-3*r*(r - 1)*(r + 24)/4
Let k(t) = 3*t**4 + 15*t**3 - 69*t**2 + 125*t - 72. Let z(q) = 5*q**4 + 22*q**3 - 103*q**2 + 188*q - 108. Let l(v) = -8*k(v) + 5*z(v). Factor l(r).
(r - 3)**2*(r - 2)**2
Suppose -16*f + 24 = -8*f. Let i(n) be the third derivative of 6*n**2 + 0*n + 0 - 1/360*n**5 - 1/144*n**4 + 0*n**f. Factor i(k).
-k*(k + 1)/6
Suppose -10*h - 65 - 45 = 0. Let m = -11 - h. Solve -1/6*g**2 + m + 0*g - 1/6*g**3 = 0 for g.
-1, 0
Suppose 0 = -5*w + 8*w - 6. Suppose -3*k = -4 - w. Factor -5*r**2 + 16*r + 3*r**2 + 4*r**k - 1 + 33.
2*(r + 4)**2
Let t(n) = 3*n**2 - 147*n - 384. Let k(h) = -4*h**2 + 149*h + 385. Let j(i) = -6*k(i) - 7*t(i). Factor j(l).
3*(l + 3)*(l + 42)
Let z(o) be the second derivative of 0 + 5*o + 0*o**3 + 0*o**2 + 1/24*o**4. Determine x, given that z(x) = 0.
0
Let w be (9 + 0 + 1)/(-14 + 12). Let v be (w/(-2))/(5/6). Factor 72/7*s**2 - 128/7*s**4 + 162/7*s + 54/7 - 160/7*s**v.
-2*(s - 1)*(4*s + 3)**3/7
Let c be (6/(-5))/((-2)/5). Suppose c*t - 13 = 4*t - 3*l, 3*l - 23 = -4*t. Let -8*d**3 + 3*d**4 - d**3 - 3*d + 2*d**2 + 7*d**t = 0. What is d?
0, 1
Let l(v) = v**3 + 8*v**2 - 10*v. Let h(u) = 2*u**3 + 19*u**2 - 21*u. Let m(r) = -2*h(r) + 5*l(r). Suppose m(q) = 0. What is q?
-4, 0, 2
Let j(u) be the first derivative of -u**5/20 + 3*u**4/4 + 9*u**2/2 - 19. Let f(n) be the second derivative of j(n). Factor f(l).
-3*l*(l - 6)
Let t(z) be the second derivative of z**9/25200 - z**8/8400 + z**7/12600 - 7*z**4/4 - 5*z. Let r(g) be the third derivative of t(g). Factor r(x).
x**2*(x - 1)*(3*x - 1)/5
Let v(x) be the second derivative of -3*x**5/20 - 13*x**4/12 - 17*x**3/6 - 7*x**2/2 - 136*x + 4. Solve v(s) = 0.
-7/3, -1
Find i such that 253 + 179 + 44*i**2 - 8*i**2 - 2*i**3 - 216*i = 0.
6
Let o(n) be the third derivative of -n**8/1680 + n**7/525 + n**6/150 - n**5/150 - n**4/40 + 9*n**2 + 4. Let o(w) = 0. What is w?
-1, 0, 1, 3
Let g(o) be the first derivative of -o**3/24 + 13*o**2/8 - 169*o/8 + 42. Factor g(r).
-(r - 13)**2/8
Let j(y) be the third derivative of y**9/15120 + y**8/1680 + y**7/420 + y**6/180 + 2*y**5/5 - 8*y**2. Let b(w) be the third derivative of j(w). Factor b(k).
4*(k + 1)**3
Let l(r) be the second derivative of r**6/660 - r**5/330 + 3*r**2/2 - 8*r + 3. Let p(d) be the first derivative of l(d). Let p(i) = 0. Calculate i.
0, 1
Let t = -2/181 - -1096/905. Let j be (88/7 - 12) + (-8)/14. Suppose 3/5 + 0*m - t*m**2 + 3/5*m**4 + j*m**3 = 0. What is m?
-1, 1
Let j be 5/(160/108) - (0/1 + 3). Factor -3/2 - j*u**2 + 3/2*u.
-3*(u - 2)**2/8
Let u(x) = 9*x**3 + 18*x**2 - 12*x - 6. Let c(h) = 2*h**3 + 2*h - 1. Let m(t) = -6*c(t) + u(t). Solve m(s) = 0 for s.
0, 2, 4
Let x be (1575/700)/((5 + -2)/(-6) - -2). Suppose 6 + 27/2*p**2 - x*p**4 + 5/2*p**3 + 16*p - 1/2*p**5 = 0. Calculate p.
-2, -1, 3
Let j = 17/10 - 6/5. Let k = 251/506 + 1/253. Factor -k*p - 1/2*p**2 + j + 1/2*p**3.
(p - 1)**2*(p + 1)/2
Solve -6/7*l**3 + 2/7*l**4 - 6/7*l**2 + 2*l + 12/7 = 0.
-1, 2, 3
Let f(v) = v**2 + 3*v + 1. Let o(w) = -8*w**2 - 169*w - 56. Let z(h) = -5*f(h) - o(h). Let z(t) = 0. Calculate t.
-51, -1/3
Let q(d) be the first derivative of -10 + 0*d**4 - 4/45*d**5 - 1/27*d**6 + 1/9*d**2 + 0*d + 4/27*d**3. Factor q(j).
-2*j*(j - 1)*(j + 1)**3/9
Let a be (-4)/3*(-7917)/84. Let k = 126 - a. Factor -2/3*x**2 + 0 + 1/3*x**3 + k*x.
x*(x - 1)**2/3
Let n(r) be the third derivative of -r**5/90 - 2*r**4/9 - 4*r**3/3 - 3*r**2 - 14*r. Factor n(x).
-2*(x + 2)*(x + 6)/3
Let g(p) be the first derivative of p**7/140 + p**6/80 - 3*p**5/40 - p**4/16 + p**3/2 - p**2/2 - 3. Let i(h) be the second derivative of g(h). Factor i(l).
3*(l - 1)**2*(l + 1)*(l + 2)/2
Suppose 5*z + 6 = 3*z. Let v(w) = -5*w**3 - 11*w**2 - 11*w. Let x(g) = 11*g**3 + 23*g**2 + 23*g. Let b(u) = z*x(u) - 7*v(u). Factor b(a).
2*a*(a + 2)**2
Let u(k) be the third derivative of -k**8/84 - 2*k**7/15 - 8*k**6/15 - 4*k**5/5 - 34*k**2. Find j, given that u(j) = 0.
-3, -2, 0
Let g(d) be the third derivative of -d**7/105 + d**6/30 + d**5/30 - d**4/6 + d**2 - 3*d. Factor g(h).
-2*h*(h - 2)*(h - 1)*(h + 1)
Let b(h) be the first derivative of -3/5*h**5 + 0*h + 0*h**3 + 3/2*h**4 + 24 + 0*h**2. Factor b(l).
-3*l**3*(l - 2)
Let j = -16 - -26. Suppose j = 4*w + 2. Factor -2 - 6*s - 3*s**w - 3 + 2.
-3*(s + 1)**2
Let c(i) be the first derivative of 2*i**5/45 - 2*i**4/9 + 2*i**3/9 - 313. Let c(a) = 0. Calculate a.
0, 1, 3
Let o(r) = r**3 - r**2 - 1. Suppose -4*c + 11 = 3. Let b(n) = 7*n**3 + n**2 - 40*n + 23. Let d(v) = c*o(v) - 2*b(v). Factor d(x).
-4*(x - 2)*(x + 3)*(3*x - 2)
Let a(v) = -6*v**5 - 9*v**4 + v**3 - v**2 - 5*v - 5. Let w(z) = -18*z + 0*z**5 + z**5 - z**4 + 19*z + 3*z**4 + 1. Let b(c) = -a(c) - 5*w(c). Factor b(p).
p**2*(p - 1)**2*(p + 1)
Let r(c) be the first derivative of -3*c**6/8 - 33*c**5/20 + 27*c**4/8 + 13*c**3 - 9*c**2 - 24*c - 387. Determine k so that r(k) = 0.
-4, -2, -2/3, 1, 2
Determine w, given that 4/5*w + 1/5*w**5 + 0 + 3*w**3 - 7/5*w**4 - 13/5*w**2 = 0.
0, 1, 4
Suppose -2*r**4 + 3*r**3 + 16*r**5 - 20*r**5 - 2*r**5 - r**4 = 0. Calculate r.
-1, 0, 1/2
Suppose 15 = -3*c + 6*c. Let p(y) = 8*y**2 + 13*y + 5. Let i(h) = -12*h**2 - 19*h - 7. Let a(u) = c*i(u) + 7*p(u). Factor a(z).
-4*z*(z + 1)
Let t(a) be the third derivative of 25*a**8/1344 + 3*a**7/28 + 61*a**6/480 - 3*a**5/20 + a**4/24 + 285*a**2. Factor t(j).
j*(j + 2)**2*(5*j - 1)**2/4
Let w(j) be the third derivative of j**9/7560 + j**8/4200 - j**3/2 - 7*j**2. Let l(u) be the first derivative of w(u). Factor l(d).
2*d**4*(d + 1)/5
Let k be 2*(6/4 - 0). Let n be 3/1 + -4 + k. Determine j so that 2 + 15*j - 19*j + 0 + n*j**2 = 0.
1
Suppose 9 = -3*o + 5*k, -16 = -3*o - 5*k + 5. Let z(x) be the first derivative of 0*x + 8/45*x**5 - 1/27*x**6 + 1 + 0*x**3 + 0*x**o - 2/9*x**4. Factor z(n).
-2*n**3*(n - 2)**2/9
Let u(w) = -42*w**3 + 87*w**2 - 48*w. Let r(i) = i**4 + 83*i**3 - 174*i**2 + 95*i. Let h(o) = -3*r(o) - 5*u(o). Factor h(d).
-3*d*(d - 1)**2*(d + 15)
Let k(a) be the first derivative of a**6/30 - a**5/25 - 378. Find n such that k(n) = 0.
0, 1
Let y be (-80)/24*(52/5 - 12). Factor 10/3 + 16/15*u**3 + 2/15*u**4 - y*u + 4/5*u**2.
2*(u - 1)**2*(u + 5)**2/15
Let k be 1*5 + 14/(-14). Factor j**k + 5*j**4 - 6*j**4 + 2*j**5 - 2*j**4.
2*j**4*(j - 1)
Determine y, given that -y**3 - 10/3*y**2 + 8/3*y + 0 + 4/3*y**4 + 1/3*y**5 = 0.
-4, -2, 0, 1
Let f(m) be the first derivative of -m**5 - 10*m**4 + 5*m**3 + 65*m**2 + 80*m + 415. Find h, given that f(h) = 0.
-8, -1, 2
Let s(q) be the third derivative of 3*q**7/35 - 5*q**6/12 + 2*q**5/5 + q**4/3 - q**2 - 46*q. Let s(t) = 0. Calculate t.
-2/9, 0, 1, 2
Let b(c) be the first derivative of -19 - 3*c**2 - 18*c + 1/2*c**3. Determine n so that b(n) = 0.
-2, 6
Suppose -14*n - 2 = -15*n. Factor -4 - 3*f**2 + 5*f + 3*f**n - 4*f**2 + 3*f**2.
-(f - 4)*(f - 1)
Find u, given that 56/11*u**2 + 10/11*u**3 - 184/11*u + 64/11 = 0.
-8, 2/5, 2
Factor -2/9*n**5 + 0*n - 2/9*n**4 + 10/9*n**3 - 2/3*n**2 + 0.
-2*n**2*(n - 1)**2*(n + 3)/9
Let h(k) be the first derivative of -4/33*k**6 + 0*k**2 - 6 + 0*k + 2/11*k**4 + 6/11*k**5 + 0*k**3. Factor h(y).
-2*y**3*(y - 4)*(4*y + 1)/11
Let g(n) = -31*n**2 + 5*n - 5. Let z be g(1). Let j(b) = -5*b - 153. Let o be j(z). Find s, given that -2/5*s**o - 6/5*s - 4/5 = 0.
-2, -1
Let j(b) = 8*b**2 + 20*b + 22. Let m(a) = a**2 - 2*a - 1. Let h(y) = -j(y) + 5*m(y). Factor h(k).
-3*(k + 1)*(k + 9)
Let c be (-2)/(-2)*-2*-6. Suppose c = 2*m + 4*y, 3*m - 14 = -4*y - 0. Factor 1 - 12*w + 10*w + w**m + 0*w**2.
(w - 1)**2
Let c = -7 - -7. Suppose d - m + 1 = c, 4*d + 2 = m + 10. Let 1/5*j**4 + 9/5*j**2 + 7/5*j + j**d + 2/5 = 0. Calculate j.
-2, -1
Suppose -25 - 20 = -15*v. Let z(m) be the third derivative of -1/2*m**v - 1/60*m**5 + 0 - 1/120*m**6 + 0*m + 5/24*m**4 - 2*m**2. Factor z(s).
-(s - 1)**2*(s + 3)
Let u be (-2)/4*-14 + (21 - 23). Let g(i) be the first derivative of 0*i + 0*i**3 + 48/25*i**u - 7/3*i**6 + 7 - 2/5*i**4 + 0*i**2. Factor g(j).
-2*j**3*(5*j - 2)*(7*j - 2)/5
Let r(h) be the first derivative of -4*h**3/9 + 38*h**2/3 - 24*h + 67. Factor r(k).
-4*(k - 18)*(k - 1)/3
Let q be (1/(-5))/(-10*16/40). Let n(d) be the third derivative of 0 + 1/120*d**6 + 0*d - q*d**5 - 1/6*d**3 - 6*d**2 + 1/8*d**4. Factor n(w).
(w - 1)**3
Let n(s) be the third derivative of s**8/3360 + s**7/180 + s**6/60 - 7*s*