5. What is x in j(x) = 0?
-1, 0, 1/2, 1
Solve 0*m - 2/9*m**2 + 4/9*m**3 + 0 = 0.
0, 1/2
Let t(g) be the first derivative of g**8/2240 + g**7/672 + g**6/720 - g**3/3 + 5. Let m(k) be the third derivative of t(k). Suppose m(w) = 0. Calculate w.
-1, -2/3, 0
Let j be 2 + (-1 - -1) - -1. Suppose 4*y - 5*x - 19 = -j, -20 = -5*y + 2*x. Factor -l**y + l**3 + 3*l**5 - l**5 + l**2 - 3*l**5.
-l**2*(l - 1)*(l + 1)**2
Let b = -1 - -3. Suppose -2*r + 9 = r. Determine h, given that -2*h**3 + 3*h**r - 4*h**3 + 2*h - h**b = 0.
-1, 0, 2/3
Let i(p) = -p**3 + 7*p**2 - 6*p + 2. Let l be i(6). Suppose -10 + 7 + 6*z - z**l - 2*z**2 = 0. Calculate z.
1
Let l(w) be the first derivative of -w**8/1260 + w**7/630 + w**6/135 + 8*w**3/3 + 2. Let g(r) be the third derivative of l(r). Factor g(c).
-4*c**2*(c - 2)*(c + 1)/3
Let n(y) = -y**3 - 9*y**2 - 21*y - 5. Let a be n(-3). Factor 0 - 1/3*q**2 + 1/3*q**3 + 0*q - 1/3*q**5 + 1/3*q**a.
-q**2*(q - 1)**2*(q + 1)/3
Suppose 0 = z + 6 - 8. Suppose -z = 2*m - 8. Factor 2/9 - 2/9*p**2 + 2/9*p - 2/9*p**m.
-2*(p - 1)*(p + 1)**2/9
Let q(j) be the first derivative of -3/4*j - 9/8*j**2 - 1/2*j**3 + 1/8*j**6 + 9/20*j**5 - 4 + 3/8*j**4. Determine t, given that q(t) = 0.
-1, 1
Suppose c = 3*k + 47, 6*k - 2*k = 5*c - 191. Let s = -35 + c. Factor 1/7*i + s - 3/7*i**2.
-i*(3*i - 1)/7
Let l(j) = -3*j**3 - j**2 + 5*j - 5. Let z(k) = 4*k**3 + 2*k**2 - 6*k + 6. Let m(b) = -6*l(b) - 5*z(b). Let m(s) = 0. Calculate s.
-2, 0
Let d be 1/4 + (-15)/(-4). Find n such that -6*n**3 - 3*n**d + 4*n**3 + 5*n**4 = 0.
0, 1
Let x = 1/602 - 136657/1806. Let j = -75 - x. Find w, given that 4/3*w**2 - j*w - 2/3 = 0.
-1/2, 1
Let j(x) = -x**3 + 8*x**2 - 6*x - 4. Let o be j(7). Factor -k**2 - 3*k**3 + 0 + 4*k**2 + o*k**5 - 3*k**4 + 0.
3*k**2*(k - 1)**2*(k + 1)
Let c be (2/3)/(16/48). Factor 4/3*k - 2/9 - 2*k**c.
-2*(3*k - 1)**2/9
Let w(y) be the second derivative of y**5/80 - y**4/24 + y**3/24 + 11*y. Find l such that w(l) = 0.
0, 1
Let x(w) be the second derivative of -5*w**4/12 - 35*w**3/6 + 8*w. Determine h, given that x(h) = 0.
-7, 0
Let i = 6 - 2. What is b in -5*b**2 + i*b**2 + 2*b**2 - 3*b + 2 = 0?
1, 2
Let i(q) be the first derivative of q**6/21 - 8*q**5/35 + 3*q**4/7 - 8*q**3/21 + q**2/7 - 3. Determine j so that i(j) = 0.
0, 1
Let b(t) be the second derivative of t**5/30 - 2*t**4/15 + 4*t**3/45 + 4*t. Suppose b(d) = 0. Calculate d.
0, 2/5, 2
Factor w + 0 + 5/3*w**2 + 1/3*w**3 - 1/3*w**4.
-w*(w - 3)*(w + 1)**2/3
Let u = 75 + -72. Factor -1/4*o - 1/2*o**2 + 0 + 7/4*o**u - o**4.
-o*(o - 1)**2*(4*o + 1)/4
Let r(a) be the third derivative of 0*a - 1/280*a**6 - 1/245*a**7 - 7*a**2 + 0*a**5 - 1/784*a**8 + 0*a**4 + 0 + 0*a**3. Find t, given that r(t) = 0.
-1, 0
Let r(f) = -2*f**3 + 7*f**2 - 9*f - 29. Let x(c) = -c**3 + 2*c**2 - 3*c - 10. Let p(l) = 4*r(l) - 11*x(l). Factor p(d).
3*(d - 1)*(d + 1)*(d + 2)
Let x(q) = 4*q**2 - 3*q + 8. Let l be x(-4). Let h be 27/l - 27/(-63). Factor 3/4*g**2 + 0 + 1/4*g**4 - h*g**3 - 1/4*g.
g*(g - 1)**3/4
Suppose 0 = 2*s - s - 25. Let c be 35/s + (-3)/(-5). Solve 2/9*r**3 - 2/3*r**c + 2/3*r - 2/9 = 0.
1
Factor -2/13*q**2 + 0 - 4/13*q.
-2*q*(q + 2)/13
Let p be (-1 + -2 - -3)/1. Factor p + 0*h**2 + 2/7*h**5 + 2/7*h**4 + 0*h + 0*h**3.
2*h**4*(h + 1)/7
Let x(j) be the third derivative of -j**9/60480 - j**8/20160 - j**5/60 + 2*j**2. Let g(r) be the third derivative of x(r). What is l in g(l) = 0?
-1, 0
Let v(z) be the first derivative of 3*z**6/2 - 21*z**5/5 + 15*z**4/4 - z**3 - 3. Factor v(j).
3*j**2*(j - 1)**2*(3*j - 1)
Let i(m) be the first derivative of 0*m - 1/4*m**2 + 7/8*m**4 - 6 - 1/3*m**3 - 2/5*m**5. Let i(k) = 0. What is k?
-1/4, 0, 1
Let i(g) be the second derivative of -1/18*g**4 + 1/30*g**5 + 0*g**3 + g + 0*g**2 + 0. Determine b so that i(b) = 0.
0, 1
Suppose -9 = 13*g - 22. Let l(k) be the first derivative of 2/21*k**3 + 1/7*k**2 - 2/7*k + g - 1/14*k**4. Factor l(r).
-2*(r - 1)**2*(r + 1)/7
Let q = -3/11668 - -129853/180854. Let j = q + 1/31. What is h in -j*h**5 + 1/4*h**4 + 0 + 0*h**2 + 0*h + 0*h**3 = 0?
0, 1/3
Solve x**3 - 4*x + 4*x**3 + 3*x**4 + 7*x**3 + 5*x**4 = 0.
-1, 0, 1/2
Let f(p) be the second derivative of 0 - 1/50*p**5 + 0*p**4 + 2*p + 0*p**3 + 0*p**2. Factor f(w).
-2*w**3/5
Let n(y) be the third derivative of 1/12*y**3 + 0 + 0*y + 3*y**2 + 0*y**4 - 1/120*y**5. Factor n(h).
-(h - 1)*(h + 1)/2
Let i(n) = -3*n**2 + 3. Let r be i(2). Let p be 6*(-2 + (-21)/r). Factor -3/2*u**3 - 5/2*u**2 + p*u**4 + 3/2*u + 1/2.
(u - 1)**2*(u + 1)*(4*u + 1)/2
Let j(c) be the second derivative of -1/6*c**4 - 1/3*c**3 + 4*c + 0 + 0*c**2. Factor j(u).
-2*u*(u + 1)
Let h(b) = 2*b**2 + 3*b. Let d be h(-2). Suppose 4*a = -3*x + 51, -2*a = -3*x + d*x + 7. Solve 8*f**5 + 3*f - f - x*f**3 + 3*f**3 = 0 for f.
-1, -1/2, 0, 1/2, 1
Suppose 0*f + 4*f - 8 = 0. Let m = f + 1. Factor -2/3 + 2/3*v**2 + 2/3*v**m - 2/3*v.
2*(v - 1)*(v + 1)**2/3
Let h = 3 + -3. Suppose -f + h*f = -3. What is z in -z**4 - 3*z**f + 2*z**3 + 2*z**4 = 0?
0, 1
Let m be (-9)/6*(-6)/(-9). Let k be 3 + (-12)/7 + m. Let -k*a + 0 + 2/7*a**2 = 0. Calculate a.
0, 1
Factor -4/13*p**2 + 0*p**3 + 2/13*p - 2/13*p**5 + 4/13*p**4 + 0.
-2*p*(p - 1)**3*(p + 1)/13
Let u = -1384 - -161927/117. Let j = u + 157/117. Factor -1/3*p + j*p**3 - p**2 + 0.
p*(p - 1)*(4*p + 1)/3
Let o(y) = -y**2 - 6*y - 2. Let s be o(-4). Let u = -6 + s. Let -3/2*l**3 + 1/2*l**4 + u - 1/2*l + 3/2*l**2 = 0. Calculate l.
0, 1
Let u(b) = -b**3 + 5*b**2 + 3*b - 5. Let x(t) = -t**3 - t**2 - t + 1. Let m(o) = -2*u(o) - 2*x(o). Factor m(l).
4*(l - 2)*(l - 1)*(l + 1)
Let m(l) = -l**3 + l**2 - l. Let r(q) = 60*q**3 - 50*q**2 - 5*q. Let x(d) = 5*m(d) + r(d). Let x(b) = 0. What is b?
-2/11, 0, 1
Suppose 5*c - 10 = -0*c. Let q(f) be the first derivative of 1/14*f**4 - 2/35*f**5 - c + 0*f**2 + 0*f + 0*f**3. What is g in q(g) = 0?
0, 1
Suppose -12/11*w - 2/11 - 18/11*w**2 = 0. Calculate w.
-1/3
Let m(t) be the first derivative of 3/10*t**5 + 3/2*t**3 - 3/2*t**4 + 1 + 3*t**2 - 6*t. Find n, given that m(n) = 0.
-1, 1, 2
Let v = 8/21 - 3/14. Let u(n) be the second derivative of -2*n - 1/18*n**3 + 1/18*n**4 - 1/126*n**7 - 1/90*n**6 + 1/30*n**5 + 0 - v*n**2. Factor u(m).
-(m - 1)**2*(m + 1)**3/3
Let v(l) be the second derivative of 5*l**4/24 + 5*l**3/6 - l. Solve v(s) = 0.
-2, 0
Suppose -41*m + y - 14 = -44*m, -5*m - 4*y + 35 = 0. Factor 2/9*t**m + 0*t + 0*t**2 - 2/9*t**4 + 0.
-2*t**3*(t - 1)/9
Let w(k) = -k**2 - 8*k. Let v be w(-6). Determine t so that v*t - 4*t**2 + 6*t**3 - 9*t**2 + 6*t**4 - 5 - 7*t**4 + 1 = 0.
1, 2
Let r(q) be the first derivative of 1/4*q**6 - 1/2*q**3 + 0*q - 3/8*q**4 - 1 + 0*q**2 + 3/10*q**5. Factor r(j).
3*j**2*(j - 1)*(j + 1)**2/2
Let g(d) be the second derivative of 2*d**6/75 - 2*d**5/25 + d**4/15 + 11*d. Find i such that g(i) = 0.
0, 1
Let z(o) be the first derivative of -o**5/90 + o**4/36 + 2*o**3/9 - o**2/2 + 3. Let g(n) be the second derivative of z(n). Factor g(t).
-2*(t - 2)*(t + 1)/3
Let g be 4/(-6)*438/(-365). Let -g*a**3 + 8/5 + 16/5*a**2 - 4*a = 0. What is a?
1, 2
Suppose -2*j - 2 = -3*a + 3, -4*a + 2 = -5*j. Let o = 6 + -2. Suppose o*y**a + 2*y**4 - 4*y**5 + 2*y**5 + 3*y**5 - 3*y**3 = 0. What is y?
-1, 0
Let q(y) be the first derivative of 0*y + 3/4*y**2 + 2 - 3/8*y**4 + 3/10*y**5 - 1/2*y**3. Suppose q(a) = 0. What is a?
-1, 0, 1
Let -3/7*s**5 - 18/7*s + 33/7*s**2 - 24/7 + 3*s**3 - 9/7*s**4 = 0. Calculate s.
-4, -1, 1, 2
Let r be ((-30)/(-50))/((-1)/(-45)). Let y = r - 22. Suppose 0 + 6*a**2 + 33/2*a**3 + 27/4*a**y + 18*a**4 + 3/4*a = 0. What is a?
-1, -1/3, 0
Let w(z) be the second derivative of 6/5*z**2 - 9/100*z**5 - 1/4*z**4 + 5*z + 2/5*z**3 + 0. Factor w(f).
-3*(f - 1)*(f + 2)*(3*f + 2)/5
Factor -2 - 8 + 8 + 3*u - u**2.
-(u - 2)*(u - 1)
Suppose 12 = -r - 2*r. Let c = 6 + r. Factor 7 - 4*t**3 - 7 + 2*t**5 + c*t.
2*t*(t - 1)**2*(t + 1)**2
Let w = -10 + 4. Let j be 8/w*(-7 - 59). What is r in j*r + 71*r**2 + 109*r**2 + 16 + 40*r**4 + 14*r**4 + 162*r**3 = 0?
-1, -2/3
Let x be (2/(-4))/((-4)/32). Let f(d) be the third derivative of 0*d**5 + 0 + 0*d - 2*d**2 - 1/360*d**6 + 0*d**3 + 1/72*d**x. Suppose f(a) = 0. Calculate a.
-1, 0, 1
Let s(a) be the third derivative of a**6/60 + a**5/15 + a**4/12 - 5*a**2. Determine v so that s(v) = 0.
-1, 0
Let l(o) be the first derivative of -o**5/20 - o**4/12 - 3