- 249. Let j = 18 + -14. Let f(g) = 7*g**2 + 14*g + 31. Let i(t) = j*r(t) + 33*f(t). Let i(q) = 0. Calculate q.
-3
Let n(c) be the second derivative of 1/210*c**5 + 0 + 0*c**4 - 2*c - 2*c**2 + 0*c**3. Let w(b) be the first derivative of n(b). Factor w(g).
2*g**2/7
Suppose -2*s = 5*b + 1993, 6*s + b + 3959 = 2*s. Let i = -6911/7 - s. What is r in 2/7*r**4 + 26/7*r**2 - i*r**3 - 24/7*r + 8/7 = 0?
1, 2
Let l(q) be the second derivative of -q**5/60 + q**3/6 - q**2/3 + 6*q. Factor l(n).
-(n - 1)**2*(n + 2)/3
Let m = -9 - -12. Factor 2*i**5 - 20 + 2*i**4 - 4*i**m + 4*i**2 + 18 + 2*i - 4*i**4.
2*(i - 1)**3*(i + 1)**2
Factor 2*a + 2/3 + 2*a**2 + 2/3*a**3.
2*(a + 1)**3/3
Find o, given that -15*o**2 - 5*o**4 + 24*o**3 - 48*o**3 - 7*o**4 - 3*o = 0.
-1, -1/2, 0
Let n = -10 - -7. Let i be (-1)/(3/(n*3)). Find f, given that -5/2*f - 4*f**2 - 2*f**i - 1/2 = 0.
-1, -1/2
Let j(i) be the second derivative of i**5/70 - i**3/21 + 23*i. Factor j(u).
2*u*(u - 1)*(u + 1)/7
Let t(p) be the second derivative of -p**7/147 + 2*p**6/21 - 4*p**5/7 + 40*p**4/21 - 80*p**3/21 + 32*p**2/7 + 32*p. Factor t(k).
-2*(k - 2)**5/7
Suppose 0 = -4*c, -4*p - 3 = -4*c + 5. Let s(r) = -r**2 + 3*r. Let h(x) = 2*x**2 - 4*x. Let a(f) = p*h(f) - 3*s(f). Solve a(m) = 0 for m.
-1, 0
Let d(h) be the second derivative of h**7/210 - h**5/50 + h**3/30 + 4*h. Factor d(k).
k*(k - 1)**2*(k + 1)**2/5
Let q(d) be the first derivative of -d**6/120 + d**5/60 + d**2 + 2. Let r(x) be the second derivative of q(x). Factor r(j).
-j**2*(j - 1)
Let u(m) be the third derivative of m**8/12 - 6*m**7/35 - m**6/6 + 3*m**5/5 - m**4/3 + 8*m**2. Find t, given that u(t) = 0.
-1, 0, 2/7, 1
Let m(b) be the third derivative of -b**8/840 + 2*b**7/525 - b**5/75 + b**4/60 - 29*b**2. Determine j, given that m(j) = 0.
-1, 0, 1
Let s(m) be the third derivative of 1/168*m**8 + 0 + 0*m**3 + 0*m - 3*m**2 - 1/60*m**6 + 0*m**4 + 1/30*m**5 - 1/105*m**7. Factor s(x).
2*x**2*(x - 1)**2*(x + 1)
Suppose -5*q + 10*q = 0. Let 2*n**5 - 6*n**5 + n**3 + q*n**2 + 3*n**5 + n**2 - n**4 = 0. What is n?
-1, 0, 1
Suppose -3*w - 6 = -6*w. Let s(n) be the first derivative of n + 1/2*n**4 - 2*n**3 + n**5 + 1/2*n**w - 2 - 1/2*n**6. Factor s(u).
-(u - 1)**3*(u + 1)*(3*u + 1)
Let g be (-8 + 5)*((-23)/(-12) + -2). Determine r so that -1/4 - g*r**2 + 1/2*r = 0.
1
Let x be (-790)/711*6/(-5). Factor x - 14/3*j - 2*j**3 + 16/3*j**2.
-2*(j - 1)**2*(3*j - 2)/3
Let m(l) = l**4 - l**3 - l**2 + l - 5. Let r(i) = -i**3 + i - 1. Let k(c) = -m(c) + 5*r(c). Factor k(u).
-u*(u - 1)*(u + 1)*(u + 4)
Let r(y) = -y**2 - 7*y + 6. Let l be r(-6). Suppose 4*k - 2 = 3*s - l, -5*k - 1 = 2*s. Factor 2/3*d**s + 2*d + 4/3.
2*(d + 1)*(d + 2)/3
Let v(l) be the third derivative of l**5/300 + l**4/60 - l**3/10 - 14*l**2. Let v(y) = 0. Calculate y.
-3, 1
Let h(m) be the first derivative of 0*m + 0*m**2 - 4/3*m**3 + 1/2*m**4 + 3. Factor h(t).
2*t**2*(t - 2)
Let p = 52 - 623/12. Let l(n) be the second derivative of -3*n + 0 + 0*n**2 - p*n**4 + 1/6*n**3. Factor l(d).
-d*(d - 1)
Suppose 0 = 5*a - 16 + 6. Suppose v = -j + 6*j, -7 = -a*v + 3*j. Find z such that -1/2*z**4 + 3/4*z**3 - 3/4*z**v + 1/2*z**2 + 0*z + 0 = 0.
-1, -2/3, 0, 1
Suppose 2*m - 13 = 5*s - 3, m + 5*s = -10. Factor 2*i**2 + m*i - 3*i + i**2.
3*i*(i - 1)
Let -300*c**4 - 144*c**5 - 99*c**3 + 4*c - 73*c**3 + 13*c - c = 0. Calculate c.
-1, -2/3, 0, 1/4
Let v be (-3)/6*1*-4. Solve t**v + 1/2*t**3 - 1 - 1/2*t = 0.
-2, -1, 1
Factor -1/4*r**3 + 3/4*r**2 + 0*r - 1.
-(r - 2)**2*(r + 1)/4
Let h(p) be the third derivative of -1/50*p**6 + 0*p + 0*p**3 + 0*p**4 + 1/420*p**8 + 3*p**2 + 0*p**7 + 0 - 2/75*p**5. Solve h(c) = 0 for c.
-1, 0, 2
Let l(r) = r + 1. Let d be l(3). Solve 3*b**3 + 8*b**4 - 6*b**2 + 6*b**4 - 2*b**d - 9*b**5 = 0.
-2/3, 0, 1
Factor -4*i - 4*i + 0*i**5 + 4*i - 8*i**2 + 8*i**4 + 4*i**5.
4*i*(i - 1)*(i + 1)**3
Let h = 6 - 4. Factor 2*l**4 - 3*l + 12*l**h - 2*l - 3*l + 2 - 8*l**3.
2*(l - 1)**4
Suppose 0 = -25*n + 31 + 19. Suppose 4/5*v + 0 - 1/5*v**5 - 4/5*v**4 + 4/5*v**n - 3/5*v**3 = 0. Calculate v.
-2, -1, 0, 1
Suppose -20*f - 2*f**2 + 2*f**2 - 20 - 5*f**2 = 0. Calculate f.
-2
Let s = -44 + 44. Factor 2/9*a**4 + 2/9*a - 2/9*a**3 + s - 2/9*a**2.
2*a*(a - 1)**2*(a + 1)/9
Suppose 2*i = -5*l + 79, 3*i = 4*l + i - 74. Suppose 6*d - l = 1. Factor -q - 1/3 - 1/3*q**d - q**2.
-(q + 1)**3/3
Let g(o) be the first derivative of o**6/5 + o**5/2 + o**4/3 + 4*o - 2. Let h(i) be the first derivative of g(i). Factor h(p).
2*p**2*(p + 1)*(3*p + 2)
Let a = 21 - 15. Let f = 8 - a. Determine s, given that -2/7 + 8/7*s**3 - 8/7*s + 2/7*s**f = 0.
-1, -1/4, 1
Let c(p) = 5*p**2 - 5*p. Let h(a) = -a**2 + 7*a + 4. Let r be h(8). Let x(q) = -4*q**2 + 4*q. Let s(b) = r*x(b) - 3*c(b). Factor s(g).
g*(g - 1)
Let f be 8/3 - (-1)/3. Let t be (-8)/20*-5*1. Suppose -15*g**t - 6*g**2 - 6*g**f + 5*g**2 - 14*g - 4 = 0. What is g?
-1, -2/3
Factor -9/7*c - 3/7*c**2 + 12/7.
-3*(c - 1)*(c + 4)/7
Let v(f) be the second derivative of -f**6/90 - f**5/20 - f**4/18 - 3*f. Factor v(k).
-k**2*(k + 1)*(k + 2)/3
Let m(v) be the second derivative of v**5/16 - 5*v**4/48 + 5*v. Solve m(c) = 0 for c.
0, 1
Let l(u) = -u**4 + u**3 + 2*u**2 - 2*u + 2. Let m(d) = -d**2 + d + 1. Let w(c) = l(c) - 2*m(c). Suppose w(p) = 0. Calculate p.
-2, 0, 1, 2
Let c = 4 + -8. Let q(j) = j**4 - j**3 + j - 1. Let v(l) = 4*l**5 - 4*l**3 + 4*l - 4. Let y(g) = c*q(g) + v(g). Solve y(z) = 0 for z.
0, 1
Let w(g) be the first derivative of g**2 - 3*g - 1/9*g**3 + 1. Determine t, given that w(t) = 0.
3
Suppose -3 = 3*n + 3*o, 4*n = 3*o - o + 14. Factor -9 + 9 + 4*i + 0*i + n*i**2.
2*i*(i + 2)
Let i = 762/221 - 56/17. Factor 10/13*x**4 - 2/13*x**2 + 4/13*x**5 + 0 - i*x + 6/13*x**3.
2*x*(x + 1)**3*(2*x - 1)/13
Let b be -2 + -1*(5 + -9). Let w(z) be the first derivative of -3 + 0*z + 1/11*z**b - 2/33*z**3. Suppose w(f) = 0. What is f?
0, 1
Factor 2/19*h**2 + 0 - 2/19*h.
2*h*(h - 1)/19
Let n be (1/(15/(-9)))/((-4)/8). Let 18/5*u**3 - 46/5*u**4 + n*u**2 - 2/5*u + 0 + 24/5*u**5 = 0. Calculate u.
-1/3, 0, 1/4, 1
Let n(f) be the third derivative of f**5/15 + f**4/6 + 16*f**2. Factor n(b).
4*b*(b + 1)
Let v = 28/9 - 47/18. Let l = -35/2 - -18. Factor v*t**2 - l*t**3 + 0 + 0*t.
-t**2*(t - 1)/2
Let t(x) be the first derivative of -2 - 1/6*x**4 - 2/3*x - 7/9*x**3 - 7/6*x**2. Find f such that t(f) = 0.
-2, -1, -1/2
Let p(a) be the second derivative of a**7/105 - 2*a**6/75 - 9*a**5/25 - 16*a**4/15 - 23*a**3/15 - 6*a**2/5 + 2*a + 33. Factor p(m).
2*(m - 6)*(m + 1)**4/5
Let d(x) be the first derivative of -10/3*x**3 + 1 + 4*x + x**2 - 1/2*x**4 + 6/5*x**5. Solve d(i) = 0.
-1, -2/3, 1
Let g(w) be the third derivative of 11/60*w**5 + 0 + 1/40*w**6 + 1/2*w**4 + 0*w + 2/3*w**3 + 7*w**2. Factor g(s).
(s + 1)*(s + 2)*(3*s + 2)
Let g = -33/8 + 181/40. Let 2/5*q**2 + 0 + g*q = 0. What is q?
-1, 0
Let u(q) be the first derivative of 2 + 0*q + 0*q**2 - 1/20*q**4 + 1/15*q**3. Factor u(p).
-p**2*(p - 1)/5
Let u be 7 - 1 - 2 - 0. Let g = u - 2. Determine b so that -37 + 2*b + 2*b**g + 37 = 0.
-1, 0
Let v(h) = 3*h - 4*h + h - h + 7. Let m be v(4). Suppose -4/13*y**2 + 0 + 0*y - 10/13*y**m = 0. Calculate y.
-2/5, 0
Suppose 122 = p + 120. Determine n, given that -1 + 3/2*n**3 + 3*n - 13/4*n**p - 1/4*n**4 = 0.
1, 2
Suppose -179 = -4*g - 19. Suppose -3*i = 5*r - 32, 0*i - 5*i + g = 5*r. Factor 0 + 2 + 3*l**3 - 3*l + i*l**2 - 6*l**2.
(l - 1)*(l + 1)*(3*l - 2)
Let d(h) be the second derivative of -4*h + 0*h**3 + 0 + 1/5*h**6 - 1/14*h**7 + 0*h**4 - 3/20*h**5 + 0*h**2. Let d(s) = 0. Calculate s.
0, 1
Let o(z) be the third derivative of z**7/490 - z**6/280 - z**5/70 - 13*z**2. Factor o(f).
3*f**2*(f - 2)*(f + 1)/7
Let x = 21 + -19. Let w(h) be the first derivative of 0*h + 2/9*h**3 + 1 - 1/3*h**4 + 0*h**x + 2/15*h**5. Factor w(o).
2*o**2*(o - 1)**2/3
Let j be ((-32)/(-10))/(1/5). Let g be j/12*3/2. Factor -3*o + 3 + o**2 + 5*o - g.
(o + 1)**2
Let v(b) be the third derivative of b**5/300 + b**4/120 - 6*b**2. What is c in v(c) = 0?
-1, 0
Let j(h) = -22*h**3 - 2*h**2 + 12*h + 12. Let v(g) = -9*g**3 - g**2 + 5*g + 5. Suppose 0 = 2*d - d - 5. Let z = 0 + d. Let l(o) = z*j(o) - 12*v(o). Factor l(a).
-2*a**2*(a - 1)
Let b be 5/(-18) + (-37)/(-74). Factor 4/9*v**2 + b*v**3 - 2/9*v - 4/9.
2*(v - 1)*(v + 1)*(v + 2)/9
Factor -11*i**4 - 3*i + 6*i 