 + 5/4*a**4 - 3*a**3 + 3. Factor c(m).
-(m - 2)*(m - 1)**3
Let c(h) be the second derivative of -2*h**7/21 - 4*h**6/75 + 2*h**5/5 + 4*h**4/15 - 2*h**3/3 - 4*h**2/5 - 19*h. Solve c(l) = 0 for l.
-1, -2/5, 1
Suppose -5 - 9 = -j. Let u = 17 - j. Factor 2/9*h**4 + 0*h**2 - 2/9*h**u + 0*h + 0.
2*h**3*(h - 1)/9
Let l(k) be the second derivative of k**5/100 - k**4/15 + 2*k**3/15 + 4*k. Factor l(s).
s*(s - 2)**2/5
Let u(h) be the first derivative of h**3/21 + 11*h**2/14 + 10*h/7 + 54. Factor u(o).
(o + 1)*(o + 10)/7
Let x(t) be the first derivative of -9/2*t**2 + 2*t + 4*t**3 - 5/4*t**4 - 6. Factor x(g).
-(g - 1)**2*(5*g - 2)
Let -6*u + 4*u**2 - 17*u**2 + 2*u - 6*u**3 + 23*u**2 = 0. Calculate u.
0, 2/3, 1
Factor 16*x**2 + 19*x**2 + x - 32*x**2 - 4*x - 6.
3*(x - 2)*(x + 1)
Let i(l) = 2*l - 4. Let b be i(2). Let s(g) be the third derivative of 0 - 1/120*g**6 + 0*g**3 - 3*g**2 + 0*g + 1/24*g**4 + b*g**5. Factor s(z).
-z*(z - 1)*(z + 1)
Let r(c) be the second derivative of 0*c**2 + 1/36*c**4 - 1/90*c**6 + 0 - 9*c + 1/60*c**5 - 1/18*c**3. Determine v, given that r(v) = 0.
-1, 0, 1
Factor 0*d + 2/7*d**4 + 0*d**3 + 2/7 - 4/7*d**2.
2*(d - 1)**2*(d + 1)**2/7
Factor 0*p**2 - 2/13*p**5 + 0*p + 0 + 4/13*p**3 - 2/13*p**4.
-2*p**3*(p - 1)*(p + 2)/13
Let u be 38/10 - 5/(-25). Let v(t) be the first derivative of 0*t + 1/5*t**2 - 4/15*t**3 + 1/10*t**u + 3. Determine d, given that v(d) = 0.
0, 1
Let a = 2743/168 - 114/7. Let i(x) be the third derivative of 1/40*x**6 + 0*x + 4*x**2 - 1/20*x**5 + a*x**4 - 1/210*x**7 + 0 + 0*x**3. Factor i(u).
-u*(u - 1)**3
Let p(u) be the first derivative of -u**6/60 + u**5/15 - u**4/12 - u**2/2 - 1. Let m(j) be the second derivative of p(j). Factor m(h).
-2*h*(h - 1)**2
Let f(s) be the first derivative of -s**7/105 + s**6/30 - s**2 - 1. Let x(t) be the second derivative of f(t). What is b in x(b) = 0?
0, 2
Let i(c) be the third derivative of c**7/840 - c**6/160 + c**5/240 + c**4/32 - c**3/12 - 21*c**2. Suppose i(x) = 0. What is x?
-1, 1, 2
Let p = 6 + -3. Suppose 3*t + 5 - 17 = 0. Factor 3*l**p - 6*l**3 + t*l**4 - 2*l**2 - 2*l**4 + 3*l**5.
l**2*(l - 1)*(l + 1)*(3*l + 2)
Suppose -3*c + 15 = 2*n, -2*n - 9 = -3*c - 2*c. Let -1 - 5/3*j**2 + 7/3*j + 1/3*j**n = 0. Calculate j.
1, 3
Let r be (-34)/(-10) - (-8)/(-20). Let b(f) be the first derivative of 10/3*f**r + 2*f**2 - 2*f**5 - f**4 + 0*f - 1. Find c, given that b(c) = 0.
-1, -2/5, 0, 1
Factor -1/8*m**4 - 125/2*m - 75/4*m**2 - 625/8 - 5/2*m**3.
-(m + 5)**4/8
Let b(x) = x + 12. Let v be b(-9). Factor -4 + 2 + 1 + v*z + z**3 - 3*z**2.
(z - 1)**3
Factor 2*f**2 + 37*f - 37*f - 2.
2*(f - 1)*(f + 1)
Let w(i) be the second derivative of 21*i**4 - 8*i**3/3 - 8*i**2 + 21*i. Factor w(g).
4*(7*g - 2)*(9*g + 2)
Let f be (-5)/(-3) - 44/(-33). Suppose 3*h - g = 14, -5*h + 4*g - 5*g = -26. Factor 2/5*w**h + 0*w**f + 0 + 0*w + 0*w**2 + 2/5*w**4.
2*w**4*(w + 1)/5
Let x = 23/4 - 5. Suppose 1/4*a**4 - 1/2 + 1/4*a**2 - 3/4*a + x*a**3 = 0. What is a?
-2, -1, 1
Let w(r) be the first derivative of 9*r**4/4 + 2*r**3 - 9*r**2/2 - 6*r - 11. Factor w(a).
3*(a - 1)*(a + 1)*(3*a + 2)
Let l(n) = -21*n**4 - 36*n**3 - 9*n**2 + 8*n. Let w(p) = -105*p**4 - 180*p**3 - 45*p**2 + 41*p. Let a(g) = 11*l(g) - 2*w(g). Factor a(b).
-3*b*(b + 1)**2*(7*b - 2)
Suppose 0*r + 4*r - 16 = 0. Let c(o) be the first derivative of -2 - 2/9*o - 1/9*o**r + 0*o**2 + 2/9*o**3. Factor c(f).
-2*(f - 1)**2*(2*f + 1)/9
Let k be ((-4)/(-20))/((-2)/(-5)). Let i be 0 - 1 - (-3 + 0). Find o such that 1/2*o + k*o**i - 1/2*o**3 - 1/2 = 0.
-1, 1
Factor -2 - 10*o**2 - 6*o**2 - 9*o + 0*o**5 - o**5 - 7*o**3 - 6*o**4 - 7*o**3.
-(o + 1)**4*(o + 2)
Let m be (-1)/(1/1 + 27/(-18)). Solve -4/7 + 0*u**m - 6/7*u + 2/7*u**3 = 0.
-1, 2
Let w(c) be the second derivative of c**6/180 - c**5/60 - c**4/72 + c**3/18 + 3*c. Factor w(u).
u*(u - 2)*(u - 1)*(u + 1)/6
Let q(s) be the third derivative of 0*s + 0 + 1/60*s**6 + 0*s**3 + 3*s**2 - 2/15*s**5 + 1/3*s**4. Factor q(i).
2*i*(i - 2)**2
Let c(q) be the third derivative of -q**8/840 + q**6/180 - q**3/6 + q**2. Let s(k) be the first derivative of c(k). Suppose s(r) = 0. What is r?
-1, 0, 1
Let j(a) = a**3 - a**2 + a. Let p(n) = -8*n**3 - 4. Let z(y) = 12*j(y) + p(y). Determine s so that z(s) = 0.
1
Let d(o) be the first derivative of -1/6*o**2 - 2/3*o + 1/9*o**3 - 1. Factor d(m).
(m - 2)*(m + 1)/3
Suppose -3*o + 11 = -5*z, -2 = -3*z - 2*o - 1. Let h be (3 - 1)/(z/(-1)). Factor 2*x**4 + 1 + 2*x**3 - x + 2*x**4 - 2*x**h - x**5 - 3*x**4.
-(x - 1)**3*(x + 1)**2
Let h(v) = -5*v**4 - 10*v**3 + 8*v**2 + 10*v. Let s(l) = -5*l**4 - 10*l**3 + 9*l**2 + 10*l. Let d(r) = 4*h(r) - 3*s(r). Factor d(q).
-5*q*(q - 1)*(q + 1)*(q + 2)
Let j(f) be the third derivative of 1/210*f**7 + 0 - 1/60*f**5 - 1/336*f**8 + 0*f**3 + 0*f**4 + 1/120*f**6 + 0*f + 2*f**2. What is m in j(m) = 0?
-1, 0, 1
Let m(a) = -3*a**3 - a**2 - a + 1. Let v(d) = d**3 + d**2 + d - 1. Let n be (-2)/10 + 8/(-10). Let r(f) = n*m(f) - 2*v(f). Suppose r(q) = 0. Calculate q.
-1, 1
Suppose 4*g - 2*g = 0. Suppose 5*x - 3*a + 12 = 0, g = -4*x + 2*x + 5*a - 20. Factor -2/9 + 2/9*u**4 + x*u**2 - 4/9*u**3 + 4/9*u.
2*(u - 1)**3*(u + 1)/9
Let p(f) be the second derivative of 0*f**3 + 0 - 1/50*f**5 + 1/150*f**6 + 0*f**2 + 1/60*f**4 - f. Let p(k) = 0. What is k?
0, 1
Let r(p) be the first derivative of -p**6 - 8*p**5/5 - p**4/2 - 6. What is b in r(b) = 0?
-1, -1/3, 0
Let w(x) be the second derivative of -x**6/60 - x**5/8 - x**4/6 + 14*x. Let w(y) = 0. What is y?
-4, -1, 0
Let a(b) = 7*b**2 + 5*b + 3. Let j(p) = 3*p**2 + 2*p + 1. Let s(o) = 2*a(o) - 5*j(o). Solve s(y) = 0.
-1, 1
Let p(q) be the third derivative of -q**5/120 - q**4/8 - 2*q**3/3 + 56*q**2. Factor p(g).
-(g + 2)*(g + 4)/2
Let d(t) be the second derivative of -3*t + 0*t**2 - 1/12*t**4 + 1/20*t**5 + 0 + 0*t**3. Suppose d(m) = 0. What is m?
0, 1
Suppose 3*y - m = -6*m - 14, 5*y + 2 = -3*m. Suppose -y*l = -3*w - 12, 0*l = 2*l - 4*w - 14. Factor -32/3*z**4 - 2/3 - 4*z - 2/3*z**2 + 16*z**l.
-2*(z - 1)**2*(4*z + 1)**2/3
Suppose 16/7 + 4/7*l - 2/7*l**2 = 0. What is l?
-2, 4
Let h(x) be the second derivative of -x**4/42 + 2*x**3/21 - x**2/7 - 22*x. Let h(z) = 0. What is z?
1
Let h = 145/42 + -20/21. Let i = 3 - h. Find p, given that 1/4 - i*p + 1/4*p**2 = 0.
1
Suppose -2 = 5*s - 6*s. Factor -2*r**2 + s*r**2 - 2*r**2 + 4*r**2.
2*r**2
Let o(d) = 44*d**2 - 24*d - 4. Let q(n) = n**3 + n**2 - n. Let j(h) = o(h) - 16*q(h). Suppose j(v) = 0. Calculate v.
-1/4, 1
Suppose -31*h**2 - 3*h**3 + 13*h + 11*h - 59*h**2 - 21*h**5 + 90*h**4 + 0*h**3 = 0. Calculate h.
-1, 0, 2/7, 1, 4
Let x(i) be the second derivative of i**4/42 - 2*i**3/21 + 5*i + 3. Factor x(g).
2*g*(g - 2)/7
Let k(n) be the second derivative of n**6/75 - n**5/50 + 23*n. Let k(m) = 0. What is m?
0, 1
Suppose -1 = 2*b - 9. Factor 0*p**3 - b*p**3 - 4*p**3 + 3*p**2 + 5*p**3.
-3*p**2*(p - 1)
Let r be (-2)/(-4)*(-1 - 21). Let t be (r/44)/(6/(-8)). Factor -t*k**2 + 0*k + 0.
-k**2/3
Let o be 0/(-3)*(-1 - (2 + -4)). Determine b, given that -2*b**2 + 0 + o*b + 6*b**3 - 9/2*b**4 = 0.
0, 2/3
Let k be 6/(-4) - 100/(-8). Suppose 3*f + p = k, -6*f + 17 = -f + p. Let -2*v**5 + 0*v - 23*v**3 - 2*v + 27*v**f = 0. Calculate v.
-1, 0, 1
Let y(m) be the third derivative of m**5/80 + 3*m**4/32 - m**2. Factor y(n).
3*n*(n + 3)/4
Let h(d) be the second derivative of 0 - 3/2*d**3 - 1/4*d**4 - 1/10*d**6 + 3*d**2 + 9/20*d**5 + 4*d. Suppose h(g) = 0. Calculate g.
-1, 1, 2
Let g(l) = -l**3 - 11*l**2 + 2*l + 22. Let x be g(-11). Factor 0*s + 0 + x*s**2 + 0*s**3 + 2/3*s**5 - 2/3*s**4.
2*s**4*(s - 1)/3
Let z be (-46)/(-10) + (-16)/(-40). Let j(p) be the second derivative of 0 - 1/21*p**3 + 1/42*p**4 + 1/70*p**z - 1/7*p**2 + p. Factor j(v).
2*(v - 1)*(v + 1)**2/7
Let g = -20 + 12. Let t(x) = x**3 + 8*x**2 - x - 6. Let i be t(g). Suppose 3*u**i - 2*u**2 + 0*u - u = 0. Calculate u.
0, 1
Let a(q) = -4*q**2 - 2. Suppose -5*y - 18 = -2*f - 7, -2*f - 10 = 2*y. Let z(l) = 5*l**2 + l + 3. Let c(w) = f*z(w) - 3*a(w). Factor c(v).
2*v*(v - 1)
Let z be (1 - 588/9) + 3. Let r = 62 + z. Factor 0*j**2 + 0 + 2/3*j - r*j**3.
-2*j*(j - 1)*(j + 1)/3
Let n(z) = -z**2 - 3*z + 4. Let q be n(-3). Let u(p) be the third derivative of -1/108*p**q - 1/270*p**5 + 0*p + 2*p**2 + 0*p**3 + 0. What is r in u(r) = 0?
-1, 0
Let z(p) be the first 