or v(j).
-j**3*(j + 1)**2
Let d(s) = -4*s**3 + 8*s**2 + 4*s + 4. Let a(z) = -z**4 + 4*z**3 - 9*z**2 - 4*z - 5. Let j(f) = -4*a(f) - 5*d(f). Factor j(o).
4*o*(o - 1)*(o + 1)**2
Let a(p) = 6*p**2 + 66*p - 44. Let b(l) = -l**2 - 13*l + 9. Let k(y) = 3*a(y) + 16*b(y). Let k(t) = 0. Calculate t.
2, 3
Let l be 8/(-24) + (-5)/(-9). Factor -4/9*c**2 + l*c**4 + 0*c**3 + 2/9 + 0*c.
2*(c - 1)**2*(c + 1)**2/9
Let q(d) be the third derivative of d**5/120 - 13*d**4/24 + 169*d**3/12 + 18*d**2. Factor q(b).
(b - 13)**2/2
Let h(k) be the third derivative of -k**7/525 - k**6/150 - k**5/150 - 5*k**2. Factor h(z).
-2*z**2*(z + 1)**2/5
Let i(o) be the second derivative of o**10/105840 - o**8/23520 - o**4/12 + 3*o. Let s(h) be the third derivative of i(h). Factor s(k).
2*k**3*(k - 1)*(k + 1)/7
Let w(l) = 2*l**2 + 2*l. Suppose 4*k = 6 - 34. Let h = -5 + 2. Let c(u) = -5*u**2 - 5*u. Let o(i) = h*c(i) + k*w(i). Find q, given that o(q) = 0.
-1, 0
Let g(j) be the third derivative of -j**6/70 - j**5/20 + j**4/4 - 3*j**3/14 + 5*j**2. Factor g(p).
-3*(p - 1)*(p + 3)*(4*p - 1)/7
Let c(i) = 60*i**2 - 48*i + 8. Let r(j) = 60*j**2 - 47*j + 8. Let y(u) = 3*c(u) - 4*r(u). Factor y(g).
-4*(3*g - 1)*(5*g - 2)
Let u(a) be the first derivative of -2*a**3/15 + 2*a**2 - 10*a - 32. Suppose u(q) = 0. Calculate q.
5
Let r(k) = 2*k**2 + 28*k - 26. Let j be r(-15). Factor 1/2*w**j + 0*w + 0*w**3 - 5/4*w**5 + 0*w**2 + 0.
-w**4*(5*w - 2)/4
Let x(z) be the first derivative of 3*z**5/5 - 9*z**4/4 + 3*z**3 - 3*z**2/2 - 5. Factor x(d).
3*d*(d - 1)**3
Determine j so that -3/2*j**2 + 0*j + 0 = 0.
0
Let c(o) be the third derivative of -o**8/168 - o**7/210 + o**6/24 + o**5/60 - o**4/8 + o**2. Solve c(x) = 0.
-3/2, -1, 0, 1
Let d = 10087 + -70912/7. Let q = -43 - d. Factor -q*g**2 + 2/7*g + 0.
-2*g*(g - 1)/7
Let c be 23 + -19 - 19/(-15) - 5. Factor 2/5*k - 2/15*k**3 + c + 0*k**2.
-2*(k - 2)*(k + 1)**2/15
Let l(n) be the second derivative of -n**5/70 - n**4/21 - 10*n. Solve l(k) = 0 for k.
-2, 0
Let c be (-3 - -5) + -1 + -1. Factor -3/4*h**3 + 1/4*h**2 + 0*h - 5/4*h**5 + c - 9/4*h**4.
-h**2*(h + 1)**2*(5*h - 1)/4
Let p = -14 + 14. Let o(w) be the second derivative of 1/3*w**3 + 1/2*w**2 + p - 2*w - 7/16*w**4. Factor o(r).
-(3*r - 2)*(7*r + 2)/4
Determine q so that -q**2 + 4*q + 5*q - 12*q**4 - 4*q**5 + 4 + 9*q**2 - 8*q**3 + 3*q = 0.
-1, 1
Let j(l) be the first derivative of -27*l**5/20 + 21*l**4/16 + 11*l**3/4 - 21*l**2/8 - 3*l/2 + 1. Let j(i) = 0. What is i?
-1, -2/9, 1
Let l(x) = -111*x**4 + 63*x**3 + 132*x**2 - 63*x + 6. Let z(u) = -16*u**4 + 9*u**3 + 19*u**2 - 9*u + 1. Let t(k) = -4*l(k) + 27*z(k). Solve t(d) = 0.
-1, -1/4, 1
Factor -2*i - 3*i - 4 + 11*i + 2*i**2 - 4*i**2.
-2*(i - 2)*(i - 1)
Let c(z) be the first derivative of 0*z - 2/55*z**5 + 3 + 0*z**3 + 0*z**2 - 1/22*z**4. Factor c(f).
-2*f**3*(f + 1)/11
Let g(u) = -u**2 + 14*u - 42. Let k be g(5). Let r(z) be the third derivative of 1/8*z**4 + 0 + 1/20*z**5 - z**k + 0*z + 3*z**2. Determine f so that r(f) = 0.
-2, 1
Let n be 2 - 4 - (-9 - 1). Let v = -8 + n. Let -2/5*u + 2/5*u**3 + 0*u**2 + v = 0. Calculate u.
-1, 0, 1
Let p(m) be the first derivative of -m**5/150 + m**3/15 + m**2 - 8. Let f(r) be the second derivative of p(r). Factor f(b).
-2*(b - 1)*(b + 1)/5
Let l = -11/6 - -5/2. Factor l + 1/3*j**4 - 1/3*j - j**2 + 1/3*j**3.
(j - 1)**2*(j + 1)*(j + 2)/3
Let p(m) = m**2 - m + 1. Let r(q) = -30*q**2 + 24*q + 3. Let h(o) = p(o) - r(o). Let x(s) = -32*s**2 + 26*s + 1. Let z(u) = -5*h(u) - 4*x(u). Factor z(g).
-3*(g - 1)*(9*g + 2)
Let j(r) be the second derivative of 0 - 1/3*r**3 + 1/12*r**4 + 3*r + 1/2*r**2. Determine g, given that j(g) = 0.
1
Let h be 138/(-24) + 6 + (-1)/(-2). Let v = 10 + -5. Let 0 + 0*m + h*m**3 + 1/4*m**v + 3/4*m**4 + 1/4*m**2 = 0. What is m?
-1, 0
Let f be ((-2)/(-150))/((-3)/18*-1). Let m(y) be the first derivative of -2 + 0*y**2 + 2/15*y**3 + 0*y + f*y**5 + 1/5*y**4. Factor m(w).
2*w**2*(w + 1)**2/5
Let h(x) be the first derivative of 2 + 2/7*x**2 + x - 3/7*x**3 - 11/42*x**4. Let b(w) be the first derivative of h(w). Determine k, given that b(k) = 0.
-1, 2/11
Suppose -3*t - 5*m + 15 = 0, -m - 10 = -3*t + 5. Suppose 2*h + 2*h - q - 4 = 0, -t*q = -20. Factor h*l**2 + 21*l + 6*l**2 - 23*l.
2*l*(4*l - 1)
Let b(k) be the first derivative of -1/3*k**3 - 1/6*k**2 + 0*k + 7 - 1/15*k**5 - 1/4*k**4. Solve b(t) = 0 for t.
-1, 0
What is b in 4/9*b**5 - 8/9*b**3 - 16/3*b**2 + 16/9*b**4 + 0 + 4*b = 0?
-3, 0, 1
Determine p, given that -24/5 - 36/5*p + 249/5*p**3 + 63/5*p**4 + 234/5*p**2 = 0.
-2, -2/7, 1/3
Let b(d) be the third derivative of 1/42*d**4 + 0 - 1/210*d**5 - 1/21*d**3 - d**2 + 0*d. Factor b(t).
-2*(t - 1)**2/7
Let l(p) = -p**3 + p. Let h be l(1). Let c be (-44)/(-12) - 5/(-15). Suppose -2 + 4 + 2*w**2 + h*w + c*w = 0. What is w?
-1
Let x(z) be the third derivative of 1/70*z**7 + 4*z**2 - 1/20*z**5 + 0*z**4 + 0 + 0*z - 1/80*z**6 + 1/224*z**8 + 0*z**3. Suppose x(w) = 0. Calculate w.
-2, -1, 0, 1
Let d(q) be the third derivative of 1/48*q**4 + 0 + 1/210*q**7 - 1/60*q**5 + 0*q + 0*q**6 - 4*q**2 - 1/672*q**8 + 0*q**3. Factor d(g).
-g*(g - 1)**3*(g + 1)/2
Let m be (6/(-40))/(4/(8/(-6))). Let b(z) be the first derivative of -2 - 3/16*z**4 - 1/8*z**2 - m*z**5 - 1/4*z**3 + 0*z. Suppose b(u) = 0. What is u?
-1, 0
Let t(d) be the second derivative of d**5/40 + d**4/16 - d**2/8 + 24*d. Factor t(l).
(l + 1)**2*(2*l - 1)/4
Let 2*r - 3/2 - 1/2*r**2 = 0. Calculate r.
1, 3
Let g(p) be the second derivative of 0 + 1/21*p**3 + 0*p**2 + 4*p - 1/42*p**4 + 1/105*p**6 - 1/70*p**5. Suppose g(x) = 0. What is x?
-1, 0, 1
Let n(k) be the second derivative of k**6/10 - k**4/2 + 3*k**2/2 + k. Factor n(g).
3*(g - 1)**2*(g + 1)**2
Let m(g) be the first derivative of -g**3/12 - g**2/4 - g/4 + 3. Factor m(u).
-(u + 1)**2/4
Factor -5 - 2*q**2 - 2 + 3*q + 5 + q.
-2*(q - 1)**2
Let m(i) be the second derivative of i**9/30240 - i**8/13440 + i**4/4 + 3*i. Let a(x) be the third derivative of m(x). Factor a(y).
y**3*(y - 1)/2
Let d(s) be the second derivative of -s**4/2 + s**3 + s. Let i(n) = -5*n**2 + 6*n - 1. Let g(z) = -2*d(z) + 3*i(z). Find y, given that g(y) = 0.
1
Solve 1/5*h**2 + 0 - 3/5*h = 0 for h.
0, 3
Suppose 0*p + 5*p = 15. Let n be (-1)/(3/9) + p. Factor 0 - 2/7*h**4 - 2/7*h**2 + n*h - 4/7*h**3.
-2*h**2*(h + 1)**2/7
Factor -7/3 + 1/6*p**2 + 5/6*p.
(p - 2)*(p + 7)/6
Let x(i) be the first derivative of -1/6*i**3 - 1/30*i**6 + 1/12*i**4 + 1 + i + 1/20*i**5 + 0*i**2. Let r(z) be the first derivative of x(z). Factor r(v).
-v*(v - 1)**2*(v + 1)
Factor 285*n**2 - 5 - 7 - 293*n**2 - 22*n.
-2*(n + 2)*(4*n + 3)
Suppose -4*j - z - 4 = 0, 0*j - 5*z = -2*j + 20. Factor -1/4 + 1/4*t**2 + j*t.
(t - 1)*(t + 1)/4
Suppose -x - 3 = -y, -x + 5 = 3*y - 4. Let h(s) = -2*s**2 - 10*s + 12. Let o be h(-6). Determine b so that 0*b**4 + 1/2*b**5 + x - b**3 + 1/2*b + o*b**2 = 0.
-1, 0, 1
Let y(x) = -x - 3. Let o be y(-5). Suppose u**o + u**4 + 2*u**4 + 4*u**4 - 4*u**4 + 4*u**3 = 0. Calculate u.
-1, -1/3, 0
Let j(m) be the first derivative of m**7/350 + 3*m**6/200 + m**5/50 + m**2 - 4. Let k(q) be the second derivative of j(q). Factor k(p).
3*p**2*(p + 1)*(p + 2)/5
Suppose 0 + 0*o + 1/4*o**2 = 0. Calculate o.
0
Let s(i) be the first derivative of -3*i**4/4 + 2*i**3/7 + 3*i**2/2 - 6*i/7 - 4. Factor s(c).
-3*(c - 1)*(c + 1)*(7*c - 2)/7
Let s(g) = -8*g**4 - 32*g**3 - 50*g**2 + 70*g. Let y(t) = 9*t**4 + 33*t**3 + 51*t**2 - 69*t. Let i(k) = -6*s(k) - 5*y(k). Factor i(u).
3*u*(u - 1)*(u + 5)**2
Let m = 2/267 - -29/89. Find b, given that m*b + 1/3*b**2 - 1/3*b**3 - 1/3 = 0.
-1, 1
Let x(d) be the second derivative of -2*d**6/45 + d**4/9 + 2*d. Factor x(q).
-4*q**2*(q - 1)*(q + 1)/3
Factor 0*n**2 - 5*n**3 + 8*n**3 + 2*n - 8*n**2 + 3*n**3.
2*n*(n - 1)*(3*n - 1)
Find l, given that 1/5*l**2 + 8/5 - 6/5*l = 0.
2, 4
Factor -1/2*p**5 + 5/2*p**4 - 5/2*p + 1/2 - 5*p**3 + 5*p**2.
-(p - 1)**5/2
Let q(n) = 2*n**3 - 6*n**2 + 6*n + 2. Let o(y) = 6*y + 1. Let m be o(1). Let f(u) = -6*u**3 + 17*u**2 - 17*u - 7. Let i(w) = m*q(w) + 2*f(w). Factor i(r).
2*r*(r - 2)**2
What is o in -66*o**3 + 10*o**4 - 5*o - 10*o**2 + 81*o**3 + 10*o**2 = 0?
-1, 0, 1/2
Let q be (-2)/(-5) - (-184)/(-10). Let r = 18 + q. Suppose 3/5*v**5 + 0*v**3 + 0*v + r*v**2 + 1/5*v**4 + 0 = 0. What is v?
-1/3, 0
Let m(j) = -j**2 + 1