et d(x) = 9*a(x) - 4*l(x). Factor d(j).
-3*j*(j - 1)*(j + 1)
Factor 13*o - o**2 - 5*o - 7*o.
-o*(o - 1)
Factor -1/2*r**2 + 1/4 - 1/4*r + 1/2*r**3 - 1/4*r**5 + 1/4*r**4.
-(r - 1)**3*(r + 1)**2/4
Let q be (14/(-70))/(2/(-30)). Let -6/5 - 12/5*z**2 + 3/5*z**q + 3*z = 0. What is z?
1, 2
Suppose 5*q**3 + 0*q**3 - 3*q**2 - 12*q**2 = 0. Calculate q.
0, 3
Let k(a) be the first derivative of a**6/30 - 7*a**5/60 + a**4/12 + a**3/6 - a**2/3 + 7*a + 2. Let m(u) be the first derivative of k(u). Factor m(c).
(c - 1)**3*(3*c + 2)/3
Let h(v) be the first derivative of -v**3/3 + 3*v**2/2 - 2*v + 12. Suppose h(t) = 0. Calculate t.
1, 2
Suppose -2*k = -0*k. Let m(v) be the third derivative of -1/35*v**7 - 1/6*v**5 + 0*v**3 + 0 + 7/60*v**6 + 1/12*v**4 + k*v - v**2. Factor m(g).
-2*g*(g - 1)**2*(3*g - 1)
Find l, given that 1465 + 5*l**5 - 5*l**4 - 10*l**3 - 1465 = 0.
-1, 0, 2
Suppose 0 = -5*f - 0*f. Determine k, given that 5*k - k - 3*k + f*k - k**3 + 1 - k**2 = 0.
-1, 1
Let b(t) be the first derivative of t**3/3 + t**2/3 - 11. Factor b(q).
q*(3*q + 2)/3
Let j be (-9)/10 + 4/10 + 1. Let i(p) be the first derivative of -1/12*p**6 + 1/3*p**5 + 1/3*p**3 - j*p**4 - 4 + 0*p - 1/12*p**2. Factor i(h).
-h*(h - 1)**3*(3*h - 1)/6
Suppose -q + 3*o = -0*q, -3*q + 3*o = -6. What is l in 0*l - 1/4*l**q + 1/2*l**2 + 0 = 0?
0, 2
Let a be (12/8 - 1) + 0. Let z(i) be the first derivative of -1/8*i**2 + 2 - 1/12*i**3 + a*i. Factor z(m).
-(m - 1)*(m + 2)/4
Suppose 0*k + 5*a + 8 = -k, 3*a + 10 = 2*k. Let i(b) be the first derivative of -2*b + 2*b**k - 2 - 2/3*b**3. Find h, given that i(h) = 0.
1
Let r(p) be the first derivative of -2*p**2 - 4 + 1/2*p**4 + 4/3*p**3 - p**5 + 1/3*p**6 + p. Factor r(w).
(w - 1)**3*(w + 1)*(2*w - 1)
Let i(f) = 4*f**2 + 2*f + 2. Let u(t) = -9*t**2 - 5*t - 5. Suppose -2*k + 9 = -1. Let z(v) = k*i(v) + 2*u(v). Suppose z(o) = 0. What is o?
0
Let c = -7 + 9. Factor 2/5*u**5 - 4/5*u**4 - 14/5*u - 4/5*u**3 + 4/5 + 16/5*u**c.
2*(u - 1)**4*(u + 2)/5
Factor 3/5*x**4 - 6/5*x**2 - 6/5*x**3 + 3/5 + 3/5*x + 3/5*x**5.
3*(x - 1)**2*(x + 1)**3/5
Let c(o) be the first derivative of o**6/150 + o**5/100 + 3*o + 3. Let u(t) be the first derivative of c(t). Determine b, given that u(b) = 0.
-1, 0
Let 15/2*f**2 - 1/2*f**3 + 125/2 - 75/2*f = 0. Calculate f.
5
Let d(a) be the second derivative of -a**7/84 + a**6/10 - 3*a**5/10 + a**4/3 + 19*a. Let d(c) = 0. What is c?
0, 2
Let t(x) be the third derivative of x**7/105 + x**6/20 + x**5/15 - 5*x**2. Suppose t(l) = 0. Calculate l.
-2, -1, 0
Factor 2*v**4 - 13*v**3 - 10*v**2 - 7*v**3 + 27*v - 7*v**4 - 7*v + 15.
-5*(v - 1)*(v + 1)**2*(v + 3)
Let v(h) = 6*h**3 - 4*h**2 + 4*h - 5. Let n = -4 + -1. Let l(y) = 6*y**3 - 3*y**2 + 3*y - 4. Let d(q) = n*l(q) + 4*v(q). Let d(r) = 0. Calculate r.
-1/2, 0, 1/3
Let f(q) = -q**5 + q**2 - 1. Let i = -15 + 10. Suppose -4*g - 3 = 1. Let o(s) = 4*s**5 - s**4 + s**3 - 4*s**2 + 5. Let a(y) = g*o(y) + i*f(y). Factor a(t).
t**2*(t - 1)*(t + 1)**2
Factor 10/9*r - 4/3*r**3 + 2/9*r**5 - 4/9*r**2 - 2/9*r**4 + 2/3.
2*(r - 3)*(r - 1)*(r + 1)**3/9
Factor 8/11*y**4 + 8/11*y**2 + 2/11*y + 0 + 12/11*y**3 + 2/11*y**5.
2*y*(y + 1)**4/11
Let a(k) be the third derivative of 1/42*k**7 - 1/12*k**4 - 3/40*k**6 - 1/336*k**8 + 0*k**3 + 0*k + 7/60*k**5 + 2*k**2 + 0. Solve a(j) = 0 for j.
0, 1, 2
Let p be 0 + ((-2)/(-8))/((-15)/(-12)). Let 1/5 + 2/5*j**3 + p*j**4 - 1/5*j - 2/5*j**2 - 1/5*j**5 = 0. Calculate j.
-1, 1
Let l(a) = -8*a**2 + 2*a + 4. Let o(x) = 4 + 4 - 19*x**2 - 2*x + 6*x + 2*x**2. Let u(n) = 13*l(n) - 6*o(n). Factor u(j).
-2*(j - 2)*(j + 1)
Let y(u) be the first derivative of 3*u**6/7 - 6*u**5/35 - u**4 + 4*u**3/21 + 5*u**2/7 + 2*u/7 + 11. Suppose y(f) = 0. What is f?
-1, -1/3, 1
Let k be (15/(-10) + 0)*-2. Factor 3/5*c**k + 3/5*c**2 + 0 - 6/5*c.
3*c*(c - 1)*(c + 2)/5
Suppose 0 = 5*l + i - 34, 2*i = 5*l - 0*i - 22. Let x(y) be the third derivative of 0*y**3 + 7/150*y**5 + 0*y + 0 + 2*y**2 - 1/30*y**4 - 1/60*y**l. Factor x(m).
-2*m*(m - 1)*(5*m - 2)/5
Let s(u) be the first derivative of 3/4*u**4 - 1 + 12*u**2 + 12*u + 5*u**3. Factor s(w).
3*(w + 1)*(w + 2)**2
Suppose 6*k + 39 = 39. Suppose 2/3*z + k - 1/3*z**2 = 0. Calculate z.
0, 2
Let l = 6/53 + 606/265. Determine r, given that -3/5*r**5 + 0 - l*r + 9/5*r**3 - 12/5*r**2 + 6/5*r**4 = 0.
-1, 0, 2
Let q = 6 + -4. Let c(t) = -t + 1. Let v be c(-7). Factor 9*a**3 - a**3 + 2*a + 0*a + v*a**q.
2*a*(2*a + 1)**2
Let m(c) be the third derivative of 0*c**3 + 0 - 2/75*c**5 - 1/840*c**8 + 1/100*c**6 + 3*c**2 - 1/15*c**4 + 0*c + 2/525*c**7. Factor m(b).
-2*b*(b - 2)**2*(b + 1)**2/5
Suppose 6 + 4 = 2*o. Solve m**2 - 4*m - o*m**2 + 3*m + 3*m**2 = 0 for m.
-1, 0
Let c(i) = i**2 - 19*i + 21. Let p be c(18). Let n(b) be the second derivative of -p*b + 3/4*b**4 + 0 - 1/2*b**3 - 3*b**2. Factor n(l).
3*(l - 1)*(3*l + 2)
Let r(g) be the second derivative of -g**6/480 + g**5/240 + 2*g**2 + 5*g. Let c(l) be the first derivative of r(l). Factor c(d).
-d**2*(d - 1)/4
Let u(t) be the third derivative of -8/105*t**7 - 4/15*t**5 - 5*t**2 + 1/84*t**8 + 0*t + 0 + 1/5*t**6 + 0*t**3 + 1/6*t**4. Factor u(n).
4*n*(n - 1)**4
Let d = -104/9 - -110/9. Factor 0 + 2/3*z - d*z**2.
-2*z*(z - 1)/3
Let z(s) be the first derivative of -1/15*s**3 - 2 - 2/5*s**2 + 1/30*s**4 - s. Let y(n) be the first derivative of z(n). Factor y(l).
2*(l - 2)*(l + 1)/5
Let m(l) be the third derivative of l**8/90720 + l**7/11340 + l**6/3240 + l**5/20 - 2*l**2. Let x(w) be the third derivative of m(w). Let x(i) = 0. What is i?
-1
Let 0 + 0*k + 0*k - k**3 - 3*k**2 + 4 = 0. What is k?
-2, 1
Let g(f) = 3*f**3 - f**2 - 2*f - 2. Let l(q) = -q**3 + q**2 + q + 1. Let x(v) = -5*g(v) - 10*l(v). Factor x(c).
-5*c**2*(c + 1)
Let h(w) be the first derivative of 1/2*w**2 + 0*w + 5 - 1/3*w**3. Suppose h(l) = 0. What is l?
0, 1
Let b(k) be the first derivative of -k**6/120 - k**5/40 - k**3 - 3. Let c(w) be the third derivative of b(w). Factor c(a).
-3*a*(a + 1)
Factor 0*x**2 + 0 - 1 + x**2.
(x - 1)*(x + 1)
Let j(x) be the third derivative of -6*x**2 + 1/210*x**5 + 4/21*x**3 + 0*x - 1/21*x**4 + 0. Determine m, given that j(m) = 0.
2
Let i(j) be the first derivative of 2*j**3/51 - 2*j/17 - 4. Factor i(l).
2*(l - 1)*(l + 1)/17
Let g(w) be the third derivative of w**7/490 + 11*w**6/840 + 2*w**5/105 - w**4/42 - 26*w**2. What is v in g(v) = 0?
-2, 0, 1/3
Let u(i) = i**3 - 12*i**2 + 12*i - 8. Let l be u(11). Let x(r) be the first derivative of 0*r**2 - 2 + 3/4*r - 1/4*r**l. Factor x(g).
-3*(g - 1)*(g + 1)/4
Let l = 3037/7 - 433. Factor 2/7*g + 2/7*g**4 + 0 + l*g**2 + 6/7*g**3.
2*g*(g + 1)**3/7
Let n(w) = -7*w**2 - 13*w - 16. Let h(a) = -20*a**2 - 40*a - 48. Let p(j) = -3*h(j) + 8*n(j). Let p(i) = 0. What is i?
-2
Let m(u) be the second derivative of u**5/30 - 5*u**4/9 + 16*u**3/9 - 3*u + 2. Factor m(l).
2*l*(l - 8)*(l - 2)/3
Let p = 61/342 + -2/171. Let m(v) be the third derivative of 0*v + p*v**4 + 0 - v**2 + 0*v**3 - 1/30*v**5. Determine w, given that m(w) = 0.
0, 2
Let d(h) be the third derivative of -h**6/240 - h**5/120 + 15*h**2 - h. Let d(t) = 0. Calculate t.
-1, 0
Suppose 2*j + 34 - 4 = 0. Let f be j/(-6) - 10/10. Factor 5/2*q**4 + f*q**5 + q**3 + 0*q + 0*q**2 + 0.
q**3*(q + 1)*(3*q + 2)/2
Suppose 5 = 3*b + 2*k + 11, 5*b + 15 = -5*k. Factor 4/3*n**2 + b*n - 2/3*n**4 + 0*n**3 - 2/3.
-2*(n - 1)**2*(n + 1)**2/3
Let h(y) be the third derivative of 1/30*y**3 + 0*y - 1/60*y**4 + 1/300*y**5 - 3*y**2 + 0. Factor h(a).
(a - 1)**2/5
Suppose 4*w - 4 = 2*l, -4*w + 7*w - 2 = 2*l. Factor -5*r**5 - r + w*r**5 + 3*r**4 + 3 - 2*r - 6*r**2 + 6*r**3.
-3*(r - 1)**3*(r + 1)**2
Let o(b) be the third derivative of -b**9/1512 - b**8/280 - b**7/140 - b**6/180 + 5*b**3/6 - 4*b**2. Let q(h) be the first derivative of o(h). Factor q(f).
-2*f**2*(f + 1)**3
Suppose -4*j + 2*r + 6 = 0, 12 = 4*j - 0*r - 4*r. Let a(t) be the third derivative of 1/16*t**4 + 1/6*t**3 + 0*t**5 - 1/240*t**6 + j - t**2 + 0*t. Factor a(g).
-(g - 2)*(g + 1)**2/2
Let d(n) = -3*n - 3. Let k(p) = 2*p + 2. Let s(y) = 3*d(y) + 4*k(y). Let r be s(-4). Factor 0 + 3/5*z**r + 0*z - 1/5*z**2.
z**2*(3*z - 1)/5
Let j(k) be the first derivative of 0*k**2 + 2 + 0*k**4 + 1/360*k**6 + 0*k - 1/120*k**5 - 2/3*k**3. Let a(v) be the third derivative of j(v). Factor a(y).
y*(y - 1)
Let n = 19 - 17. Let l(p) be the s