 Find p, given that -9*p**5 - 12*p + 33*p**c + 12*p**2 - 18*p**5 + 6*p**4 - 24*p**4 = 0.
-1, 0, 2/3
Let y(q) = 2*q**4 + 16*q**3 - 28*q**2 + 16*q - 4. Let i(w) = w**4 + w**3 - w**2 - 1. Let j(h) = 4*i(h) - y(h). Solve j(v) = 0.
0, 2
Let i**5 + 169*i - 2*i**4 + 4*i**2 - 2 - 2*i**5 - 170*i + 2*i**3 = 0. What is i?
-2, -1, 1
What is b in -1/2*b**2 + 0 - 1/2*b = 0?
-1, 0
Suppose 0*y = -3*y. Let f be ((-10)/(-4) + -2)*4. Factor 2/9*q + y + 2/9*q**f.
2*q*(q + 1)/9
Let k = -76/31 + 5791/124. Let d = k + -44. Solve 0 + 1/4*j + 0*j**3 + 1/2*j**4 - 1/2*j**2 - d*j**5 = 0 for j.
-1, 0, 1
Factor -1/2*r**2 + 0*r + 0 + 1/2*r**3.
r**2*(r - 1)/2
Factor 0 + 32/11*q - 16/11*q**2 + 2/11*q**3.
2*q*(q - 4)**2/11
Let h(k) be the first derivative of -169*k**4/6 - 442*k**3/9 - 56*k**2/3 - 8*k/3 + 9. Solve h(p) = 0.
-1, -2/13
Let h(a) be the first derivative of -2/27*a**3 + 1 - 4/9*a + 1/3*a**2. Determine f so that h(f) = 0.
1, 2
Let m = -2/1559 + 9368/10913. Let -4/7*v + m - 2/7*v**2 = 0. What is v?
-3, 1
Factor 13/2 + 1/2*m**2 + 7*m.
(m + 1)*(m + 13)/2
Let a(x) = 2*x**2 + 4*x - 1. Let v(h) = 0 + 6*h**2 + 1 - 3 + 12*h. Let z(t) = -8*a(t) + 3*v(t). Solve z(m) = 0.
-1
Let m(i) be the first derivative of 2*i**3/15 + 2*i**2/5 - 6. Factor m(u).
2*u*(u + 2)/5
Suppose 6*z - 3*z + 7 = 5*n, 3 = -n + 5*z. Factor -22/5*h**n + 4/5*h - 26/5*h**3 + 0.
-2*h*(h + 1)*(13*h - 2)/5
Determine s, given that -3/10 + 1/10*s**2 - 1/5*s = 0.
-1, 3
Let j(h) be the second derivative of h**7/21 - 2*h**6/45 - 2*h**5/15 + h**4/9 + h**3/9 + 14*h. Let j(f) = 0. What is f?
-1, -1/3, 0, 1
Let z(j) be the second derivative of -125*j**7/84 - 305*j**6/12 - 74*j**5 - 271*j**4/3 - 172*j**3/3 - 20*j**2 - 34*j. Find k such that z(k) = 0.
-10, -1, -2/5
Let u be (-10)/(-1)*1/2. Suppose -u*t = -2*t - 9. Let 3*m**t + 8*m**3 + m + m + 9*m**2 - 2*m**3 = 0. Calculate m.
-2/3, -1/3, 0
Let d(y) be the third derivative of -y**6/540 + y**4/36 - 2*y**3/27 + 8*y**2. What is x in d(x) = 0?
-2, 1
Let w(k) be the third derivative of 1/24*k**3 + 1/40*k**5 - 1/24*k**4 + 5*k**2 + 0 - 1/120*k**6 + 1/840*k**7 + 0*k. Factor w(r).
(r - 1)**4/4
Factor 2/3*q**2 + 10/9*q - 2/9*q**4 + 4/9 - 2/9*q**3.
-2*(q - 2)*(q + 1)**3/9
Suppose 0 = b + 2*d + 4, -4*d + 2*d + 4 = 3*b. Suppose c + b*c = 0. Factor -1/4*k**4 - 1/4*k + c + 1/4*k**2 + 1/4*k**3.
-k*(k - 1)**2*(k + 1)/4
Let f(s) be the third derivative of s**6/120 - s**5/40 + s**3/12 - 7*s**2. Determine m so that f(m) = 0.
-1/2, 1
Let f(r) be the second derivative of 5*r**4/12 - 20*r**3/3 + 40*r**2 - 33*r. Determine j, given that f(j) = 0.
4
Suppose 709*g = 717*g - 16. Let 4 + 8/3*z - 4/3*z**g = 0. What is z?
-1, 3
Let g(h) be the first derivative of h**4/14 - 8*h**3/21 + 5*h**2/7 - 4*h/7 + 57. Suppose g(v) = 0. What is v?
1, 2
Let a(d) = 2*d**5 - 6*d**3 + 2*d**2 - 2. Let r(x) = -x**4 + x**3 - x**2 + 1. Let z(y) = a(y) + 2*r(y). Determine p, given that z(p) = 0.
-1, 0, 2
Let w = 81/68 + 18/17. Suppose 9/4*i + i**4 - 1/2 - 1/2*i**2 - w*i**3 = 0. Calculate i.
-1, 1/4, 1, 2
Let j(f) be the third derivative of 1/90*f**5 + 0*f**3 + 0 + 0*f + 1/360*f**6 + 1/72*f**4 - 4*f**2. Factor j(i).
i*(i + 1)**2/3
Factor 2*o**3 - 6*o**2 + 21*o + 13*o - 2 - 10*o**2 - 18.
2*(o - 5)*(o - 2)*(o - 1)
Let b(t) be the third derivative of -t**6/360 + t**4/72 - 9*t**2. Factor b(i).
-i*(i - 1)*(i + 1)/3
Suppose -3*n = -5*t + 13, 5*n + 3*t - 44 = -9. Let w be n/6*(-108)/(-40). Factor 3/5*j**3 + w*j - 9/5*j**2 - 3/5.
3*(j - 1)**3/5
Let k(o) be the third derivative of -o**2 + 1/21*o**4 + 0 - 1/210*o**5 + 0*o - 1/7*o**3. Let k(y) = 0. Calculate y.
1, 3
Let o(s) = s**2 - s + 4. Let v(t) = -t**2 + 2*t - 5. Let f(k) = 5*o(k) + 4*v(k). Find r, given that f(r) = 0.
-3, 0
Let z(w) be the third derivative of 0*w + 0 + w**2 + 1/180*w**5 + 1/18*w**3 + 1/36*w**4. Factor z(a).
(a + 1)**2/3
Let o(i) = 8*i**3 + 16*i**2 + 5*i + 5. Let x(l) = 12*l**3 + 24*l**2 + 8*l + 8. Let f(c) = 8*o(c) - 5*x(c). Find t such that f(t) = 0.
-2, 0
Let q(x) be the second derivative of -7*x - 1/9*x**4 + 0 + 1/63*x**7 + 1/15*x**5 - 1/3*x**2 - 1/3*x**3 + 1/15*x**6. Factor q(c).
2*(c - 1)*(c + 1)**4/3
Let m = -13 + 20. Let l(f) = f**2 - 7*f + 4. Let a be l(m). Suppose 3*d**4 - 3*d**3 + 2*d**a - 3*d**4 + d**2 = 0. Calculate d.
0, 1/2, 1
Suppose -f - 6 = -3*f. Factor 2*k**f + 8*k + 2*k**4 + 2 - 6*k**2 - 10*k + 2.
2*(k - 1)**2*(k + 1)*(k + 2)
Let b = -2339/7 + 335. Let m be 33/(-84) - 10/(-8). Factor m*j**2 + 2/7*j**3 + b*j + 2/7.
2*(j + 1)**3/7
Let u(x) be the first derivative of -x**8/28 - x**7/70 + x**6/10 + x**5/20 - x**2/2 + 2. Let q(y) be the second derivative of u(y). Suppose q(f) = 0. What is f?
-1, -1/4, 0, 1
Let t be (4/6)/(4/24). Let b(x) be the second derivative of 1/60*x**6 + 0*x**5 + x + 1/4*x**2 + 0*x**3 + 0 - 1/12*x**t. Factor b(i).
(i - 1)**2*(i + 1)**2/2
Let c(u) = u**2 - 11*u + 12. Let h be c(10). Let k(l) = 0 + 2 + 4 - 8*l**h. Let f(w) = 9*w**2 - 7. Let x(a) = 6*f(a) + 7*k(a). Factor x(t).
-2*t**2
Let g(q) = q**4 - q**2 + q - 1. Let n(o) be the second derivative of -o**6/5 + o**4/2 - 2*o**3/3 + 2*o**2 - 2*o. Let y(i) = -4*g(i) - n(i). Factor y(t).
2*t**2*(t - 1)*(t + 1)
Let j(p) = -p**4 + p**3 + p**2 - p - 1. Let h(n) = -41*n**4 - 6 + 36*n**3 + 7*n**4 - 8*n**2 - 3*n**2 + 13*n**3 - 4*n. Let c(x) = -h(x) + 6*j(x). Factor c(k).
k*(k - 1)*(4*k - 1)*(7*k - 2)
Let l(w) be the second derivative of -w**4/15 - 2*w**3/15 - 12*w. Find z such that l(z) = 0.
-1, 0
Let u(l) = l**3 + 4*l**2 + 2*l + 1. Let v be u(-3). Suppose -2*o = -4*o + v. Factor 0*y - 2/7*y**5 + 0*y**4 + 0*y**o + 0 + 2/7*y**3.
-2*y**3*(y - 1)*(y + 1)/7
Factor -64/9*w - 2/9*w**3 + 20/9*w**2 + 64/9.
-2*(w - 4)**2*(w - 2)/9
Let w be 6/21 + (-54)/(-7). Factor -p**3 + 7*p**4 + w*p**2 - 11*p**3 + 5*p**5 - 2*p - 7*p**5 + p**4.
-2*p*(p - 1)**4
Let x = 1321/15 + -88. Let o(w) be the second derivative of -w - 1/100*w**5 + 0 + x*w**3 + 0*w**2 + 1/60*w**4. Find v such that o(v) = 0.
-1, 0, 2
Let f be ((-27)/12)/3 + (-2)/(-2). Let v(i) be the first derivative of -f*i + 1/16*i**4 - 1/8*i**2 + 1 + 1/12*i**3. Factor v(x).
(x - 1)*(x + 1)**2/4
Solve 1/3*x**2 - 4/3 + 0*x = 0.
-2, 2
Suppose 5*w - 13 = b, 5*w + 3 = 4*b + 25. Factor -3*i**w + 4*i - 1 - 2 + 2*i.
-3*(i - 1)**2
Let m(u) be the second derivative of -3*u**5/140 - u**4/14 + 3*u**3/14 + 32*u. Find c such that m(c) = 0.
-3, 0, 1
Let r(v) = v**3 + 2. Let b(y) = y**2 - 5*y - 5. Let d(i) = 2*i**2 - 9*i - 9. Let u(c) = 11*b(c) - 6*d(c). Let p(s) = r(s) + u(s). Suppose p(o) = 0. Calculate o.
-1, 1
Let u(a) = a**2 - a - 2. Let o be u(4). Suppose 0 = -l + 3*l - o. Find t such that -4*t**3 + 3*t**4 + t**4 + t**3 - t**l + t**2 - t**4 = 0.
0, 1
Let d(f) be the third derivative of -25*f**8/84 - 26*f**7/21 - 7*f**6/8 + 3*f**5/2 - 9*f**2. Factor d(b).
-5*b**2*(2*b + 3)**2*(5*b - 2)
Let d(t) be the first derivative of t**5/20 - t**4/4 + 5*t**3/12 - t**2/4 + 1. Factor d(g).
g*(g - 2)*(g - 1)**2/4
Suppose -3*z = -4*p + 11, 3*z + p = 13 + 1. Factor -3*a**3 - a**2 - 5*a**3 + a**4 + 7*a**z + a.
a*(a - 1)**2*(a + 1)
Let l be (-2 - -7) + -2 - -1. Factor 4*j**4 - l*j**2 - 4*j**3 + 4*j**3 + 2*j**5 - 2*j.
2*j*(j - 1)*(j + 1)**3
Let u(y) = -14*y**4 - 4*y**3 - 14*y**2 + 8*y. Let f(p) = -5*p**4 - p**3 - 5*p**2 + 3*p. Let o(m) = 8*f(m) - 3*u(m). Factor o(l).
2*l**2*(l + 1)**2
Let c(u) be the first derivative of -u**6/2 + 3*u**4/2 - 3*u**2/2 - 8. Factor c(g).
-3*g*(g - 1)**2*(g + 1)**2
Suppose -3*k + 40 = 7*k. Factor 4/7*j**3 - 2/7*j + 0 + 0*j**k - 2/7*j**5 + 0*j**2.
-2*j*(j - 1)**2*(j + 1)**2/7
Suppose -18 = -6*f - 6. Let q(k) be the second derivative of -12*k**3 - 15/4*k**5 - 6*k**f + 0 - 45/4*k**4 + 4*k. Determine g, given that q(g) = 0.
-1, -2/5
Let u(j) = -19*j**3 - 16*j**2 + 25*j + 8. Let a(s) = -13*s**3 - 11*s**2 + 17*s + 5. Let x(n) = 7*a(n) - 5*u(n). Determine m so that x(m) = 0.
-1, 5/4
Suppose 1 = -y, -4*y + 18 = -4*t + 94. Let b be t/(-30) - (-6)/10. Factor -1/4*l + b - 1/4*l**3 + 1/2*l**2.
-l*(l - 1)**2/4
Let g = -1 - -4. Let r be 1 - ((-22)/(-6) - g). Factor -r - 16/3*u**4 - 1/3*u**2 - 2*u + 8*u**3.
-(u - 1)**2*(4*u + 1)**2/3
Let m(d) be the second derivative of -3*d**6/5 - 3*d**5/10 + 4*d**4/3 + 4*d**3/3 - 5*d. Determine g, given that m(g) = 0.
-2/3, 0, 1
Let p(o) be the first derivative of -o**5/36 + o**4/72 - o**2/2 + 6. Let n(k) be the second derivative 