ose 38*u = 34*u + 16. Let q(w) = t*d(w) + u*s(w). Factor q(x).
3*x*(x + 2)
Let s be (-2)/(-10)*65*(-94)/(-611). Suppose -6/13*h**s + 56/13 + 80/13*h = 0. Calculate h.
-2/3, 14
Let z(r) be the third derivative of -r**8/84 + 11*r**7/210 + 13*r**6/40 + 29*r**5/60 + 5*r**4/24 - 48*r**2. Find d, given that z(d) = 0.
-1, -1/4, 0, 5
Let q = 211722349/30069 - 63371/9. Let p = 1683954/16705 + q. Factor -436/5*f**2 - 196/5*f**4 - 16/5 + 144/5*f + p*f**3.
-4*(f - 1)**2*(7*f - 2)**2/5
Let i = -692 + 145321/210. Let h(b) be the second derivative of -1/30*b**4 - i*b**7 + 1/25*b**5 + 1/5*b**2 - 4*b + 0*b**6 - 1/10*b**3 + 0. Factor h(g).
-(g - 1)**3*(g + 1)*(g + 2)/5
Find r such that 50 + 47 + 4*r**2 - 72*r - 22 - 7 = 0.
1, 17
Suppose 1 = -w, 3*d + 5*w + 23 = 4*d. Factor d + 99 + 5*k**2 - 50*k + 8.
5*(k - 5)**2
Suppose -19*z + 17*z = 2. Let u be (4 - 4) + z + 3. Let -386 - 18*l**3 - 12*l**u - 12*l**4 - 3*l**5 - 3*l + 386 = 0. What is l?
-1, 0
Suppose 116*n - 93*n = -294*n. Determine g, given that n*g + 10/17*g**2 - 2/17*g**3 + 0 = 0.
0, 5
Let v(h) be the third derivative of 2*h**6/15 - 8*h**5/15 - h**4/2 + 6*h**3 - 27*h**2. Let v(d) = 0. Calculate d.
-1, 3/2
Let p(l) = -3*l - 36. Let j be p(-12). Suppose j = i - 4*s + 12, -6*i + 2*i + 3 = s. Find z such that 0*z - 1/4*z**2 + i + 3/4*z**3 - 3/4*z**4 + 1/4*z**5 = 0.
0, 1
Let r(p) be the second derivative of -p**8/2240 + p**7/280 - p**6/120 + 25*p**4/12 + p. Let l(y) be the third derivative of r(y). Factor l(b).
-3*b*(b - 2)*(b - 1)
Let i(w) be the first derivative of -2*w**5/5 - 11*w**4/2 - 46*w**3/3 + 11*w**2 + 48*w - 538. Let i(p) = 0. Calculate p.
-8, -3, -1, 1
Let f(s) = -s**2 + 5. Let x(c) = 1. Let o be (-14 - -14) + (0 - (0 - 1)). Let d(m) = o*f(m) - 4*x(m). Suppose d(i) = 0. Calculate i.
-1, 1
Find c such that 3/5*c**4 + 0*c**2 + 0*c**3 + 0*c + 0 + 3/5*c**5 = 0.
-1, 0
Let t(k) = 2*k**3 - 43*k**2 - 45*k + 10. Let h(o) = o**3 - 21*o**2 - 22*o + 4. Let l(j) = -15*h(j) + 6*t(j). Let l(u) = 0. Calculate u.
-1, 0, 20
Suppose -5*s - 5*l = 5, -13*l - 28 = -2*s - 9*l. Solve -10/3*y**2 - 2/3*y**s - 8/3*y**3 + 0 - 4/3*y = 0.
-2, -1, 0
Factor 24*i**3 + 270*i + 162 + 3/2*i**4 + 261/2*i**2.
3*(i + 1)*(i + 3)*(i + 6)**2/2
Let a(r) = 7*r**2 + 19*r + 22. Let n(o) = -o**2 + o. Suppose 4*c - 2 = -6. Let f(m) = c*a(m) - 5*n(m). Factor f(p).
-2*(p + 1)*(p + 11)
Let a be ((-20)/1)/((-2170)/124). Solve -12/7*y**2 - 4/7*y**3 + 4/7*y**4 + 4/7*y + a = 0 for y.
-1, 1, 2
Let a be 33/55 + 3/15*17. Let s(o) be the third derivative of -1/120*o**5 + 0*o - 1/12*o**a - 1/3*o**3 + 0 + 2*o**2. Factor s(w).
-(w + 2)**2/2
Suppose 43*t - t**2 + 5*t**3 + 9*t**2 + 27*t**3 - 47*t = 0. Calculate t.
-1/2, 0, 1/4
Let c(i) = -i**3 + 17*i**2 + 16*i + 33. Let s be c(18). Let z = s - -5. Determine b so that 2/11*b**z - 4/11 + 2/11*b = 0.
-2, 1
Let j(k) = 4*k**2 + 16*k + 14. Let a(x) be the first derivative of -8*x**3/3 - 16*x**2 - 29*x + 19. Let p(g) = 2*a(g) + 5*j(g). Factor p(c).
4*(c + 1)*(c + 3)
Factor -4 - 2/9*c**2 - 2*c.
-2*(c + 3)*(c + 6)/9
Let u = 55 + -26. Suppose 2*d - 5*s - 35 = -3*d, u = 5*d + s. Factor -y**3 + d*y**2 - 3*y**2 - 5*y**2 - y**3.
-2*y**2*(y + 1)
Let f be -8 - (-1020)/48 - 13. Find p, given that 0*p + 0 - 3/4*p**3 - 1/2*p**2 - f*p**4 = 0.
-2, -1, 0
Let t(p) = -4*p**2 + 3*p - 24*p - 3*p + 16*p**2 + 3. Let r(y) = -y**2 + y + 1. Let d(a) = 3*r(a) + t(a). Let d(q) = 0. Calculate q.
1/3, 2
Let j(m) be the second derivative of 55/6*m**3 - 5/3*m**4 + 0 - 22*m + 15/2*m**2. Let j(a) = 0. Calculate a.
-1/4, 3
Let t(s) be the second derivative of -s**4/3 + 20*s**3/3 + 48*s**2 - 3*s - 3. Suppose t(u) = 0. Calculate u.
-2, 12
Suppose -5*d - 32 + 897 = 0. Let n = d - 173. Factor n - 2/5*s**2 - 2/5*s.
-2*s*(s + 1)/5
Let q be ((-1 + -1)*(-9)/(-6))/(-9). Let g(l) be the second derivative of -1/36*l**4 + 0 + q*l**2 - 1/18*l**3 + 5*l. Factor g(h).
-(h - 1)*(h + 2)/3
Let i = -19826 + 19826. Factor -8/3*t**4 - 10/3*t**3 - 2/3*t**5 + i*t - 4/3*t**2 + 0.
-2*t**2*(t + 1)**2*(t + 2)/3
Let k = 955/6 + -159. Let l(o) be the third derivative of -k*o**3 + 1/60*o**5 + 0*o + 0 + 1/120*o**6 - 1/24*o**4 + 3*o**2. Let l(i) = 0. Calculate i.
-1, 1
Let z(r) be the second derivative of r**7/6720 - r**6/320 - r**4/12 + 37*r. Let t(q) be the third derivative of z(q). Factor t(w).
3*w*(w - 6)/8
Let t be 2*2 - (21 - 22). Factor -2*a**3 + 0*a**3 + 5*a**4 + 5*a - 8*a**3 + a**5 - 10*a**2 + 5 + 4*a**t.
5*(a - 1)**2*(a + 1)**3
Let c(o) = o**2 - 5*o - 10. Let v be c(7). Suppose 0 = 5*y + v - 19. Factor 6*f**y + 6*f**4 - 3 + 0 - 6*f**2 + 3*f**5 + 3*f**4 - 9*f.
3*(f - 1)*(f + 1)**4
Let q(j) be the third derivative of j**5/105 + 13*j**4/42 + 24*j**3/7 + 76*j**2. Find p, given that q(p) = 0.
-9, -4
Determine m so that 15 + 65/4*m + 5/4*m**2 = 0.
-12, -1
Suppose 0 = 3*l + y - 3, -2*l - 24 = -3*y - 26. Let t(c) be the first derivative of l - 3/4*c**4 + 0*c + 0*c**2 + 1/6*c**6 + 0*c**5 + 2/3*c**3. Factor t(h).
h**2*(h - 1)**2*(h + 2)
Let h be 8/36 + 295/9. Suppose 0 = -b - 0*b + h. Suppose 24*z**4 + 15*z**2 + 5*z**4 - b*z**3 + 26*z**5 - 2*z - 35*z**5 = 0. What is z?
0, 2/9, 1
Let m(q) be the second derivative of -q**7/1008 + q**6/540 + q**5/720 + 17*q**3/6 + 12*q. Let o(i) be the second derivative of m(i). Solve o(b) = 0 for b.
-1/5, 0, 1
Let x(d) be the first derivative of -d**6/540 + d**4/36 + 2*d**3/27 + 11*d**2/2 + 1. Let t(b) be the second derivative of x(b). Factor t(g).
-2*(g - 2)*(g + 1)**2/9
Let d be (4 + (-14)/3)*-3. Find f such that d*f**2 + 1 + 4*f**2 + 8*f - 4*f**2 + 5 = 0.
-3, -1
Let y = 2 - -2. Suppose 2*g + 2*x = 7 + 1, 4*g = y*x + 8. What is z in -z - 27*z**2 + 25*z**2 + 2*z**3 - g*z = 0?
-1, 0, 2
Let p(c) be the third derivative of -c**5/140 + 67*c**4/28 - 4489*c**3/14 - 39*c**2. What is u in p(u) = 0?
67
Let h = -333/4 - -1677/20. Let z = -1533/20 - -345/4. Factor z + 24/5*x + h*x**2.
3*(x + 4)**2/5
Suppose -6 = -3*j + j. Let j*w**3 - 216*w + 3*w**2 + 216*w = 0. What is w?
-1, 0
Let n = 42 - 22. Factor 3*x**5 - 2*x**3 + x - x + 3*x + n*x**3 + 12*x**4 + 12*x**2.
3*x*(x + 1)**4
Factor 0*v + 0 - 7/3*v**3 + 2/3*v**2 + 5/3*v**4.
v**2*(v - 1)*(5*v - 2)/3
Suppose -4*g - 4 = 4*u, -4*u + u + 18 = -4*g. Factor -2/13*r - 4/13 + 2/13*r**u.
2*(r - 2)*(r + 1)/13
Let x(d) = -2*d**2 + 45*d + 25. Let c be x(23). Let i(f) = f**3 - f**2 + 7*f - 16. Let l be i(c). Factor 6/7*b**l + 2/7*b**3 + 0*b - 8/7.
2*(b - 1)*(b + 2)**2/7
Let g be (-14)/(-49) - (-752)/14. Suppose 57*f = g*f. What is b in 3/5*b**2 + 0*b + f + 3/5*b**3 = 0?
-1, 0
Suppose 4*o - 78 = -46. Suppose o*q - 48 = -8*q. Factor -1/5*b**2 + 0*b + 0 + 1/5*b**q.
b**2*(b - 1)/5
Factor -10*u**3 - 5 - 3 + 3 + 0*u**4 - 15 - 6*u**2 + 34*u + 2*u**4.
2*(u - 5)*(u - 1)**2*(u + 2)
Let p(q) = -q**4 - 11*q**3 + q**2 + 11*q - 2. Let l(a) = -a**4 - 23*a**3 + a**2 + 23*a - 5. Let c(t) = 2*l(t) - 5*p(t). Factor c(o).
3*o*(o - 1)*(o + 1)*(o + 3)
Let w(c) be the second derivative of c**7/21420 - c**6/3060 + c**5/1020 - 5*c**4/3 - 2*c. Let z(p) be the third derivative of w(p). Suppose z(h) = 0. What is h?
1
Let 637*b**2 + 57 - 368*b - 79 - 169*b**3 + 50 + 598*b**2 = 0. What is b?
2/13, 7
Let k(o) be the third derivative of o**6/90 + 47*o**5/45 - o**2 + 30*o. Factor k(v).
4*v**2*(v + 47)/3
Suppose x + 4 = 11. Let r = x - 5. Factor 3*a**3 + 4*a**2 + 2*a - a**r - a + a**4.
a*(a + 1)**3
Factor -42/13*s + 2/13*s**3 - 90/13 + 2/13*s**2.
2*(s - 5)*(s + 3)**2/13
Let z be (-5 - (-3 + -1))*88/(-77). Factor -4/7*j**2 - z*j - 4/7.
-4*(j + 1)**2/7
Factor 4*f + 10*f**3 + 3*f**3 + 2*f**3 - 6*f**2 - 13*f**3.
2*f*(f - 2)*(f - 1)
Let n(r) = -r**3 + r**2. Let b(h) = 16*h**3 - 191*h**2 + 450*h + 125. Let s(j) = b(j) - 4*n(j). Factor s(k).
5*(k - 5)**2*(4*k + 1)
Let x(g) be the second derivative of g**6/50 + 6*g**5/25 + 13*g**4/20 + 3*g**3/5 - 23*g. Factor x(p).
3*p*(p + 1)**2*(p + 6)/5
Suppose -4*a + 5 = -3. Let x(f) be the first derivative of -1/11*f**a + 0*f - 4/55*f**5 + 1/33*f**6 + 0*f**4 + 4/33*f**3 + 1. Find b, given that x(b) = 0.
-1, 0, 1
Let f = 346 - 2419/7. Let t(k) be the first derivative of 0*k - 9 - 16/21*k**3 + f*k**4 - 8/7*k**2. Solve t(q) = 0 for q.
-2/3, 0, 2
Let b be ((1 - 2) + 0)*-3. Let r be (b - 0) + (0 - 0). Factor -2*g - 2*g + r*g**2 - g + 6*g - 2.
(g + 1)*(3*g - 2)
Let n(b) = -16*b**3 + 7*b**2 + 11*b - 7. Let k(t) = 39*t**3 - 18*t**2