show correct solution factor each of the polynomial.1.2x²-8x2.-3s²+9s3.4x+20x²4.5t-10f²5.s²+8s+126.x²-10x+21
Answer (1)
Answer:Let's factor each of the polynomials step-by-step:1. \( 2x^2 - 8x \)Step 1: Find the greatest common factor (GCF) of the coefficients: 2.Step 2: Factor out the GCF:\[ 2x(x - 4) \]Answer: \(\boxed{2x(x - 4)}\)2. \( -3s^2 + 9s \)Step 1: GCF of coefficients: 3, and note the negative sign.Step 2: Factor out \(-3s\):\[ -3s(s - 3) \]Answer: \(\boxed{-3s(s - 3)}\)3. \( 4x + 20x^2 \)Step 1: GCF of coefficients: 4x.Step 2: Factor out \( 4x \):\[ 4x(1 + 5x) \]Answer: \(\boxed{4x(1 + 5x)}\)4. \( 5t - 10f^2 \)Step 1: GCF of coefficients: 5.Step 2: Factor out 5:\[ 5(t - 2f^2) \]Answer: \(\boxed{5(t - 2f^2)}\)5. \( s^2 + 8s + 12 \)Step 1: Find two numbers that multiply to 12 and add to 8: 2 and 6.Step 2: Factor as:\[ (s + 2)(s + 6) \]Answer: \(\boxed{(s + 2)(s + 6)}\)6. \( x^2 - 10x + 21 \)Step 1: Find two numbers that multiply to 21 and add to -10: -3 and -7.Step 2: Factor as:\[ (x - 3)(x - 7) \]Answer: \(\boxed{(x - 3)(x - 7)}\)
