- 18. Find d, given that f(d) = 0.
-1, 1/4, 1
Let v(t) = t**2 - t + 1. Let a(k) = -6*k**2 + 15*k - 15. Let y(s) = -s + 5. Let g be y(4). Let q(c) = g*a(c) + 3*v(c). Solve q(r) = 0.
2
Factor -4 - l + l**2 + 1 + 1 + 0*l**2.
(l - 2)*(l + 1)
Let c(u) = u**3 + 11*u**2 - 6*u + 5. Let m(r) = r**2 - r. Let b(i) = c(i) - 6*m(i). Let p be b(-5). Factor 0*w**3 + 0*w**2 + 0 - 1/4*w**p + 0*w**4 + 0*w.
-w**5/4
Suppose 5*s = -n + 30, -s + 5 = -0. Suppose -n = -3*t + 7. Factor 2*d**4 + 2*d**2 + 2*d**3 - d**2 - d**t.
d**2*(d + 1)**2
Suppose 3 = -3*i - 3*j, -30*i + 31*i = 4*j + 19. Factor 0*r + 0 + 2/7*r**i + 0*r**2 - 2/7*r**4.
-2*r**3*(r - 1)/7
Let r(o) be the first derivative of -o**5/10 + o**4/8 - 2. Find y such that r(y) = 0.
0, 1
Let g(y) be the first derivative of -y**4/2 - 34*y**3/9 + 8*y**2/3 + 8*y + 20. Find o such that g(o) = 0.
-6, -2/3, 1
Suppose 1 = x + p - 5, 14 = -3*x + 5*p. Factor 1/4*o**3 + 3/4*o + 1/4 + 3/4*o**x.
(o + 1)**3/4
Let f(v) be the third derivative of 0*v - 1/6*v**3 + v**2 - 1/336*v**8 - 1/24*v**4 + 1/60*v**6 + 0 - 1/210*v**7 + 1/30*v**5. Find w such that f(w) = 0.
-1, 1
Let w = 127/3 + -42. Solve 0 + 0*o + w*o**3 - 1/3*o**2 = 0 for o.
0, 1
Let g(l) be the first derivative of -2/3*l**4 + 4/3*l + 26/9*l**3 + 3 - 11/3*l**2. Factor g(z).
-2*(z - 2)*(z - 1)*(4*z - 1)/3
Let n(t) be the first derivative of -5*t**3/12 + 5*t**2/2 - 5*t - 10. Factor n(l).
-5*(l - 2)**2/4
Suppose 7 = -2*t + 4*t + 3*x, 3*t - 9 = -3*x. Let m(a) be the first derivative of 1/3*a**t - 1 + 2/9*a**3 + 0*a. Factor m(p).
2*p*(p + 1)/3
Suppose -3*r + 1 = -4*g, 8 + 3 = -2*g + 5*r. Let y(h) be the second derivative of -1/6*h**g + 0*h**3 - 4*h + 1/36*h**4 + 0. Determine m so that y(m) = 0.
-1, 1
Solve 2*a**3 - a**3 - a**4 + a**2 + a**2 = 0.
-1, 0, 2
Let f = -2 + 4. Find u such that -2*u + 3*u**5 + u**4 + 5*u + 4*u**f - 6*u**3 - 3*u**4 - 2 + 0*u = 0.
-1, 2/3, 1
Let z(n) be the first derivative of -2*n**6/15 + 8*n**5/25 - 8*n**3/15 + 2*n**2/5 + 16. Factor z(r).
-4*r*(r - 1)**3*(r + 1)/5
Factor -2/9*z**3 + 0 + 0*z + 10/9*z**2.
-2*z**2*(z - 5)/9
Let f(p) be the third derivative of -p**6/660 - p**5/330 + p**4/132 + p**3/33 - 4*p**2. Factor f(t).
-2*(t - 1)*(t + 1)**2/11
Factor -240 + 7*a - 2*a - 5*a**3 - 3*a**2 - a**4 + 244.
-(a - 1)*(a + 1)**2*(a + 4)
Suppose -4*s = -s + 339. Let j = s + 235/2. Solve 3/2*x**5 + 11/2*x**4 + 15/2*x**3 + j*x**2 + 0 + x = 0 for x.
-1, -2/3, 0
Let p be (-4)/2 - 1*14. Let v be 2/(-4) + (-56)/p. Factor -2/5*j**4 + 2/5*j - 6/5*j**2 + 0 + 6/5*j**v.
-2*j*(j - 1)**3/5
Let s(z) = 6*z**4 + 5*z**3 - 11*z**2 + 17. Let n(o) = -2*o**4 - 2*o**3 + 4*o**2 - 6. Let c = -4 + -2. Let k(h) = c*s(h) - 17*n(h). Factor k(t).
-2*t**2*(t - 1)**2
Suppose -2/9*u**3 + 4/9 + 2/9*u - 4/9*u**2 = 0. What is u?
-2, -1, 1
Let c be (-1)/((-1)/6*2). Determine o so that 2*o**3 - c*o**3 - o + 2*o**3 = 0.
-1, 0, 1
Let s(i) be the second derivative of 2*i - 1/12*i**4 - 1/40*i**5 + 1/8*i**2 + 1/40*i**6 + 1/12*i**3 + 0. Factor s(c).
(c - 1)**2*(c + 1)*(3*c + 1)/4
Let o(n) be the third derivative of n**7/1470 - n**5/420 + 4*n**2. Factor o(m).
m**2*(m - 1)*(m + 1)/7
Let h be 6/15 - 24/(-15). Determine t, given that 8*t - 25*t**4 - 1 - 2*t - 6*t**3 - 4*t**h + 30*t**4 = 0.
-1, 1/5, 1
Factor 1/5*j**2 + 0*j - 1/5.
(j - 1)*(j + 1)/5
Determine y, given that -32/7*y + 16/7 - 4/7*y**3 + 20/7*y**2 = 0.
1, 2
Let t be (5/4 + 0)/(93/124). Suppose -2/3 + t*r**5 - 10/3*r**3 + 5/3*r + 4/3*r**2 - 2/3*r**4 = 0. Calculate r.
-1, 2/5, 1
Let c be (-60)/(-3)*39/208. What is n in -3/2*n**2 - 15/4*n**3 + 3/2 + c*n = 0?
-1, -2/5, 1
Suppose r + 0*r**3 + 4*r**2 + r - r**2 + r**3 = 0. What is r?
-2, -1, 0
Let h(a) = -2*a**2 + 12*a - 8. Let j(i) = -i**2 + 4*i - 3. Let b(w) = -3*h(w) + 8*j(w). Solve b(y) = 0.
-2, 0
Let u(c) be the third derivative of -c**7/10080 - c**6/1440 - c**5/480 + c**4/8 + 8*c**2. Let z(n) be the second derivative of u(n). Factor z(y).
-(y + 1)**2/4
Let w(r) be the first derivative of 2*r**5/15 + r**4/2 - 14*r**3/9 - 5*r**2 + 12*r + 9. Let w(d) = 0. Calculate d.
-3, 1, 2
Let d(g) be the third derivative of g**8/672 - g**7/84 + g**6/30 - g**5/30 + 5*g**2. Suppose d(q) = 0. What is q?
0, 1, 2
Let j(a) be the second derivative of 0 - 1/5*a**5 + 1/3*a**4 + 8*a + a**2 - 1/21*a**7 - 1/5*a**6 + a**3. Factor j(c).
-2*(c - 1)*(c + 1)**4
Suppose 4*i + 3*b = 31, 6*i + 2*b - 26 = 2*i. Suppose -3*l + i = -l. Factor -10/9*f**3 + 0*f + 2/3*f**4 + 4/9*f**l + 0.
2*f**2*(f - 1)*(3*f - 2)/9
Let x(d) be the first derivative of -d**5/20 + d**3/12 + 1. Factor x(a).
-a**2*(a - 1)*(a + 1)/4
Let o(u) = -u**2 + 3. Let j(q) = -q. Let p(f) = -4*j(f) - o(f). Let t be p(-5). Factor 0*c + 2*c**2 - 1 - c - c**t + c**3.
(c - 1)*(c + 1)**2
Let u = 491/170 + -3/34. Determine q, given that 0 + 32/5*q**3 + 4/5*q + 22/5*q**2 + u*q**4 = 0.
-1, -2/7, 0
Let l = 267 + -513/2. Factor -75/2*m**2 - 6 - l*m**4 + 24*m + 57/2*m**3 + 3/2*m**5.
3*(m - 2)**2*(m - 1)**3/2
Let y(n) be the second derivative of -3*n**5/50 + 19*n**4/30 - 11*n**3/5 + 9*n**2/5 - 11*n. Factor y(t).
-2*(t - 3)**2*(3*t - 1)/5
Let v(n) be the first derivative of -2*n**3/9 - 2*n**2/3 - 2*n/3 - 5. Factor v(m).
-2*(m + 1)**2/3
Let 16/5*b**4 + 0*b - 8/5*b**2 + 28/5*b**3 + 0 = 0. What is b?
-2, 0, 1/4
Let k be (-55)/183 + (-4)/(-12). Let b = 112/305 + k. Factor 1/5 + 0*h - b*h**2 + 0*h**3 + 1/5*h**4.
(h - 1)**2*(h + 1)**2/5
Let j(n) be the first derivative of -9/4*n**2 - 3 + n - 11/6*n**3. Determine m so that j(m) = 0.
-1, 2/11
Let a = 65 - 33. Let p be 2 + a/(-10) + 2. Factor 2/5*l**5 + 0*l**2 + 2/5*l - p*l**3 + 0 + 0*l**4.
2*l*(l - 1)**2*(l + 1)**2/5
Suppose 6*m - 4*m = 0. Let h = 1 + 1. Solve 1 - 3*c**h + m - 2*c**2 + 4*c**2 = 0.
-1, 1
Let a(o) be the third derivative of o**7/2100 + o**6/1200 - o**5/200 - o**4/240 + o**3/30 + 12*o**2. Suppose a(l) = 0. What is l?
-2, -1, 1
Suppose 0 = -27*a + 24*a + 9. Let a - 3/4*s**3 - 9/4*s**2 + 0*s = 0. What is s?
-2, 1
Let t(n) be the second derivative of -2*n + 0 + 0*n**3 + 0*n**2 - 1/18*n**4. Factor t(l).
-2*l**2/3
Let o(h) = 4*h - 6. Let i be o(4). Suppose -3*k = -5*d + i, 2*d + 3*k - 1 = 3. Factor 0 - 1/3*l + 1/3*l**5 - 2/3*l**d + 2/3*l**4 + 0*l**3.
l*(l - 1)*(l + 1)**3/3
Let t(u) be the first derivative of 2*u**3/51 - 2*u/17 - 7. Solve t(k) = 0.
-1, 1
Factor 3*q**2 + 3*q + 6*q**4 - 3*q**3 + 5*q**4 - 14*q**4.
-3*q*(q - 1)*(q + 1)**2
Suppose -x - 2*x + 23 = 5*g, -3*g + 3 = 0. Suppose 3*h + 3 + x = -5*t, 25 = 5*h - 5*t. Solve -w**h + 1/3 + 2/3*w = 0.
-1/3, 1
Let d(c) = 1 + 0*c + c**2 + 0*c. Let x(o) = o**3 - 10*o**2 - 9. Let i be (-74)/(-4) + 6/(-12). Let u(h) = i*d(h) + 2*x(h). Factor u(s).
2*s**2*(s - 1)
Suppose 3*a = -0*a + 9. Let d(f) = f - 1. Let o be d(a). Factor 0 - 1/3*t + 1/3*t**3 + 1/3*t**o - 1/3*t**4.
-t*(t - 1)**2*(t + 1)/3
Let u = -846 + 848. Factor -1/5*s**u + 0 + 1/5*s.
-s*(s - 1)/5
Let d(o) be the third derivative of o**6/240 + o**5/30 + o**4/12 + 9*o**2. Solve d(n) = 0.
-2, 0
Let p(s) = s + 10. Let u be p(-7). Let t be (2 - -1) + 6 + -7. Factor 5*q**t + 2*q - 2 - q**u - 10*q + 6.
-(q - 2)**2*(q - 1)
Factor 2/7*n**4 + 16/7*n**3 + 0 + 40/7*n**2 + 32/7*n.
2*n*(n + 2)**2*(n + 4)/7
Suppose -i = 2*i - 105. Let l be i/50 - 1/2. Factor 4/5*s**4 + s**3 - s - 3/5*s**2 - l.
(s - 1)*(s + 1)**2*(4*s + 1)/5
Factor -7*a - 4*a + 3*a**3 + 6*a + 5*a**2 - 4 + a.
(a - 1)*(a + 2)*(3*a + 2)
Let t(a) be the second derivative of -3*a**5/10 - 5*a**4/12 + a**3 - 34*a. Determine m, given that t(m) = 0.
-3/2, 0, 2/3
Suppose -4*x + 0*x = 36. Let v be 1*3*(-6)/x. Factor -2*k**2 - 2*k - k**2 + k**v.
-2*k*(k + 1)
What is v in 2/11*v**2 - 4/11 - 2/11*v = 0?
-1, 2
Let x = -305 + 613/2. Let p be -2 + (-14)/(-4)*1. Factor -f + x*f**5 + 3/2*f**2 - 7/2*f**4 + 0 + p*f**3.
f*(f - 1)**3*(3*f + 2)/2
Let g(v) be the second derivative of -1/70*v**5 + 0*v**2 + 1/105*v**6 - 6*v - 1/42*v**4 + 0*v**3 + 1/147*v**7 + 0. What is h in g(h) = 0?
-1, 0, 1
Suppose n - 36 = -11*n. What is p in -1/2*p**n - 3/2*p**2 + 0 - p = 0?
-2, -1, 0
Let v(t) be the second derivative of 0*t**2 - 3*t + 0*t**4 + 0 + 1/30*t**5 + 0*t**3. Suppose v(p) = 0. Calculate p.
0
Let c(r) = 3*r + 3. Let x(k) = k**2 - 2*k - 2. Let l(t) = -3*c(t) - 4*x(t). Let h(b) = 5*b**2 + 2*b + 2. Let u(q) = 4*h(q) + 6*l(q). Solve u(d) = 0.
-1/2, 1
Let t be (-8)/(-12) + 435/(-18). Let u = -22 - t. Determine d s