**4*(x - 1)
Let o(s) be the first derivative of 11*s**4/3 + 6*s**3 - 4*s**2 + 9*s + 8. Let j(p) be the first derivative of o(p). Factor j(k).
4*(k + 1)*(11*k - 2)
Let z be ((-14)/42)/((-1)/6). Let x(m) be the second derivative of 2/3*m**3 + 0 + z*m + 1/6*m**4 + 0*m**2. Factor x(i).
2*i*(i + 2)
Let d = -69 - -69. Let f(b) be the second derivative of 0 + 1/18*b**4 + b - 1/18*b**3 + 0*b**2 - 1/45*b**6 + d*b**5 + 1/126*b**7. Factor f(i).
i*(i - 1)**3*(i + 1)/3
Let d(n) = 3*n**4 - 7*n**3 + 2*n**2 + 7*n. Let s(a) = 2*a**4 - 6*a**3 + 2*a**2 + 6*a. Let v(b) = -4*d(b) + 5*s(b). Solve v(o) = 0.
-1, 0, 1
Suppose 4 = -2*h + 10. Let k(s) be the second derivative of 0*s**5 + 1/5*s**2 - 1/15*s**4 + 1/75*s**6 + 0*s**h + 0 - 2*s. Factor k(w).
2*(w - 1)**2*(w + 1)**2/5
Let c(p) be the third derivative of -p**5/12 + 5*p**4/8 + 10*p**3/3 + 2*p**2 - 2. Factor c(o).
-5*(o - 4)*(o + 1)
Let k = -22 - -43. Let n(z) = z**2 - z + 1. Let d(c) = c**3 - 5*c**2 + 8*c - 7. Let g(w) = k*n(w) + 3*d(w). Suppose g(s) = 0. Calculate s.
-1, 0
Let q be (0 - (-2)/4)/2. Find g such that -1/2*g - 1/4 - q*g**2 = 0.
-1
Let f(a) = -2*a**2 + 4*a - 10. Let x(s) = -1. Suppose -64 = 6*h - 2*h. Let m = 8 + h. Let i(j) = m*x(j) + f(j). Factor i(u).
-2*(u - 1)**2
Let l = 253/3 - 84. Let 0 + 1/3*i - l*i**4 - i**2 + i**3 = 0. What is i?
0, 1
Let b(c) be the second derivative of 3*c**5/20 + 3*c**4/4 + 3*c**3/2 + 3*c**2/2 + 5*c. Factor b(y).
3*(y + 1)**3
Let i(p) be the second derivative of -3*p**5/20 + p**4/4 + p**3/2 - 3*p**2/2 - 9*p. Factor i(s).
-3*(s - 1)**2*(s + 1)
Let a(r) be the first derivative of -r**8/5040 - r**7/2520 + 2*r**3/3 + 2. Let l(i) be the third derivative of a(i). Find t, given that l(t) = 0.
-1, 0
Let 2*j**3 + 0*j + 7*j**4 - 2*j - j**4 + 4 - 10*j**2 + 0 = 0. What is j?
-1, 2/3, 1
Let i(f) = -63*f**3 - 5*f**2 + 5. Let t(q) = -94*q**3 - 7*q**2 + 7. Let k(s) = -7*i(s) + 5*t(s). Let p be k(-1). Let -d**2 - d**2 + p*d - 31*d = 0. Calculate d.
-1, 0
Let b(o) be the first derivative of 18*o**2 + 15*o**5 + 12*o - 45/2*o**4 + 1 - 11*o**3. Factor b(m).
3*(m - 1)**2*(5*m + 2)**2
Determine y so that 2/9*y**2 + 1/9*y**3 + 0*y + 0 = 0.
-2, 0
Factor 1/10*c**4 + 3/10*c**3 - 3/10*c - 1/2*c**2 + 2/5.
(c - 1)**2*(c + 1)*(c + 4)/10
Let t(u) be the third derivative of u**5/60 - 7*u**4/24 + 2*u**3/3 + u**2. Let l be t(7). Find o such that -6 - l*o**2 + 9*o - 3*o**2 + 3*o**2 + o**2 = 0.
1, 2
Factor 2/11 + 0*t - 2/11*t**2.
-2*(t - 1)*(t + 1)/11
Let d(g) be the second derivative of g**6/120 - g**5/30 + g**4/24 + g**2/2 + g. Let m(b) be the first derivative of d(b). Factor m(s).
s*(s - 1)**2
Suppose -8*n + 21 = -5*n - 3*m, 2*n + 4*m + 10 = 0. Determine q so that 1/2 + 1/4*q**n + 5/4*q + q**2 = 0.
-2, -1
Let d(x) = x**4 + x**3 + x + 1. Let p(i) = -6*i**4 - 6*i**3 + i**2 - 4*i - 5. Let a(w) = -5*d(w) - p(w). Factor a(v).
v*(v - 1)*(v + 1)**2
Suppose -4*i + 5*i**2 + 3*i**2 - 2*i - 2*i**3 = 0. What is i?
0, 1, 3
Let l(q) = -q**3 - 11*q**2 - 10*q - 6. Let c be l(-10). Let m = 8 + c. Factor -z - 1 - 1/4*z**m.
-(z + 2)**2/4
Let o(s) be the third derivative of 0*s**3 + 1/96*s**4 - 1/480*s**6 + 0 + 0*s + 0*s**5 - 4*s**2. Factor o(p).
-p*(p - 1)*(p + 1)/4
Determine b, given that 3/2*b - 3*b**3 + 3/2*b**5 + 3*b**4 + 3 - 6*b**2 = 0.
-2, -1, 1
Let d(v) be the third derivative of v**6/720 + 5*v**2. Factor d(s).
s**3/6
Let g(x) be the first derivative of -2/15*x**3 + 0*x - 2/5*x**2 + 1/10*x**4 + 3. Find j such that g(j) = 0.
-1, 0, 2
Let m be (3/(-6))/(2/4). Let j = 3 + m. Factor -2*g**5 + 7*g**5 - 9*g**3 - 2*g**5 - 4*g + j*g*