st derivative of -o**3/12 - o**2 - 4*o - 5. Factor b(q).
-(q + 4)**2/4
Let g(b) be the second derivative of -2*b**7/105 - 2*b**6/75 + 3*b**5/25 + b**4/3 + 4*b**3/15 - 15*b. Suppose g(h) = 0. What is h?
-1, 0, 2
Let r(j) = j + 6. Let y be r(-7). Let z be 1/((-1)/3)*y. Factor -10/3*k**2 - 4/3*k**z - 2/3*k + 4/3.
-2*(k + 1)*(k + 2)*(2*k - 1)/3
Let -4/3*u**2 + 4/3 + 4/3*u - 4/3*u**3 = 0. What is u?
-1, 1
Let t be (-198)/(-540) - (-4)/30. Factor 1/4*w + 1/4*w**2 - t.
(w - 1)*(w + 2)/4
Suppose 2*i - i = 4*g + 14, 2*i = 4*g + 20. Let m(j) be the third derivative of -j**2 + 0*j**5 + 0*j - 1/30*j**i + 0 + 0*j**3 - 1/35*j**7 + 0*j**4. Factor m(p).
-2*p**3*(3*p + 2)
Factor 5*u - 13*u - u**3 + 6*u - 6 + 6*u**2 + 3*u**3.
2*(u - 1)*(u + 1)*(u + 3)
Suppose 2*j = -14*c + 18*c + 2, 5*j = 2*c + 21. Let b(n) be the first derivative of 4 - 3/4*n**c + 0*n + 3/8*n**4 + 0*n**3. Factor b(u).
3*u*(u - 1)*(u + 1)/2
Factor 2/17*x**3 + 8/17 - 2/17*x - 8/17*x**2.
2*(x - 4)*(x - 1)*(x + 1)/17
Let t(z) be the second derivative of z**7/14 + 13*z**6/30 + 11*z**5/10 + 3*z**4/2 + 7*z**3/6 + z**2/2 - 6*z. Factor t(q).
(q + 1)**4*(3*q + 1)
Let r(s) = -3*s**3 + 4*s + 2*s**4 + 10*s**2 - s**4 + 0*s**3 - 4. Let k(u) = 3*u**3 - 9*u**2 - 3*u + 3. Let o(t) = -4*k(t) - 3*r(t). Find j such that o(j) = 0.
-2, 0, 1
Let l(t) = 6*t**2 + 6*t - 2. Let w(r) = -5*r**2 - 6*r + 3. Let p = -2 - -9. Let k(c) = p*w(c) + 6*l(c). What is f in k(f) = 0?
3
Let l(h) = -155*h**3 + 285*h + 220. Let d(t) = 7*t**3 - 13*t - 10. Let i(x) = -45*d(x) - 2*l(x). Factor i(w).
-5*(w - 2)*(w + 1)**2
Find x, given that 9*x - 4*x + x**2 + x**2 - 7*x = 0.
0, 1
Let f(k) be the second derivative of -k**5/4 + 25*k**4/6 - 80*k**3/3 + 80*k**2 - 19*k. Solve f(t) = 0.
2, 4
Suppose -2/5*t**5 + 14/5*t**2 + 48/5*t - 46/5*t**3 - 32/5 + 18/5*t**4 = 0. What is t?
-1, 1, 4
Determine s, given that -10/3*s**3 + 2/3*s**4 + 4/3 - 14/3*s + 6*s**2 = 0.
1, 2
What is i in -1 + 5 - 41*i**2 + 2*i**3 + 49*i**2 + 10*i = 0?
-2, -1
Factor 2*n + 0*n**2 + 5*n**2 + 8*n**2 - 9*n**2 + 2*n**3.
2*n*(n + 1)**2
Let t(z) be the first derivative of 8*z**3/39 + z**2/13 - 15. Factor t(g).
2*g*(4*g + 1)/13
Factor 1152*p**5 - 60*p**3 + 12*p**2 + 30*p**4 + 38*p**2 - 1157*p**5 - 18*p + 3*p.
-5*p*(p - 3)*(p - 1)**3
Let o(c) = c**4 - c**3 + c**2 + c + 1. Let y(v) = 2*v**5 + 5*v**4 - 9*v**3 + 5*v**2 + 7*v + 5. Let a(z) = -5*o(z) + y(z). Factor a(p).
2*p*(p - 1)**2*(p + 1)**2
Let y(f) = 26*f**4 - 16*f**3 - 10*f**2 + 16. Let n(q) = 5*q**4 - 3*q**3 - 2*q**2 + 3. Let a(z) = 16*n(z) - 3*y(z). Factor a(x).
2*x**2*(x - 1)*(x + 1)
Let n = 111 - 108. What is t in -15/2*t + n - 21/2*t**2 = 0?
-1, 2/7
Let n(t) be the second derivative of -t**5/80 - t**4/48 + t**3/12 - 18*t. Factor n(x).
-x*(x - 1)*(x + 2)/4
Let h be (40/10)/(-1 - -3). Let u be (h/15)/((-7)/(-245)). Solve -14/3*n + u*n**3 + 4/3*n**2 - 4/3 = 0 for n.
-1, -2/7, 1
Let p = -1029/10 + 103. Let u(r) be the first derivative of 0*r**2 - 1/3*r**3 + 1/2*r + 0*r**4 + p*r**5 + 1. Factor u(j).
(j - 1)**2*(j + 1)**2/2
Let k(d) be the second derivative of -1/21*d**4 + 0*d**2 - 2*d - 1/21*d**3 + 0. Solve k(i) = 0 for i.
-1/2, 0
Let v be -2*((-77)/429 + (-2)/13). Determine t, given that -4/3*t + v*t**5 + 2*t**4 + 0 - 2*t**2 + 2/3*t**3 = 0.
-2, -1, 0, 1
Let p(u) be the second derivative of -u**7/336 - u**6/120 - u**5/160 - 11*u. Determine o so that p(o) = 0.
-1, 0
Factor -4/3 + 8/3*h - h**2 + 1/3*h**4 - 2/3*h**3.
(h - 2)*(h - 1)**2*(h + 2)/3
What is h in 2 + 6*h**2 - 2*h**2 + 4*h - 5*h**2 - 3*h = 0?
-1, 2
Let p(t) be the third derivative of 2*t**5/15 + 7*t**4/12 - 2*t**3/3 - 9*t**2. Find m, given that p(m) = 0.
-2, 1/4
Suppose 3*j - 5*s - 31 = 0, -7*s = 2*j - 2*s + 21. Solve -5*a**2 - 3*a**j + a**2 - 4 - a**3 - 8*a + 2*a**2 = 0.
-2, -1
Suppose 3*v - 9 = 0, 2*v = 5*h + 3 - 37. Let f = -8 + h. Factor -2/3*w**2 + f*w + 2/3.
-2*(w - 1)*(w + 1)/3
Let a(n) be the third derivative of n**8/26880 - n**7/5040 + n**4/24 - 8*n**2. Let g(f) be the second derivative of a(f). Factor g(l).
l**2*(l - 2)/4
Let r be (-114)/(-57) - (-16)/(-9). Factor -r*h**2 - 4/9 + 2/3*h.
-2*(h - 2)*(h - 1)/9
Let u(i) = 25*i**2 + 76*i + 3. Let g be u(-3). Factor 0*y + 0*y**2 - 1/2*y**3 + 1/2*y**5 + g + 0*y**4.
y**3*(y - 1)*(y + 1)/2
Let n = 13 - 10. Suppose -2/5*x + 0 + 2/5*x**n + 0*x**2 = 0. Calculate x.
-1, 0, 1
Factor -6/13*f**4 + 0 - 2/13*f**2 + 2/13*f**5 + 6/13*f**3 + 0*f.
2*f**2*(f - 1)**3/13
Let a(j) = -j**3 - j**2 + 4*j - 2. Let f be a(1). What is q in f + 4/9*q + 2/9*q**2 = 0?
-2, 0
Suppose -x = -5*x - 12. Let q = x - -7. Factor -2*o**3 + q - 4 - 2*o**2.
-2*o**2*(o + 1)
Let c be 209/133 - (1 + 0). Factor 2/7*q**4 + 0 + 0*q + 2/7*q**2 - c*q**3.
2*q**2*(q - 1)**2/7
Let y be (-16)/(-3) + -3 + 2 + -4. Find b, given that y*b + 0 - 1/3*b**2 = 0.
0, 1
Suppose -2*b + 0 = -4. Factor 2/5*t**b + 0 + 2/5*t - 4/5*t**3.
-2*t*(t - 1)*(2*t + 1)/5
Let m(w) = -w + 13. Let j be m(11). Factor -5*z**2 - 3*z + 4 + z**4 + 7*z - 2*z**3 + 2*z**j.
(z - 2)**2*(z + 1)**2
Let p be 4/(-6) + (-280)/(-60). Let m(d) be the second derivative of 0 - 1/63*d**7 + 0*d**2 - 1/9*d**p + 0*d**5 + 2*d + 1/9*d**3 + 2/45*d**6. Factor m(q).
-2*q*(q - 1)**3*(q + 1)/3
Let k(j) be the second derivative of -j**7/63 - 4*j**6/45 - j**5/5 - 2*j**4/9 - j**3/9 - 2*j. Let k(d) = 0. Calculate d.
-1, 0
Let k(z) = 2*z**2 - z - 1. Let g be k(-1). Suppose -19*l + 8*l**4 + 8 - 10*l - 25*l + 74*l**g + 6*l - 42*l**3 = 0. Calculate l.
1/4, 1, 2
Let o(l) = -3*l - l**2 + 1 + l**2 - l**2. Let f be o(-2). Factor 4/9*c**2 + 0 - 22/9*c**f + 0*c.
-2*c**2*(11*c - 2)/9
Suppose -25 = 2*c - 5*w - 9, c - 5*w + 18 = 0. Factor -30*i**2 + 2*i + 33*i**c + 3 - 8*i.
3*(i - 1)**2
Let t(q) be the third derivative of q**5/24 - 5*q**4/12 + 5*q**3/4 + 2*q**2. Factor t(s).
5*(s - 3)*(s - 1)/2
Let l(s) be the second derivative of -s**2 - 1/6*s**4 + 2/3*s**3 + s + 0. Solve l(m) = 0.
1
Let t = 18 + -10. What is a in 8*a - 5 - 3 + t*a**2 - 28*a**3 + 0*a + 20*a = 0?
-1, 2/7, 1
Let a(k) be the third derivative of k**7/210 + k**6/30 + k**5/12 + k**4/12 + 17*k**2. Solve a(w) = 0.
-2, -1, 0
Suppose -6/5*d**3 + 0 - 2/5*d**4 + 0*d - 4/5*d**2 = 0. What is d?
-2, -1, 0
Let d(b) = -4*b**2 + 54*b + 26. Suppose 3*w - 102 = -0*w. Let p = w - 20. Let z(f) = -f**2 + 11*f + 5. Let i(u) = p*z(u) - 3*d(u). Factor i(o).
-2*(o + 2)**2
Let j = 105 + -103. Factor -10/3*n**2 + j + 4/3*n.
-2*(n - 1)*(5*n + 3)/3
Let c be 3 + (-7)/(-5) - (-44)/(-11). Factor c*f**2 + 0 + 0*f - 2/5*f**3.
-2*f**2*(f - 1)/5
Factor 0*r + 3/4*r**4 - 3/2*r**3 + 0*r**2 + 0.
3*r**3*(r - 2)/4
Factor 1/2*x**3 + 1/4*x**2 - 1/4*x**4 + 0 - 1/2*x.
-x*(x - 2)*(x - 1)*(x + 1)/4
Let h(i) be the second derivative of 2/5*i**6 - 2/35*i**7 + 2*i**3 + 12/5*i**2 - 1/2*i**4 - 3/4*i**5 + 2*i + 0. Suppose h(m) = 0. Calculate m.
-1/2, 2
Factor 0*z + 1/5*z**3 - 1/5*z**4 + 2/5*z**2 + 0.
-z**2*(z - 2)*(z + 1)/5
Let o = -1248/5 + 251. Let 0 + o*w**2 + 2/5*w - 7/5*w**4 - 2/5*w**3 = 0. What is w?
-1, -2/7, 0, 1
Let v(k) be the third derivative of -2*k**7/105 - k**6/5 - 13*k**5/15 - 2*k**4 - 8*k**3/3 - 20*k**2. Let v(y) = 0. What is y?
-2, -1
Factor 10/3*n**4 + 0*n**3 - 10/3*n**2 + 5/3*n**5 - 5/3*n + 0.
5*n*(n - 1)*(n + 1)**3/3
Suppose 6 + 6 = 4*u. Find g, given that 4*g**2 + g**5 + 6*g**u + 3*g - 2*g - g + 4*g**4 + g = 0.
-1, 0
Let z(g) be the second derivative of g**4/6 + 2*g**3/3 + g**2 - 40*g. Factor z(f).
2*(f + 1)**2
Let z(b) be the third derivative of -1/90*b**6 + 2*b**2 + 0 + 0*b - 1/105*b**7 + 0*b**4 + 1/252*b**8 + 2/45*b**5 - 1/9*b**3. Suppose z(i) = 0. What is i?
-1, -1/2, 1
Let s be 10/45 - 16/(-9). Let j(o) be the first derivative of -1/3*o**3 + 1 - o**s - o. Factor j(x).
-(x + 1)**2
Suppose 3*u = -9, -2*l = -5*u + 2*u - 27. Suppose 18*h**2 + 2*h - 26*h**3 + h**4 + 9 - 13 + l*h**4 = 0. What is h?
-2/5, 1
Let d(p) be the third derivative of -p**5/40 + p**4/8 - p**3/4 + 2*p**2. Let d(i) = 0. Calculate i.
1
Let l(g) be the first derivative of 1 + 1/12*g**4 - 1/6*g**2 - 2/9*g**3 + 2/3*g. Solve l(f) = 0.
-1, 1, 2
Let h(y) = y**2 + 8*y + 10. Let w be h(-7). Let -4/7 - 26/7*t**w + 6/7*t + 18/7*t**4 + 10/7*t**2 - 4/7*t**5 = 0. Calculate t.
-1/2, 1, 2
Let w(f) = -f**2 - 8*f - 5. Suppose l + 3 = -4*y + 2*y, l - 4*y + 15 = 0. Let b be w(l). Let -p + 0*p + 3*p - 2*p**b = 0. Calculate p.
0, 1
Let i(g) = -7*g**3 + 8*g**2 