- 1). Factor -1/6*a**4 - 1/6 - 2/3*a**3 - a**2 - l*a.
-(a + 1)**4/6
Let d(w) be the first derivative of 9*w**3 + 33*w**2/2 + 6*w - 3. Factor d(z).
3*(z + 1)*(9*z + 2)
Find s such that 16/9*s - 10/9*s**2 + 2/9*s**3 - 8/9 = 0.
1, 2
Let m(o) be the second derivative of 3*o + 1/210*o**5 + 3/2*o**2 - 1/42*o**4 + 0 + 0*o**3. Let i(r) be the first derivative of m(r). Factor i(q).
2*q*(q - 2)/7
Suppose -a + 4*p + 2 = -8, -3*p - 6 = 0. Let n(k) be the first derivative of 3 + 2/33*k**3 - 6/11*k**a + 18/11*k. Suppose n(w) = 0. What is w?
3
Let v(x) be the second derivative of x**5/180 - x**4/72 - x**3/9 - x**2 + x. Let y(a) be the first derivative of v(a). Factor y(b).
(b - 2)*(b + 1)/3
Suppose -g = -6 + 3. Factor 1 - 2*j**3 - 4*j**2 + j**g - 2 - 3*j + j**2.
-(j + 1)**3
Let y(j) be the first derivative of -j**3/6 + j**2/4 + j + 5. Factor y(d).
-(d - 2)*(d + 1)/2
Let n(b) be the second derivative of -b**4/60 + b**3/30 + 19*b. Let n(l) = 0. Calculate l.
0, 1
Let 0*l**3 + 1/6*l + 0 + 1/3*l**4 - 1/6*l**5 - 1/3*l**2 = 0. What is l?
-1, 0, 1
Find u, given that 3*u + u**3 + 5*u**3 - 9*u**3 + 6*u**2 - 6 = 0.
-1, 1, 2
Let r(o) = -o + 21. Let s be r(17). Let f(m) be the second derivative of -1/5*m**2 - 2*m + 0 + 1/15*m**3 + 1/30*m**s - 1/50*m**5. Find g such that f(g) = 0.
-1, 1
Let a(b) be the third derivative of -b**6/30 + 4*b**5/15 + b**4/6 - 8*b**3/3 + 29*b**2. Factor a(v).
-4*(v - 4)*(v - 1)*(v + 1)
Suppose -x + 6 = 2*g - 15, 0 = 5*g - 25. Suppose 3*u - s - 3 = 0, -3*s - x + 2 = -3*u. Suppose -4*a + 3*a**2 + 2*a**2 - 4 + u - 6*a**2 = 0. What is a?
-2
Let h = 37 - 331/9. Factor h*y**4 - 2/9*y**2 + 2/9*y**3 + 0 - 2/9*y.
2*y*(y - 1)*(y + 1)**2/9
Suppose 2*y + 2*y = 52. Find p, given that -y*p**3 + 5*p**3 - 5*p**4 + 4*p**2 + 9*p**4 = 0.
0, 1
Let r(x) be the third derivative of -x**6/1080 - x**5/360 - x**3/6 + 4*x**2. Let g(l) be the first derivative of r(l). Let g(u) = 0. Calculate u.
-1, 0
Let l(a) be the second derivative of -a**7/168 + 13*a**6/120 - 29*a**5/40 + 53*a**4/24 - 85*a**3/24 + 25*a**2/8 - 53*a. Find u, given that l(u) = 0.
1, 5
Suppose -4*b + 2*n + 2 = 0, b = -3*n + 7 + 11. Let g be b/(-6)*(-8)/2. Factor -2/9*s + 0 + 2/9*s**g.
2*s*(s - 1)/9
Suppose 1689*i + 39 = 1702*i. What is u in -2/13*u**4 - 2/13*u**i + 4/13*u**2 + 0 + 0*u = 0?
-2, 0, 1
Factor 3*m**3 - 6*m**3 - 4*m + m - 6*m**2.
-3*m*(m + 1)**2
Let a(f) be the first derivative of -4/5*f**5 + 8/3*f**3 - 4*f + 0*f**4 + 7 + 0*f**2. Let a(s) = 0. Calculate s.
-1, 1
Suppose 0 = 4*y - 9 + 1. Let j(c) be the first derivative of 3/5*c**y - 4/5*c - 2/15*c**3 + 1. Factor j(u).
-2*(u - 2)*(u - 1)/5
Let b(j) be the first derivative of -2/9*j + 0*j**2 + 2/27*j**3 - 2. Factor b(c).
2*(c - 1)*(c + 1)/9
Let u = 28 + -82/3. Determine n so that u*n**3 + 0 - 2/3*n**2 - 2/3*n + 2/3*n**4 = 0.
-1, 0, 1
What is r in 1 + 9*r - 1 - 3*r**2 - 1 - 5 = 0?
1, 2
Suppose 3*b + 3 = 0, -5*j - 4*b + 5 = b. Factor 2*k**2 + 6*k**4 + 0*k**2 - 4*k**3 + j*k**5 + 10*k**3.
2*k**2*(k + 1)**3
Find d such that 2*d**3 + 0 + 0*d - 4/13*d**2 - 12/13*d**4 = 0.
0, 1/6, 2
Let i(z) be the first derivative of z**3/3 + 9*z**2/2 - 9. Let g be i(-9). Determine s so that -1/2*s**2 + 1/2*s**5 + 1/2*s**4 + 0 + g*s - 1/2*s**3 = 0.
-1, 0, 1
Let u(p) be the second derivative of 1/180*p**6 - 1/2*p**2 - 1/36*p**4 + p + 1/90*p**5 + 0 - 1/9*p**3. Let a(h) be the first derivative of u(h). Factor a(q).
2*(q - 1)*(q + 1)**2/3
Let k(f) be the first derivative of 3*f**4/4 - 2*f**3 - 39*f**2/2 - 30*f - 53. Factor k(r).
3*(r - 5)*(r + 1)*(r + 2)
Factor 0 - 6/11*g + 2/11*g**2.
2*g*(g - 3)/11
Let v(p) be the third derivative of 1/8*p**4 + 0*p + 0 - 1/40*p**6 + 1/20*p**5 - 1/2*p**3 - 7*p**2. Suppose v(b) = 0. What is b?
-1, 1
Let l be 16 + (-3 - (4 + -5)). Let k = -12 + l. Let -2/7*q**k + 0 + 0*q = 0. What is q?
0
Factor -5/3*c**2 - 2/3 + 7/3*c.
-(c - 1)*(5*c - 2)/3
Let b(g) be the third derivative of g**6/200 - g**5/100 + 13*g**2. Factor b(o).
3*o**2*(o - 1)/5
Suppose 3 = g + 3*i, 4*i + 3 + 9 = 0. Factor -9*z - 4*z**3 + 3 - g*z**2 - 2 - 3*z - 5.
-4*(z + 1)**3
Let o(c) be the third derivative of c**7/420 + c**6/90 - c**5/60 - c**4/6 + c**3/3 + 4*c**2. Let x(h) be the first derivative of o(h). Factor x(p).
2*(p - 1)*(p + 1)*(p + 2)
Let v be 10/25*(-1 + 6). Let g(j) be the first derivative of 5/16*j**4 - 1/20*j**5 + 7/8*j**2 - 1/2*j + v - 3/4*j**3. Factor g(d).
-(d - 2)*(d - 1)**3/4
Let r be 12/3 - 52/16. Determine i, given that 3/4*i**2 - r*i + 0 = 0.
0, 1
Suppose 0 = -3*r + 5*t + 11, -3*r + 2 + 5 = -t. Let u(k) = -k**3 + 4*k**2 - 3*k. Let j be u(3). Suppose 4*s**r + s - 3*s**2 + j*s + 1 - 3*s = 0. What is s?
1
Let p = 1/1457 + 1373/122388. Let q(f) be the second derivative of p*f**7 + 0 + 0*f**3 + 0*f**4 + 0*f**2 + 1/40*f**5 + 1/30*f**6 - 2*f. Solve q(z) = 0 for z.
-1, 0
Let c be 1*(4 - 0)/2. Determine i, given that 2*i**2 + 0*i**2 - 3*i**5 - 2*i**c - i**4 = 0.
-1/3, 0
Find g such that 0 + 2/15*g - 2/15*g**3 + 0*g**2 = 0.
-1, 0, 1
Let g(z) = 2*z - 2. Let u be g(1). Let n(l) be the first derivative of -3/7*l**4 + u*l - 1/21*l**6 + 8/35*l**5 + 2 + 8/21*l**3 - 1/7*l**2. Factor n(t).
-2*t*(t - 1)**4/7
Let y(s) be the third derivative of s**11/166320 + s**10/37800 - s**8/5040 - s**7/2520 - s**5/15 - s**2. Let o(j) be the third derivative of y(j). Factor o(h).
2*h*(h - 1)*(h + 1)**3
Let u = 6 - -16. Suppose -u = -2*x - 3*f - f, -4*f = -4*x - 16. Factor 4*a + a - a**2 - x - 3*a.
-(a - 1)**2
Let d be (11/(-5) + 2)/(15/(-50)). Let p be (-1)/2 - (-22)/12. Factor p*f**3 - d*f**2 + 0 - 2/3*f**4 + 0*f.
-2*f**2*(f - 1)**2/3
Factor -5703*n**3 - 7 - 48*n + 5679*n**3 + 52*n**2 + 23 + 4*n**4.
4*(n - 2)**2*(n - 1)**2
Factor -2/13 + 2/13*h + 4/13*h**2.
2*(h + 1)*(2*h - 1)/13
Factor -7252*w**2 + 7252*w**2 + 4*w**5 + 4*w**4.
4*w**4*(w + 1)
Let s(m) be the first derivative of -m**8/4200 + m**7/525 - m**6/180 + m**5/150 + 5*m**3/3 - 2. Let j(r) be the third derivative of s(r). Factor j(a).
-2*a*(a - 2)*(a - 1)**2/5
Suppose 5 - 4 - 2*o + 2*o**3 + 0*o**3 - o**4 = 0. What is o?
-1, 1
Let v(f) be the third derivative of -5*f**5/24 - 5*f**4/8 - 3*f**3/4 + 27*f**2. Solve v(h) = 0 for h.
-3/5
Let p(t) = 2*t + 14. Let u be p(-7). Factor 0 + u*i + 2/3*i**3 + 10/3*i**4 + 0*i**2 + 8/3*i**5.
2*i**3*(i + 1)*(4*i + 1)/3
Let f be ((-4)/6)/((-1)/2). Let r(w) = w**3 - 3*w**2 - 6*w + 8. Let c be r(4). Factor c - 2*m**4 + 2/3*m**2 + f*m - 8/3*m**3.
-2*m*(m + 1)**2*(3*m - 2)/3
Let h be (-1)/((-76)/75 - -1). Let c be 10/h*(318 + 2). Determine d so that 8*d - 2/3 - 32*d**2 + c*d**3 = 0.
1/4
Let v(m) be the first derivative of 7*m**2 - m**2 + 2 + m**3 + 4 + 12*m. Solve v(w) = 0.
-2
Let a(o) = -o**3 + 5*o**2 - 3*o - 4. Suppose -5*l = 4*q - 41, 2*l + 0*l - 6 = q. Let u be a(q). Factor u + 0*c + 4/3*c**2 - 2/3*c**3.
-2*c**2*(c - 2)/3
Let t = 70 + -279/4. Factor 0*l - t*l**2 + 1/4.
-(l - 1)*(l + 1)/4
Let q be 1*((-1225)/(-20))/(-7). Let l = q - -41/4. Determine o so that 5*o**4 + 0 + 6*o**3 + 1/2*o + l*o**5 + 3*o**2 = 0.
-1, -1/3, 0
Let b(i) = -3*i**5 + 8*i**4 - 8*i**2 + 3*i. Let s(y) = -48*y**5 + 129*y**4 - 129*y**2 + 48*y. Let t(v) = -33*b(v) + 2*s(v). Factor t(r).
3*r*(r - 1)**3*(r + 1)
Let q(a) = a**3 + 5*a**2 + 4*a + 2. Let o be q(-4). Factor 0*m**2 + 0*m + o*m - 2*m**2.
-2*m*(m - 1)
Factor 4*o**5 + 39*o**3 + 20*o + 20*o**4 + 40*o**2 - 8 + 12 + o**3.
4*(o + 1)**5
Let x(y) = 26*y**2 - 6*y - 4. Let o(h) = -h + 5*h**2 + 3 - 1 - 3. Let u(t) = 16*o(t) - 3*x(t). Find c, given that u(c) = 0.
-2, 1
Suppose 5*o - 25 = 10. Find p such that 4*p**3 - 6*p - o*p + 8 + p = 0.
-2, 1
Factor -4*a - 9*a + 3*a + 5*a**2.
5*a*(a - 2)
Let s(k) = 3*k**3 - 8*k + 5 - 29*k**2 - 9*k + 7*k**3. Let q(h) = 9*h**3 - 30*h**2 - 18*h + 6. Let b(d) = -5*q(d) + 6*s(d). Find u such that b(u) = 0.
-2/5, 0, 2
Let h(w) be the second derivative of -16/165*w**6 - 12/55*w**5 + 0*w**2 + 0 - 1/33*w**3 + 2*w - 3/22*w**4. Let h(r) = 0. What is r?
-1, -1/4, 0
Let s = -2 - -4. Factor 2*g**s + 2*g**4 + 4*g**2 - 3 - 2*g**4 - 3*g**4.
-3*(g - 1)**2*(g + 1)**2
Suppose 36 = 4*n + 5*p, -2*p + 12 = -2*n + 3*n. Suppose -n*d + 3 + 9 = 0. Determine k, given that -2*k**3 - d*k - 2 - 9*k**2 - 7*k**3 + 2 - 3*k**4 = 0.
-1, 0
Let g(v) be the second derivative of 9/2*v**3 + 9/2*v**4 + 3*v - 243/10*v**6 - 243/14*v**7 - 81/10*v**5 + 3/2*v**2 + 0. Factor g(q).
-3*(3*q - 1)*(3*q 