*3 - 4*r**2 - 3*r + 4. Let y(f) = -15*f + 0*f**3 + 21 - 6*f**3 - 8*f**2 - 13*f**2. Let l(k) = 21*g(k) - 4*y(k). Factor l(s).
3*s*(s - 1)*(s + 1)
Let m(h) be the third derivative of -h**7/630 + h**6/60 - h**5/20 - 4*h**2. What is n in m(n) = 0?
0, 3
Let m(t) be the second derivative of 0*t**3 + 2/45*t**6 + 0 + 0*t**2 - 1/30*t**5 + 0*t**4 - 1/63*t**7 - 2*t. Solve m(n) = 0.
0, 1
Let d - 8*d**2 - 4*d**3 + 4*d + 3*d + 8 - 4*d = 0. What is d?
-2, -1, 1
Let n = -7 + 1. Let j(i) = -i**4 - i**3 - i**2 + i - 1. Let v(k) = -4*k**4 - 3*k**3 + 5*k - 3. Let o(u) = n*j(u) + 2*v(u). Solve o(b) = 0.
-1, 0, 2
Let m be -14 + 11 + (0 - -6). Let -2*y - y**2 + m*y**2 + 2*y - 2 = 0. Calculate y.
-1, 1
Let 145/3*c**2 + 4/3 + 76/3*c**3 + 64/3*c**5 + 44/3*c - 208/3*c**4 = 0. Calculate c.
-1/4, 2
Let 0*f**2 + 0*f + 2/7*f**4 + 0 + 1/7*f**3 + 1/7*f**5 = 0. Calculate f.
-1, 0
Let g(j) be the second derivative of -j**6/60 + j**5/8 - j**4/3 + j**3/3 - 5*j. Find d, given that g(d) = 0.
0, 1, 2
Let w(j) be the second derivative of j**3/6 - 7*j**2/2 + 3*j. Let n be w(7). Factor 2/7*c**3 + n*c + 0 + 2/7*c**2.
2*c**2*(c + 1)/7
Let f(l) be the third derivative of l**8/20160 + l**7/2016 + l**6/720 + 7*l**5/60 + 9*l**2. Let z(g) be the third derivative of f(g). Find p such that z(p) = 0.
-2, -1/2
Let i(g) = -g + 13. Suppose 3 = 2*o - 13. Let u be i(o). What is f in u*f**3 - 5*f**4 - 2*f**2 + 0*f**2 - f**3 + 3*f**4 = 0?
0, 1
Let s(p) be the second derivative of p**7/5040 - p**5/720 - p**3/6 + 2*p. Let d(v) be the second derivative of s(v). Factor d(w).
w*(w - 1)*(w + 1)/6
Let f(s) be the first derivative of -s**4/12 + s**3/3 - s**2/2 + s/3 + 4. Solve f(j) = 0.
1
Let n(l) be the third derivative of l**6/300 + l**5/150 - l**4/60 - l**3/15 + 8*l**2. Suppose n(c) = 0. Calculate c.
-1, 1
Let x = -1419/10 - -142. Let b(q) be the first derivative of 0*q**3 + 0*q**2 + x*q**5 + 0*q**4 + 2 + 0*q. Factor b(l).
l**4/2
Factor -1/2*c**4 - 1/2 + 0*c + c**2 + 0*c**3.
-(c - 1)**2*(c + 1)**2/2
Suppose -3*f + 4*f - 6 = 3*m, -3*f + m = -2. Solve f + 123*v**3 + 30*v + 63*v**4 + 79*v**2 - 9*v + 2 = 0.
-1, -1/3, -2/7
Find p, given that 0*p - 3/4*p**3 - 3/2*p**2 + 0 = 0.
-2, 0
Factor 2*n - 8*n - n**2 - 16 + 5*n - 7*n.
-(n + 4)**2
Let z(u) be the second derivative of u**7/420 - u**5/60 - u**3/3 + 2*u. Let v(i) be the second derivative of z(i). Factor v(r).
2*r*(r - 1)*(r + 1)
Let h(y) = 21*y**4 + 114*y**3 + 147*y**2 - 54*y. Let o(v) = v**3 + v**2. Let m(c) = -h(c) - 6*o(c). Factor m(r).
-3*r*(r + 3)**2*(7*r - 2)
Let t(g) be the third derivative of -2/3*g**7 - 25/168*g**8 + 0*g + 0 - 23/20*g**6 + 5*g**2 - 1/3*g**4 + 0*g**3 - 14/15*g**5. Factor t(m).
-2*m*(m + 1)**2*(5*m + 2)**2
Suppose 0 = -2*o - 5*y + 15, o + y = -0*o + 6. Let w = -2 + o. Factor -g + 1 - 2*g**w + 2*g**2 + 3*g - 3.
-2*(g - 1)**2*(g + 1)
Determine w so that 6/11*w**3 - 2/11*w**2 - 6/11*w**4 + 2/11*w**5 + 0*w + 0 = 0.
0, 1
Suppose 3*k - k = 30. Let a be ((-3)/25)/((-3)/k). Factor 0 + 1/5*m + a*m**2.
m*(3*m + 1)/5
Let z(g) be the third derivative of 0*g - 1/120*g**5 + 1/168*g**8 + 0*g**3 - 3/140*g**7 + 0*g**4 + 4*g**2 + 0 + 1/40*g**6. Factor z(h).
h**2*(h - 1)**2*(4*h - 1)/2
Let z = 161 + -161. Find t, given that 0*t + z - 1/2*t**2 = 0.
0
Let l be 15/99 + 2/11. Let m(f) be the first derivative of -4/9*f**3 + 1/6*f**4 - 2 + 0*f + l*f**2. Factor m(t).
2*t*(t - 1)**2/3
Factor -12*a**4 - 10 + 24 - 10 - 12*a + 8*a**2 + 8*a**3 + 4*a**5.
4*(a - 1)**4*(a + 1)
Suppose -a + 4 = -1. Let x(j) be the third derivative of -1/210*j**a + 0*j + 0 + 0*j**4 + 1/21*j**3 + j**2. Factor x(f).
-2*(f - 1)*(f + 1)/7
Let a be (6 + 91/(-14))/(-1). Let d(m) = m**2 + 5*m. Let k be d(-5). Factor k + 0*y - 1/2*y**3 - a*y**2.
-y**2*(y + 1)/2
Let g(z) be the first derivative of z**6/30 + 3*z**5/25 + 3*z**4/20 + z**3/15 - 3. Factor g(k).
k**2*(k + 1)**3/5
Let r = -27 - -17. Let g be ((-2)/6)/(r/12). Find v such that -4/5*v**3 + 0*v + g*v**2 + 0 + 2/5*v**4 = 0.
0, 1
Let d(t) = -2*t**3 - 4*t**2 + 2*t + 8. Let a = 17 - 9. Suppose a = -0*o + 2*o. Let p(v) = 1. Let m(f) = o*p(f) - d(f). Find j, given that m(j) = 0.
-2, -1, 1
Suppose -2*d + 2*f = -6, 18 = d + 2*f - 0. Let z(s) be the first derivative of -4*s**2 + 3 - 2/3*s**3 - d*s. Solve z(o) = 0.
-2
Let d(t) be the first derivative of 0*t + 0*t**2 - 1/7*t**4 - 2/7*t**3 + 1 + 2/7*t**5. Find b, given that d(b) = 0.
-3/5, 0, 1
Let h(k) be the third derivative of -27*k**8/224 - 33*k**7/70 + k**6/48 + 19*k**5/12 + 19*k**4/12 + 2*k**3/3 + 13*k**2. Solve h(d) = 0.
-2, -1, -2/9, 1
Let a(b) be the second derivative of -5*b**4/12 + 4*b**3/3 + 2*b**2 + 6*b. Solve a(v) = 0.
-2/5, 2
Factor 3/8*s**2 + 9*s + 54.
3*(s + 12)**2/8
Let m = 667/5 - 133. Factor 0*u**2 - m*u + 2/5*u**3 + 0.
2*u*(u - 1)*(u + 1)/5
Let b(v) = -v**4 + v**3 + v - 1. Let i(f) = f**5 - 4*f**4 + 2*f**3 + f**2 + 3*f - 3. Let d(j) = 3*b(j) - i(j). Solve d(w) = 0 for w.
-1, 0, 1
Let f(t) be the first derivative of 0*t - 1 + 0*t**2 - 5*t**4 - 32/3*t**6 - 2/3*t**3 - 64/5*t**5. Suppose f(y) = 0. Calculate y.
-1/2, -1/4, 0
Let k(m) = -m**3 + 7*m**2 - m + 11. Let l be k(7). Let x be (l/6)/(2 - -1). Solve 0*v + 0*v**2 + 2/9*v**3 + 0 - x*v**5 + 0*v**4 = 0.
-1, 0, 1
Factor 5*b - 351*b**3 - 28*b**2 + 367*b**3 - 13*b.
4*b*(b - 2)*(4*b + 1)
Let d(p) = -p**2 + 1. Let s(o) = 7*o**2 + 6*o - 16. Let n(r) = -6*d(r) - s(r). Let b be n(-7). Factor -5*k**b + k**2 - 5*k**4 - k**3 + 8*k - k**3 - k**5 + 4.
-(k - 1)*(k + 1)**2*(k + 2)**2
Let h(y) be the second derivative of -y**7/28 - 13*y**6/20 - 171*y**5/40 - 95*y**4/8 - 25*y**3/2 - 12*y - 2. What is q in h(q) = 0?
-5, -2, -1, 0
Let d(p) be the third derivative of -p**8/6720 + p**6/720 + p**4/8 + 3*p**2. Let b(g) be the second derivative of d(g). Find a, given that b(a) = 0.
-1, 0, 1
Suppose 6*u - 3*u = 15. Factor 15*x**2 + 4*x + 6*x - u*x - 2*x + 12*x**3.
3*x*(x + 1)*(4*x + 1)
Suppose o = -3*o + 8. Let u = 1/84 - -163/420. Factor -u*z + 16/5*z**o - 2*z**3 - 4/5.
-2*(z - 1)**2*(5*z + 2)/5
Suppose 4*v + 5*z + 8 = 5*v, 2*z + 11 = 3*v. Let 3*g**4 + g**5 - 5 + g**2 + 1 + 4 + v*g**3 = 0. What is g?
-1, 0
Let o(f) be the first derivative of -4/5*f**5 - 5 - 1/4*f**4 + 0*f + 1/2*f**2 + 4/3*f**3. Factor o(v).
-v*(v - 1)*(v + 1)*(4*v + 1)
Let f(t) = -t**2 + 3*t + 4. Let u(c) = 2*c**2 - 7*c - 9. Let w be (-12)/(-4) + 1 + 0. Let z be 8*-1*(-3)/w. Let s(p) = z*u(p) + 14*f(p). Solve s(r) = 0.
-1, 1
Let w(m) be the second derivative of 4*m + 0*m**4 - 1/35*m**5 + 1/105*m**6 + 0 - 1/7*m**2 + 2/21*m**3. What is q in w(q) = 0?
-1, 1
Let m(s) be the second derivative of -s**4/6 - 4*s**3/3 - 4*s**2 - 19*s. Factor m(r).
-2*(r + 2)**2
Factor -15*q**4 - 5*q + 3*q**2 + 3*q**3 + 0*q**2 + 2*q + 12*q**4.
-3*q*(q - 1)**2*(q + 1)
Let l(h) be the third derivative of h**8/80640 - h**7/10080 - h**5/60 - 4*h**2. Let m(w) be the third derivative of l(w). Solve m(y) = 0.
0, 2
Find f such that -92*f - 145*f**2 - 180*f**3 + 22*f - 5*f**4 + 100*f**3 = 0.
-14, -1, 0
Let g(t) = 8*t**5 - 16*t**4 - 4*t**3 + 20*t. Let y(v) = v**5 - v**3 + v. Let i(z) = g(z) - 20*y(z). Factor i(x).
-4*x**3*(x + 2)*(3*x - 2)
Let w(p) be the first derivative of -3*p**4/34 - 10*p**3/51 - p**2/17 + 2*p/17 - 8. Factor w(y).
-2*(y + 1)**2*(3*y - 1)/17
Let c(g) = -9*g**2 - 12*g - 3. Let o(z) = 10*z**2 + 12*z + 2. Let t = -22 + 16. Let d(f) = t*c(f) - 5*o(f). Factor d(l).
4*(l + 1)*(l + 2)
Determine i, given that -4/5*i**3 - 16/5*i - 6/5*i**4 + 24/5*i**2 + 2/5*i**5 + 0 = 0.
-2, 0, 1, 2
Let f be (0 + 1)/1 + 10/(-20). Suppose f*j**2 - 1/2 + 1/4*j**3 - 1/4*j = 0. Calculate j.
-2, -1, 1
Let t(o) be the third derivative of 2*o**7/525 - 2*o**6/75 + 2*o**5/75 + 2*o**4/15 - 2*o**3/5 - 20*o**2. Factor t(b).
4*(b - 3)*(b - 1)**2*(b + 1)/5
Let i(n) = -n**2 + 5*n + 2. Let m = 21 - 16. Let y be i(m). Find x such that -4/7 - 10/7*x**2 - y*x = 0.
-1, -2/5
Let p = 1/43 - -41/86. Factor 3/2*b**4 + 0*b - p*b**2 + b**3 + 0.
b**2*(b + 1)*(3*b - 1)/2
Let t = -71/12 + 6. Let p(o) be the third derivative of -t*o**3 + 1/96*o**4 + 0 + 1/240*o**5 + 0*o + o**2. Determine l so that p(l) = 0.
-2, 1
Factor 19*t**2 - t**2 - 10 - 35*t + 27*t**2.
5*(t - 1)*(9*t + 2)
Let m(f) be the third derivative of -f**6/24 + 5*f**4/8 + 5*f**3/3 - f**2 - 20*f. Solve m(w) = 0 for w.
-1, 2
Let s(o) be the second derivative of -o**5/150 + o**4/90 + 3*o. Factor s(y).